| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.21 |
| Score | 0% | 64% |
Convert z-4 to remove the negative exponent.
| \( \frac{1}{z^{-4}} \) | |
| \( \frac{1}{z^4} \) | |
| \( \frac{-4}{z} \) | |
| \( \frac{-1}{-4z^{4}} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
How many 1\(\frac{1}{2}\) gallon cans worth of fuel would you need to pour into an empty 6 gallon tank to fill it exactly halfway?
| 2 | |
| 4 | |
| 7 | |
| 2 |
To fill a 6 gallon tank exactly halfway you'll need 3 gallons of fuel. Each fuel can holds 1\(\frac{1}{2}\) gallons so:
cans = \( \frac{3 \text{ gallons}}{1\frac{1}{2} \text{ gallons}} \) = 2
What is \( \frac{1}{8} \) ÷ \( \frac{1}{6} \)?
| \(\frac{4}{15}\) | |
| \(\frac{1}{12}\) | |
| \(\frac{1}{27}\) | |
| \(\frac{3}{4}\) |
To divide fractions, invert the second fraction and then multiply:
\( \frac{1}{8} \) ÷ \( \frac{1}{6} \) = \( \frac{1}{8} \) x \( \frac{6}{1} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{1}{8} \) x \( \frac{6}{1} \) = \( \frac{1 x 6}{8 x 1} \) = \( \frac{6}{8} \) = \(\frac{3}{4}\)
What is \( \frac{35\sqrt{8}}{5\sqrt{2}} \)?
| 4 \( \sqrt{\frac{1}{7}} \) | |
| \(\frac{1}{4}\) \( \sqrt{7} \) | |
| 4 \( \sqrt{7} \) | |
| 7 \( \sqrt{4} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{35\sqrt{8}}{5\sqrt{2}} \)
\( \frac{35}{5} \) \( \sqrt{\frac{8}{2}} \)
7 \( \sqrt{4} \)
If \( \left|b - 8\right| \) + 3 = -9, which of these is a possible value for b?
| -4 | |
| -11 | |
| -19 | |
| 12 |
First, solve for \( \left|b - 8\right| \):
\( \left|b - 8\right| \) + 3 = -9
\( \left|b - 8\right| \) = -9 - 3
\( \left|b - 8\right| \) = -12
The value inside the absolute value brackets can be either positive or negative so (b - 8) must equal - 12 or --12 for \( \left|b - 8\right| \) to equal -12:
| b - 8 = -12 b = -12 + 8 b = -4 | b - 8 = 12 b = 12 + 8 b = 20 |
So, b = 20 or b = -4.