Question

Help me please! These are due today.

Answer 1

Answer:

${x}^{2} + 3x$

Step-by-step explanation:

1.

Area of shaded region = Area of external rectangle - Area of internal rectangle

$= 4x(x + 2) - x(3x + 5) \\ = 4 {x}^{2} + 8x - 3 {x}^{2} - 5x \\ = 4 {x}^{2} - 3 {x}^{2} + 8x - 5x \\ = {x}^{2} + 3x$

2.

Let the width of the rectangle be x inches.

Therefore, length of the rectangle = (x + 3) inches

A.

Area of rectangle

$=(x + 3)\times x\\=x^2 + 3x$

B.

Width of rectangle = 4 inches

Length of rectangle = 4 + 3 = 7 inches

Area of rectangle = 7*4 = 28 square inches.