| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.09 |
| Score | 0% | 62% |
Which of the following expressions contains exactly two terms?
monomial |
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binomial |
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quadratic |
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polynomial |
A monomial contains one term, a binomial contains two terms, and a polynomial contains more than two terms.
When two lines intersect, adjacent angles are __________ (they add up to 180°) and angles across from either other are __________ (they're equal).
obtuse, acute |
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vertical, supplementary |
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acute, obtuse |
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supplementary, vertical |
Angles around a line add up to 180°. Angles around a point add up to 360°. When two lines intersect, adjacent angles are supplementary (they add up to 180°) and angles across from either other are vertical (they're equal).
The endpoints of this line segment are at (-2, -5) and (2, -3). What is the slope-intercept equation for this line?
| y = x - 4 | |
| y = -\(\frac{1}{2}\)x - 4 | |
| y = \(\frac{1}{2}\)x - 4 | |
| y = 2x + 3 |
The slope-intercept equation for a line is y = mx + b where m is the slope and b is the y-intercept of the line. From the graph, you can see that the y-intercept (the y-value from the point where the line crosses the y-axis) is -4. 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, -5) and (2, -3) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(-3.0) - (-5.0)}{(2) - (-2)} \) = \( \frac{2}{4} \)Plugging these values into the slope-intercept equation:
y = \(\frac{1}{2}\)x - 4
Order the following types of angle from least number of degrees to most number of degrees.
acute, right, obtuse |
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acute, obtuse, right |
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right, acute, obtuse |
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right, obtuse, acute |
An acute angle measures less than 90°, a right angle measures 90°, and an obtuse angle measures more than 90°.
Solve for a:
a2 - 10a + 16 = -2a + 1
| 4 or 1 | |
| 3 or 5 | |
| -3 or -8 | |
| -1 or -3 |
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 - 10a + 16 = -2a + 1
a2 - 10a + 16 - 1 = -2a
a2 - 10a + 2a + 15 = 0
a2 - 8a + 15 = 0
Next, factor the quadratic equation:
a2 - 8a + 15 = 0
(a - 3)(a - 5) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (a - 3) or (a - 5) must equal zero:
If (a - 3) = 0, a must equal 3
If (a - 5) = 0, a must equal 5
So the solution is that a = 3 or 5