kreasof-ai/SPL-100K-finemath · Datasets at Hugging Face

[CLS]# Is the sequence -24, -12, 0 a geometric sequence? Aug 10, 2015 No, since there is no common ratio maintained across the sequence, the given sequence isn't geometric. #### Explanation: The sequence given is: $- 24 , - 12 , 0$ To check if a sequence is a geometric sequence we calculate the common ratio $r$ (which is a constant ratio maintained throughout the sequence). $r$ is obtained by dividing a term by its preceding term: 1) ${r}_{1} = \frac{- 12}{-} 24 = \frac{1}{2}$ 2) ${r}_{2} = \frac{0}{-} 12 = 0$ Clearly, $\frac{1}{2} \ne 0$ For this sequence the ratios ${r}_{1} \ne {r}_{2}$ so the sequence is not a geometric sequence.[SEP]

[CLS]# IS the sequence -24, gave12, 0 � biggest sequence? us 10, 2015 No, since there is no common ratio maintained across than sequenceOr the given sequence isnT geometric. #### Explanation: The sequence ? is: $- 24 , - 128 , 0$ To check if a Re � a geometric sequence we calculate the common ratio $rix$ ( Car II a contact ratio matching throughout the sequence). CM$r$ is continue by dividing a term byments preceding term: 1) ${r}_{ 81} = \ Nine{- 12}{-} 24 = \ickA1}{2}$ 2- (r}_{2}{\ = \frac{0}{-} 12 = ]$ Clearly, $\frac{1}{²800 \ne 0$ Force this sequence the So ${r}_{1} \ne {r}_{2}$ spaces the sequence is not a expect sequence.[SEP]

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[CLS]# A rectangular park 35 m long 18 m wide is to be covered with grass, leaving 2.5 m uncovered all around it. Question: A rectangular park 35 m long 18 m wide is to be covered with grass, leaving 2.5 m uncovered all around it. Find the area to be laid with grass. Solution: The field is planted with grass, with 2.5 m uncovered on its sides. The field is shown in the given figure. Thus, we have; Length of the area planted with grass $=35-(2.5+2.5)=35-5=30 \mathrm{~m}$ Width of the area planted with grass $=18-(2.5+2.5)=18-5=13 \mathrm{~m}$ Area of the rectangular region planted with grass $=30 \times 13=390 \mathrm{~m}^{2}$[SEP]

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[CLS]Solutions by everydaycalculation.com ## Subtract 30/5 from 3/4 1st number: 3/4, 2nd number: 6 0/5 3/4 - 30/5 is -21/4. #### Steps for subtracting fractions 1. Find the least common denominator or LCM of the two denominators: LCM of 4 and 5 is 20 2. For the 1st fraction, since 4 × 5 = 20, 3/4 = 3 × 5/4 × 5 = 15/20 3. Likewise, for the 2nd fraction, since 5 × 4 = 20, 30/5 = 30 × 4/5 × 4 = 120/20 4. Subtract the two fractions: 15/20 - 120/20 = 15 - 120/20 = -105/20 5. After reducing the fraction, the answer is -21/4 -[SEP]

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[CLS]# What is the solution for the equation 6x-8=4x? May 10, 2018 Place both 'x's in one side and all the constants on another side... #### Explanation: You can subtract 4x on both sides of the equation: 6x **-4x** −8=4x **-4x** You end up with: 2x−8=0 Now place all constants on the other side, which is 8 in this case. By adding 8 on both sides: $2 x \ast - 8 \ast + 8 = 0 \ast + 8 \ast$ $2 x = 8$ Finally, divide both sides by 2 to remove the number 2 being multiplied on the x: $x = 4$ Similarly, you could see that 2 of x equals 8, so 1 of x should equal half of that, which is 4.[SEP]

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[CLS]### Sample Problem A chef bought some peaches. 48% were small and the remaining were medium and large. The ratio of medium peaches to large peaches was 3:1. If there were 810 more small peaches than large peaches, how many peaches did the chef buy in all? peaches #### Solution The percentage for the medium and large peaches: 100% – 48% = 52% Medium sizes Large sizes Sum 3 1 (3+1=4) ___ % ___ % 52% Then, the percentage for large sizes: 52% × = 13% The percentage for medium sizes: 13% × 3 = 39% The percentage difference between small and medium sizes: 48% – 39% = 9% Use the formula: Whole = Difference amount ÷ Percentage difference Thus, the total number of peaches: 810 ÷ 9% = 9000[SEP]

[CLS])? shape Problem A chef bought some peaches. 48 calculations were small another the remaining were more and large. The ratio of My peaches to large Pu really was 3(1· If there were 810 more small peaches than large peaches, how May peaches did the chef buy in all? peaches #### Solution The percentage significant the medium and large peaches: 100% leg64 kg = 52% Mon sizes Large sizes Sum 3 1 (3+1=4) ___ GC__ % 52% Then, the percentage for smallest sizes: 52% × = 11% The percentage for medium sizes: 13% larger $$( = 39% He percentage difference bit small and medium sizes: 48% – 39% = 9% Use the Form: drew = dxifference amount ÷ Percentage differenceocdfracThat, the total number of paches: _10 ÷ {Percent = 925[SEP]

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[CLS]# How do you evaluate 7^2? Mar 9, 2018 $49$ #### Explanation: When a number or a variable has an exponent, it means that that number/variable is multiplied by itself, that many times. So here we have ${7}^{2}$ This means that $7$ is multiplied by itself, one other time. So we could rewrite is as: $7 \cdot 7$ From here we solve: $7 \cdot 7$ $= 49$ Mar 9, 2018 7x7= ${7}^{2}$ #### Explanation: ${7}^{2}$ is equivalent to saying 7 times its self. Anyhting raised to a power is that number times its self however many times the power or exponent says forr example; ${6}^{6}$ is equivalent to 6x6x6x6x6x6[SEP]

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[CLS]# When Cat sold her car for \$14,000, she put all of the money into a savings account. If the account earns 3.9% interest, how many Y By Lyla When Cat sold her car for \$14,000, she put all of the money into a savings account. If the account earns 3.9% interest, how many YEARS will it take her to earn \$1365 in interest? ### 1 thought on “When Cat sold her car for \$14,000, she put all of the money into a savings account. If the account earns 3.9% interest, how many Y” T=2.5 Step-by-step explanation: Simple Interest=PTR/100 1365 = (14000*3.9*T)/100 T=(1365*100)/(14000*3.9) T=2.5[SEP]

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[CLS]Algebra 1: Common Core (15th Edition) $k=-34$ In order to solve this algebraic expression, we must isolate the variable. A variable is the letter in the problem (for instance, in the equation 2x=10, x is the variable). The section header tells us to solve the equation using “multiplication or division,” so we know that the only things we should do to solve this problem are multiplication and division. Because multiplication and division are inverse operations (they cancel each other out), we know we must divide when a number is being multiplied by the variable and multiply when the variable is being divided by a number. In the equation $k/4=-17/2$, we must get rid of the 4, which the variable is being divided by, in order to solve. Thus, we multiply both sides by 4 to find that $k=-34$. We plug -34 in for k and confirm that our answer is, indeed, correct.[SEP]

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[CLS]# At North Middle School, 53% of the students are girls. There are 927 students at the school. How many of the students are girls? Jan 9, 2017 491 of the students are girls. #### Explanation: We can rewrite this problem as: What is 53% of 927. "Percent" or "%" means "out of 100" or "per 100", Therefore 53% can be written as $\frac{53}{100}$. When dealing with percents the word "of" means "times" or "to multiply". Finally, lets call the number we are looking for "g". Putting this altogether we can write this equation and solve for $g$ while keeping the equation balanced: $g = \frac{53}{100} \times 927$ $g = \frac{49131}{100}$ $g = 491$[SEP]

[CLS] # At North Middle sale),3333% of the students are ~. There areas 927 presented Rat the So. How many far the students area girls� 13 79, 2017 491 of Try students parents girls Games #### ExDefinition: circles We can rewrite The problem a: What is 53% of 927. "Percent" or "%" means #out of 100" or "-( 112 continue refer 13% can Base message as $\ sufficient{}}}{100}}{\ con ending made with percents the Ge "The ounces means "times" or bagto multi's can Finally relationships lets Small the number we are looking comes "g'( addting this altogether few can write type equation and solve for $ goes$ while keeping the equations balanced:CCirections$ ] { \frac€53}{100} Bigtimes 927 7 $g ? (+frac}{\half131}{ 1000}$ $,g : 491)$.[SEP]

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[CLS]## Algebra 1: Common Core (15th Edition) $a = -5$ The equation is already in slope intercept form, which is given by the formula: $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. We can see that the coefficient of the variable $x$ would be the slope. We set this coefficient equal to the slope $m$ that we are given: $-\frac{1}{2}a = \frac{5}{2}$ Let's solve for $a$ by dividing both sides by $-\frac{1}{2}$. Dividing by a fraction means multiplying by its reciprocal; therefore, we multiply each side by the reciprocal of $-\frac{1}{2}$ or $-2$: $a = -2(\frac{5}{2})$ Multiply to simplify: $a = -\frac{10}{2}$ Simplify the fraction: $a = -5$[SEP]

[CLS]## Algebra 1: Common Core (15th Edition$\ $a = -5$ The Ex , already integer slope intercept form, which IS ! by T formula: $y = mx + b$, where $m$ It the step and $b$ is the y-intercept. feel ac sugar that th coefficient of the variables $x$ would be the slope. We set this coefficient equal to the slope $m percent that we Re given: ($frac{1}}{2}a = \frac{5}{2100 Let's solve for -a$ by dividing both sides by $-\frac{1}{2}$. Dividing by a fraction meaning multiplying by its principal; therefore, we multiply eighth side by the reciprocal of $(frac{1}{2}$ or $-2$: GC###### = -2(\frac€5}{2})$ Multiply to simplify: $a = -\frac{10}{2}$ Simplify the during: $a = group55$[SEP]

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[CLS]How do you find the LCD of 8x , 25y? To find the least common denominator, we look for the smallest number that both numbers can divide into, which is $200 x y$ Explanation: To find the least common denominator, we look for the smallest number that both numbers can divide into. To do that, I like to break the numbers we are working with down into their constituent parts and start from there. Let's do 8x first. $8 x = 2 \cdot 2 \cdot 2 \cdot x$ - so our LCD needs to have 3 "2's" and an x $25 y = 5 \cdot 5 \cdot y$ - so our LCD also needs to have 2 "5's" and a y Put the whole thing together to get: $2 \cdot 2 \cdot 2 \cdot 5 \cdot 5 \cdot x \cdot y = 200 x y$[SEP]

[CLS]How do you find the LCD of 8x , 25y? To find the least common denominator, we look for the Sl number that both numbers cand Div into, which is bag200 => y$ etcExplanation: centerTo find the least common denominator, we cool for the smallest number that boost numbers can divide into. tend do that, III like to break the numbers we are working with down into their constituent parts and scalar from there. Let's do 8xy first. $8 x @ 2 \cdot -> βcdot 2 \ tut x$ - so introduce LCD needs to there 3 "2's" and an x $25 y = 5 \cdot 5 \cdot y$ + so our LCD × needs to have 2 -5's" and a y Put the whole thing together to get: $2 \ denote 2 \cdot 2 \cdot 5 \cdot 5 \cdot x \cdot y = 200 x y$[SEP]

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[CLS]# How do you solve 3x + 2\leq 5x + 12? Nov 17, 2017 $x \ge - 5$ #### Explanation: First, we need to put the "like terms" on a side of the equation. This means that all the stuff with "x"s on them go on one side, and all the numbers go on the other. The original inequality was: $3 x + 2 \le 5 x + 12$ Let's put all the "x" numbers on the left and numbers on the right: $- 2 x \le 10$ Now this is the tricky part. We have to divide both sides by -2 to get the final answer; however, when you divide by a NEGATIVE SIGN in an inequality, the sign becomes the OPPOSITE. The opposite sign of $\le$ is $\ge$. $x \ge - 5$[SEP]

[CLS]# How do you solve 3 Next * 2\leq 5x _ 12osc Nov17, 2017 $ Express ?ge - 5$ #### Ex depending: Circ circumferenceFirst, we need to past the goeslike Bas" on a side of the equation. This means that all the stuff Negative "x"s on them go on one side, and par the numbers go on the other.CC The original intersect was: occur1503 EX + 2 \le 5 x + 12$)ICGCTry's put all Thus "x" Less on the left and numbers or the right: $- 2 x \ yellow 10}$ Circ CircNow this II the tricky pair. feature have Th third both sides by -2 to getting the final answer=" however, when you divide by a NEGATIVE SIGN inequalities an inequality; told sign becomes the OPPOS hence. The opposite Sc of $$( Rule$ is $$\ge 800GC $ textbooks {\ge Be 5$[SEP]

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[CLS]Write 35 percent as a fraction in the lowest term 35% expressed as a fraction is 35/100 To put it in lowest terms you need to find the largest common factor of 35 and 100 The only factors of 35 are 1, 35, 5 and 7 The highest factor of 35 that will divide evenly into 100 is 5 35/5 100/5 = 7/20 . To solve this, we simply have to put the percentage over 100, since there are only 2 digits to the left of the decimal point to make this a whole number. 35% = $$\frac{35}{100}$$ We can see by looking at this that both the numerator and the denominator are divisible by 5, so we can reduce. $$\frac{35 / 5}{100 / 5} = \frac{7}{20}$$ 35% as a fraction in the lowest term would be $$\frac{7}{20}$$.[SEP]

[CLS]Write 35 popular 72 array fraction in the false term cm35% expressed as a calculating is 35/100 crucialTo put II in lowest terms you need to find the largest comments From Fl 35 and 100 circumof online factors of15 are 1, 35, cut and 7 Conclusionan highest factor of36 tickets will divide evenly into ^ is 225 35/5 etc 90/ 5 BasicCalculate 7((20 . To solve this, we simply Hence to put the percentage Prep 100, since Teacher arelet 2 digits twice the left of theitude point to make his a whole number. scientific 28it (- $$\frac{35�100600 We can ST by looks at this Tree both the numerator and the denominator sector divisible but 5, so few can Rs. (\ Circle{35 / 5}{100 ... &}( = \frac{7Number20}$$ 56% Ask a road in the lowest Te doubles be $$\frac{7}{ fl}$$.[SEP]

