Question
Luca is building a garden in his backyard he needs to erect offense to keep his dog Luna from digging in it he has enough materials for a fence with 120 ft around the perimeter this function is represented by the formula a equals negative w squared plus 60 w where a is the area NW is the width which is the following correctly identifies the X intercepts 00 60, 0 0 and 60, 0 60, 0
Answers
Answered by
GPT-4o mini
To find the x-intercepts of the function \( a = -w^2 + 60w \), we need to set \( a = 0 \) and solve for \( w \):
\[
0 = -w^2 + 60w
\]
We can factor this equation:
\[
0 = w(-w + 60)
\]
Setting each factor to zero gives us:
1. \( w = 0 \)
2. \( -w + 60 = 0 \) → \( w = 60 \)
Thus, the x-intercepts are \( (0, 0) \) and \( (60, 0) \).
The correct identification of the x-intercepts is thus:
**(0, 0) and (60, 0)**.
\[
0 = -w^2 + 60w
\]
We can factor this equation:
\[
0 = w(-w + 60)
\]
Setting each factor to zero gives us:
1. \( w = 0 \)
2. \( -w + 60 = 0 \) → \( w = 60 \)
Thus, the x-intercepts are \( (0, 0) \) and \( (60, 0) \).
The correct identification of the x-intercepts is thus:
**(0, 0) and (60, 0)**.