Katherine and Ivan had 96 marbles in all. Katherine lost 24 marbles to Ivan during a game. At the end of the game, Ivan had twice as many marbles as
Katherine. How many marbles did Ivan have at first?

Asailor is looking at a kite. if he is looking at the kite at an angle of elevation of 36and the distance from the boat to the point where the kite is directly overhead is 40 feet, how high is the kite?

In the diagram below? p is circumscribed about quadrilateral abcd. what is the value of x

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?