| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.20 |
| Score | 0% | 64% |
For this diagram, the Pythagorean theorem states that b2 = ?
c2 + a2 |
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c2 - a2 |
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c - a |
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a2 - c2 |
The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c2) is equal to the sum of the two perpendicular sides squared (a2 + b2): c2 = a2 + b2 or, solved for c, \(c = \sqrt{a + b}\)
The dimensions of this cube are height (h) = 6, length (l) = 4, and width (w) = 8. What is the volume?
| 49 | |
| 192 | |
| 84 | |
| 36 |
The volume of a cube is height x length x width:
v = h x l x w
v = 6 x 4 x 8
v = 192
The endpoints of this line segment are at (-2, 9) and (2, -1). What is the slope of this line?
| -1 | |
| 1 | |
| 1\(\frac{1}{2}\) | |
| -2\(\frac{1}{2}\) |
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, 9) and (2, -1) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(-1.0) - (9.0)}{(2) - (-2)} \) = \( \frac{-10}{4} \)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.)
If angle a = 25° and angle b = 24° what is the length of angle d?
| 114° | |
| 155° | |
| 141° | |
| 145° |
An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite:
d° = b° + c°
To find angle c, remember that the sum of the interior angles of a triangle is 180°:
180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 25° - 24° = 131°
So, d° = 24° + 131° = 155°
A shortcut to get this answer is to remember that angles around a line add up to 180°:
a° + d° = 180°
d° = 180° - a°
d° = 180° - 25° = 155°