Please show work I will give brainiest

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?

Find two numbers if their sum is 91 and the ratio is 6: 7?

The distance between two points is 6.5cm and scale of map is 1: 1000 what's the distance between the two points