Given f(x)=x^2+kx-19 and the remainder when f(x)is divided by x-7 is −5, then what is the value of k

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?

Mason and christian go to the movie theater and purchase refreshments for their friends. mason spends a total of $45.75 on 3 bags of popcorn and 6 drinks. christian spends a total of $71.50 on 6 bags of popcorn and 4 drinks. write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink. using these equations, determine and state the price of a drink, to the nearest cent.

Susan is paying $0.30 per $100 on her $483,000 home in homeowners insurance annually. if her annual homeowners insurance premium is divided into twelve equal monthly installments to be included on each of her monthly mortgage payments of $2,128.00, what is her total monthly payment?