Question is in picture

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?

Select the correct answer from each drop-down menu. consider the following polynomials equations. 3x^2(x-1) and -3x^3+ 4x^2-2x+1 perform each operation and determine if the result is a polynomial. is the result of a + b a polynomial? yes or no is the result of a - b a polynomial? yes or no is the result of a · b a polynomial? yes or no

(10. in the figure, a aabc is drawn tocircumscribe a circle of radius 3 cm ,such thatthe segments bd and dc are respectively oflength 6 cm and 9 cm. find the length ofsides ab and ac.