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When solving the following questions, show each step of the solution along with the final results. If there is no work to show, be sure to fully explain your solution method.
1. Simplify the following algebraic operations:
a) 7x – 2(x – 2) + 5(x + 3)
b) (x + 2)(x – 4) + 3x + 1
2. Suppose a student has earned the following grades on her first four quizzes: 83, 72, 89, 78. What must she score on her fifth quiz in order to have a mean of 80 on all of her quizzes?
3. The perimeter of a rectangle is twice the length plus twice the width. The area of a rectangle is the product of its length and width. Suppose we let l represent the length and w represent the width of a rectangle.
a) Write an algebraic expression that represents the perimeter.
b) Write an algebraic expression that represents the area.
c) Calculate the perimeter of a rectangle 12 inches long and 20 inches wide.
d) Calculate the area of the rectangle described in Part C.
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