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)

Question

Responses

A=2(w2+3)
cap A is equal to 2 times open paren w squared plus 3 close paren

A=6w2
cap A is equal to 6 w squared

A=2w2+3w
cap A is equal to 2 w squared plus 3 w

A=2w+3
cap A is equal to 2 w plus 3

Answer 1

To find the relationship between the width (w) of the frame and the area (A) in square inches, we start by using the information given.

1. The length (L) of the frame is stated to be 3 inches longer than 2 times the width. Therefore, we can express this relationship as: \[ L = 2w + 3 \]

2. The area (A) of a rectangle is given by the formula: \[ A = L \times w \]

3. Substituting the expression for L into the area formula, we have: \[ A = (2w + 3) \times w \]

4. Simplifying this, we get: \[ A = 2w^2 + 3w \]

So, 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 correct response is: A = 2w² + 3w (cap A is equal to 2 w squared plus 3 w)