(1.) A triangular prism and a triangular pyramid have congruent bases and heights. The volume of the prism is 174 cubic units. What is the volume of the pyramid? Show your work.

Abouncy ball is released from a certain height. on the first bounce, it travels 32cm. with each subsequent bounce, it travels 9/10 the distance of the previous bounce. what is the total distance that the ball has traveled when it completes its 25th bounce?

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?

You have a square piece of cardboard that measures 14 inches on each side. to build a box, you cut congruent squares out of each corner of the cardboard. use the picture to find the area of the cardboard you were used to build the box