What is the vertical shift of the function? f(x) = sin x − 3/2

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?

You dug a hole that was 8 feet deep. after taking a short break, you dug down 3 more feet in the same hole. when finished digging, a tractor accidentally filled the hole with 4 feet of dirt. how deep is your hole now?

The following numbers will result in a quotient that is less than 1 when it is divided by ? a.2% e. 1 and 2/3 b.x2 f. 1/5 c. 3/10 g. 7/15 d. 5/9