Answer: A. 76 sq. units
Step-by-step explanation:
1. You can use the following formula for calcualte the area of the parallelogram:
Where 
is the base and 
is the height of the parallelogram
and 
2. The formula for calculate the area of a rectangle is:
Where 
is the base and 
is the height of the rectanngle.
and 
3. Then, the area of the figure is the sum of the area of the parallelogram and the area of the rectangle:
Step-by-step explanation:
First, let's move all of the terms with an 
to the left-hand side of t he equation, and everything else to the right-hand side of the equation.
Next, let's divide both sides by 
to isolate the variable by itself on the left-hand side of the equation:
Answer:
She should aim 6 feet down the wall
Explanation:
The diagram attached sketches the situtation.
Since the angle with which the ball hits the wall is the same with which it bounces, angle β is the same for the two shown triangles.
Then, since both are right triangles, then all the angles are congruent and the triangles are similar. Hence, you can equal the ratios of the sides, to make an equation:
x/4 = y/2 ⇒ x = 2y
You have other equation:
x+ y = 18
Substitute
2y + y = 18
3y = 18
y = 18/3
y = 6 ← this is the distance down the wall where the ball should hit
x = 2(6) = 12
Then, she should aim 6 feet down the wall.
We have 112.5 = 225/2; cos112.5 < 0 because 90 < 112.5 < 180;
cos 112.5 = cos(225/2);
We use the trigonometric formula: cos(x/2) = -
;
Then, cos(225/2) = -
;
We have the formula: cos(270 - x) = -sinx (because cos(a-b) = cosacosb + sinasinb);
Then, cos225 = cos(270-45) = -sin45 = -
Finally, cos112.5 = -
The answer is C.
hope this helps
