The length of a rectangular dog run is 2 feet more than twice the width, w, and the perimeter of the dog run is 32 feet. Solve the equation 2w + 2(2w + 2) = 32 to find the width, w, of the dog run. Then find the length, 2w+2, of the dog run.

Complex numbers multiply √-4 * √-25 and show all intermediate steps. alternative notation is sqrt(-4) * sqrt(-25).

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?

Drag the tiles to the correct boxes to complete the pairs. not all tiles will be used. identify the domain for each of the given functions.