| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.57 |
| Score | 0% | 71% |
Convert z-4 to remove the negative exponent.
| \( \frac{-4}{-z} \) | |
| \( \frac{1}{z^4} \) | |
| \( \frac{1}{z^{-4}} \) | |
| \( \frac{4}{z} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
What is \( \frac{18\sqrt{12}}{9\sqrt{3}} \)?
| 2 \( \sqrt{4} \) | |
| \(\frac{1}{2}\) \( \sqrt{4} \) | |
| \(\frac{1}{4}\) \( \sqrt{\frac{1}{2}} \) | |
| \(\frac{1}{4}\) \( \sqrt{2} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{18\sqrt{12}}{9\sqrt{3}} \)
\( \frac{18}{9} \) \( \sqrt{\frac{12}{3}} \)
2 \( \sqrt{4} \)
If a car travels 520 miles in 8 hours, what is the average speed?
| 40 mph | |
| 50 mph | |
| 70 mph | |
| 65 mph |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)Damon loaned Charlie $900 at an annual interest rate of 2%. If no payments are made, what is the interest owed on this loan at the end of the first year?
| $90 | |
| $24 | |
| $20 | |
| $18 |
The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:
interest = annual interest rate x loan amount
i = (\( \frac{6}{100} \)) x $900
i = 0.02 x $900
i = $18
What is \( \frac{5}{2} \) + \( \frac{2}{8} \)?
| 2 \( \frac{1}{8} \) | |
| 2 \( \frac{5}{8} \) | |
| \( \frac{9}{18} \) | |
| 2\(\frac{3}{4}\) |
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 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [8, 16, 24, 32, 40] making 8 the smallest multiple 2 and 8 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{5 x 4}{2 x 4} \) + \( \frac{2 x 1}{8 x 1} \)
\( \frac{20}{8} \) + \( \frac{2}{8} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{20 + 2}{8} \) = \( \frac{22}{8} \) = 2\(\frac{3}{4}\)