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−6A=5w−6cap A is equal to 5 w minus 6 A=5(w2−6)A=5(w2−6)cap A is equal to 5 times open paren w squared minus 6 close paren A=5w2A=5w2cap A is equal to 5 w squared A=5w2−6w

Answer 1

To find the relationship between the width \( w \) of the garden plot and the area \( A \), we start with the information given:

1. The length \( l \) of the garden plot is described as "6 meters less than 5 times the width." Mathematically, this can be expressed as:
\[
l = 5w - 6
\]

2. The area \( A \) of a rectangle is given by the formula:
\[
A = l \times w
\]

Now, substituting the expression for \( l \) into the area formula, we get:
\[
A = (5w - 6) \times w
\]
This simplifies to:
\[
A = 5w^2 - 6w
\]

This means 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**.