Consider the sets below.
u = {x | x is a real number}
a= {x | x is an odd integer}
r= {x | x = 3, 7, 11, 27}
is r c a?

Ametalworker has a metal alloy that is 30? % copper and another alloy that is 55? % copper. how many kilograms of each alloy should the metalworker combine to create 90 kg of a 50? % copper? alloy?

One of the same side angles of two parallel lines is 20° smaller than the other one. find the measures of these two angles.

1- 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.2- 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 the first question?