Determine whether each of the following relations is an equivalence relation, an order relation, or neither. If it is an order, determine whether it is strict and whether it is partial or total. The universe is the set of positive integers.

a. {hx, yi : y is a multiple of x}
b. {hx, yi : the greatest common factor of x and y is 5}
c. {hx, yi : x and y have the same number of prime factors}
d. {hx, yi : when written in base 10, x has at least as many digits than y}

What is the first step of an indirect proof of a number that is divisible by two

How many verticies does a triangular prims have

Mrs. julien’s and mrs. castillejo’s classes are selling cookie dough for a school fundraiser. customers can buy packages of macadamia nut chip cookie dough and packages of triple chocolate cookie dough. mrs. julien’s class sold 25 packages of macadamia nut chip cookie dough and 30 packages of triple chocolate cookie dough for a total of $221.25. mrs. castillejo’s class sold 5 packages of macadamia nut chip cookie dough and 45 packages of triple chocolate cookie dough for a total of $191.25. (a) write the system of equations that model the problem. be sure to explain which equation represents which situation. (b) find the cost of each type of cookie. show your work. (c) explain which method you used to solve the system and why you chose that method.