| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.29 |
| Score | 0% | 66% |
The total water usage for a city is 30,000 gallons each day. Of that total, 28% is for personal use and 48% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 6,000 | |
| 7,500 | |
| 8,000 | |
| 3,450 |
48% of the water consumption is industrial use and 28% is personal use so (48% - 28%) = 20% more water is used for industrial purposes. 30,000 gallons are consumed daily so industry consumes \( \frac{20}{100} \) x 30,000 gallons = 6,000 gallons.
What is \( \frac{20\sqrt{15}}{4\sqrt{5}} \)?
| 5 \( \sqrt{3} \) | |
| \(\frac{1}{3}\) \( \sqrt{5} \) | |
| \(\frac{1}{3}\) \( \sqrt{\frac{1}{5}} \) | |
| 5 \( \sqrt{\frac{1}{3}} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{20\sqrt{15}}{4\sqrt{5}} \)
\( \frac{20}{4} \) \( \sqrt{\frac{15}{5}} \)
5 \( \sqrt{3} \)
What is \( \sqrt{\frac{81}{25}} \)?
| \(\frac{5}{7}\) | |
| 1\(\frac{4}{5}\) | |
| 1\(\frac{1}{2}\) | |
| 1\(\frac{1}{3}\) |
To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:
\( \sqrt{\frac{81}{25}} \)
\( \frac{\sqrt{81}}{\sqrt{25}} \)
\( \frac{\sqrt{9^2}}{\sqrt{5^2}} \)
\( \frac{9}{5} \)
1\(\frac{4}{5}\)
If \( \left|a + 7\right| \) - 6 = 0, which of these is a possible value for a?
| -1 | |
| -10 | |
| 5 | |
| 6 |
First, solve for \( \left|a + 7\right| \):
\( \left|a + 7\right| \) - 6 = 0
\( \left|a + 7\right| \) = 0 + 6
\( \left|a + 7\right| \) = 6
The value inside the absolute value brackets can be either positive or negative so (a + 7) must equal + 6 or -6 for \( \left|a + 7\right| \) to equal 6:
| a + 7 = 6 a = 6 - 7 a = -1 | a + 7 = -6 a = -6 - 7 a = -13 |
So, a = -13 or a = -1.
Convert a-3 to remove the negative exponent.
| \( \frac{-3}{a} \) | |
| \( \frac{1}{a^3} \) | |
| \( \frac{-1}{-3a} \) | |
| \( \frac{-1}{-3a^{3}} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.