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

The dog run must have a width between 0 and 60 feet.
The dog run must have a width between 0 and 60 feet.
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Answer 1

A-intercepts solve 0 = −w^2 + 60w → w(−w + 60) = 0, so w = 0 or w = 60. Thus the feasible widths giving positive area are between 0 and 60 feet.

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