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=5w−6
A=5(w^2−6)
A=5w^2−6w
A=5w^2
Responses
A=5w−6
A=5(w^2−6)
A=5w^2−6w
A=5w^2
Answers
GPT-4o mini
To establish the relationship between the width \( w \) of the garden plot and the area \( A \), we can start by expressing the length \( l \) in terms of \( w \). The problem states that the length is 6 meters less than 5 times the width. Therefore, we can write:
\[
l = 5w - 6
\]
Next, the area \( A \) of the rectangle (garden plot) can be calculated using the formula:
\[
A = l \times w
\]
Substituting the expression for \( l \) into the area formula gives:
\[
A = (5w - 6) \times w
\]
This simplifies to:
\[
A = 5w^2 - 6w
\]
Therefore, the equation that describes the relationship between the width \( w \) and the area \( A \) is:
\[
A = 5w^2 - 6w
\]
Thus, the correct response is:
**A = 5w^2 - 6w**
\[
l = 5w - 6
\]
Next, the area \( A \) of the rectangle (garden plot) can be calculated using the formula:
\[
A = l \times w
\]
Substituting the expression for \( l \) into the area formula gives:
\[
A = (5w - 6) \times w
\]
This simplifies to:
\[
A = 5w^2 - 6w
\]
Therefore, the equation that describes the relationship between the width \( w \) and the area \( A \) is:
\[
A = 5w^2 - 6w
\]
Thus, the correct response is:
**A = 5w^2 - 6w**