Alocal hamburger shop sold a combined total of 712 hamburgers and cheeseburgers on tuesday. there were 62 more cheeseburgers sold than hamburgers. how many hamburgers were sold on tuesday?

Arecipe uses 2 cups of sugar to make 32 brownies. how many cups of sugar are needed to make 72 brownies?

Each month, a shopkeeper spends 5x + 14 dollars on rent and electricity. if he spends 3x−5 dollars on rent, how much does he spend on electricity? for which value(s) of x is the amount the shopkeeper spends on electricity less than $100? explain how you found the value(s).

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?