| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.29 |
| Score | 0% | 66% |
If side a = 7, side b = 3, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{97} \) | |
| \( \sqrt{58} \) | |
| 5 | |
| \( \sqrt{50} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 72 + 32
c2 = 49 + 9
c2 = 58
c = \( \sqrt{58} \)
If a = c = 1, b = d = 2, and the blue angle = 54°, what is the area of this parallelogram?
| 12 | |
| 35 | |
| 72 | |
| 2 |
The area of a parallelogram is equal to its length x width:
a = l x w
a = a x b
a = 1 x 2
a = 2
Factor y2 + 2y - 63
| (y + 7)(y + 9) | |
| (y - 7)(y - 9) | |
| (y - 7)(y + 9) | |
| (y + 7)(y - 9) |
To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce -63 as well and sum (Inside, Outside) to equal 2. For this problem, those two numbers are -7 and 9. Then, plug these into a set of binomials using the square root of the First variable (y2):
y2 + 2y - 63
y2 + (-7 + 9)y + (-7 x 9)
(y - 7)(y + 9)
The formula for volume of a cube in terms of height (h), length (l), and width (w) is which of the following?
2lw x 2wh + 2lh |
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h2 x l2 x w2 |
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lw x wh + lh |
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h x l x w |
A cube is a rectangular solid box with a height (h), length (l), and width (w). The volume is h x l x w and the surface area is 2lw x 2wh + 2lh.
A(n) __________ is two expressions separated by an equal sign.
problem |
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expression |
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equation |
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formula |
An equation is two expressions separated by an equal sign. The key to solving equations is to repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.