1+ cos(12x) = a. 2sin^2(6x) b. 2sin^2(12x) c. 2cos^2(12x) d. 2cos^2(6x)

You are cycling around europe with friends. a cycling festival is starting soon in barcelona. it will take 4.5 hours to cycle there. how many minutes in total is this?

In a class, there are 12 girls. if the ratio of boys to girls is 5: 4 how many boys are there in the class

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?