| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.97 |
| Score | 0% | 59% |
What is 5y6 - 4y6?
| -y-6 | |
| 9y36 | |
| y6 | |
| -y6 |
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:
5y6 - 4y6
(5 - 4)y6
y6
The total water usage for a city is 40,000 gallons each day. Of that total, 23% is for personal use and 56% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 13,200 | |
| 8,400 | |
| 14,000 | |
| 10,500 |
56% of the water consumption is industrial use and 23% is personal use so (56% - 23%) = 33% more water is used for industrial purposes. 40,000 gallons are consumed daily so industry consumes \( \frac{33}{100} \) x 40,000 gallons = 13,200 gallons.
If a rectangle is twice as long as it is wide and has a perimeter of 12 meters, what is the area of the rectangle?
| 128 m2 | |
| 8 m2 | |
| 32 m2 | |
| 18 m2 |
The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 12 meters so the equation becomes: 2w + 2h = 12.
Putting these two equations together and solving for width (w):
2w + 2h = 12
w + h = \( \frac{12}{2} \)
w + h = 6
w = 6 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 6 - 2w
3w = 6
w = \( \frac{6}{3} \)
w = 2
Since h = 2w that makes h = (2 x 2) = 4 and the area = h x w = 2 x 4 = 8 m2
Convert b-5 to remove the negative exponent.
| \( \frac{-1}{-5b} \) | |
| \( \frac{1}{b^5} \) | |
| \( \frac{-5}{-b} \) | |
| \( \frac{1}{b^{-5}} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
| 6.3 | |
| 3.6 | |
| 2.4 | |
| 1 |
1