| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.23 |
| Score | 0% | 65% |
A factor is a positive __________ that divides evenly into a given number.
integer |
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improper fraction |
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mixed number |
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fraction |
A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.
If \( \left|b - 2\right| \) - 7 = 9, which of these is a possible value for b?
| 3 | |
| 18 | |
| -4 | |
| -11 |
First, solve for \( \left|b - 2\right| \):
\( \left|b - 2\right| \) - 7 = 9
\( \left|b - 2\right| \) = 9 + 7
\( \left|b - 2\right| \) = 16
The value inside the absolute value brackets can be either positive or negative so (b - 2) must equal + 16 or -16 for \( \left|b - 2\right| \) to equal 16:
| b - 2 = 16 b = 16 + 2 b = 18 | b - 2 = -16 b = -16 + 2 b = -14 |
So, b = -14 or b = 18.
The total water usage for a city is 20,000 gallons each day. Of that total, 35% is for personal use and 52% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 17,500 | |
| 4,200 | |
| 3,400 | |
| 4,400 |
52% of the water consumption is industrial use and 35% is personal use so (52% - 35%) = 17% more water is used for industrial purposes. 20,000 gallons are consumed daily so industry consumes \( \frac{17}{100} \) x 20,000 gallons = 3,400 gallons.
Simplify \( \sqrt{75} \)
| 5\( \sqrt{3} \) | |
| 3\( \sqrt{3} \) | |
| 6\( \sqrt{3} \) | |
| 7\( \sqrt{6} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{75} \)
\( \sqrt{25 \times 3} \)
\( \sqrt{5^2 \times 3} \)
5\( \sqrt{3} \)
What is \( \frac{-9y^5}{3y^2} \)?
| -3y2\(\frac{1}{2}\) | |
| -3y-3 | |
| -\(\frac{1}{3}\)y7 | |
| -3y3 |
To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:
\( \frac{-9y^5}{3y^2} \)
\( \frac{-9}{3} \) y(5 - 2)
-3y3