| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.37 |
| Score | 0% | 67% |
If side a = 2, side b = 9, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{17} \) | |
| \( \sqrt{85} \) | |
| \( \sqrt{162} \) | |
| \( \sqrt{40} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 22 + 92
c2 = 4 + 81
c2 = 85
c = \( \sqrt{85} \)
Simplify (y + 8)(y - 1)
| y2 + 9y + 8 | |
| y2 - 7y - 8 | |
| y2 - 9y + 8 | |
| y2 + 7y - 8 |
To multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses:
(y + 8)(y - 1)
(y x y) + (y x -1) + (8 x y) + (8 x -1)
y2 - y + 8y - 8
y2 + 7y - 8
The endpoints of this line segment are at (-2, 0) and (2, -6). What is the slope-intercept equation for this line?
| y = -2\(\frac{1}{2}\)x + 3 | |
| y = \(\frac{1}{2}\)x + 1 | |
| y = -1\(\frac{1}{2}\)x - 3 | |
| y = -1\(\frac{1}{2}\)x + 0 |
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, 0) and (2, -6) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(-6.0) - (0.0)}{(2) - (-2)} \) = \( \frac{-6}{4} \)Plugging these values into the slope-intercept equation:
y = -1\(\frac{1}{2}\)x - 3
Which of the following is not a part of PEMDAS, the acronym for math order of operations?
addition |
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division |
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exponents |
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pairs |
When solving an equation with two variables, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)
Breaking apart a quadratic expression into a pair of binomials is called:
factoring |
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deconstructing |
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normalizing |
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squaring |
To factor a quadratic expression, apply the FOIL (First, Outside, Inside, Last) method in reverse.