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 irrational number is? if the rational number were 0, would it give us the same result we found in part b?

Part B seems to be missing, but I think I have enough information to be able to answer.

Let's say we had two numbers x and y. Let x be rational and y be irrational.

If x is some nonzero number, then x*y is irrational. The proof for this is a bit lengthy so I'll leave it out.

For instance,

x = 2 is rational, y = sqrt(3) is irrational, x*y = 2*sqrt(3) is irrational.

If we made x = 0, then

x*y = 0*y = 0

This is true for any value of y that we want. The y value doesnt even have to be irrational. It can be any real number.

So the distinction is that if x = 0, then x*y = 0 is rational since 0 is rational. Otherwise, x*y is irrational.

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.

step-by-step explanation:

se a cavasery6