| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.09 |
| Score | 0% | 62% |
Which of the following expressions contains exactly two terms?
polynomial |
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monomial |
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binomial |
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quadratic |
A monomial contains one term, a binomial contains two terms, and a polynomial contains more than two terms.
If side a = 3, side b = 7, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{58} \) | |
| \( \sqrt{52} \) | |
| \( \sqrt{80} \) | |
| \( \sqrt{53} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 32 + 72
c2 = 9 + 49
c2 = 58
c = \( \sqrt{58} \)
The endpoints of this line segment are at (-2, -3) and (2, 1). What is the slope-intercept equation for this line?
| y = -2\(\frac{1}{2}\)x + 1 | |
| y = \(\frac{1}{2}\)x + 1 | |
| y = -x - 2 | |
| y = x - 1 |
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 -1. 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, 1) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(1.0) - (-3.0)}{(2) - (-2)} \) = \( \frac{4}{4} \)Plugging these values into the slope-intercept equation:
y = x - 1
Solve for a:
5a - 3 < -6 - 7a
| a < -\(\frac{2}{5}\) | |
| a < -\(\frac{1}{4}\) | |
| a < \(\frac{1}{5}\) | |
| a < -\(\frac{1}{7}\) |
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.
5a - 3 < -6 - 7a
5a < -6 - 7a + 3
5a + 7a < -6 + 3
12a < -3
a < \( \frac{-3}{12} \)
a < -\(\frac{1}{4}\)
Simplify (2a)(5ab) - (4a2)(6b).
| 34a2b | |
| 14ab2 | |
| -14a2b | |
| 34ab2 |
To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.
(2a)(5ab) - (4a2)(6b)
(2 x 5)(a x a x b) - (4 x 6)(a2 x b)
(10)(a1+1 x b) - (24)(a2b)
10a2b - 24a2b
-14a2b