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=5(w2−6) cap A is equal to 5 times open paren w squared minus 6 close paren A=5w−6 cap A is equal to 5 w minus 6 A=5w2 cap A is equal to 5 w squared A=5w2−6w
Answers
GPT-4o mini
To find the equation that describes the relationship between the width \( w \) of the garden plot and the area \( A \), we start with the information given.
1. Let the width of the garden plot be \( w \).
2. According to the problem, the length \( l \) of the plot is \( 6 \) meters less than \( 5 \) times the width:
\[
l = 5w - 6
\]
3. The area \( A \) of the rectangle is given by the formula:
\[
A = \text{length} \times \text{width} = l \times w
\]
Substituting for \( l \):
\[
A = (5w - 6) \cdot w
\]
\[
A = 5w^2 - 6w
\]
So, the correct equation that describes the relationship between the width \( w \) of the plot and the area \( A \) in square meters is:
\[
A = 5w^2 - 6w
\]
This corresponds to:
\[
A = 5w^2 - 6w
\]
Thus, the correct response is: **A = 5w² - 6w**.
1. Let the width of the garden plot be \( w \).
2. According to the problem, the length \( l \) of the plot is \( 6 \) meters less than \( 5 \) times the width:
\[
l = 5w - 6
\]
3. The area \( A \) of the rectangle is given by the formula:
\[
A = \text{length} \times \text{width} = l \times w
\]
Substituting for \( l \):
\[
A = (5w - 6) \cdot w
\]
\[
A = 5w^2 - 6w
\]
So, the correct equation that describes the relationship between the width \( w \) of the plot and the area \( A \) in square meters is:
\[
A = 5w^2 - 6w
\]
This corresponds to:
\[
A = 5w^2 - 6w
\]
Thus, the correct response is: **A = 5w² - 6w**.