Given: <2 and <4 are vertical angles
Prove: <2 ≅ <4

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?

Which of the expressions (on the photo document i inserted) together represent all solutions to the following equation? 8cos(12x)+4=-4 *the answer should be in degrees.* > i would like for someone to explain the process to find the solutions for this.

1. evaluate 8x(2)y9(-2) for x=-1 and y=2 2. simplify the equation. -() 3. simplify the expression. [tex]\frac{5}{x(-2) y9(5)}[/tex]