Determine the location of the vertex and determine the nature of the vertex for the graphs of: y = x^3 - 6x^2 -15x + 7

For each expression use a property to write an equivalent expression.

What is the equation of a vertical line passing through the point (−5, −1)? y = −5 y = −1 x = −5 x = −1

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?