| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.37 |
| Score | 0% | 67% |
If \( \left|x + 6\right| \) + 1 = -2, which of these is a possible value for x?
| -3 | |
| 0 | |
| -6 | |
| 10 |
First, solve for \( \left|x + 6\right| \):
\( \left|x + 6\right| \) + 1 = -2
\( \left|x + 6\right| \) = -2 - 1
\( \left|x + 6\right| \) = -3
The value inside the absolute value brackets can be either positive or negative so (x + 6) must equal - 3 or --3 for \( \left|x + 6\right| \) to equal -3:
| x + 6 = -3 x = -3 - 6 x = -9 | x + 6 = 3 x = 3 - 6 x = -3 |
So, x = -3 or x = -9.
The total water usage for a city is 15,000 gallons each day. Of that total, 34% is for personal use and 61% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 3,500 | |
| 6,000 | |
| 4,050 | |
| 3,450 |
61% of the water consumption is industrial use and 34% is personal use so (61% - 34%) = 27% more water is used for industrial purposes. 15,000 gallons are consumed daily so industry consumes \( \frac{27}{100} \) x 15,000 gallons = 4,050 gallons.
If a car travels 210 miles in 6 hours, what is the average speed?
| 15 mph | |
| 65 mph | |
| 35 mph | |
| 60 mph |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)
| 1.8 | |
| 2.5 | |
| 1 | |
| 2.1 |
1
Simplify \( \frac{20}{44} \).
| \( \frac{1}{3} \) | |
| \( \frac{5}{11} \) | |
| \( \frac{1}{2} \) | |
| \( \frac{10}{19} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 20 are [1, 2, 4, 5, 10, 20] and the factors of 44 are [1, 2, 4, 11, 22, 44]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{20}{44} \) = \( \frac{\frac{20}{4}}{\frac{44}{4}} \) = \( \frac{5}{11} \)