| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.31 |
| Score | 0% | 66% |
Solve for b:
b2 - 18b + 55 = -3b - 1
| 7 or 8 | |
| -1 or -6 | |
| 3 or -6 | |
| 5 or -8 |
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:
b2 - 18b + 55 = -3b - 1
b2 - 18b + 55 + 1 = -3b
b2 - 18b + 3b + 56 = 0
b2 - 15b + 56 = 0
Next, factor the quadratic equation:
b2 - 15b + 56 = 0
(b - 7)(b - 8) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (b - 7) or (b - 8) must equal zero:
If (b - 7) = 0, b must equal 7
If (b - 8) = 0, b must equal 8
So the solution is that b = 7 or 8
Which of the following is not a part of PEMDAS, the acronym for math order of operations?
exponents |
|
division |
|
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.)
What is 8a3 + 8a3?
| 16a3 | |
| 0 | |
| 16 | |
| 64a3 |
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.
8a3 + 8a3 = 16a3
The dimensions of this cube are height (h) = 8, length (l) = 1, and width (w) = 2. What is the surface area?
| 166 | |
| 52 | |
| 126 | |
| 104 |
The surface area of a cube is (2 x length x width) + (2 x width x height) + (2 x length x height):
sa = 2lw + 2wh + 2lh
sa = (2 x 1 x 2) + (2 x 2 x 8) + (2 x 1 x 8)
sa = (4) + (32) + (16)
sa = 52
The formula for volume of a cube in terms of height (h), length (l), and width (w) is which of the following?
lw x wh + lh |
|
h x l x w |
|
h2 x l2 x w2 |
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2lw x 2wh + 2lh |
A cube is a rectangular solid box with a height (h), length (l), and width (w). The volume is h x l x w and the surface area is 2lw x 2wh + 2lh.