Ali was asked to simplify the expression 3(x - 6) + (4x + 12) - 6x. His work is shown below. 3(x - 6) + (4x + 12) - 6x

3x - 9 + 4x + 12 - 6x

(3x + 4x - 6x) + (-9 + 12)

x + 3

What is the logarithmic function modeled by the following table? x f(x) 9 2 27 3 81 4

If x=-3 is the only x-intercept of the graph of a quadratic equation, which statement best discribes the discriminant of the equation?

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?