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
cap A is equal to 5 w squared
A=5w2−6w
cap A is equal to 5 w squared minus 6 w
A=5w−6
cap A is equal to 5 w minus 6
A=5(w2−6)
Responses
A=5w2
cap A is equal to 5 w squared
A=5w2−6w
cap A is equal to 5 w squared minus 6 w
A=5w−6
cap A is equal to 5 w minus 6
A=5(w2−6)
Answers
GPT-4o mini
To find the relationship between the width \( w \) of the garden plot and its area \( A \), we start with the information given in the problem.
We are told that the length \( l \) of the garden plot is 6 meters less than 5 times the width \( w \). This can be expressed as:
\[
l = 5w - 6
\]
The area \( A \) of a rectangle is given by the formula:
\[
A = l \times w
\]
Substituting the expression for length into the area formula gives:
\[
A = (5w - 6) \cdot w
\]
Now we can distribute \( w \):
\[
A = 5w^2 - 6w
\]
Thus, 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** (cap A is equal to 5 w squared minus 6 w)
We are told that the length \( l \) of the garden plot is 6 meters less than 5 times the width \( w \). This can be expressed as:
\[
l = 5w - 6
\]
The area \( A \) of a rectangle is given by the formula:
\[
A = l \times w
\]
Substituting the expression for length into the area formula gives:
\[
A = (5w - 6) \cdot w
\]
Now we can distribute \( w \):
\[
A = 5w^2 - 6w
\]
Thus, 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** (cap A is equal to 5 w squared minus 6 w)