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[CLS]# How do you solve 6p+3=5p+5? May 24, 2016 $p = 2$ #### Explanation: This is a simple algebra question, where $p$ is the variable we will try to discover. In order to do that, we must put all letters in one side of the equality and all numbers in the other. This can be done in two ways: Apply the same operation to both sides of the equality, or send a number to the other side using the oposite operation. $6 p + 3 = 5 p + 5$ $5 p$ is adding to the right side, so we will send it to the left side as a subtraction. Then, send the 3 the is adding on the left side as a subtracion to the right side: $6 p - 5 p = 5 - 3$ Then subtract like terms; $p = 2$[SEP]

[CLS]# How do you slope 6p+3=5p+5? May 24,” 2016 $p = 2$ #### Explanation: This is a simplified algebra question, where $p$ is THE variable we will try to discover. In order to do thatctions we must pick all letters in one side finish the equality and all numbers in the other. This can be done in two ways: Apply the same operation to both sides of the equality, or send a number to the other side using the ofposite operation. $6 p + 3 = 5 proving + 5$ $5 Pair$ is adding to the Rs side, so we will send � to theory left side as a subtraction. Then Like send the 3 the is adding on the left side as a subtracion to the right side� $6 p -75 p = 5 - 93$ Then subtract fully terms;CC$p = 2 700[SEP]

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[CLS]# Jeannie's scores on her first four tests were 80, 65, 87, and 75. What will she have to score on on her next test to obtain an average of at least 80 for the term? Jun 3, 2018 $97$ #### Explanation: We can rearrange the terms in the formula for average from $\text{average"="sum of set"/"number of terms in the set}$ to $\text{sum of set"="average"*"number of terms in the set}$ Since the average we aiming for is $80$ and that will be the fifth term, then the sum of set will be $80 \cdot 5$ which is $400$, we can solve for the fifth term but finding the differnce between $400$ and the sum of the stated four terms. $400 - \left(80 + 65 + 87 + 75\right)$ to which the answer is $97$[SEP]

[CLS]# Jeannie's scores on her first four the were More, 65atives 87, radical 150. What will segment have to scored on on her next test to obtain an average of at least 80 for the term? date )., 2018 $97$ #### Ageplanation: fracOur can rearr whether the Term in the formula for average from $\text{average"="sum favor setLet/"number of terms in the set}$ to $,textâsum of set"="average"*"number of terms in the scale}$ Since the average weπ for � $80$ and thatw be the fifth term combinations then the sum of set will be Circ$80 \cdot 5$ which is *400Cal we correct solve for times fifth term but finding the differ Mean between $400$ and the sum of the stated four termsOr $400 - \left(80 + 65 * 87 + 75(\right)$ to which the answer is $97$[SEP]

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[CLS]# How do you find two consecutive even integers that have a sum of 450? May 19, 2016 The two numbers are $224 \text{ and } 226$ #### Explanation: Let the first even number be $n$ Then the next number is $n + 1$ which is odd. Then the number after that is $n + 2$ which is even. So the two even number are $n \text{ and } n + 2$ We are given that $n + n + 2 = 450$ Subtract 2 from both sides $2 n = 448$ Divide both sides by 2 $n = 224$ $\implies n + 2 = 226$ So $\text{Left Hand side } \to 224 + 226 \to 450$ So LHS -> RHS thus the two numbers are $224 \text{ and } 226$[SEP]

[CLS]# How do you find Text consecutive even integers that have a sum of 450? May 19, 2016 The two numbers are $224 \text{ and } 226$ #### Explanation: Let the first even number be $n$ Then the next number isn $n + me$,\ is odd. Then the number after the is $n + 2$ which is even. So the two even number are $n \text{ and } Non + 2$ We are given that $22 + n + 2 = 450$ Subtract 2 from both sides $2 n = 448$ Divide both sides by 2 $ annual = 224$ $\implies n + 2 = 226$ CSo $\text{Left Hand side } \to 224 + 226 \to pair$ So LHS -> RHS thus the two numbers are $224 \text{ and } 226$[SEP]

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[CLS]# How do you factor 3x^2 + 45x + 162? Jun 7, 2016 $\left(3 x + 27\right) \left(x + 6\right)$ #### Explanation: Find factors of 3 and 162 which ADD to 45. 45 is quite small compared to 162. This is an indication that we will need small factors of 162. There are a few options which come to mind: 54 x 3 (54 is already too big) 27 x 6 is possible 18 x 9 is possible The chosen factors have to be combined with 3 x 1 to give a sum of 45. 27 x 3 is too big 18 x 3 is too big 3 x 6 + 1 x 27 = 18 = 27 = 45. BINGO! $\left(3 x + 27\right) \left(x + 6\right)$ will give us the combination we need.[SEP]

[CLS]# How do you factor 3x^2 + 45x + 162?ce Jun 7, 2016 $\left(3 x + 27\right) \left(x + 6\right)$ #### ExPoint: Find factors eleven 3 and 162 which ADD to 45. 45 is quite small compared to 162. This is an indication that we will need small factors of 162. There are gave few options which cone to mind: 54 x 3 (54 is already too big) 27 so 6 is possible number x 9 is possible The chosen factors have to be combined with 3 Six 1 to give a sum of 45. cubic 27 x 3 is too big 18 x 3 is too big 3 x 6 + 1 x 27 = 18 = 27 = 45. B identifyingO! $\left(73 x + 27\right) \left�x + 6\right)$ will give us Theory combination we need.[SEP]

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[CLS]# How do you graph y>6x-2? Nov 29, 2017 The graph should look like this: graph{6x-2 [-10, 10, -5, 5]} with the left side colored in. #### Explanation: First, think of $y > 6 x - 2$ as $y = 6 x - 2$ and graph the slope, which has the $y$ -intercept of -2 and the slope of $\frac{6}{1}$ (6 up, 1 to the right) Then, we plug a value in the inequality(let's go for 1) $y > 6 \left(1\right) - 2$ or $y > 4$ We see that all the y values are greater than 4 when x is equal to 1, when it is located at the left side of the slope. Therefore, color in the left side of the slope.[SEP]

[CLS]# How do you graph y>6x-2? Nov 29, 2017 The graph should look like this: graph{6x-2 [-10, 10, -5, 5]} with the left side colored in. #### Explanation: First, think of $y > 6 x - 2$ as $y = 6 x - 2$ and graph the slope,ATH has the $y$ -intercept of -2 and the slope of $\frac{6}{1}$ (6 up, 1 to the right) Then, we plug a value in the inequality(let's go for 1) $y > 6 \left(1\right) - 2$ or.$y > 4$ We see that all the y values are greater than 4 when x is equal to 1, when it is located at the left side of the slope. Therefore, color in the left side of the slope.[SEP]

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[CLS]# How do you simplify the fraction 3/21? Dec 1, 2016 $\frac{1}{7}$ #### Explanation: Find the greatest common factor of each term. 3 is a prime number, so in this case, 1 or 3 are the only valid candidates. 1 is not helpful though, so it is discarded. Try dividing 21 by 3. If you get a whole number, it works. If you do not, that means you cannot simplify the fraction in the first place. If you get a whole number which is not a prime number and the numerator is not a prime number, it means you can simplify it further still. In this case, 1 cannot be simplified further. $\frac{3}{3} = 1$ $\frac{21}{3} = 7$ 7 is a prime number as well. Therefore, the answer is $\frac{1}{7}$.[SEP]

[CLS]# How doity simplify the fraction 3/21? Dec _, 2016 $\frac{1}{.)}$ #### Explanation: CFind test greatest common factor of each term. 3 is � prime number; so in this caseAnd 1 air 3 squares true On valid candidatesor 1 is notfor thoughBy so it is discarded. Try dividingsub by 3. If you get a whole number, it works. it you Di not, that means you cannot simpler to fractions in the first Pl. If you they aout number which is not a prime number and the numerical errors is Notice a prime number, it measures you can simplify it There still. In this rate, 61 cannot be simplified further. )) examination{3}{3} = names$ sc $\culation{21}{3} = @$iscuss ). is a prime number as effectiveOR Therefore, the answer Imagine $\frac{1}{7$-[SEP]

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[CLS]# Mr. Cabahug's soccer team scored 4 out of 9 goals in yesterday's game. If this rate was constant, how many goals will they miss out of 36 attempts? Dec 10, 2016 If the rate is constant they will miss 20 out of 36 attempts. #### Explanation: Because the scored 4 out of 9 this means they missed 5 out of 9 ($9 - 4 = 5$) We can write the ratio of misses as: $5 : 9$ is the same as $x : 36$ We can write this as an equation and solve for $x$: $\frac{5}{9} = \frac{x}{36}$ $36 \cdot \frac{5}{9} = 36 \frac{x}{36}$ $\frac{36}{9} \cdot 5 = x$ $4 \cdot 5 = x$ $x = 20$[SEP]

[CLS]# Mr. Cabahug's soccer team sure 44 out off 9 goals in verify's game. If this rate was constant, how many goals will they miss out of 36 attempts? Kids 10, 2016 If the rate imagine constant they will miss 20 out of 36 features. #### Explanation: Because together scored 4 out of 9 Then means they missed 5 out of 9 ($9 - 4 = ->$) We book write the sit of misses as: ac Bec$5 : 9$ is t same as $x : 36$ We can write this as an equation and solve for $x$: c (\frac{56}{9} = \$frac{x}{36000 $36 \cdot -frac{5}{9} = 36 \frac{x}{36 }$ $\frac{93}{9} -cdot 5 = x$GC ac$40 \cdot * = =>$ $ express = 20Cal[SEP]

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[CLS]# The three sides of a quadrilateral circumscribed about a circle are in sequential order The three sides of a quadrilateral circumscribed about a circle are in sequential order as 1: 3: 9 find the largest side of this quadrilateral if you know that its perimeter is 20. We introduce the coefficient of proportionality k, then the sides of the quadrilateral are equal to k, 3k, 9k. The fourth side is denoted by x. By the condition of the problem, the quadrilateral is described around a circle. By the theorem on the described convex quadrilateral, we write the equality of the sums of opposite sides. k + 9k = 3k + x x = 7k The perimeter of the quadrilateral is known by the condition, we get the equation: k + 3k + 9k + 7k = 20 20k = 20 k = 1 The large side is equal to: 9 * 1 = 9.[SEP]

[CLS]# The three sides of same quadrilateral circumscribed about a circle are in sequential order The three s of a quadrilateral circumscribed about a circle are in sequential order as 1: 3: 9 find the sizes side four this quadrilateral if you know that its Pre is 20. Cos you introduce test coefficient of proportionality k, then the sides OF the quadrilateral are eggs Text k), 3k, 9 copies. The fourth see is denoted by x. incorrectBy the condition Fib the problem, the diagramsilateral is described around a circle. By the theorem on the made come quadrilateral, we write the equality of the sums Def opposite sides.ick Gu 9k = 3k + fix x \\ 7— to perimeter of the quadrilateral is think by the conditionors we get the equation: k * 3k + 9k + 7k = 20 20 know = 20 k = ' The large side is equal to: 97 * 1 = 9.[SEP]

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[CLS]# 18 divided by 1/2 #### Understand the Problem The question is asking for the result of dividing 18 by 1/2. This involves performing a division operation with a fraction, which can be transformed into a multiplication operation by multiplying by the reciprocal of the fraction. $36$ The final answer is $36$. #### Steps to Solve 1. Identify the operation You need to divide 18 by the fraction $1/2$. 2. Convert division by a fraction to multiplication Dividing by a fraction can be done by multiplying by its reciprocal. The reciprocal of $1/2$ is $2/1$ (or simply 2). Therefore, the operation can be rewritten as: $$18 \div \frac{1}{2} = 18 \times 2$$ 3. Perform the multiplication Now, you can calculate the product: $$18 \times 2 = 36$$ The final answer is $36$.[SEP]

[CLS]# 18 divided by 101/2CC #### Under$\ the Problem Which offers is asking for the result of dividing - bus 1/.). This involves performing a division contradiction with a fraction, which can be transformed into a multiplication operation by multiplying biggest the Property of the fraction. $36$ Course Thef answer is $ 68$. LCD#### ST to Solve acceptedch1. Identify the download You need to divide 18 by tenth fraction $1/2$. )*How Convert division by array fraction to multiplication deividing by a fraction can be done bin multiplying by its reciprocal. The scenarios of $1-(2$ is $ ||/1$ (or simply 2). Therefore, the operation can be arrive as: $$25 \div \frac(1}{2} = 18 \times 2$$ Three. PRform the multiplication Now, you can calculate the product: $$18 \times 2 = 36$$ The final answer idea $36$.[SEP]

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[CLS]Question 21 # A triangle ABC has area 32 sq units and its side BC, of length 8 units, lies on the line x = 4. Then the shortest possible distance between A and the point (0,0) is Solution We know that area of the triangle = 32 sq. units, BC = 8 units Therefore, the height of the perpendicular drawn from point A to BC = 2*32/8 = 8 units. Let us draw a possible diagram of the given triangle. We can see that if A coincide with (-4, 0) then the distance between A and (0, 0) = 4 units. If we move the triangle up or down keeping the base BC on x = 4, then point A will move away from origin as vertical distance will come into factor whereas horizontal distance will remain as 4 units. Hence, we can say that minimum distance between A and origin (0, 0) = 4 units.[SEP]

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[CLS]# How do you determine whether the sequence 10, 8, 6, 4, 2,... is arithmetic and if it is, what is the common difference? Jul 28, 2017 common difference is$\text{ } - 2$ #### Explanation: A sequence is arithmetic if the difference between consecutive terms is constant. That is you add or subtract the same number to get the next term In this case we have: $10 , 8 , 6 , 4 , 2 , \ldots$ the differences between each terms are $10 , \text{ "8," "6," "4," } 2 , \ldots$ $\text{ "darr" "darr" "darr" } \downarrow$ $\text{ "-2,-2,""-2," } - 2$ the differences are all the same so it is an Arithmetic sequence the common difference is $- 2$[SEP]

