The lengths of two sides of a triangle are shown below:

Side 1: 8x2 − 5x − 2

Side 2: 7x − x2 + 3

The perimeter of the triangle is 4x3 − 3x2 + 2x − 6.

Part A: What is the total length of the two sides, 1 and 2, of the triangle?

Part B: What is the length of the third side of the triangle?

Part C: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? Justify your answer.

Quick! a survey of 57 customers was taken at a bookstore regarding the types of books purchased. the survey found that 33 customers purchased mysteries, 25 purchased science fiction, 18 purchased romance novels, 12 purchased mysteries and science fiction, 9 purchased mysteries and romance novels, 6 purchased science fiction and romance novels, and 2 purchased all three types of books. a) how many of the customers surveyed purchased only mysteries? b) how many purchased mysteries and science fiction, but not romance novels? c) how many purchased mysteries or science fiction? d) how many purchased mysteries or science fiction, but not romance novels? e) how many purchased exactly two types of books?

Last month, a 770 g box of cereal was sold at a grocery store for $3.10. however, this month, the cereal manufacturer launched the same cereal in a 640 g box, which is being sold at $2.50. what is the percent change in the unit price?

Two line segments are shown in the figure below. suppose that the length of the line along the x-axis is 6, and the length of the hypotenuse of the triangle is 10. what is the equation of the hypotenuse line (shown in red, below)?