Colby and danielle clean pools for extra money over the summer. colby's income is determined by f(x) = 3x + 12, where x is the number of hours. danielle's income is g(x) = 5x + 10. if colby and danielle were to combine their efforts, their income would be h(x) = f(x) + g(x). assume colby works 4 hours. create the function h(x), and indicate if colby will make more money working alone or by teaming with danielle.

Abby is preparing fruit punch for her party. she starts with a bowl filled with liquid that has 1/2 fruit juice and 1/2 sprite, but she decides it's too fruity. so she pours out 1/4 of the liquid, and then fills the bowl up again with sprite. what fraction of the punch is now sprite?

The tuition costs, c, for a local community college are modeled by c(h) = 250 + 200h, where h represents the number of credit hours taken. the local state university has tuition costs, s, modeled by the function s(h) = 300 + 180h. how many credit hours will a student have to take for the two tuition costs to be equal? round the answer to the nearest tenth of an hour.

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?