Molly is having her birthday party at pizza party palace. the costs involved are listed below. pizza party palace requires a 10% deposit prior to the date of the event. if the deposit has been paid, how much is still owed for molly's party?

The parabola y = x² - 4 opens: a.) up b.) down c.) right d.) left

Given: and prove: what is the missing reason in the proof? given transitive property alternate interior angles theorem converse alternate interior angles theorem

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?