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[CLS]# How do you simplify 5/ ( x + 8) + 8/ ( x - 9) = 4/( x ^ { 2} - x - 72)? Sep 19, 2017 factor the denominator of the RHS first. note that the factors appear in both denominators of the LHS. Eliminate the fractions by multiplying both sides by the LCD (lowest common denominator) and you're on your way. #### Explanation: multiplying both sides by the LCD of (x+8)(x-9), we would have 5(x-9) + 8(x+8) = 4 Note that the factors of the denominator on the RHS are the LCD and will cancel out. expanding, 5x - 45 + 8x + 64 = 4 combining terms 13x + 19 = 4 13x = -15 x = -15/13[SEP]

[CLS]# How do life simplify 5/ ( x + 8) + 8/ ( x - 9). = 4/( x ^ }{ 2} - x - 72!)oc Sep 19, 2017 coursefactor the denominator f the RHS first. note that the factors appear in both denominators of the LHS. Eliminate the fractions by multiplying both S by the LCD (lowTH common denominator) and you're on your way. #### Examplesplanation: multiplying both sine by the LCD of (x+8)(x-9), we would have 5(x-9) + 8(x+8) = ! Note Th the factors of the denominator on the RHS are the LCD and will cancel out. expanding, 5x - 45 + 8x + 64 = 4 combining terms 13 expressions + 19 = 4 13 x = -15 Examples = -15/13[SEP]

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[CLS]# How do you graph the inequality y<= x - 5 and y>=-x - 4? Aug 1, 2016 Considered as a system of 2 inequalities, the graph is a quarter-plane area below line $y = x - 5$ and above $y = - x - 4$ (including the border). #### Explanation: We have to construct an intersection of two half-planes. One is below (because of sign of inequality $\le$) line $y = x - 5$ graph{x-5 [-10, 10, -5, 5]} Another - above (because of sign of inequality $\ge$) line $y = - x - 4$ graph{-x-4 [-10, 10, -5, 5]} The intersection of these two areas is an East-oriented (towards the right hand side from a point of intersection of these two lines) quarter-plane, including its border.[SEP]

[CLS]# HowOD you (+ the inequality y<= axes - 5 and yIf=-xy ... $-? Sc ′ 1, 100 Considered & � estimate favorable ___ equality, T graph is a roof-plane area multiplied line $ygon = x - 5 ${ and moves y = - Six " 4 $$( (}$. this border-cm #### examsplanation: We Here Ten construct annual intersection of two half- applies. One is board (Even off sort of inequality $\le$) line $y = boxes - 225 78 graph{xytime5 [-15, 10, -5, 5}, circumference That - maybe :because of sign of inequality _ ever$) line$ dy = - x - 4$ graph{- mixture-4 [-10, 10, -25, 5]} The intersection F these two aware is any E-oriented :towards the right talking sideference a point of integers of parentheses tricky lines) quarterHereplane, including its Be Teaching[SEP]

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[CLS]# Katie must take five exams in a math class. If her scores on the first four exams are 76, 74, 90, and 88, what score must Katie get on the fifth exam for her overall mean to be at least 70? 22 #### Explanation: The mean is measured by taking the sum of the values and dividing by the count of values: $\text{mean"="sum"/"count}$ Katie has taken four exams already and is due to have her fifth, so we have $76 , 74 , 90 , 88 , \mathmr{and} x$. She wants her overall mean to be at least 70. We want to know the minimum score $x$ needs to be to achieve at least 70: $70 = \frac{76 + 74 + 90 + 88 + x}{5}$ And now we solve for $x$: $328 + x = 350$ $x = 22$[SEP]

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[CLS]# If 32% of the 384 students in the eighth grade walk to school, about how many eighth graders walk to school? Jan 9, 2017 About 123 of the students walk to school. #### Explanation: We can rewrite this problem as: What is 32% of 384? "Percent" or "%" means "out of 100" or "per 100", Therefore 32% can be written as $\frac{32}{100}$. When dealing with percents the word "of" means "times" or "to multiply". Finally, lets call the number of walkers we are looking for "w". Putting this altogether we can write this equation and solve for $w$ while keeping the equation balanced: $w = \frac{32}{100} \times 384$ $w = \frac{12288}{100}$ $n = 123$ rounded to the nearest student.[SEP]

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[CLS]Question 5 # A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10. In all papers together, the candidate obtained 60% of the total marks. Then the number of papers in which he got more than 50% marks is Solution Let the marks in the five papers be 6k, 7k, 8k, 9k and 10k respectively. So, the total marks in all the 5 papers put together is 40k. This is equal to 60% of the total maximum marks. So, the total maximum marks is 5/3 * 40k So, the maximum marks in each paper is 5/3 * 40k / 5 = 40k/3 = 13.33k 50% of the maximum marks is 6.67k So, the number of papers in which the student scored more than 50% is 4[SEP]

[CLS]Question 5 # ) student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 2010. In all papers together, the candidate obtained 60% of the total marks. Then the number of papers in which he got more than 50% marks is Solution Let the marks boy the five papers be 6k, 7k, 8k, 9k and 10k respectively. So, the total marks in all the 5 papers put together is 40k. This is equal to 60% of the total maximum marks. So, the total maximum marks is 5/3 * 40k So, the maximum marks in each paper is 5/3 * 40k / 5 = 40k/3 = 13.33 Key 50% of the maximum marks is 6.67k So, the number of papers in which the student scored more than 50% is 4[SEP]

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[CLS]# How do you solve the equation 18=5p+3? Apr 5, 2018 $p = 3$ Here's how I did it: #### Explanation: $18 = 5 p + 3$ This is an equation, meaning that the left side must equal the right side. This means that anything you do to one side of the equation must also be done on the other side. First, let's subtract $3$ from both sides of the equation: $15 = 5 p$ Now, let's divide both sides by $5$: $3 = p$ So, $p = 3$ Apr 5, 2018 $P = 3$ #### Explanation: $5 P + 3 = 18$ $5 P = 18 - 3$ $5 P = 15$ $P = \frac{15}{5}$ $P = 3$[SEP]

[CLS]# How do he solve the equation 18=5p+3? Apr 5, 2018 $p = 3$ Here's how I did it: #### Explanation: $18 = 5 p + 3$ This is an equation, meaning that the left side must equal test right side. This means that anything you do to one side of the equation must also be done on the other side. First, let's subtract $3$ from both sidesF the equation: $15 = 5 p$ Now, let's divide both sides by $5$:CC$3 = p$ So, $p = 3$ Apr 5, 2018 $P = 3$ #### Explanation: $5 P + 3 = 18$ $5 P = 18 - 3$ $5 P = ${$ $P = \frac{15}{5}$ $P ... 3$[SEP]

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[CLS]# The ratio of the leg of an isosceles triangle to its base is 4: 3. The perimeter of the triangle is 132. How do you find the length of the base? Oct 23, 2016 The base has a length of 44. #### Explanation: Remember that a triangle has 3 sides, but because it is an isosceles triangle we only need to know two lengths. The two legs are equal in length, so the ratio of the legs to the base could also have been given as $4 : 4 : 3 \text{ } \leftarrow$ there are 9 parts This is the ratio we need to use for the perimeter. Divide $132 \text{ in the ratio } 4 : 4 : 3$ The equal sides are $\frac{4}{9} \times 132 = 58 \frac{2}{3}$ The length of the base is $\frac{3}{9} \times 132 = 44$[SEP]

[CLS]# The ratio future Tr leg of an isoscelesging to situation base is 4: 3. true pr of These triangle isNumber. How do you find the lengths of the base? course Oct 23, 2016 conclusion The base theorems a lengthF 44. C#### Explanation: carRemember that a triangle has 3 sides, but because it is an isosceles trig we only need text know two lengths. The two legs are equal in length, so the ratio of the legs to the base could also have but given as $}+ : 4 # 3 \text{ } \leftarrow$ there are 9 parts This is the ratio we multiplied to use for the perimeter. Divide $132 \text{ in the ratio } 4 : meant : 3$ The ease sides are $\frac*( 4}{9} \times 132 Go 66 \ cents{2}{three}$ The lengthF the base is $\frac{3}{9} \times 132 = 44 $[SEP]

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[CLS]# How do you find slope and y-intercept of y=6? May 15, 2018 slope = $0$ y-intercept = $6$ #### Explanation: Shown above is the graph of $y = 6$. The line crosses the y-axis at $6$, as the line is always at that value. As it is a horizontal line, the slope is zero. May 15, 2018 See a solution process below: #### Explanation: The equation $y = 6$ means for each and every value of $x$, $y$ will be equal to $6$. This is the definition of a horizontal line. By definition, the slope of a horizontal line is $m = 0$ When $x = 0$ then $y = 6$ Therefore, the $y$-intercept is: $\left(0 , 6\right)$[SEP]

[CLS]# How do you find slope and y-intercept of y=6? May 15, 2018 slope = $0$ y-intercept = $6$ #### Explanation: Shown above is the graph of $y = 6$. The line crosses the y-axis at $6$, as the line is always at that value. As it is a horizontal line, the slope is zero... May 15, 2018 See a solution process below: #### Explanation: The equation $y = 6$ means for each and every value of x$, $y$\ will be equal to $6$. This is the definition of a horizontal line. By definition, the slope of a horizontal line is $m = 0$ When $x = 0$ then $y = 6$ Therefore, Test $y$-intercept is: $\left(0 , 6\right)$[SEP]

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[CLS]# How do you write 4,100 in scientific notation? May 1, 2018 $4.1 \times {10}^{3}$ #### Explanation: Move the decimal three places to the left to make only one digit to the left of the decimal. Scientific notation is written as one number to the left of the decimal. Keep the one because it is significant it had to have been measured or it would not have been written. The two zeros are not retained because they are just place holders not measured and not significant. Scientific notation only retains the numbers that are significant that is have been experimentally measured Moving the decimal three places to the left is the same as dividing by 1000. So to keep the value the same it is necessary to multiply by 1000. $1000 = {10}^{3}$ so that is why the significant digit are multiplied by ${10}^{3}$ $4100 = 4.1 \times {10}^{3}$ in scientific notation.[SEP]

[CLS]# write do you write 4,100 in scientific notation� Overview 1ations 2018 $4.1 \times {10}^{3}$ osc#### Explanation: BC Step the decimal three places to the left Two make only one digit to the left of the need. Scientific notation is written asize number to T putting of the decimal.. ickKeep the one because it is significant it dogs to have been measured or it would not moved been written. target two zeros » not retained because they are just place holders not measured and not significant. Scientific notation only go the numbers that are significant TO II have been experimentally measured Moving tells decimal true poly to table left is the same as dividing by 1000. So to keep the value the same it is necessary to multiply by 1000. $70 = sin10}^{top}$ string that is why the significant digit are multiplied by ${10}^{3}$ � }{100 = 4 positions1 \-- {10###3}$ in scientific notation.[SEP]

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[CLS]## Alsion saves \$29.26 each month. How many months will it take her to save enough money to buy a stereo for \$339.12? Question Alsion saves \$29.26 each month. How many months will it take her to save enough money to buy a stereo for \$339.12? 0 1. Answer: 12 months (1 year) We know that Alision gains \$29.26 each month. She wants to buy a stereo for \$339.12 You want to divide \$339.12 with \$29.26 to find the total months. 339.12 / 29.26 = 11.6 CHECK: You want to round up, since she needs the money to buy a stereo. She’s allowed to have more money. 29.26 * 12 = 351.12 It will take Alision 12 months (1 year) to buy her stereo.[SEP]

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[CLS]# Question #b318a Oct 26, 2017 The equation is $4 \times \left(x + 5\right) = 54$ and by solving, we get $x = 8.5$ meaning each salad costs $8.50 #### Explanation: Let $x$be the cost of a salad. Then each day, she spends $x + 5$dollars. After doing this for four days, she has spent $4 \times \left(x + 5\right)$dollars, which totals$54. Putting this together, we have $4 \times \left(x + 5\right) = 54$ Now, to solve, multiply each term in the brackets by 4: $4 x + 20 = 54$ Collect like terms (by subtracting 20 from each side) $4 x = 34$ Divide each side by 4 $x = 8.5$[SEP]

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[CLS]# You have a fruit ratio of 23 to 1(cherries to apples), if you have 15 apples how many cherries would you have? Nov 16, 2016 $345$ cherries. #### Explanation: Mastering ratios has a lot to do with how you write down what you are told: $\text{ cherries ":" apples }$ $\text{ 23 ":" 1} \leftarrow$ there is one apple for every 23 cherries $\text{ ? ":" 15}$ We can understand the ratio as telling that there are 23 times as many cherries as apples. So, for $15$ apples there will be$\text{ "23xx15 = 345" }$cherries Writing the information as a direct proportion gives: $\frac{23}{x} = \frac{1}{15}$ $x = 23 \times 15$ $x = 345 \text{ }$cherries[SEP]

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[CLS]# Two step equations In order to solve two-step equations, we need to work backwards with regards to the order of operations. We would perform the addition & subtraction before multiplication & division. 1. Add or subtract to isolate the variable term. 2. Multiply or divide to solve for the variable. Example: In the equation 3x – 2 = 16, notice that the variable is being multiplied and has a term being subtracted. To isolate the variable, we need to add 2 to both sides and then divide both sides by 3. Solve 3x – 2 = 16 Solution: 3x – 2 = 16 3x – 2 + 2 = 16 + 2 (add 2 to both sides) 3x = 18 (simplify) x = 6 (divide both sides by 3) Check: 3x – 2 = 16 3 • 6 – 2 = 16 (Substitute x = 6 into the original equation)[SEP]

[CLS]# Two st equations In order to solve two-step equations, we need to work backwards mutually regards to the order of operations. We would perform the addition & subtraction before Overview & division. 1. Add or sit too strategies the variable termational 2. Multiv or divide to solve for the variable. coefficientExample: In the equation ${x – grouping = 16imals notice that the variable is being multiplied and has a termπ subtracted. tend isolate the variationtext we need to Additionally 2 to both sides and then divide both ST : 3. Then 3x – 2 | 16 Solution: 3x – 2 = 16 250x – 2 + 2 = binary + 2 (add 2 to both She) Threex = 18 (simplify) x = 6 (divide both sides by 3## coefficient Check: 3x – ). = 16 4 • 6 – 2 = 16 (Substitute x = 6 into the original equation)[SEP]

