A soccer team has 20 members. The team wants to purchase a mixture of sweatshirts and jackets so that each team member receives either a sweatshirt or a jacket. • The soccer team spends $816.
• Each sweatshirt costs $32, and each jacket costs $54.

Two parallel lines are crossed by a transversal. what is the value of x? x = 40 x = 70 x = 110 x = 130

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?

Parabolas y=−2x^2 and y=2x^2 +k intersect at points a and b that are in the third and the fourth quadrants respectively. find k if length of the segment ab is 5.