4. What line is the line of reflection used to reflect triangle MNP and to its image, triangle M'N'P'?

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- 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. 3- 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 part b?

For problems 29 - 31 the graph of a quadratic function y=ax^2 + bx + c is shown. tell whether the discriminant of ax^2 + bx + c = 0 is positive, negative, or zero.

Javier bought a painting for $150. each year, the painting's value increases by a factor of 1.15. which expression gives the painting's value after 77 years?