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=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
Answers
GPT-4o mini
To find the equation that describes the relationship between the width \( w \) of the plot and the area \( A \), we first need to express the length of the garden plot in terms of the width \( w \).
According to the problem, the length \( l \) is described as:
\[
l = 5w - 6
\]
The area \( A \) of a rectangle (which is the shape of the garden plot) is given by the formula:
\[
A = l \times w
\]
Substituting the expression for \( l \) into the area formula gives:
\[
A = (5w - 6) \times w
\]
Expanding this expression, we get:
\[
A = 5w^2 - 6w
\]
So the equation that describes the relationship between the width \( w \) of the plot and the area \( A \) is:
\[
A = 5w^2 - 6w
\]
From the options provided, the correct one is:
**A = 5w² - 6w (A is equal to 5 w squared minus 6 w)**.
According to the problem, the length \( l \) is described as:
\[
l = 5w - 6
\]
The area \( A \) of a rectangle (which is the shape of the garden plot) is given by the formula:
\[
A = l \times w
\]
Substituting the expression for \( l \) into the area formula gives:
\[
A = (5w - 6) \times w
\]
Expanding this expression, we get:
\[
A = 5w^2 - 6w
\]
So the equation that describes the relationship between the width \( w \) of the plot and the area \( A \) is:
\[
A = 5w^2 - 6w
\]
From the options provided, the correct one is:
**A = 5w² - 6w (A is equal to 5 w squared minus 6 w)**.