Find the coordinates of the image under the transformation (x – 4, y + 6) for ∆XYZ at X(-6, 1), Y(4, 0), Z(1, 3) A. X’(-10, 7) Y’(0, 6) Z’(-3, 9)
B. X’(10, -7) Y’(0, -6) Z’(3, -9)
C. X’(-8, 7) Y’(-2, 0) Z’(-5, 8)
D. X’(-3, 2) Y’(1, 3) Z’(-3, 5)

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?

What is the image of c for a 90° counterclockwise rotation about a? (3, 7) (-1, 3) (7, 3)

Use the ratio test to determine whether ∑n=14∞n+2n! converges or diverges. (a) find the ratio of successive terms. write your answer as a fully simplified fraction. for n≥14, limn→∞∣∣∣an+1an∣∣∣=limn→∞.