| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.04 |
| Score | 0% | 61% |
What is 2\( \sqrt{5} \) x 3\( \sqrt{8} \)?
| 6\( \sqrt{13} \) | |
| 5\( \sqrt{40} \) | |
| 12\( \sqrt{10} \) | |
| 5\( \sqrt{5} \) |
To multiply terms with radicals, multiply the coefficients and radicands separately:
2\( \sqrt{5} \) x 3\( \sqrt{8} \)
(2 x 3)\( \sqrt{5 \times 8} \)
6\( \sqrt{40} \)
Now we need to simplify the radical:
6\( \sqrt{40} \)
6\( \sqrt{10 \times 4} \)
6\( \sqrt{10 \times 2^2} \)
(6)(2)\( \sqrt{10} \)
12\( \sqrt{10} \)
What is the greatest common factor of 68 and 16?
| 10 | |
| 15 | |
| 4 | |
| 12 |
The factors of 68 are [1, 2, 4, 17, 34, 68] and the factors of 16 are [1, 2, 4, 8, 16]. They share 3 factors [1, 2, 4] making 4 the greatest factor 68 and 16 have in common.
Convert c-3 to remove the negative exponent.
| \( \frac{1}{c^3} \) | |
| \( \frac{-3}{c} \) | |
| \( \frac{-3}{-c} \) | |
| \( \frac{-1}{-3c^{3}} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
The total water usage for a city is 50,000 gallons each day. Of that total, 30% is for personal use and 62% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 16,000 | |
| 6,750 | |
| 2,850 | |
| 3,200 |
62% of the water consumption is industrial use and 30% is personal use so (62% - 30%) = 32% more water is used for industrial purposes. 50,000 gallons are consumed daily so industry consumes \( \frac{32}{100} \) x 50,000 gallons = 16,000 gallons.
What is \( \frac{3}{2} \) + \( \frac{5}{6} \)?
| 2 \( \frac{7}{12} \) | |
| 2\(\frac{1}{3}\) | |
| 1 \( \frac{1}{6} \) | |
| 2 \( \frac{2}{10} \) |
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60]. The first few multiples they share are [6, 12, 18, 24, 30] making 6 the smallest multiple 2 and 6 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{3 x 3}{2 x 3} \) + \( \frac{5 x 1}{6 x 1} \)
\( \frac{9}{6} \) + \( \frac{5}{6} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{9 + 5}{6} \) = \( \frac{14}{6} \) = 2\(\frac{1}{3}\)