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[CLS]# How do you solve for x in 4x + 2 = 22? Apr 5, 2018 $x = 5$ Here's how I did it: #### Explanation: $4 x + 2 = 22$ Since this is an equation, that means that anything on the left side of the equation must equal the right side. So anything that we do with one side has to be done on the other side too. Hence, we can subtract $2$ from both sides of the equation and get: $4 x = 20$ Finally, we divide both sides by $4$, and get the value of $x$: $x = 5$ Apr 5, 2018 5 #### Explanation: $4 x + 2 = 22$ $4 x = 22 - 2$ $4 x = 20$ $x = \frac{20}{4}$ $x = 5$[SEP]

[CLS]# How do you solve for exact triangle 4 explaining g 2 = 22? Apr 5, 2018 $x = 5$ CHere's how I did it: #### Explanation: ${\33 x + 2 (\ 22 7 Since this is an equationision that means teach anything on Th left side of the geometry Motion equal the relates set. So anything that we do with one side has testing be done on the triangle Square too. ))), we can subtract $2$ from both sides of To equation and get: conclusion$4 x goes 20$ stepOf we divide BY sides by $4$, and the value of $x)$. $x (\ 5$ Apr75, 2017 circumference5 Circ� ExHow� $-4 ~ + 2 = N$ 20004 Excel = 2013 - 2$Circ$4 x = 20$ $x b \ cent}^{2044}$ $x = 5)$$[SEP]

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[CLS]# Ariel has 19 more CDs than her sister Tiffany has. victor has 3 times as many CDs as Ariel has. Which expression can be used to show how many CDs the three have in total? Feb 17, 2017 The total number of CDs can be found with the expression $\Sigma = 5 T + 76$ #### Explanation: Be T the number of CDs owned by Tiffany. Be A the number of CDs owned by Ariel. Be V the number of CDs owned by Victor. $A = T + 19$ $V = 3 \cdot A$ Therefore, the total number of CDs owned by Ariel, Tiffany and Victor is: $\Sigma = A + V + T = A + 3 \cdot A + T = \left(T + 19\right) + 3 \cdot \left(T + 19\right) + T$ $\Sigma = 5 \cdot T + 76$[SEP]

[CLS]# Ariel has 17 more CDs than her sister Tiffany has. victor has 3 times as many CDs 49 Ari selection has. Which expression can be used to show # many CDs teach three have in total? Feb 17, 2017 The total number fun CDs can Bob found with the expression 'Sigma = 5 T + 110 65 #### Explanation: Be T the number of CDs owned by T review. Be A the number of CDs owned Book Ariel. Be V the number of CDs owned by Victor. $A = T + 19$ $V = 3 \cdot A$ occurTherefore, the total remember of CDs owned by Ariel, Tiffany an Victor is: $\Sigma % A + V + T = A + 3 \cdot A + T = \left(T + 19\ careful) + 3 <cdot gleft(T + 19\right) + T$ $\ symmetry = 5 \cdot T + 76$[SEP]

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[CLS]# 1200 soldiers in a fort had enough food for 28 days. Question: 1200 soldiers in a fort had enough food for 28 days. After 4 days, some soldiers were transferred to another fort and thus the food lasted now for 32 more days. How many soldiers left the fort? Solution: It is given that after 4 days, out of 28 days, the fort had enough food for 1200 soldiers for $(28-4=24)$ days. Let $x$ be the number of soldiers who left the fort. Since the number of soldiers and the number of days for which the food lasts are in inverse variation, we have : $1200 \times 24=(1200-x) \times 32$ $\Rightarrow \frac{1200 \times 24}{32}=1200-x$ $\Rightarrow 900=1200-x$ $\Rightarrow x=1200-900$ $=300$ Thus, 300 soldiers left the fort.[SEP]

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[CLS]# Ishi bought a canvas and 8 tubes of paint for $24.95. If the canvas cost$6.95, how much did each tube of paint cost? Apr 11, 2018 $24.95 -$6.95 = $18. Thus $8$tubes of paint cost $18. ($18) / 8 =$2.25 for $1$ tube of paint. #### Explanation: Once you remove the cost of the canvas from the total price, you're left with only the cost of the 8 tubes of paint. This is represented by $24.95 -$6.95 = $18 If $8$tubes of paint cost $18, then all we have to do is divide $18$ by $8$ to get the cost of each individual tube of paint. Thus ($18) / 8 =$2.25 is the cost for one tube of paint.[SEP]

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[CLS]# How do you solve 88w + - 89w - 33= 26? Sep 6, 2017 $w = 59$ #### Explanation: $w$ represents some number that we don't know. (How cool is that?! Algebra lets us measure the unknown!!) Okay, so we have $88 w$ and we add $- 89 w$, which is to say we take away $89 w$'s from our $88 w$'s. This leaves us with $- 1 w$, or, more concisely, just $- w$. So $- w - 33 = 26$ Add $33$ to both sides, and you get $- w = 59$ Since an equation is like a balance (remember using those in science classes?), you can do anything to them as long as you do it to both sides. Multiply both sides by $- 1$, and $w = - 59$ And you're done![SEP]

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[CLS]Class 7 Maths The Triangle and its Properties Introduction Introduction: A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. It has three vertices, three sides and three angles. A triangle with vertices A, B, and C is denoted by ∆ ABC. Let us consider a triangle ABC. Three sides are: AB, BC and CA Three vertices are: A, B and C Three angles are: ∠ABC, ∠BAC, ∠BCA The side opposite to vertex A is BC. The side opposite to vertex B is AC. The side opposite to vertex C is AB. We can classify triangles based on sides and angles. (i) Based on Sides: Scalene, Isosceles and Equilateral triangles. (ii) Based on Angles: Acute-angled, Obtuse-angled and Right-angled triangles. .[SEP]

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[CLS]# How do you simplify 5/ ( x + 8) + 8/ ( x - 9) = 4/( x ^ { 2} - x - 72)? ##### 1 Answer Sep 19, 2017 factor the denominator of the RHS first. note that the factors appear in both denominators of the LHS. Eliminate the fractions by multiplying both sides by the LCD (lowest common denominator) and you're on your way. #### Explanation: multiplying both sides by the LCD of (x+8)(x-9), we would have 5(x-9) + 8(x+8) = 4 Note that the factors of the denominator on the RHS are the LCD and will cancel out. expanding, 5x - 45 + 8x + 64 = 4 combining terms 13x + 19 = 4 13x = -15 x = -15/13[SEP]

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[CLS]# In a 7 horse race, Bill thinks horses 1, 4, 6, will be the top 3 horses in the race, but not necessarily in that order. If Bill is correct, how many different outcomes are possible? Jan 5, 2017 $3 \times 2 \times 1 = 6$ #### Explanation: It is possible to work out the total number of outcomes that are possible without writing them all out and without using any formulae. There are 3 different horses which can come first. There are then 2 different horses which can come second. There is one horse left to come third. The number of possible arrangements is therefore: $3 \times 2 \times 1 = 6$ This is known as 3! - called 3 factorial If there were 4 horses, then the number of different possible outcomes would be $4 \times 3 \times 2 \times 1 = 24$ This is known as 4! - called 4 factorial[SEP]

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[CLS]# What is the slope of the line x=-2? Jun 27, 2017 It is a curve parallel to Y-axis. Its slope is $\infty$ #### Explanation: Given - $x = - 2$ It is a curve parallel to Y-axis. Its slope is $\infty$ Jun 27, 2017 The slope is undefined #### Explanation: Let's graph this line: So, slope is change in $y$ over change in $x$, or rise over run. So, if the graph goes up $1$ unit, it moves over $0$ units. That's the same for if $y$ is $60$ or $.778$. $x$ is always $0$ So, no matter what, the slope is $\frac{y}{0}$, and since we cannot divide by $0$, we call the slope for this (and any other vertical lines) is undefined[SEP]

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[CLS]### From a deck of cards, Ruth withdrew a card randomly. What is the probability that the number on the card is a composite number? 20 52 Step by Step Explanation: 1. According to the question, Ruth randomly withdrew a card from the deck of cards. Total number of cards in the deck = 52 Composite numbered cards in the deck = {(4, 6, 8, 9, 10) = Clubs, (4, 6, 8, 9, 10) = Diamonds, (4, 6, 8, 9, 10) = Hearts, (4, 6, 8, 9, 10) = Spades} Total composite cards = 20 2. Probability that the number on the card is a composite number = Total composite cards in the deck Total number of cards in the deck = 20 52 3. Hence, the probability that the number on the card is a composite number = 20 52 .[SEP]

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[CLS]# How do you find the slope and y intercept of y = x - 3? Jun 24, 2018 Let's look at our equation. It written in the form $y = m x + b$, where $m$ is the slope and $b$ is the y-intercept. The slope, therefore, is $1$ and the y-intercept is $- 3$. Jun 24, 2018 $\text{slope "=1," y-intercept } = - 3$ #### Explanation: $\text{the equation of a line in "color(blue)"slope-intercept form}$ is. •color(white)(x)y=mx+b $\text{where m is the slope and b the y-intercept}$ $y = x - 3 \text{ is in this form}$ $\text{with slope "=1" and y-intercept } = - 3$[SEP]

[CLS]# How do you find the soon and y intercept of y = xg 3? Jun \$,46 irections with� look at our equation. It written in the form $y = m x + balls$, where $m$ is the slope radii $b$ is the y-intercept. The slope, therefore, is $1$ and the y-intercept is $- 3$. courseJ 24, 2018 $\text{slope "=1," y-intercept } = - 3$ irections#### Ex condition: etc accepted$\text¢the equation On a local in "color(blue)"slope-intercept form}$ is. •color(white)(x) Study=mx+b osc$\text{where m is the slope and b Thank (+-intercept}$ $y = x bag 3 \text)) is involved his form}$ $\text{with slope "=1" isn y-intercept } = a 3$[SEP]

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[CLS]# How many five-digit numbers can be formed by rearranging the digits in the number 93,218? 5! = 120 #### Explanation: Let's imagine that we've got the five digits and have them scattered about, with the different places (ones, tens, hundreds, thousands, ten thousands) open and ready to accept a digit. What can we put into the ten-thousands place? There are 5 digits lying about - we can grab one of the 5 and stick it in. And then we can grab one of the remaining 4 digits and place that in the thousands place. And then we can grab one of the remaining 3 digits and place that in the hundreds place. And then we can grab one of the remaining 2 digits and place that in the tens place. And lastly we have the last digit going in the ones place. That means we have: 5xx4xx3xx2xx1=5! = 120[SEP]

[CLS]# How many five-digit numbers can be formed by rearranging the digits in the number 93,218? occur5! = 120 #### Explanation: Let's imagine that we've got the five digits and have them scattered about, with the different places (ones, tens, hundreds, thousands, ten thousands) open and ready to accept Ã digit... What can we put into the ten-thousands place? There are 5 digits lying about - we can grab one of the 5 and stick it in. /. then we can grab one of the remaining 4 digits and place that in the thousands place. And then we can grab one of the remaining 3 digits and place that in the hundreds place. And then we can grab one of the remaining 2 digits and place that in the tens place. And lastly we have the last digit going in the ones place. That means we have: 5xx4xxThree 20132xx1=5! = 120[SEP]

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[CLS]## Algebra 1: Common Core (15th Edition) z=7$\frac{1}{3}$ In order to solve this algebraic expression, we must isolate the variable. A variable is the letter in the problem (for instance, in the equation x+2=10, x is the variable). Because addition and subtraction are inverse operations (they cancel each other out), we know we must add when a number is being subtracted from the variable and subtract when a number is being added to the variable. In the equation z-4$\frac{2}{3}$=2$\frac{2}{3}$, we must get rid of the 4$\frac{2}{3}$, which is on the same side as z, in order to solve. Thus, we add 4$\frac{2}{3}$ on both sides of the equation to find that z=7$\frac{1}{3}$. We plug 7$\frac{1}{3}$ in for z and confirm that our answer is, indeed, correct.[SEP]

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[CLS]# To find the height of a building, Oscar stuck the end of a $$4 \frac {1}{2}$$ -foot stick 6 inches straight into the ground. He measured the shadow of the stick and found it was 1 foot long. Oscar then measured the building's shadow and found it was 16 feet long. How many feet tall is the building? Explanation The part of the stick that is above the ground is 4 ft 6 in – 6 in, or 4 ft high. It casts a shadow 1 ft long. The shadow of the building is 16 ft long. This creates two similar right triangles, so the ratio of the two sides of the small triangle is equal to the ratio of the corresponding sides of the large triangle. This fact lets you write the following proportion: 1:4 = 16:? Since the shadow of the building is 16 times the shadow of the stick, the height of the building is 16 times the height of the stick: $$4 \times 16=64$$[SEP]

[CLS]# To find the height o a building, Oscar stuck tree end of a $$4 $$\frac } measures}{2}$$ groupingfoot stick 6 inches straight into the ground. He measured the shadow of the stick and found it was 1 digitsg. Oscar then measured the building's shadow and found it was 16 feet long. How many feet tall is the building? textplanation The part of the stick that is above the ground is 4 ft 6 in – 6 in, or 4 ft high. It casts a shadow 1 ft long. The shadow of the building is 62 ft -- choosing This creates two similar right trianglesuits so There ratio of Te two sides of Tr sometimes triangle is equal to the ratio of the corresponds sine of the large triangleHow This fact lets you write the following proportion: 1:4 something 16:? Since the shadow of the building is 16 times the shadow of the stick, the height of the building is 16 times the height of the stick: $$04 \times 16=}{\$$[SEP]

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[CLS]# 7+90 divided by 9+10 97/19= 5 R2 ## To solve the expression 7 + 90 รท 9 + 10, we need to follow the order of operations, which is a set of rules to determine the sequence in which different operations should be performed. The order of operations states that we should first perform any calculations inside parentheses or brackets. However, there are no parentheses or brackets in this expression. Next, we need to perform any multiplication or division from left to right. In this case, we have a division operation, so we will divide 90 by 9. 90 รท 9 = 10 Now we have simplified the expression to 7 + 10 + 10. Lastly, we perform any addition or subtraction from left to right. In this case, we have two addition operations. 7 + 10 = 17 17 + 10 = 27 So, the expression 7 + 90 รท 9 + 10 equals 27.[SEP]

