The figure below shows triangle pqr and some of its transformed images on a coordinate grid: a coordinate plane is shown with five triangles. triangle pqr has vertices 2 comma 1, 5 comma 1, and 2 comma 4. triangle a has vertices negative 2 comma 1, negative 5 comma 1, and negative 5 comma 4. triangle b has vertices negative 6 comma 1, negative 6 comma 4, and negative 9 comma 1. triangle c has vertices negative 2 comma negative 1, negative 2 comma negative 4, negative 5 comma negative 4. triangle d has vertices 2 comma negative 1, 5 comma negative 1, and 5 comma negative 4. which of the four triangles was formed by a translation of triangle pqr?

Which of the following expressions is equal to 2x^2+8

How many kilometers are equal to 5 miles? use 1 mile ≈ 1.61 kilometers. !

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?