Ineed . see picture: "number of solutions to equations challenge"

Step-by-step explanation:

Put the values of P and Q to the equation Px - 45 = Qx + 75:

15x - 45 = 15x + 75     subtract 15x from both sides

-45 = 75   FALSE

In other cases, we get some value x.

Example:

A. P = -45 and Q = -75

-45x - 45 = -75x + 75     add 45 to both sides

-45x = -75x + 120      add 75x to both sides

25x = 120       divide both sides by 25

x = 4.8

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

answer: .64

step-by-step explanation

set up the formula for standard deviation for this set of numbers, then simplify