| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.21 |
| Score | 0% | 64% |
How many 2 gallon cans worth of fuel would you need to pour into an empty 12 gallon tank to fill it exactly halfway?
| 3 | |
| 3 | |
| 6 | |
| 9 |
To fill a 12 gallon tank exactly halfway you'll need 6 gallons of fuel. Each fuel can holds 2 gallons so:
cans = \( \frac{6 \text{ gallons}}{2 \text{ gallons}} \) = 3
Simplify \( \sqrt{75} \)
| 4\( \sqrt{3} \) | |
| 4\( \sqrt{6} \) | |
| 5\( \sqrt{3} \) | |
| 6\( \sqrt{3} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{75} \)
\( \sqrt{25 \times 3} \)
\( \sqrt{5^2 \times 3} \)
5\( \sqrt{3} \)
What is \( \sqrt{\frac{16}{81}} \)?
| \(\frac{7}{9}\) | |
| \(\frac{4}{9}\) | |
| 1 | |
| 1\(\frac{1}{4}\) |
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:
\( \sqrt{\frac{16}{81}} \)
\( \frac{\sqrt{16}}{\sqrt{81}} \)
\( \frac{\sqrt{4^2}}{\sqrt{9^2}} \)
\(\frac{4}{9}\)
Convert c-2 to remove the negative exponent.
| \( \frac{1}{c^{-2}} \) | |
| \( \frac{-1}{-2c^{2}} \) | |
| \( \frac{2}{c} \) | |
| \( \frac{1}{c^2} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
What is -a2 - 9a2?
| -10a-2 | |
| 10a-2 | |
| -10a2 | |
| 10a2 |
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:
-1a2 - 9a2
(-1 - 9)a2
-10a2