| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.28 |
| Score | 0% | 66% |
What is -9y5 x 7y4?
| -2y20 | |
| -63y9 | |
| -2y5 | |
| -63y20 |
To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:
-9y5 x 7y4
(-9 x 7)y(5 + 4)
-63y9
12 members of a bridal party need transported to a wedding reception but there are only 2 5-passenger taxis available to take them. How many will need to find other transportation?
| 5 | |
| 4 | |
| 2 | |
| 1 |
There are 2 5-passenger taxis available so that's 2 x 5 = 10 total seats. There are 12 people needing transportation leaving 12 - 10 = 2 who will have to find other transportation.
The total water usage for a city is 50,000 gallons each day. Of that total, 14% is for personal use and 37% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 6,400 | |
| 3,500 | |
| 11,500 | |
| 5,850 |
37% of the water consumption is industrial use and 14% is personal use so (37% - 14%) = 23% more water is used for industrial purposes. 50,000 gallons are consumed daily so industry consumes \( \frac{23}{100} \) x 50,000 gallons = 11,500 gallons.
What is -5c2 + 2c2?
| 7c2 | |
| -3c2 | |
| -7c2 | |
| -7c-2 |
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:
-5c2 + 2c2
(-5 + 2)c2
-3c2
If all of a roofing company's 12 workers are required to staff 3 roofing crews, how many workers need to be added during the busy season in order to send 7 complete crews out on jobs?
| 18 | |
| 10 | |
| 17 | |
| 16 |
In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 12 workers at the company now and that's enough to staff 3 crews so there are \( \frac{12}{3} \) = 4 workers on a crew. 7 crews are needed for the busy season which, at 4 workers per crew, means that the roofing company will need 7 x 4 = 28 total workers to staff the crews during the busy season. The company already employs 12 workers so they need to add 28 - 12 = 16 new staff for the busy season.