Functions f(x) and g(x) are shown below:

f(x) = x2
g(x) = x2 − 8x + 16

in which direction and by how many units should f(x) be shifted to obtain g(x)?
a. left by 4 units
b. right by 4 units
c. left by 8 units
d. right by 8 units

The following division is being performed using multiplication by the reciprocal find the missing numbers is 5/12 divided by x/3 equals 5/12 times x/10 equals 1/x

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?

At the electronics store you have a coupon for 20% off up to 2 cds you buy for cds with the original cost of $10.99 each the sales tax is 5% what is the total cost of your purchase