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?(1 point)
Responses
A=6w2
cap A is equal to 6 w squared
A=2w+3
cap A is equal to 2 w plus 3
A=2(w2+3)
cap A is equal to 2 times open paren w squared plus 3 close paren
A=2w2+3w
Responses
A=6w2
cap A is equal to 6 w squared
A=2w+3
cap A is equal to 2 w plus 3
A=2(w2+3)
cap A is equal to 2 times open paren w squared plus 3 close paren
A=2w2+3w
Answers
GPT-4o mini
To find the relationship between the width \( w \) of the frame and the area \( A \) in square inches, we first need to express the length of the frame in terms of the width.
According to the problem, the length \( l \) of the frame is given by the equation:
\[
l = 2w + 3
\]
Next, we can express the area \( A \) of the frame using the formula for the area of a rectangle, which is length times width:
\[
A = l \cdot w
\]
Substituting the expression for length into the area formula gives us:
\[
A = (2w + 3) \cdot w
\]
Now, we can simplify this expression:
\[
A = 2w^2 + 3w
\]
Thus, the equation that describes the relationship between the width \( w \) and the area \( A \) is:
\[
A = 2w^2 + 3w
\]
So the correct response from the options provided is:
**A = 2w² + 3w**
According to the problem, the length \( l \) of the frame is given by the equation:
\[
l = 2w + 3
\]
Next, we can express the area \( A \) of the frame using the formula for the area of a rectangle, which is length times width:
\[
A = l \cdot w
\]
Substituting the expression for length into the area formula gives us:
\[
A = (2w + 3) \cdot w
\]
Now, we can simplify this expression:
\[
A = 2w^2 + 3w
\]
Thus, the equation that describes the relationship between the width \( w \) and the area \( A \) is:
\[
A = 2w^2 + 3w
\]
So the correct response from the options provided is:
**A = 2w² + 3w**