Question
The length of a rectangle is 2 inches less than 3 times the width. Which equation describes the relationship between w, the width of the rectangle in inches, and A, the area in square inches?(1 point)
Responses
A=3w2−2w
cap A is equal to 3 w squared minus 2 w
A=2w2−3
cap A is equal to 2 w squared minus 3
A=2w2−3w
cap A is equal to 2 w squared minus 3 w
A=3w2−2
Responses
A=3w2−2w
cap A is equal to 3 w squared minus 2 w
A=2w2−3
cap A is equal to 2 w squared minus 3
A=2w2−3w
cap A is equal to 2 w squared minus 3 w
A=3w2−2
Answers
GPT-4o mini
To express the relationship between the width \( w \) and the area \( A \) of the rectangle, we first need to define the length of the rectangle based on the given information.
The problem states that the length \( l \) is "2 inches less than 3 times the width." This can be represented mathematically as:
\[
l = 3w - 2
\]
The area \( A \) of a rectangle is calculated using the formula:
\[
A = l \times w
\]
Substituting the expression for the length into the area formula gives us:
\[
A = (3w - 2) \times w
\]
Expanding this:
\[
A = 3w^2 - 2w
\]
Thus, the equation that describes the relationship between \( w \) and \( A \) is:
\[
A = 3w^2 - 2w
\]
Therefore, the correct choice from your provided responses is:
**A=3w²−2w**
The problem states that the length \( l \) is "2 inches less than 3 times the width." This can be represented mathematically as:
\[
l = 3w - 2
\]
The area \( A \) of a rectangle is calculated using the formula:
\[
A = l \times w
\]
Substituting the expression for the length into the area formula gives us:
\[
A = (3w - 2) \times w
\]
Expanding this:
\[
A = 3w^2 - 2w
\]
Thus, the equation that describes the relationship between \( w \) and \( A \) is:
\[
A = 3w^2 - 2w
\]
Therefore, the correct choice from your provided responses is:
**A=3w²−2w**