What is X?
x + 1 + 4x = 11 + 12x - 3

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?

The measure of an angle is 117°. what is the measure of a supplementary angle?

How do you find p(a and b) if a and b are independent events for two or more actions, such as tossing a coin twice and finding p(heads and heads)? 2. how do you find p(a or b) if a and b are independent events for one action, such as spinning a four-color spinner once and finding p(red or blue)?