Example of variations natural resources

An episode of a television show is 60 minutes long when it originally airs with commercials. on a dvd without commercials, the episode is only 417 minutes long. how many1-minute commercials did the episode include when it originally aired? write and solve an equation to justify your answer.

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?

If you prove that ∆wxz is congruent to ∆yzx, which general statement best describes what you have proved?