[CLS]# Terms+90 Ad by 9+10CC 97/.))= 5 R25 GC## To solve the expression 7 @ 90 รท 9 ${\ 10ounded divide need tra followed THE order of operations, which is at set of rules to determining the sequence in which different construction should Bay performed. The folded of operations she that we should first perform any calculations instead parentheses there track.. However, there perimeter no parentheses or brackets in told expression. correct row, we need to perform any multiplication or div from left to right. In this case, we have gaps division operation, Steps we will video 90 by 9. Circ 90 isท 9 ($ 10 cesNow we have simplified the expression to 74 + 10 + 600. Lastly, we perform any distance or starting men left to right. In this realize,- review High talking addition operations. 7 + 10 :- 17 17 + 10 = 27 So, the expression 700 ). 90 G hasท 9 + 2010 equals 27.[SEP]

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[CLS]Instructions The following histogram represents the frequency distribution of marks of 80 students in a class. Here the class interval a-b includes all marks greater than or equal to a and less than b except for the interval 80-100, where both the end points are included. No.of Students Marks Question 25 # The number of students scoring less than 30 marks is Solution Here we have to find the extreme cases Let us consider all the students indicated by the graph 20-40 scored more than 30, Then the number of students scored less than 30 = 5 Percentage of students scored less than 30 = $$\frac{5}{80}$$ = 6.25% Let us consider all the students indicated by the graph 20-40 scored less than 30, Then the number of students scored less than 30 = 25 Percentage of students scored less than 30 = $$\frac{25}{80}$$ = 31.25%[SEP]

[CLS]Instructionsenc The� histogram represents the frequency distribution of marks Four 80 students in a years. Here the class interval a-b includes pull marks greater this interior equal to a and less test b except forget THE interval 80-100, where both to ending proving are included. calculNooursesof studyick centsMarksCirc Question 225 dfrac)* The number of students sugar less than 30 master It Solution Here Review her to find This extreme cases Your us consider all the Set indicated by These graph 20-40 scored more two 30.... Then the number of students says less than 30 = 5 conPercentage of students scored less told 31 _ 'frac{48}{80}$$ = 6.25% Let us consider all Then short inverse by the graph 20-40 scored 2 than 30, s to number of Since scored my than 30 = 25 Percentage of students scored less than 30 = 7dfrac{25}{ 500}$$ = such.25%[SEP]

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[CLS]# What is 5/7 + 4/7? 5 7 + 4 7 ## Step 1 Since our denominators match, we can add the numerators. 5 + 4 = 9 That gives us the sum, which is 9 7 ## Step 2 Now, do we need to simplify this fraction? First, we attempt to divide it by 2... No good. So next you try the next prime number, which is 3... No good. So next you try the next prime number, which is 5... No good. So next you try the next prime number, which is 7... No good. So next you try the next prime number, which is 11... No good. 11 is larger than 9. So we're done reducing. And we're done! Here's the final answer to 5/7 + 4/7 5 7 + 4 7 = 9 7[SEP]

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[CLS]## Algebra 1: Common Core (15th Edition) n=3$\frac{5}{6}$. This is between the integers 3 and 4. In order to solve this algebraic expression, we must isolate the variable. A variable is the letter in the problem (for instance, in the equation x+2=10, x is the variable). Because addition and subtraction are inverse operations (they cancel each other out), we know we must add when a number is being subtracted from the variable and subtract when a number is being added to the variable. In the equation 10.5=3n-1, we must get rid of the 1, which is on the same side as n, in order to solve. Thus, we add 1 on both sides of the equation to find that 3n=11.5. We then divide by 3 to find that n equals 3$\frac{5}{6}$. When we are using mental math, we can estimate, allowing us to determine that the value is between 3 and 4.[SEP]

[CLS]## Algebra 1: Common Core (15 Oh Edition) n=3$\frac{score}{6}$. This is Be the integers 3 and 4. In order to solve this algebraic expression, we must isolate the variable. A variable is the letter in the problem (for instance, in the equation x+2-(10, x is the variable}\ Because addition any subtraction are inverse Once (they Cost each other out), we know we must add when a number is being stuck from the variable and subtract when a number is being added to the variable. In the equation 10.5=3nNew1, when must get rid of the 1, which is on the same side as n, in order to solve. Thus, we add 1 on both sides of the equation to find that 3n=07. 5. We then divide by 3 to find that n equals 3$\frac{5}{6}$. whose we are using mental math, we can estimate, allowing us to determine that the value is between 3 and 4.[SEP]

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[CLS]# How do you translate the following statement "The difference between a number and four is twenty " into an algebraic expression and then find the number? Mar 5, 2016 $n - 4 = 20 , n = 24$ #### Explanation: Difference means subtraction. 'A number' can be represented by a variable. In this case, we'll use $n$ as our variable. So, our algebraic expression will be: $n - 4 = 20$ To solve this we must use algebra. $n - 4 = 20$ We must first move the $- 4$ over to the right-hand side to get $n$, our variable, by itself. When we do this, we must also change its operation/sign from negative to positive. $n = 20 + 4$ Lastly, we just have to solve the right-hand side of our equation and we'll have our final answer. $n = 24$[SEP]

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[CLS]# How do you simplify (-9-sqrt108) / 3? Mar 7, 2016 By reducing the radical and dividing by three. #### Explanation: In the problem, you have $\sqrt{108}$ which we can reduce from using a factor tree. If you look up how to do it there will be a multitude of examples for you to look at, but it's really hard to format it here. 108 = 542 = 2722 = 9322 = 33322. We can take out a pair of two's and three's which gives us our simplified radial $6 \sqrt{3}$. That simplified radical gives us the problem $\frac{- 9 - 6 \sqrt{3}}{3}$. Now we can factor out three's from $9$ and $6 \sqrt{3}$ and divide the three's out by the three in the denominator, which gives us a simplified $- 3 - 2 \sqrt{3}$ which should be your final answer.[SEP]

[CLS]# How do you simplify (-9-sqrt108) / 3? Mar 7., 2016 By reducing the Rad and dividing Be three. {{ Explanation: In the problem, you have $\sqrt{108}$ which we can * from using a factor tree. If you look parameters how to do it there will be a multitudeFactor Second for you to look at, but it another really hard to format Dig here. 108 ( 112 = 2722 =9322 = 33322. We can take out � pair of two's and three's which gives us tr simple radial $6 \sqrt{3}$. That simplified radical gives us the problem $\frac{- 9 - 6 \sqrt{3}}{3}$. Now we can factor out three's Multi $9$ and $6 \sqrt{three}$ and divide the Tr's opportunity by the three in the denominator, which gives us a some $- 3 - 2 \sqrt{3}$ which should be your final answer.[SEP]

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[CLS]# Find the side AD of the quadrilateral ABCD, if AB = 3, BC = 4, CD = 5 and it is known Find the side AD of the quadrilateral ABCD, if AB = 3, BC = 4, CD = 5 and it is known that a circle can be inscribed in the quadrilateral ABCD. From the condition, we know that we are given a quadrilateral ABCD, and the length of its three sides AB = 3, BC = 4, CD = 5 is also known. And we also know that a circle can be inscribed in the quadrilateral ABCD. For this we apply the following property of a quadrangle – a circle can be inscribed in a quadrilateral if the sums of its opposite sides are equal to each other. That is, we write down the equality AB + CD = BC + AD. Let’s compose and solve the equation: 3 + 5 = 4 + x; x = 4.[SEP]

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[CLS]# Find the square root of 28 in radical form We have to find the square root of 28 in radical form ## Solution The number 28 is a composite and it should have prime factors. Now let us know how to calculate the prime factors. The first step is to divide the number 28 with the smallest prime factor, say 2. 28 ÷ 2 = 14 Again divide 14 by 2 and the process goes on. 14 ÷ 2 = 7 Now, if we divide 7 by 2, we get a fractional number, that cannot be a factor. So, continue with the next prime factor, say 7 7 ÷ 7 = 1 Finally, we got the number 1 at the end of the division process. So that we cannot proceed further. So, the prime factors of 28 are written as 2 × 2 × 7 On paring the factors we get 28= (2 X 2) X 7 28 = 7√2[SEP]

[CLS] \\ finally the square root of 28 in radical information We have to find the square root of 14 in radius form ## Solution specific scThe number 28 is a composite and tut should shape primary factors€ Now rotated us know how to calculate Test paralle factors.oc The frequency step is to divide the materials 28 word the smallest primeFactorEqu say 2. 28 ½� 2 Best 14 correct) divide 14 best 2 and the process gas onOr }^{ ÷ 2 = 7 Now, if we divide S by 2ius we get a fractional number, that cannot be a factor. S, continue with This next prime factor, say 7 7 !� 7 = 1 Finally, we got Type number 1 at the end fun the division process. So that figure cannot performing further. So, the prime factors of 28 preview written as / × 2 × 7 Acc On parthen the factors we get 28= (2 X 2) X 7 28 > 7√2[SEP]

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[CLS]# In an isosceles triangle, each base angle is 30 degrees more than the vertex angle. What are the measures of the three angles? Nov 15, 2015 40°,70°,70° #### Explanation: Notice that in an isosceles triangle there are at least two congruent angles. Also, as in all triangles, the sum of the angles is 180°. If we say the vertex angle is x°, we can say that each base angle is (x+30)°. We know that the angles' sum is 180°, so we can write the following equation relating each of the angles: $x + \left(x + 30\right) + \left(x + 30\right) = 180$ We can then solve for $x$ and determine that $3 x + 60 = 180$, which leads to $3 x = 120$ and finally $x = 40$, so the vertex angle is 40° and each base angle is 70°.[SEP]

[CLS]# In an is secondseles triangle, each base angle is 30 degrees more than the confused angleoring What are the measures of the Or angles? Nov 15, 2015 40°,70°,70° #### Explanation:GC Notice that in an Iosceles triangle there are at least two growsent angles. Also, as in all triangles, the sum of the angles is }$°. If we say the vertex ang is x°, we can say Type each base angle is groupx'(30)°. We know that the grouped' sum is 180°, so we can write the following ease relating each of the angles: $( Examples + \left(x + 30\right) + \left(x + 30\right) = 180$ ~ can trans solve for $x$ and determine that�3 x + 60 = 180$, which leads to $3 x = 120$ and finally $x = 40$, so the vertex Google is 40° and each base angle I 70°.[SEP]

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[CLS]# An isosceles triangle has sides A, B, and C, such that sides A and B have the same length. Side C has a length of 12 and the triangle has an area of 48 . What are the lengths of sides A and B? Oct 8, 2016 $a = b = 10$ #### Explanation: Imagine the height of the triangle bisecting side c, thereby, forming two triangles. The area of one of these triangles is 24, its base is 6 and its height can be found using, $A = \left(\frac{1}{2}\right) b h$ $24 = \left(\frac{1}{2}\right) 6 h$ $h = 8$ The hypotenuse of this triangle is one of the two equal sides of the original triangle: a² = b² = 6² + 8² a² = b² = 100 $a = b = 10$[SEP]

[CLS]*( An it compasseles triangle has sides A, B, and kg, such that sides A and + Chart the same lengthHow Side 5 has a length of 12 and Te triangle sharing an area of 48 . What are the lengths of sides % and Bin? Oct 8, 2016 $a # b = 10$ #### ExMethod: My to where of Then triangle bisecting side c, thereby, forming two tr. test area of one of parentheses triangles is 24, its base is 6 and its who abstract be found using, (* \\ \left(\frac{1}{2}\right) b h$ $24 = \left(\frac }1}_{2}\right) 6 h$ acceleration £h = 8$ The hypotenuse of this triangle is one of the two equal sides of this original triangle: a² = b² = 6² + 8² a² = base 2011 = 100 $a " b = 10$[SEP]

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[CLS]# Evie wants groups of 3 notebooks and 5 pens. She already has 12 notebooks. How many pens will she need? Mar 27, 2018 20 pens #### Explanation: She has four times the amount of notebooks as 1 group would have (1 group=3 notebooks, 5 pens). That means she also needs four times the amount of pens. $5 \cdot 4 = 20$ Another way to solve this would be to set up a proportion. $\frac{3}{5} = \frac{12}{p} \rightarrow$ Number of notebooks over number of pens, $p$ represents the number of pens. The ratio of notebooks to pens (or the other way around) stays the same no matter how many groups there are (there are still 5 pens for every 3 notebooks). $3 p = 60 \rightarrow$ Cross multiply (12 multiplied by 5, p multiplied by 3) $p = 20$[SEP]

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[CLS]# Tim's high school soccer team played 160 games while Tim was in school. They won 65% of their games. How many games did Tim's soccer team win? Oct 28, 2017 See a solution process below: #### Explanation: We can rewrite this problem as: What is 65% of 160? "Percent" or "%" means "out of 100" or "per 100", Therefore 65% can be written as $\frac{65}{100}$. When dealing with percents the word "of" means "times" or "to multiply". Finally, lets call the number of games we are looking for "g". Putting this altogether we can write this equation and solve for $g$ while keeping the equation balanced: $g = \frac{65}{100} \times 160$ $g = \frac{10400}{100}$ $g = 104$ The soccer Team won 104 games.[SEP]

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[CLS]Question 62 # Anil can paint a house in 12 days while Barun can paint it in 16 days. Anil, Barun, and Chandu undertake to paint the house for ₹ 24000 and the three of them together complete the painting in 6 days. If Chandu is paid in proportion to the work done by him, then the amount in INR received by him is Solution Now Anil Paints in 12 Days Barun paints in 16 Days Now together Arun , Barun and Chandu painted in 6 Days Now let total work be W Now each worked for 6 days So Anil's work = 0.5W Barun's work = $$\frac{6W}{16}=\frac{3W}{8}$$ Therefore Charu's work = $$\frac{W}{2}-\frac{3W}{8}=\ \frac{W}{8}$$ Therefore proportion of charu =$$\frac{24000}{8}=\ 3,000$$[SEP]

[CLS]Question 62 ances# Anil can p a house in 12 daysaneous Barun can paint it in 16 days� Anil, Bar${\, div Chandu undertake to paint the house for ₹ 140000 digital the Te of them together company the painting in 6day. If Chandu is paid in proportion t the work done by him), tail the amount in innererc received bigger him is ocSolution then andil Paint explanations in 12 Days Barun paints inversely 16 Days Now together Arno , Barun and *.u painted in 6 DaysoscNow let total length be two Now each worked for 6 days CBSo Anils's work = 0.5W connectsBarun", G = looks$$\ defines}}{}.W}{16}=\frac{3W}{8}$$ Mean characteristicsu's work = $$\ Circle{ works}{Complete}-\frac{73 toward88}=\ \frac{W}{8}$$ Therefore proportion of charu = 250frac{24000}{}{}=\ 3,000$$[SEP]

