| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.00 |
| Score | 0% | 60% |
Solve for a:
a2 + 17a + 31 = 5a - 4
| 5 or -1 | |
| -9 or -9 | |
| 1 or 1 | |
| -5 or -7 |
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:
a2 + 17a + 31 = 5a - 4
a2 + 17a + 31 + 4 = 5a
a2 + 17a - 5a + 35 = 0
a2 + 12a + 35 = 0
Next, factor the quadratic equation:
a2 + 12a + 35 = 0
(a + 5)(a + 7) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (a + 5) or (a + 7) must equal zero:
If (a + 5) = 0, a must equal -5
If (a + 7) = 0, a must equal -7
So the solution is that a = -5 or -7
On this circle, line segment AB is the:
radius |
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diameter |
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circumference |
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chord |
A circle is a figure in which each point around its perimeter is an equal distance from the center. The radius of a circle is the distance between the center and any point along its perimeter. A chord is a line segment that connects any two points along its perimeter. The diameter of a circle is the length of a chord that passes through the center of the circle and equals twice the circle's radius (2r).
If the base of this triangle is 6 and the height is 6, what is the area?
| 32 | |
| 39 | |
| 18 | |
| 105 |
The area of a triangle is equal to ½ base x height:
a = ½bh
a = ½ x 6 x 6 = \( \frac{36}{2} \) = 18
A(n) __________ is two expressions separated by an equal sign.
formula |
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problem |
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expression |
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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.
The endpoints of this line segment are at (-2, -3) and (2, 5). What is the slope of this line?
| -1 | |
| 2 | |
| 2\(\frac{1}{2}\) | |
| -1\(\frac{1}{2}\) |
The slope of this line is the change in y divided by the change in x. The endpoints of this line segment are at (-2, -3) and (2, 5) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(5.0) - (-3.0)}{(2) - (-2)} \) = \( \frac{8}{4} \)