Question
The length of a frame is 3 inches longer than 2 times the width. Which of the following equations describes the relationship between the width (w) of the frame in inches, and the area (A) in square inches? 2w+3(1 point)
Responses
Responses
Answers
GPT-4o mini
To describe the relationship between the width \( w \) of the frame and the area \( A \) in square inches, we start with the information given: the length \( l \) of the frame is 3 inches longer than 2 times the width.
We can express the length as:
\[
l = 2w + 3
\]
The area \( A \) of a rectangle is calculated using the formula:
\[
A = l \times w
\]
Substituting the expression for \( l \) into the area formula, we get:
\[
A = (2w + 3) \times w
\]
Simplifying this:
\[
A = 2w^2 + 3w
\]
Therefore, the equation that describes the relationship between the width \( w \) of the frame and the area \( A \) in square inches is:
\[
A = 2w^2 + 3w
\]
This equation indicates that the area \( A \) is a function of the width \( w \).
We can express the length as:
\[
l = 2w + 3
\]
The area \( A \) of a rectangle is calculated using the formula:
\[
A = l \times w
\]
Substituting the expression for \( l \) into the area formula, we get:
\[
A = (2w + 3) \times w
\]
Simplifying this:
\[
A = 2w^2 + 3w
\]
Therefore, the equation that describes the relationship between the width \( w \) of the frame and the area \( A \) in square inches is:
\[
A = 2w^2 + 3w
\]
This equation indicates that the area \( A \) is a function of the width \( w \).