Write a real world example that could be solved by using the inequality 4x+8≥32.then solve the inequality

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?

Asporting good store is offering 30 percent off of the original price(x) of football cleats. the discount will be reduced by an another $7 before sales tax.

Which term describes the point where the perpendicular bisectors of the three sides of a triangle intersect?