| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.50 |
| Score | 0% | 70% |
Solve for z:
z2 - 2z - 8 = -4z - 5
| 3 or -2 | |
| -6 or -8 | |
| 1 or -3 | |
| 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:
z2 - 2z - 8 = -4z - 5
z2 - 2z - 8 + 5 = -4z
z2 - 2z + 4z - 3 = 0
z2 + 2z - 3 = 0
Next, factor the quadratic equation:
z2 + 2z - 3 = 0
(z - 1)(z + 3) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (z - 1) or (z + 3) must equal zero:
If (z - 1) = 0, z must equal 1
If (z + 3) = 0, z must equal -3
So the solution is that z = 1 or -3
Which of the following is not a part of PEMDAS, the acronym for math order of operations?
exponents |
|
addition |
|
division |
|
pairs |
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 angle a = 24° and angle b = 34° what is the length of angle c?
| 122° | |
| 77° | |
| 101° | |
| 83° |
The sum of the interior angles of a triangle is 180°:
180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 24° - 34° = 122°
What is 3a + 2a?
| 5a | |
| 6a | |
| 6a2 | |
| 1 |
To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.
3a + 2a = 5a
If the base of this triangle is 1 and the height is 2, what is the area?
| 1 | |
| 45\(\frac{1}{2}\) | |
| 66 | |
| 17\(\frac{1}{2}\) |
The area of a triangle is equal to ½ base x height:
a = ½bh
a = ½ x 1 x 2 = \( \frac{2}{2} \) = 1