| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.28 |
| Score | 0% | 66% |
Solve for c:
c2 + 8c + 10 = -c - 4
| -2 or -7 | |
| 1 or -9 | |
| 7 or -6 | |
| 6 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:
c2 + 8c + 10 = -c - 4
c2 + 8c + 10 + 4 = -c
c2 + 8c + c + 14 = 0
c2 + 9c + 14 = 0
Next, factor the quadratic equation:
c2 + 9c + 14 = 0
(c + 2)(c + 7) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (c + 2) or (c + 7) must equal zero:
If (c + 2) = 0, c must equal -2
If (c + 7) = 0, c must equal -7
So the solution is that c = -2 or -7
The dimensions of this cube are height (h) = 9, length (l) = 7, and width (w) = 1. What is the volume?
| 210 | |
| 63 | |
| 144 | |
| 36 |
The volume of a cube is height x length x width:
v = h x l x w
v = 9 x 7 x 1
v = 63
Solve for c:
-c - 2 < \( \frac{c}{-8} \)
| c < -1\(\frac{1}{5}\) | |
| c < 2\(\frac{5}{29}\) | |
| c < -2\(\frac{2}{7}\) | |
| c < -1\(\frac{1}{13}\) |
To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the < sign and the answer on the other.
-c - 2 < \( \frac{c}{-8} \)
-8 x (-c - 2) < c
(-8 x -c) + (-8 x -2) < c
8c + 16 < c
8c + 16 - c < 0
8c - c < -16
7c < -16
c < \( \frac{-16}{7} \)
c < -2\(\frac{2}{7}\)
A(n) __________ is two expressions separated by an equal sign.
problem |
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expression |
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formula |
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equation |
An equation is two expressions separated by an equal sign. The key to solving equations is to repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.
Order the following types of angle from least number of degrees to most number of degrees.
acute, obtuse, right |
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right, obtuse, acute |
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right, acute, obtuse |
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acute, right, obtuse |
An acute angle measures less than 90°, a right angle measures 90°, and an obtuse angle measures more than 90°.