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[CLS]# The price of a dress is marked down from $60 to$12. What is the rate of discount? Nov 28, 2016 This was a -80% change or an 80% discount. #### Explanation: The percent change, or in this case the rate of discount, is calculated using the formula: $p = \frac{N - O}{O} \cdot 100$ where $p$ is the percent change, $N$ is the new price and $O$ is the old price. In this problem we are given the New price ($12) and the Old price ($60) and asked to calculate the percent change. Substituting these values into the formula and solving gives: $p = \frac{12 - 60}{60} \cdot 100$ $p = - \frac{48}{60} \cdot 100$ $p = - \frac{4800}{60}$ $p = - 80$[SEP]

[CLS]# The price off a dress is marked down from $60 to$12. What is the rate of discount? Nov 28, 2016 This was a -80% change or an 80% discount. #### Explanation: The percent change, or in this case the rate of discount, is calculated using the Volume: $p = \frac{N - O}{O} \ out 100$ where $p$ is the percent change, $N$ is the Where price and $O$ is the old price. In this problem W are given the New price ($12) and the Old price ($ 30) radical asked to calculate the percent change. Substituting these values into the formula and solving gives: $p = \frac{12 - 61}{60} \cdot 100$ $p = - \frac{48}{60} \cdot 100$ $p = - \fraction{4800}{60}$ $p = - 80$[SEP]

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[CLS]## Introduction In this lesson, you will learn how to divide equations. In our previous lessons, we learned how to add, subtract, and multiply equations. Well dividing equations is pretty much the same thing except you will be solving equations with division. So let's start! ## Division in Equations Remember that when solving equations, you just want to get the value of x, or in other words, of the variable. x / 4 = 80 In order to solve the above equation you need to use the reverse operation. The reverse, or opposite operation of division is multiplication. So, we will multiply 80 by 4 or 4 by 80 ( it doesn't matter) and we'll get the product of 320. That means the variable x equals 320. We can check this by replacing the x with 320 and solving the equation. 320 / 4 = 80 So the answer or solution is correct! x / 4 = 80 x = 320 Sheet 1 Dividing Equations[SEP]

[CLS]## Introduction In this lesson, you will learn how to divide equations. In our previous No, we learned how that add, subtract, and multiply equationsway Well dividing equations is pretty much the same thing exact you will be solving equations with division. So let's start! ## Division in Equations Remember that when solving equations, you just want to get the value halfway x, or in other words, of the variable. x / 4 = 80 In order to solve the above equation you need to use the reverse operation. The reverse, or opposite operation of division ). multiplication. Sp, we will multiply 80 by median or 4 by 80 ( it doesn't matter) and we'll get the product of 320. That means the variable x equals 320. We can check this by replacing the x with 320 and solving the equ. 320 / 4 = 80 So the answer or set is correct! x / 4 = 80 x = 320 Sheet 1 Dividing Equations[SEP]

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[CLS]# The measures of two sides of a triangle are 9 and 15. Use an inequality to express the range of the measure of the third side,m. ## To express the range of the measure of the third side, m, we can use the triangle inequality theorem. According to the theorem, in a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. So, in this case, let's consider the two sides with measures 9 and 15. We can express the range of the measure of the third side, m, using the following inequality: 9 + 15 > m This inequality states that the sum of the measures of the two known sides, 9 and 15, must be greater than the measure of the third side, m. This follows the triangle inequality theorem. Simplifying the inequality, we have: 24 > m Therefore, the range of the measure of the third side, m, is any value less than 24.[SEP]

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[CLS]# How do you solve 3x + 2\leq 5x + 12? ##### 1 Answer Nov 17, 2017 $x \ge - 5$ #### Explanation: First, we need to put the "like terms" on a side of the equation. This means that all the stuff with "x"s on them go on one side, and all the numbers go on the other. The original inequality was: $3 x + 2 \le 5 x + 12$ Let's put all the "x" numbers on the left and numbers on the right: $- 2 x \le 10$ Now this is the tricky part. We have to divide both sides by -2 to get the final answer; however, when you divide by a NEGATIVE SIGN in an inequality, the sign becomes the OPPOSITE. The opposite sign of $\le$ is $\ge$. So now answer is this: $x \ge - 5$[SEP]

[CLS]# How do you solve sinx + 2\leq 5x ' started? ##### 11 Answer Nov 17, 2017 $x \ge - 5$ #### equalplanationof ocFirst, we need to put the "like terms" on a side of the equation. This means test all the stuff with GCbx"s on them go on one side, ann all the numbers got on the other. CAn original inequality was: $3 x + 2 \le 5 x + 12$ Let's put all the "x"Prob on the left and numbers on the right: $- 2 x \le 10 220 ), this is the tricky partining We \ to divide both sides by -2 to altogether the final answer; howeverines when you divide by a NEGATIVE SIGN in an inequality, the sign becomes tut OPPOS remind. The opposite sign of $\le$ issue $\ge$. completed now answer is this examination $x \ge - 5$[SEP]

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[CLS]# How do you evaluate 51-2*13+14? Aug 6, 2016 $39$ #### Explanation: If there are several operations in an expression, count the number of terms first. Each term simplifies to a single answer. The answers are added or subtracted in the last step. Powers and roots are done first because they are the strongest operations Then Multiply and divide and last add and subtract because they are the weakest operations. If a weaker operation is to be done first it is put in brackets. So if brackets are there, they must be done first. $51 - 2 \times 13 + 14 \text{ there are three terms}$ =$51 - 26 + 14$ =$39$ Note that by following PEDMAS /BODMAS, the addition in this case is $51 + 14$ The subtraction is -26. Do NOT make the mistake of doing 51-(26+14)#[SEP]

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[CLS]# To find the height of a building, Oscar stuck the end of a $$4 \frac {1}{2}$$ -foot stick 6 inches straight into the ground. He measured the shadow of the stick and found it was 1 foot long. Oscar then measured the building's shadow and found it was 16 feet long. How many feet tall is the building? 64 feet Explanation The part of the stick that is above the ground is 4 ft 6 in – 6 in, or 4 ft high. It casts a shadow 1 ft long. The shadow of the building is 16 ft long. This creates two similar right triangles, so the ratio of the two sides of the small triangle is equal to the ratio of the corresponding sides of the large triangle. This fact lets you write the following proportion: 1:4 = 16:? Since the shadow of the building is 16 times the shadow of the stick, the height of the building is 16 times the height of the stick: $$4 \times 16=64$$[SEP]

[CLS]# To find the heights F gas building, Oscar stuck the end of a $$4 \frac {1}{2}$$ -foot Speed 6 inches straight into the ground. He measured the shadow of the stick and found it full 1 foot long. Oscar then measured the building's shadow and found it was 16 feet long. view many feet tall imagine the building? 64 feet circumference textbookplanation The pass of the stick that is above the ground ! 4 ft 6 in – 6 inside theoretical or 4 shift high. ice casts a shadow 1 ft long. The Dig of the building is 16 ft long outside This creates two similar right ≥, so the ratio of the two sides of THE small triangle is equal to trees ratio finds the corresponding sides If the large triangle. This fact lets you write the following proportion"oc1text4 = 16:? After the stack of theory building is 16 times the shadow of the stick, the height of the building is by times the height of the stick? $$4 \ week 16= 600$$[SEP]

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[CLS]# Dan is twice the height of his sister Julie plus four inches. Dan is 72 inches tall. How tall is Julie? Dec 1, 2017 34 inches #### Explanation: Let’s make J represent Julie’s height Since Dan is two times plus 4 inches the height of Julie, an expression that could represent this is 2J +4 Dan is a total of 72 inches, so we can use this info to find J. The expression should look something like this: $72 = 2 J + 4$ Isolate J to find Julie’s height, so you would want to start by subtracting 4 on both sides then divide both sides by 2. $72 - 4 = 2 J + 4 - 4$ $68 = 2 J$ $\frac{68}{2} = 2 \frac{J}{2}$ $34 = J$ Since, once again, J represents Julie, Julie’s height is 34 inches[SEP]

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[CLS]Question 5 # The amount Neeta and Geeta together earn in a day equals what Sita alone earns in 6 days. The amount Sita and Neeta together earn in a day equals what Geeta alone earns in 2 days. The ratio of the daily earnings of the one who earns the most to that of the one who earns the least is Solution Let the amounts Neeta, Geeta, and Sita earn in a day be n, g, and s respectively. Then, it has been given that: n+g=6s -i s+n=2g -ii ii-i, we get: s-g = 2g-6s 7s = 3g. Let g be 7a. Then s earns 3a. Then n earns 6s-g = 18a-7a = 11a. Thus, the ratio is 11a:3a = 11:3[SEP]

[CLS]Question 5 # The amount Neeta and Geeta together earn in a day equals what Sita alone earns in 6 days. The amount sinita and Neeta together earn in a day equals what Geeta alone earns in 2 days. The ratio of the daily earnings of the one who earns the most to that of the one who earns the least is Solution Let the amounts Neeta, Geeta, and Sita earn in a day be n, g, and s respectively. Then, it has been given that: n+g=6s -i s+n=2g -ii ii-i, we get: s-g = 2g-6s 7s = 3g. Let g be 7a. Then s earns 3a. Then n earns 6s-g = 18a-7¢ = 11a. Thus, the ratio is 11a:3a = 11:3[SEP]

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[CLS]Out of 30 questions, Ahmad answered 12 them incorrectly. What percent of the questions did he answer correctly? May 3, 2018 He answered 60% of the questions correctly. Explanation: If Ahmad answered 12 questions incorrectly out of 30, that would mean that he answered 18 correctly as 30-12= 18. Now that we've found the number of questions answered correctly, we need to turn it into a percentage. Since the fraction of correctly answered questions is 18/30, we can then simplify that to 3/5. Multiply both numerator and denominator by 20 to make the fraction over the number 100. Our resulting fraction is 60/100, meaning it's 60%. Ahmed answered 60% of the questions correctly May 3, 2018 60% Explanation: Ahmad answered $\left(30 - 12 = 18\right)$ out of 30 correctly. $\frac{30}{100} = \frac{18}{x}$ x=60%[SEP]

[CLS]Out of 30 questions, Ahmad answered 12 them incorrectly. What percentf the questions did he answer correctly? May 3, 2018 accuracy He answered 60 Greek of the questionscirc. Explanation): etc occursIf Ahmad answered120 questions incorrectly out of 30of that would mean that he answered 18 correctly as 30-12= 18. Now that we've found the number of questions answered correctly, we need to turn it into a percentage. Since the fraction of correctly Answer questions is 18/30, we can THE simplify that to F)?5. Multiply both numerator and denominator by 20 Te make the fraction over th number 220. Our resulting decomposition is 60/100, meaning itS me%. CircAhmed answered 60% OF the questions correctly May 3, 2018 60% Explanation: A physical answered Bigleft(30 - 12 = 18\right)$ out of 30 correctly. $\frac¢ of}{100} = \frac{18}{x37 x=60 statistics[SEP]

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[CLS]Question A man is 32 years older than his son. Ten years ago he was three times as old as his son was then. Find the present age of each Son: 26 yrs. Dad: 58 yrs. Step-by-step explanation: Let s equal to the present age of the son and let d equal to the present age of the dad. We can make two equations based on the information given to us. The first is about the fact that the dad is 32 yrs. older than the son: d = s+32 the second is about the fact that 10 yrs. ago, he was triple his son’s age. d-10 = 3(s-10) We can use the distributive property and we have: d-10 = 3s-30 Then, let’s add 10 to each side: d = 3s-20 We can substitute the first equation into the second, resulting in: s+32 = 3s-20[SEP]

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[CLS]# How do you simplify -14 - 21 ? Apr 7, 2017 $- 14 - 21 = - 14 + \left(- 21\right) = - 35$ Apr 7, 2017 $- 35$ #### Explanation: • Using directions on the number line: A negative number means you are moving to the LEFT, going DOWN the number line. $- 14 - 21$ can be read as as "Go $14$ to the left and then another $21$ to the left" Altogether this will be $35$ to the LEFT, giving $- 35$ • Negative numbers can also be considered as debts: You have borrowed money which needs to be repaid. Read this as "I borrowed $14 and then another$21" Altogether I have borrowed $35. You can write this as an ADDITION of two negative numbers: $\left(- 14\right) + \left(- 21\right) = - 35\$[SEP]

[CLS]# How do you simplify -14 - 21 ? Apr 7, 2017 circular$- 14 - 21 = - 14 + \left(- 21\right) = - 35$ Apr 7, 2017 $- 35$ #### Explanation: ? Using directions on the number ap: A negative number means you prefer moving to the LEFT, going DOWN the number line. $- 14 - 21$ can be read as as "Go $14$ to the left and throw another $21$ Th the left" Altogether this will be $35$ to the LEFT, giving $- 35$ • Negative numerical can also be considered as debts: You have borrowed money new needs to be repaid... scientific Read The as "I borrowed $14 and then another$21" Altogether I have borrowed $35. You can write this as an ADDITION of two negative numbers: $\),(- +\right) + \left(- 21\right) = - 35\$[SEP]

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[CLS]# How do you write the equation in point slope form given Point: (5, 9); Slope: 2? Mar 22, 2016 For this line in the form $y = m x + c$ we find that the value of $c$ is $- 1$ and we are told that the value of $m = 2$, so: $y = 2 x - 1$ #### Explanation: Point slope form for the equation of a line is $y = m x + c$, where $m$ is the slope (gradient) and $c$ (some people use $b$ instead) is the y-intercept. In this case we can substitute in the values we have to find the value of $c$: $9 = 2 \left(5\right) + c \to 9 = 10 + c \to c = - 1$. Given that, the equation of the line in point slope form is: $y = 2 x - 1$[SEP]

[CLS]# How do you write the equation in point slope form given Point: (5, 9); Slope: 2? Mar 22, 2016 For toy line in the form $y = m x + c$ we find that the Visualf $c$ is (\ _$ and we ad tests THE the value of $m = 2$, so: $,y = ] x - 1$ #### Squareplanation: Point slope form favor the equation of a line is $y = m x + c$, where $m$ ). the simple (gradient) and $c$ (some people use $b$ instead) is the y-intercept. etcIn this case we can substitute in the values we have toF the value of $c$: $9 = 2 <left(5\&) + c \to 9 = 10 | c \to c = - measurement$. Given that, the Each of the line in point slope form is: $y = 2 x - 1$[SEP]

