Christopher’s backyard is shaped like a rectangle with a length of 2x + 5 feet and a width of 4x - 7 feet.
a. use the foil method to write an expression for the area of his backyard

8x² + 6x - 35

Step-by-step explanation:

A = (2x + 5)(4x - 7)

Front: 2x * 4x = 8x²

Outside: 2x * (-7) = -14x

Inside: 5 * 4x = 20x

Last: 5 * -7 = -35

Add up: 8x² - 14x + 20x -35

Simplify: 8x² + 6x - 35

The perimeter of the kite WXYZ is 33.94 square units

Step-by-step explanation:

Step 1; First we plot the points W, X, Y, Z on the graph. We need to find the distance between the opposite sides i.e W and Y, X and Z. To find the distance between W and Y, X and Z we use the formula

Distance = √ (x2 - x1)² + (y2 - y1)².

So for W (-3, 3) and Y (4, -4) where W is (x1, y1) and Y is (x2, y2).

Distance = √(4 - (-3))² + (-4 -3)² = √49 + 49 = √98 = 9.899.

Distance between X (2, 3) and Z (-3, -2) where X is (x1, y1) and Z is (x2, y2).

Distance = √(-3 -2)² + (-2 -3)² = √25 + 25 = √50 = 7.071.

Step 2; The parameter of a kite is given by 2 times the sum of the two distances between opposite sides.

Parameter = 2 × (9.899 + 7.071) = 2 × 16.97 = 33.94 square units.