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^2
cap A is equal to 5 w squared
A=5(w^2−6)
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=5w^2−6w
Responses
A=5w^2
cap A is equal to 5 w squared
A=5(w^2−6)
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=5w^2−6w
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 need to first express the length in terms of the width.
Given that the length \( L \) is 6 meters less than 5 times the width, we can write:
\[
L = 5w - 6
\]
The area \( A \) of the garden plot is given by the formula:
\[
A = L \times w
\]
Substituting the expression for length \( L \) into the area formula:
\[
A = (5w - 6) \times w
\]
Expanding this gives:
\[
A = 5w^2 - 6w
\]
So the correct equation that describes the relationship between the width \( w \) and the area \( A \) is:
\[
A = 5w^2 - 6w
\]
Therefore, the correct response is:
**A=5w^2−6w** (cap A is equal to 5 w squared minus 6 w).
Given that the length \( L \) is 6 meters less than 5 times the width, we can write:
\[
L = 5w - 6
\]
The area \( A \) of the garden plot is given by the formula:
\[
A = L \times w
\]
Substituting the expression for length \( L \) into the area formula:
\[
A = (5w - 6) \times w
\]
Expanding this gives:
\[
A = 5w^2 - 6w
\]
So the correct equation that describes the relationship between the width \( w \) and the area \( A \) is:
\[
A = 5w^2 - 6w
\]
Therefore, the correct response is:
**A=5w^2−6w** (cap A is equal to 5 w squared minus 6 w).