| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.18 |
| Score | 0% | 64% |
What is -6x5 x x7?
| -6x35 | |
| -5x7 | |
| -6x12 | |
| -6x7 |
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:
-6x5 x x7
(-6 x 1)x(5 + 7)
-6x12
What is \( 5 \)\( \sqrt{32} \) - \( 3 \)\( \sqrt{2} \)
| 2\( \sqrt{16} \) | |
| 17\( \sqrt{2} \) | |
| 2\( \sqrt{-12} \) | |
| 15\( \sqrt{32} \) |
To subtract these radicals together their radicands must be the same:
5\( \sqrt{32} \) - 3\( \sqrt{2} \)
5\( \sqrt{16 \times 2} \) - 3\( \sqrt{2} \)
5\( \sqrt{4^2 \times 2} \) - 3\( \sqrt{2} \)
(5)(4)\( \sqrt{2} \) - 3\( \sqrt{2} \)
20\( \sqrt{2} \) - 3\( \sqrt{2} \)
Now that the radicands are identical, you can subtract them:
20\( \sqrt{2} \) - 3\( \sqrt{2} \)The total water usage for a city is 40,000 gallons each day. Of that total, 11% is for personal use and 30% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 2,400 | |
| 3,600 | |
| 7,600 | |
| 9,600 |
30% of the water consumption is industrial use and 11% is personal use so (30% - 11%) = 19% more water is used for industrial purposes. 40,000 gallons are consumed daily so industry consumes \( \frac{19}{100} \) x 40,000 gallons = 7,600 gallons.
A factor is a positive __________ that divides evenly into a given number.
improper fraction |
|
mixed number |
|
integer |
|
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.
What is -2z2 + 3z2?
| z2 | |
| -5z-2 | |
| 5z2 | |
| 5z-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:
-2z2 + 3z2
(-2 + 3)z2
z2