| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.30 |
| Score | 0% | 66% |
What is -c5 - 9c5?
| -10c5 | |
| 8c10 | |
| -10c-5 | |
| 8c-10 |
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:
-1c5 - 9c5
(-1 - 9)c5
-10c5
What is \( 8 \)\( \sqrt{48} \) + \( 3 \)\( \sqrt{3} \)
| 11\( \sqrt{144} \) | |
| 24\( \sqrt{144} \) | |
| 24\( \sqrt{3} \) | |
| 35\( \sqrt{3} \) |
To add these radicals together their radicands must be the same:
8\( \sqrt{48} \) + 3\( \sqrt{3} \)
8\( \sqrt{16 \times 3} \) + 3\( \sqrt{3} \)
8\( \sqrt{4^2 \times 3} \) + 3\( \sqrt{3} \)
(8)(4)\( \sqrt{3} \) + 3\( \sqrt{3} \)
32\( \sqrt{3} \) + 3\( \sqrt{3} \)
Now that the radicands are identical, you can add them together:
32\( \sqrt{3} \) + 3\( \sqrt{3} \)A factor is a positive __________ that divides evenly into a given number.
mixed number |
|
integer |
|
fraction |
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improper 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 a car travels 165 miles in 3 hours, what is the average speed?
| 45 mph | |
| 25 mph | |
| 55 mph | |
| 30 mph |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)The total water usage for a city is 5,000 gallons each day. Of that total, 13% is for personal use and 29% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 800 | |
| 750 | |
| 8,000 | |
| 3,900 |
29% of the water consumption is industrial use and 13% is personal use so (29% - 13%) = 16% more water is used for industrial purposes. 5,000 gallons are consumed daily so industry consumes \( \frac{16}{100} \) x 5,000 gallons = 800 gallons.