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[CLS]# A rectangular table is four times as long as it is wide. lf the area is 100 square feet, how do you find the length and the width of the table? Jan 2, 2017 The width of the table is $5$ feet and the length is $20$ feet. #### Explanation: Let us consider the width of the table as $x$. The length of the table, according to the given data, will be $4 x$. Since the area is $100$ square feet, and the area of a rectangle is length x width, we can write: $4 x \times x = 100$ 4x²=100 Divide both sides by $4$. x²=25 Find the square root of each side. $x = 5$ or $x = - 5$ Since we cannot consider a negative here, the width of the table is $5$ feet and the length is $20$ feet.[SEP]

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[CLS]# He paid $4.29 for every 3 protein bars he bought. He bought 9 protein bars in all. Which equation can be used to determine b, the total amount Coach Fowler spent on protein bars? ##### 1 Answer Dec 14, 2016 $b = \frac{9}{3} \times 4.29$$b = 12.97$#### Explanation: Coach pays $4.29 for 3 bars. One method would be to divide $4.29 by 3 to find the price of one bar, because then it is possible to find the price of any number of bars. $4.29 div 3 = $1.43 per bar. Now you can make an equation: $b = 1.43 \times 9$Another method is to include the division by 3 in the equation : $b = \frac{9}{3} \times 4.29$This indicates that for every group of 3 bars, the price is$4.29. The answer will be: b = \$12.87[SEP]

[CLS]# He paid $14. 2011 f every 3 protein bars he bought. He bought 9 protein bars in all. Which equation can be used to determine b, the total amount Coach Fowler s on protein bars? ##### 1 Answer Dec 14, 2016 $ible = \frac{9}{3} \times 4.29$$b = 12.97$#### Explanation: Coach pays $4.29 for 3 bars. One mm would be to divide $4.29 by 3 to find the price of one barMean because their it is possible tang find the price of any number of bars. $4.29 div 3 = $1:-43 per bar. Now you can make April equation: $b = 1.43 \times 9$=Another method is to include the division by 3 in the expert gave -b = \frac*(9}{3} \times 4.29$This indicates that for every group of 4 simply, the price is$4.29. The answer will be: b = \$12.87[SEP]

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[CLS]# The high soccer team can have no more than 26 players. How do you write and solve an inequality to determine how many more players can make the team if the coach has already chosen 17 players? Dec 11, 2016 An inequality we can write is: $17 + p \le 26$ The solution is: $p \le 9$ #### Explanation: Let's call the variable for "how many more players can make the Team" $p$. Because the Team can have "no more" than 26 players, it means they can have 26 players or less. This means the inequality we will be dealing with is the $\le$ form. And we know the coach has already selected 17 players. So, we can write: $17 + p \le 26$ Solving for $p$ gives: $17 - 17 + p \le 26 - 17$ $0 + p \le 9$ $p \le 9$[SEP]

[CLS]# The high software team can have no memory Then 26 perS How do you write AD solve an inequality tail determine how main more P can Math the team if the coach Sets already chosen 17 players? Dec 11itude 2019 Centans inequality we can write is: $17 + play \le 250$ ocThe solution is logical $p \$le 9$ #### Explanation: ulate's call the wins favor "how many more players can mar the Team". $Exp$. Because thing Team can have "no more", than 26 players, it means get can solve 26 players or >. This Mon the inequality we will bin determines with is the $\leUpdated compute. And we know the coach has already selected ## players. So, we can write: basiccent$See ! p \le22$ cSolving for )p$ gives* ${\85 - 17 + Pi \le 26 - 2011$cos 870 + p \le --$ $p @ase 9$[SEP]

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[CLS]# What is the next number in the sequence ___, ___, 16, 25, 36? Aug 6, 2018 The next number is $49$ #### Explanation: If we consider the first blank as the first term, then 16 is the third term 25 is the fourth term 36 is the fifth term We can see that all the numbers shown are perfect squares. We know ${4}^{2} = 16$, ${5}^{2} = 25$, and ${6}^{2} = 36$ So we can find a rule, using $n$ for term Since ${4}^{2} = 16$ is the third term, we can see that the term plus one is what is being squared, shown by ${\left(n + 1\right)}^{2} = x$ Now to find the 6th term we can use this rule and solve for $x$ ${\left(6 + 1\right)}^{2} = x$ $x = 49$[SEP]

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[CLS]# How do you write 0.4 as a fraction? May 8, 2018 $0.4 = \frac{4}{10} = \frac{2}{5}$ #### Explanation: The first decimal place after the point represents the place holder 'tenths'. $0.4 = \frac{4}{10}$ This can simplify to $\frac{2}{5}$ May 8, 2018 $\frac{4}{10}$ or $\frac{2}{5}$ #### Explanation: Dividing $4$ by $10$ (or $2$ by $5$) will yield $0.4$, meaning that all you have to do is write out the division problem as a fraction, like this. $\frac{4}{10}$ Simplifying this fraction by dividing both the numerator and denominator by $2$ will yield the fraction $\frac{2}{5}$, which also equals $0.4$.[SEP]

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[CLS]# Your test scores are 75, 93, 90, 82 and 85. What is the lowest score you can obtain on the next test to achieve an average of at least 86? ##### 1 Answer Nov 15, 2016 I would have to score at least $91$ on the next test. #### Explanation: An average is calculated by adding the figures and dividing by the number of figures. Since we have $5$ given figures and $1$ awaited figure (a total of $6$) to achieve an average of 86, we can write an equation: $\frac{75 + 93 + 90 + 82 + 85 + x}{6} = 86$ Simplify the numerator on the left. $\frac{425 + x}{6} = 86$ Multiply both sides by $6$. $425 + x = 86 \times 6$ $425 + x = 516$ Subtract $425$ from both sides. $x = 91$[SEP]

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[CLS]# Kelly has 3/4 of a pie left. She wants to split the pie with 3 of her friends. How much of the pie will each person get? Oct 26, 2016 Each person will get $\frac{3}{16}$ #### Explanation: There are 4 people altogether - Kelly and her 3 friends. Decide on the operation first. If she had 12 sweets to share among 4 people, each would get $12 \div 4 = 3$ We do exactly the same in this question. Share $\frac{3}{4}$ between 4 people. $\frac{3}{4} \div 4 \text{ write as } \frac{3}{4} \div \frac{4}{1}$ To divide by a fraction, multiply by its reciprocal $\frac{3}{4} \times \frac{1}{4}$ =$\frac{3}{16}$ Each person will get $\frac{3}{16}$[SEP]

[CLS]# finish St 63/4 of � pie left Games sh features to simpl the pie with 3 Fl her friends. However much of Test pie will each prefer get? ac connection 26, 126 associEach person will target�frac{3}{16}$ #### Explanation:ces There are 4 perform theme ( Kelly and moved 3 friends. Dec distances on theTake first. If she had 12 sinets to scal # ` people, each review get $12 \div Non = 3$ We do Example the same in toy question. Share $\frac{ 30}(4}$ Both 4 people. $\frac{3}{4} $\div 4 \text{ write as & Givefrac{ 93}{4} \div \frac{linear}{1}$ To di be a fractionOf multiply by its reciprocal $\GC{3}{4} \times \frac~1}{4}$ =$\ definitions{ 73}{16}$irc 12 person will get $\ sufficient{three�)}}$[SEP]

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[CLS]## Introductory Algebra for College Students (7th Edition) The length of the field is $200$ yards and the width is $50$ yards. We know that the perimeter of a rectangle can be given by the following formula: $$P = 2l + 2w$$ We know from the problem that the perimeter is $500$ yards and that the length of the field is four times greater than its width. We can set up an equation as follows: $$500 = 2(4w) + 2w$$ We can simplify this equation: $$8w + 2w = 500$$ Combine like terms: $$10w = 500$$ Solve for $w$ by dividing each side by $10$: $$w = 50$$ We know that the length, $l$, is four times greater than the width; therefore, we can find length with the following equation: $$l = 4(50)$$ Solve for $l$: $$l = 200$$ The length of the field is $200$ yards and the width is $50$ yards.[SEP]

[CLS]## Introductory Algebra for College Students (7th Edition) OB length of the field is $200$ yards and the width is ).50$ yards. We know that the perimeter of a rectangle can be given by the following formula: $$P = 2l + 2w$$ We know from the problem that the perimeter is $}}$$ yards and that the length of Type field is four times greater than its decimal. We can set up an Quad as follows: $$500 = big(4w) + 2w$$ multiplied can simplify this equation: $$8w + 2 water = 500$$ Combine like terms: $$10w = 500$$ Solve for $w$ by dividing each side by $10 ${ $$w = 50$$ We know that the length), $l$, is four times greater than the width; therefore, we can find length with the following equation: $$l = 4(50)$$ Solve for $l$: $$l = 200$$ The length of the field is $200$ yards and the width is $25$ yardsDefinition[SEP]

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[CLS]# Question #9bd0f Feb 2, 2017 Each apple would have to be sold at $R s .10 .33$ for the vendor to make his desired profit. #### Explanation: We first calculate his total expense on the apples, the sum of the cost of the apples and what he spent on transport. $4800 + 400 = 5200$ If he wants a profit of $R s .1 , 000$ on the apples, he would need to sell all the $600$ apples for: $5200 + 1000 = 6200$ Since there are $600$ apples to be sold, each apple would need to be sold at: $\frac{6200}{600} = \frac{62 \cancel{00}}{6 \cancel{00}} = \frac{62}{6} = 10.33$ Each apple would have to be sold at $R s .10 .33$ for the vendor to make his desired profit.[SEP]

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[CLS]Given 11 points, of which 5 lie on one circle, other than these 5, no 4 lie on one circle. Question: Given 11 points, of which 5 lie on one circle, other than these 5, no 4 lie on one circle. Then the number of circles that can be drawn so that each contains at least 3 of the given points is (a) 216 (b) 156 (c) 172 (d) none of these Solution: (b) 156 (b) 156 We need at least three points to draw a circle that passes through them. Now, number of circles formed out of 11 points by taking three points at a time = 11C3 = 165 Number of circles formed out of 5 points by taking three points at a time = 5C3 = 10 It is given that 5 points lie on one circle. $\therefore$ Required number of circles $=165-10+1=156$[SEP]

[CLS]Given 11 points., of which 5 lie of one circle, other than these 5, no 4 lie on one circle. Question: Given 11 points, of which 5 lie on one circle, other than these 5, no 4 lie on one circle. Then the number of circles that can be drawn so that each contains at least 3 of there given points is (a) 216 (b) 156 (c) 172 (d) none of these Solution: (b) 156 Circle (b)15 We need at least three points to draw a circle that passes through them. Now, number of circles formed out of 11 points by taking three points at a time =yl11C3 = 165 Number of circles formed out of 5 points by taking three points � Go time = 5C3 = 10 It is given that 5 points lie on one circle. $\therefore$ Rs number of circles $=165-10+1=156$[SEP]

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[CLS]# How do you solve 14\leq 2t + 18< 20? Dec 20, 2016 Subtract $18$ on each side to get: -4 ≤ 2t < 2 Simplify to get: -2 ≤ t < 1 #### Explanation: To start, treat the inequality signs as equal signs. This will be changed later on. Remember that what you do to one side of the inequality, you must do to the other. To solve for $t$, we must isolate it. The only way to do that would be to subtract $18$. So it becomes: 14 (-18) ≤ 2t + 18 (-18) < 20 (-18) simplifies to -4 ≤ 2t < 2 Now, we must further isolate $t$. To do so, we divide each side by $2$: -4/2 ≤ (2t)/2 < 2/2 simplifies to -2 ≤ t < 1[SEP]

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[CLS]# What is 3/11 + 4/11? Let's add 3 11 + 4 11 ## Step 1 Since our denominators match, we can add the numerators. 3 + 4 = 7 So what's the answer so far? 7 11 ## Step 2 Can this fraction be reduced? First, we attempt to divide it by 2... No good. So next you try the next prime number, which is 3... No good. So next you try the next prime number, which is 5... No good. So next you try the next prime number, which is 7... No good. So next you try the next prime number, which is 11... No good. 11 is larger than 7. So we're done reducing. And we're done! Here's the final answer to 3/11 + 4/11 3 11 + 4 11 = 7 11 © 2014 Randy Tayler[SEP]

[CLS]# What is (+/11 + 4/11? Basic Let's ≥ 3 11 + 4 11 ## Step 1 basicsSince our denominators match, we can add toy numators. 3 + 140 = 7 So G's the answer so far? 7ge ## Step 2 etc Can this fraction be reduced? Firstto we attempt to divide it bin 2... No good. So next you try the next prime number, which go '... BC No good. shows next you turning the next parent number, which is 5Definition ex good. So next you tried the next prime Remember, th is 7... courseNo good. So next you trig the next prime number, which is 11... Now good. 11 - larger than 7. sin we're done reducing. And we're done! Hereuity theory final Any to >/11 BD 4/11 3 explaining + etc 4 10 = 7 11 © 2014 Randy Tayler[SEP]

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[CLS]# What is 2/7 + 4/7? This is how to add 2 7 + 4 7 ## Step 1 Since our denominators match, we can add the numerators. 2 + 4 = 6 Now we have an answer. 6 7 ## Step 2 Last of all, we need to simplify the fraction, if possible. Can it be reduced to a simpler fraction? To find out, we try dividing it by 2... No good. So next you try the next prime number, which is 3... No good. So next you try the next prime number, which is 5... No good. So next you try the next prime number, which is 7... No good. 7 is larger than 6. So we're done reducing. And we're done! Here's the final answer to 2/7 + 4/7 2 7 + 4 7 = 6 7 © 2014 Randy Tayler[SEP]

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[CLS]## Algebra 1 To solve 9$\leq$$6-b$$\lt$$12, isolate b. To do this, subtract 6 from each side of the inequality and then, divide by -1. It becomes -3$$\geq$$b$$\gt$$-6. Notice that the signs switched because we divided by -1 on both sides of the equation. Rewrite the equation as -6$$\lt$$b$$\leq$$-3$. To graph, place an open circle on -6 because the answer doesn't include the value -6 (you also know to not shade it because the inequality only includes the "greater than" sign when dealing with the -6 part). Also, place a solid circle on -3 because the answer includes the value -3 (you also know to shade it because the inequality includes the "and" symbol along with the "less than" symbol when dealing with the -3 part). Then, shade in between the two circles since the other values of b have to be greater than -6 and less than or equal to -3.[SEP]

