| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.10 |
| Score | 0% | 62% |
Which of the following expressions contains exactly two terms?
binomial |
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quadratic |
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monomial |
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polynomial |
A monomial contains one term, a binomial contains two terms, and a polynomial contains more than two terms.
Which of the following statements about math operations is incorrect?
all of these statements are correct |
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you can add monomials that have the same variable and the same exponent |
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you can subtract monomials that have the same variable and the same exponent |
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you can multiply monomials that have different variables and different exponents |
You can only add or subtract monomials that have the same variable and the same exponent. For example, 2a + 4a = 6a and 4a2 - a2 = 3a2 but 2a + 4b and 7a - 3b cannot be combined. However, you can multiply and divide monomials with unlike terms. For example, 2a x 6b = 12ab.
Solve for a:
a2 - a - 15 = -4a + 3
| 3 or -6 | |
| -2 or -6 | |
| 6 or 4 | |
| 4 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 - a - 15 = -4a + 3
a2 - a - 15 - 3 = -4a
a2 - a + 4a - 18 = 0
a2 + 3a - 18 = 0
Next, factor the quadratic equation:
a2 + 3a - 18 = 0
(a - 3)(a + 6) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (a - 3) or (a + 6) must equal zero:
If (a - 3) = 0, a must equal 3
If (a + 6) = 0, a must equal -6
So the solution is that a = 3 or -6
When two lines intersect, adjacent angles are __________ (they add up to 180°) and angles across from either other are __________ (they're equal).
supplementary, vertical |
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acute, obtuse |
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obtuse, acute |
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vertical, supplementary |
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, 4) and (2, 2). What is the slope-intercept equation for this line?
| y = 1\(\frac{1}{2}\)x - 4 | |
| y = -2\(\frac{1}{2}\)x + 1 | |
| y = 3x + 1 | |
| y = -\(\frac{1}{2}\)x + 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 3. 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, 4) and (2, 2) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(2.0) - (4.0)}{(2) - (-2)} \) = \( \frac{-2}{4} \)Plugging these values into the slope-intercept equation:
y = -\(\frac{1}{2}\)x + 3