Find the distance between the points (0,4) and (3,0).
We use the distance formula: $\sqrt{(3 - 0)^2 + (0 - 4)^2} = \sqrt{9 + 16} = \boxed{5}$.

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We note that the points $(0, 4)$, $(3, 0)$, and $(0, 0)$ form a right triangle with legs of length 3 and 4. This is a Pythagorean triple, so the hypotenuse must have length $\boxed{5}$.
5
Level 2
Algebra
Problem: Find the distance between the points (0,4) and (3,0).
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To find the distance between two points in a Cartesian coordinate system, we use the distance formula, which is derived from the Pythagorean theorem. The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by the formula:

d = √((x_2 - x_1)² + (y_2 - y_1)²)

In this case, the points are (0,4) and (3,0). Assigning the coordinates, we have \( x_1 = 0 \), \( y_1 = 4 \), \( x_2 = 3 \), and \( y_2 = 0 \).

Now, we calculate the differences in the x and y coordinates:

x_2 - x_1 = 3 - 0 = 3
y_2 - y_1 = 0 - 4 = -4

Next, we square these differences:

(3)² = 9
(-4)² = 16

We then add these squared values:

9 + 16 = 25

Finally, we take the square root of the sum to find the distance:

d = √(25) = 5

Thus, the final answer is 5.<|END_OF_LATENT|> The final answer is $5$.