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
A=2w+3
cap A is equal to 2 w plus 3
A=2w2+3w
cap A is equal to 2 w squared plus 3 w
A=2(w2+3)
cap A is equal to 2 times open paren w squared plus 3 close paren
A=6w2
Responses
A=2w+3
cap A is equal to 2 w plus 3
A=2w2+3w
cap A is equal to 2 w squared plus 3 w
A=2(w2+3)
cap A is equal to 2 times open paren w squared plus 3 close paren
A=6w2
Answers
GPT-4o mini
To find the relationship between the width \( w \) of the frame, and the area \( A \) in square inches, we need to first express the length in terms of the width.
The problem states that the length \( l \) of the frame is 3 inches longer than 2 times the width:
\[
l = 2w + 3
\]
The area \( A \) of the frame can be calculated using the formula for the area of a rectangle, which is the length multiplied by the width:
\[
A = l \times w
\]
Substituting the expression for length \( l \) into the area formula gives us:
\[
A = (2w + 3) \times w
\]
This expands to:
\[
A = 2w^2 + 3w
\]
Now, looking at the responses provided, 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** (the second response).
The problem states that the length \( l \) of the frame is 3 inches longer than 2 times the width:
\[
l = 2w + 3
\]
The area \( A \) of the frame can be calculated using the formula for the area of a rectangle, which is the length multiplied by the width:
\[
A = l \times w
\]
Substituting the expression for length \( l \) into the area formula gives us:
\[
A = (2w + 3) \times w
\]
This expands to:
\[
A = 2w^2 + 3w
\]
Now, looking at the responses provided, 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** (the second response).