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 30 feet. The dog run must have a width between 0 and 30 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 sidth between 0 and 120 feet,
The correct analysis of the x-intercept is: The dog run must have a width between 0 and 60 feet.
To find the x-intercept, we set A (the area) equal to zero and solve for w (the width):
0 = -w^2 + 60w
Simplifying this equation, we get:
w(w - 60) = 0
So, either w = 0 or w - 60 = 0.
If w = 0, it means that the width of the dog run is 0 feet, which is not possible.
If w - 60 = 0, it means that the width of the dog run is 60 feet, which is within the possible range.
Therefore, the dog run must have a width between 0 and 60 feet.