| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.34 |
| Score | 0% | 67% |
If the base of this triangle is 6 and the height is 5, what is the area?
| 15 | |
| 25 | |
| 78 | |
| 56 |
The area of a triangle is equal to ½ base x height:
a = ½bh
a = ½ x 6 x 5 = \( \frac{30}{2} \) = 15
If side a = 2, side b = 1, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{145} \) | |
| \( \sqrt{37} \) | |
| \( \sqrt{58} \) | |
| \( \sqrt{5} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 22 + 12
c2 = 4 + 1
c2 = 5
c = \( \sqrt{5} \)
A(n) __________ is two expressions separated by an equal sign.
formula |
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equation |
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expression |
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problem |
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.
Factor y2 - 8y + 15
| (y - 5)(y - 3) | |
| (y + 5)(y + 3) | |
| (y + 5)(y - 3) | |
| (y - 5)(y + 3) |
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 15 as well and sum (Inside, Outside) to equal -8. For this problem, those two numbers are -5 and -3. Then, plug these into a set of binomials using the square root of the First variable (y2):
y2 - 8y + 15
y2 + (-5 - 3)y + (-5 x -3)
(y - 5)(y - 3)
The dimensions of this cube are height (h) = 4, length (l) = 1, and width (w) = 2. What is the volume?
| 108 | |
| 8 | |
| 70 | |
| 36 |
The volume of a cube is height x length x width:
v = h x l x w
v = 4 x 1 x 2
v = 8