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I am the yeast of thoughts and minds
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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?

What is the value of x? assume that the line is tangent to the circle.

In each diagram, line p is parallel to line f, and line t intersects lines p and f. based on the diagram, what is the value of x? ( provide explanation)