Question

The base of a rectangle shown below measures 3x+4 in and the height measures x-2 in. The area of the rectangle shown below is 2x² + 4x - 7 in². What is the Area of the shaded region?

A. 7x - 11 square inches
B. 5x - 9 square inches
C. 3x² - 4x - 7 square inches
D. 6x² + 6x - 7 square inches

Answer 1

The area of the shaded region is -x² + 14x - 15 square inches.

Step-by-step explanation:

To find the area of the shaded region, we need to subtract the area of the smaller rectangle from the area of the larger rectangle. The area of the larger rectangle is given as 2x² + 4x - 7 square inches, and the area of the smaller rectangle is (3x+4)(x-2) square inches.

To find the area of the shaded region, we can subtract the area of the smaller rectangle from the area of the larger rectangle:

Shaded area = Area of larger rectangle - Area of smaller rectangle

Shaded area = (2x² + 4x - 7) - (3x+4)(x-2)

Simplifying the expression:

Shaded area = 2x² + 4x - 7 - (3x²- 2x - 8x +8)

Shaded area = 2x² + 4x - 7 - 3x² +10x -8

Shaded area = -x² + 14x - 15

Therefore, the area of the shaded region is -x² + 14x - 15 square inches.