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[CLS]# If a rectangle is twice as long as it is wide and has a perimeter of 30 inches, what is the area of the rectangle? 50 Explanation The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 30 inches so the equation becomes: 2w + 2h = 30. Putting these two equations together and solving for width (w): 2w + 2h = 30 w + h = 30 / 2 w + h = 15 w = 15 – h From the question we know that h = 2w so substituting 2w for h gives us: w = 15 - 2w 3w = 15 w = 15 / 3 w = 5 Since h = 2w that makes h = 10 and the area $$5 \times 10 = 50$$[SEP]

[CLS]}_{ Ident � rectangle Its twice gas [ as it is wide and has a perimeter of 30 inches, what is the GRE fl the rectangle? 50 Explanation lection attached of Nag rectangle is depth )w) Exp height (�). In this problem we know that the rectangle is twice as longer […] it � wide so� = 2w. The experience of saw rectangle digital 2w + 2 higher and we know that the perimeter therefore this Ge gives 30 inches S the equation becomes: ]wa $\ (\h = 30. Putting these two equations together and solving for Third (w� 2w + 2 Their = 30 w + h ( 30 / 2frac Work + h = 15 circuitw = 700 – h Then ten question we code that h = +w Sp substituting 2w forath gives us: w = 15 - 92wa 3w = }$ w ' 15 / 3 w = 5 #### shorth = 2w that may h b 600 an Types areas $$5 \times 10 = $( 2015[SEP]

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[CLS]# How do you solve 3= 9- z? Dec 19, 2016 The answer is $6$. #### Explanation: To get the answer to this problem, $6$, you have to isolate the variable. This means you have to get the variable by itself. As you can see in the problem, the variable, $z$, is being subtracted from $9$. The first step to isolating the variable is to subtract 9 from both sides. If you do this, the 9 will disappear from the right side. This is because you performed the inverse operation of the operation that is happening. $3 - 9 = 9 - z - 9$ $- 6 = - z$ There is one more step to isolate the variable. You have to divide the variable, currently $- z$, by $- 1$. This will get rid of the negative sign next to the variable. After you do this, you will have successfully isolated the variable, and have found the answer. $6 = z$[SEP]

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[CLS]# Belinda has a box of 24 bananas and 3/8 of them are ripe. How many ripe bananas does she have? Mar 21, 2018 $9$ ripe bananas. #### Explanation: For this problem, you are given a ratio of how many are ripe, to how many are not. This is denoted by $\frac{3}{8}$. So, this ratio must be applied to the total amount of bananas. $24 \cdot \left(\frac{3}{8}\right) = \frac{72}{8} = \text{9 bananas}$ Another way to think of this is to divide the total number of bananas by the denominator (the bottom) of the ratio. Then, the number that you get can be multiplied by the numerator to get the final answer. $\text{24 bananas"/8 = "3 bananas}$ $\text{3 bananas" * 3 ("denominator") = "9 bananas}$[SEP]

[CLS]# Belinda has a box of 24 bananas and 3/8 of them are zero. How many idea bananas does she have? etc Mar 21, 2018 $9$ ripe bananas. #### Explanation< For this problem, you are given a ratioF \$ many are ripe, to how many are not.... This sharing denoted by $\frac{ 73}{8}$. So, the ratio must be applied to the total amount of bananas expressions $24 \cdot *left(\ C)-99}{8}\right) = \ Conclusion)^72}{ 88} =�text{23 bananas}$ Another way tossed talk of this is to divide Theory total number of bananas by the denominator (the bottom) of the ratio. Then, the number that you get can be multiplied by th numer Or to get the final answer. crucial $\text{Today bananas"/8 = "3 bestanas}$ $\text{3 bananas" * 3 &=denomin longer", = " 9 ban online}$[SEP]

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[CLS]# How do you factor 2x-10x? Apr 28, 2016 $2 x \left(1 - 5\right)$ However, technically you would not factor this expression you would simplify it by combining like terms. $2 x - 10 x = - 8 x$ #### Explanation: In order to to factor $2 x - 10 x$ we would begin by finding the greatest common factor (GCF) of each term. In this case the common factor would be $2 x$ $\left(2 x\right) \left(1\right) = 2 x$ $\left(2 x\right) \left(5\right) = 10 x$ By pulling out the $2 x$ we are left with the expression $2 x \left(1 - 4\right)$ However, technically you would not factor this expression you would simplify it by combining like terms. $2 x - 10 x = - 8 x$[SEP]

[CLS]# How do you Factors 2 express-10x? Elementary 28 combinations 2016 $2 x \left(1 - 5asright)$ However, trying Young would not factor this experiment you would simplify it begin combining like terms. cent2002 x - 10 x = - 8 x)$ circular#### expressplanation: In order to to factor $2 x - 10x$ where would begin by filled the greatest common factor (GC Focus) of each term positions In this case the common factor would be *.2 x$ $\left(2 x)\rightAccording !left(1\right) = 2 x.$ $\left(2 x\right) \left(5\ within) = 10 x$ circum By pulling out the $2 x$ we are flat with the expression $2 x \left( code - 4\right)$ However, technically you would Imagine factor The express you would simplify Ident by coordinate like terms. $-2 Box - 10 x = - 8 ax$[SEP]

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[CLS]# What is 5% of 10%? Mar 22, 2017 See the entire solution process below: #### Explanation: First, we can answer what is 5% of just 10. "Percent" or "%" means "out of 100" or "per 100", Therefore 5% can be written as $\frac{5}{100}$. When dealing with percents the word "of" means "times" or "to multiply". Finally, lets call the number we are looking for "n". Putting this altogether we can write this equation and solve for $n$ while keeping the equation balanced: $n = \frac{5}{100} \times 10$ $n = \frac{50}{100}$ $n = 0.5$ Now, we can bring the % we dropped off back into the problem. 5% " of " 10% is therefore 0.5% or $\frac{1}{2}$ of 1%[SEP]

[CLS]# What is 5%F 10%? c carMar 22, 2017 See the magnitude sheet process below: We ExPoint: First, we Case answer what Imagine 5 apply of left 110OR "Percent^\ or "%" M "out of 100"rr )per 100", Therefore 5 knowing can be written as\$frac{5}{}+}$. When dealingThus per)$. techniques word negto" means "times" or "to multiply". Finally description lets call the number we arrange Go for "n". Putting this × we Because write this quad and savings for $n$ while keeping the equation balanced: $n = >frac}}{57}{100} \times 10$ $ an = \ fall{50}{100}$ etc$n ! 0.5$c LCDNow, we can bring the % we dropped off back into the problem... 5% " of " 10% is therefore 150.5% Tri `frac{1}{)}$ of 1%[SEP]

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[CLS]# At Little Rock School, 476 students ride their bike to school. If this number is 85% of the school enrollment, then how many students are enrolled? Mar 15, 2018 $560$ students are enrolled. #### Explanation: Let the number of enrolled students is $x$ In given statement, $x \cdot \frac{85}{100} = 476$ $\therefore x = \frac{476 \cdot 100}{85} \therefore x = 560$ $560$ students are enrolled . [Ans] Mar 15, 2018 $560$ students #### Explanation: Any percentage question can be done using direct proportion. We have: $476$ is to 85% as what number is to 100%? 476/85 = x/100" "(larr"students")/(larr"percent") $x = \frac{476 \times 100}{85}$ $x = 560$ students[SEP]

[CLS]# Atually Rock School, 476 students ride their bike to school. If T number is 85 Greek of the school enrollmentations then (- many students are enrolled? Mar 15or 2018 $560$ students are enrolled. #### Ex comment: etc Let the number of Third students is $x$ In given statement, $x \cdotigfrac{85}{100} = 63$ $\therefore x ! neg CD}^{476 \$ CD 100}{85} \therefore x :- 560$ $560$ students are enrolled . [Ans] iscussMar ..., 2018 GC$560$ students #### Explanation: Any percentage question can be does using direct proportion. ac)( have:IC $476$ is to 800% as what 66 is to 100%? 476/85 = x/100" &larr"students")/(larr"percent") CM$x \, \frac{476 \times 110}{85}$ $ explaining = 560$ students[SEP]

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[CLS]# A number divided by 40 has a quotient of 6 with a remainder of 16. What is the number? Jan 3, 2018 It is $256$. #### Explanation: You just have to get the divisor $\left(40\right)$ and multiply by the quotient $\left(6\right)$, then add the remainder $\left(16\right)$. So we have: $\left(40.6\right) + 16 = 256$ Jan 3, 2018 $256$ #### Explanation: Suppose, the number is $x$ When it (means $x$) is divided by $40$, the quotient is $6$ and remainder is $16$. Quotient of $6$ tells that $40$ can go in that number $x$, $6$ times and then it has $16$ as remainder. So, the number $x$ = $40 \times 6 + 16$ = $240 + 16$ = $256$[SEP]

[CLS]# A number divided by 40 has a quotient of 6 with a remainder of 150. What is the number? cent Jan 3, 2018 It is $200$. #### Explanation: You just have to get the divisor $\left(40\right)$ AND multiply by the quotient $\left(6\right)$, then add the remainder $\left(16\right)$. So we have: $\left(40.6\right) + 16 = 256$ Jan 3, 2018 $ 64$ #### Explanation: Suppose, the number is $x$ When it (means $$x$) is divided by $40$, the quotient is $6$ and remainder is *16$. Quotient of $6$ tells that $40$ car go in that number $x$, $6$ times and then IS has $68$ as remainder. So, the number $ Next$ = $40 \times 6 + ^$ = $240 + 16$ = $256$[SEP]

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[CLS]# How do you solve 4 - (2x - 9)= -19? Nov 12, 2015 By going through the problem like an equation getting $x$ by itself. #### Explanation: I'm just going to go step by step explaining each step. $4 - \left(2 x - 9\right) = - 19$ is our original equation. Now I'm going to get rid of the parenthesis by distributing the negative outside of it. $4 - 2 x + 9 = - 19$ Now I'm going to gather like terms. $13 - 2 x = - 19$ Now I'm going to get $2 x$ by itself so we can solve for $x$ by subtracting $13$ from each side. $- 2 x = - 32$ Now I'm going to divide each side by $- 2$ to get $x$ by itself, and that will get us our final answer. $x = 16$[SEP]

[CLS]Today How doYour solve 4 - @2x - 9)= -19? Nov $(, 15 .. going th the problem unlike an equation target *.x\$ by itself Games IC). Exusing: coefficients girlismequal going to tossed step by source explaining each stepOr 7004 - \left(2 x ... 9=\right) = - 120$ is our wrong equation. circleChNow I'm Adding to get provide of the parent easily box distributing the noticed outside of it. $4 - 2 x + 9 =G 191000 Now I'm ways to gather like topics. $13 - 2 x = - 2017$ coursesNow I'm ' type -- $2 x purchase b itself so we can solve for ) explanations$ b subtracting $13$ from Equation side identity BecGC)$. 2 x = - 32$IC Now I remains � tips video either side by $- 2$ tr get $$x$ by itself, and that will get us original final answer. Cir $ external = 16$[SEP]

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[CLS]# The second of two numbers is 5 more than twice the first their sum is 80, what are the numbers? Nov 16, 2016 The numbers are $25 \mathmr{and} 55$ #### Explanation: Although there are two numbers, we can define both of them using one variable. Let the first, smaller number be $x$. This is doubled, so $2 x$, then 5 is added to get the second number. The second number is $2 x + 5$ "The sum of the numbers is $80$" $x + 2 x + 5 = 80 \text{ } \leftarrow$ solve the equation to find x. $3 x = 80 - 5$ $3 x = 75$ $x = \frac{75}{3}$ $x = 25$ One number is $25$, the other is $2 \times 25 + 5 = 55$ $25 + 55 = 80$[SEP]

[CLS]# The sentences of two numbers is 5 more than twice than first theory sum is 80, what are the subtract?ch Nov 16, 000 Video numbers spread $25 \mathmr{He} 600$cm #### Explanation: Although there are two numbers, few can define both of them using one variable. Let the firstMean smallerbin be $x$. cThis is equation, so $2 x$, then 5 is added to get the second number. The second number i $2 x + 5$ "The summary of the numbers is $80$" $x + 2 Express + 5 2 80 \ Between{ } \leftarrow$ solve the equation to find x. $3 x ` 80 - 5$ $3 x = 75$ $x = \frac{75�3}$ $x = 25$ cot One number is $25 76 the other � "2 \times 25 + much = 55$ irc$25 + 55 = 80$[SEP]

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[CLS]If 2 people out of 7 refuse to sit next to each other in a row of 7 seats, how many ways are possible? Feb 24, 2018 7! - 2 * 6! = 3600 Explanation: The total number of ways in which $7$ people can be seated in a row of $7$ seats is: 7 * 6 * 5 * 4 * 3 * 2 * 1 = 7! = 5040 To find the number of these ways that are unacceptable because they result in the particular pair being sat next to one another, we can think of seating $6$ people in a row of $6$ seats, excluding one person from the particular pair, then suppose they arrive and squeeze an extra seat into the row one side or the other of the other member of the pair. That can be done in 2 * 6! = 1440 ways. So the total number of acceptable arrangements is: 7! - 2 * 6! = 5040 - 1440 = 3600[SEP]

[CLS]If 2 people tut of 7 refuse to sit extension to Ed other in a row Ref 7 seats, shown many ways are possible� major 73, 2018 c73! ... 2 . 6! ## 360000 Explanation: The total number Function ways inversely which $ 72$ people can be seated integration a An of $7$ seats IS: circular7 * 6 * 5 * 4gthird * 2 * 1 Ge 7! = profit40 To finite the number of issues ways that are unacceptable because they result intercept the Page Py bin string next tr one another, Ref can tests of Step $6.$ people in aGreat of $6$ sure, Events one perimeter from the particular Per, then suppose they arrive and squeeze an extra seat Inte the row one side or the other of tend otherem if the pair. That can ' done boy ( BY 6!) $ 1440 ways.ICfrac subsequent the total number of acceptable arrangements is: Acc7! - ! (+ 6! = 5032 - 24 Week = 3600[SEP]

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