act-dog

A. Incorrect. Let s represent the initial speed of the car, in miles per hour, and l represent the length of the skid in feet. The equation that models the situation is then $s\approx \sqrt{35l}$. Remember to multiply, not add, the values underneath the square root.

B. Incorrect. Let s represent the initial speed of the car, in miles per hour, and l represent the length of the skid in feet. The equation that models the situation is then $s\approx \sqrt{35l}$. Remember that, when simplifying a radical such as $a\sqrt{b^{2}c}$, the constants outside of the radical will multiply, not add: $\left(a\times b\right)\sqrt{c}$, not $\left(a+b\right)\sqrt{c}$.

C. Correct. Let s represent the initial speed of the car, in miles per hour, and l represent the length of the skid in feet. The equation that models the situation is then $s\approx \sqrt{35l}$. Substitute $l=108$ into the equation: $s\approx \sqrt{35\left(108\right)}\to s\approx \sqrt{3,780}$. Simplify the radical by factoring $3,780=36\left(105\right)$ and using the property $\sqrt{ab}=\sqrt{a}\sqrt{b}$ to yield $\sqrt{3,780}=\sqrt{36}\sqrt{105}=6\sqrt{105}$.

D. Incorrect. Let s represent the initial speed of the car, in miles per hour, and l represent the length of the skid in feet. The equation that models the situation is then $s\approx \sqrt{35l}$. You may have used the equation $s\approx 35\sqrt{l}$.