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^2−6w
cap A is equal to 5 w squared minus 6 w

A=5w^2
cap A is equal to 5 w squared

A=5w−6
cap A is equal to 5 w minus 6

A=5(w^2−6)
cap A is equal to 5 times open paren w squared minus 6 close paren

Answer 1

To find the equation that describes the relationship between the width \( w \) of the garden plot and the area \( A \), you first need to express the length in terms of the width.

The problem states that the length \( l \) is 6 meters less than 5 times the width. Thus, you can express the length as follows:

\[
l = 5w - 6
\]

The area \( A \) of a rectangle can be calculated using the formula:

\[
A = l \times w
\]

Substituting \( l \) from the first expression into the area formula gives:

\[
A = (5w - 6) \times w
\]

Expanding this expression:

\[
A = 5w^2 - 6w
\]

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=5w^2−6w** (cap A is equal to 5 w squared minus 6 w)