Question

Nora is creating a dog run in her backyard for her dog, Max. She has enough materials to create a run with a perimeter of 120 feet. This is represented by the function A=−w2+60w
, where A
is the area of the run and w is the width. Which of the following best analyzes the meaning of the x-intercept?(1 point)
Responses

The dog run must have a width between 0 and 60 feet.
The dog run must have a width between 0 and 60 feet.

The dog run must have a width between 0 and 120 feet.
The dog run must have a width between 0 and 120 feet.

The dog run must have a width between 0 and 900 feet.
The dog run must have a width between 0 and 900 feet.

The dog run must have a width between 0 and 30 feet.

Answer 1

Answer: The dog run must have a width between 0 and 60 feet.

Reason: A = −w^2 + 60w = w(60 − w), so the x‑intercepts are w = 0 and w = 60. Those are the widths that give area 0, so valid (nonnegative) widths lie between 0 and 60 feet.