Paul has two label-printing machines. each machine can print 30 labels per minute. on day 1, only the first machine was used, and it printed 90 labels. on the following day, the first machine printed for x minutes and the second machine printed for y minutes. which expression shows the total number of labels printed by both machines during these two days?
120x + 30y
90 + 30x + 30y
30 + 90x + y
90x + 60y

Fine the area of the kite. a. 90 sq. units b. 9 sq. units c. 180 sq. units d. 45 sq. units

Marina baked cookies. she gave 3/4 of the cookies to the scout bake sale. she shared the remaining 6 cookies with her friends. how many cookies did marina bake?

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?