Question
The length of a garden plot is 6 meters less than 5 times the width. Which equation describes the relationship between the width `w` of the plot in meters, and the area `A` in square meters?(1 point)
Responses
A=5w2−6w
cap A is equal to 5 w squared minus 6 w
A=5w2
cap A is equal to 5 w squared
A=5w−6
cap A is equal to 5 w minus 6
A=5(w2−6)
cap A is equal to 5 times open paren w squared minus 6 close paren
Responses
A=5w2−6w
cap A is equal to 5 w squared minus 6 w
A=5w2
cap A is equal to 5 w squared
A=5w−6
cap A is equal to 5 w minus 6
A=5(w2−6)
cap A is equal to 5 times open paren w squared minus 6 close paren
Answers
GPT-4o mini
To find the relationship between the width \( w \) of the garden plot and the area \( A \), we start by using the information given.
1. **Length**: The length of the garden plot \( L \) is defined as \( L = 5w - 6 \) (6 meters less than 5 times the width).
2. **Area**: The area \( A \) of a rectangle is given by the formula \( A = \text{length} \times \text{width} \).
Using the relationship for length, we can express the area as follows:
\[
A = L \cdot w = (5w - 6) \cdot w
\]
Expanding this gives:
\[
A = 5w^2 - 6w
\]
This shows that the equation that describes the relationship between the width \( w \) and the area \( A \) is:
\[
A = 5w^2 - 6w
\]
So the correct response is:
**A=5w²−6w**
1. **Length**: The length of the garden plot \( L \) is defined as \( L = 5w - 6 \) (6 meters less than 5 times the width).
2. **Area**: The area \( A \) of a rectangle is given by the formula \( A = \text{length} \times \text{width} \).
Using the relationship for length, we can express the area as follows:
\[
A = L \cdot w = (5w - 6) \cdot w
\]
Expanding this gives:
\[
A = 5w^2 - 6w
\]
This shows that the equation that describes the relationship between the width \( w \) and the area \( A \) is:
\[
A = 5w^2 - 6w
\]
So the correct response is:
**A=5w²−6w**