What translation rule can be used to describe the result of the composition of (x, y) → (x-9, y -2) and (x, y) + (x + 1, y-2)?
(x, y) = (x+8, y– 4)
(x, y) = (x – 10, y +0)
(x, y) → (x–8. y - 4)
(x, y) = (x - 4. y - 8)

The depth of a lake at a certain point, wich is a function of the distance of that point from shore, is 30 feet.

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?

Identify the number as a rational or irrational.explain. 127