| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.32 |
| Score | 0% | 66% |
Solve for x:
x2 + 10x + 23 = -x + 5
| -2 or -9 | |
| 3 or -8 | |
| 3 or -7 | |
| 2 or -5 |
The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:
x2 + 10x + 23 = -x + 5
x2 + 10x + 23 - 5 = -x
x2 + 10x + x + 18 = 0
x2 + 11x + 18 = 0
Next, factor the quadratic equation:
x2 + 11x + 18 = 0
(x + 2)(x + 9) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (x + 2) or (x + 9) must equal zero:
If (x + 2) = 0, x must equal -2
If (x + 9) = 0, x must equal -9
So the solution is that x = -2 or -9
The dimensions of this cylinder are height (h) = 7 and radius (r) = 2. What is the volume?
| 80π | |
| 72π | |
| 28π | |
| 324π |
The volume of a cylinder is πr2h:
v = πr2h
v = π(22 x 7)
v = 28π
Factor y2 - 9y + 14
| (y - 7)(y - 2) | |
| (y + 7)(y - 2) | |
| (y - 7)(y + 2) | |
| (y + 7)(y + 2) |
To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce 14 as well and sum (Inside, Outside) to equal -9. For this problem, those two numbers are -7 and -2. Then, plug these into a set of binomials using the square root of the First variable (y2):
y2 - 9y + 14
y2 + (-7 - 2)y + (-7 x -2)
(y - 7)(y - 2)
Which of the following is not a part of PEMDAS, the acronym for math order of operations?
division |
|
exponents |
|
pairs |
|
addition |
When solving an equation with two variables, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)
If BD = 11 and AD = 19, AB = ?
| 6 | |
| 11 | |
| 18 | |
| 8 |
The entire length of this line is represented by AD which is AB + BD:
AD = AB + BD
Solving for AB:AB = AD - BD