Question
The length of a rectangular 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?(1 point)
Responses
A=2w+3
cap A is equal to 2 w plus 3
A=2w^2+3w
cap A is equal to 2 w squared plus 3 w
A=6w^2
cap A is equal to 6 w squared
A=2(w^2+3)
Responses
A=2w+3
cap A is equal to 2 w plus 3
A=2w^2+3w
cap A is equal to 2 w squared plus 3 w
A=6w^2
cap A is equal to 6 w squared
A=2(w^2+3)
Answers
GPT-4o mini
To find the correct equation that describes the relationship between the width \( w \) of the rectangular frame and the area \( A \), we start with the information given:
1. The length (L) of the frame is 3 inches longer than 2 times the width:
\[
L = 2w + 3
\]
2. The area (A) of a rectangle is calculated as:
\[
A = \text{length} \times \text{width} = L \times w
\]
Substituting the expression for length into the area formula:
\[
A = (2w + 3) \times w
\]
Expanding this, we have:
\[
A = 2w^2 + 3w
\]
So, the correct equation that describes the relationship between the width \( w \) and the area \( A \) is:
\[
A = 2w^2 + 3w
\]
Thus, the response is:
**A=2w^2+3w**.
1. The length (L) of the frame is 3 inches longer than 2 times the width:
\[
L = 2w + 3
\]
2. The area (A) of a rectangle is calculated as:
\[
A = \text{length} \times \text{width} = L \times w
\]
Substituting the expression for length into the area formula:
\[
A = (2w + 3) \times w
\]
Expanding this, we have:
\[
A = 2w^2 + 3w
\]
So, the correct equation that describes the relationship between the width \( w \) and the area \( A \) is:
\[
A = 2w^2 + 3w
\]
Thus, the response is:
**A=2w^2+3w**.