The hypotenuse of a right triangle is 10m long. the shorter leg is 2m shorter than the longer leg. find the side lengths of the triangle.

Suppose that the price p (in dollars) and the weekly sales x (in thousands of units) of a certain commodity satisfy the demand equation 4p cubedplusx squaredequals38 comma 400. determine the rate at which sales are changing at a time when xequals80, pequals20, and the price is falling at the rate of $.20 per week.

Some boys and girls were asked if they had a pet. one third of the group were boys. there were 20 boys. 20% of the girls had a pet. boys with a pet : girls with a pet = 1 : 5 i need to know how many girls there are.

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.