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 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 120 feet.
The dog run must have a width between 0 and 120 feet.
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The correct answer is "The dog run must have a width between 0 and 60 feet."
To find the x-intercept of the function, we set A equal to 0 and solve for w:
0 = -w^2 + 60w
w(-w + 60) = 0
w = 0 or -w + 60 = 0
w = 0 or w = 60
Since a negative width doesn't make sense in this context, we only consider the positive solution. Therefore, the dog run must have a width between 0 and 60 feet.