| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.45 |
| Score | 0% | 69% |
| 2.1 | |
| 1.2 | |
| 1 | |
| 7.2 |
1
If a car travels 150 miles in 2 hours, what is the average speed?
| 70 mph | |
| 45 mph | |
| 60 mph | |
| 75 mph |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)Simplify \( \frac{32}{76} \).
| \( \frac{10}{19} \) | |
| \( \frac{8}{19} \) | |
| \( \frac{1}{3} \) | |
| \( \frac{6}{17} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 32 are [1, 2, 4, 8, 16, 32] and the factors of 76 are [1, 2, 4, 19, 38, 76]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{32}{76} \) = \( \frac{\frac{32}{4}}{\frac{76}{4}} \) = \( \frac{8}{19} \)
Convert c-2 to remove the negative exponent.
| \( \frac{-1}{-2c^{2}} \) | |
| \( \frac{-1}{c^{-2}} \) | |
| \( \frac{1}{c^2} \) | |
| \( \frac{2}{c} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
What is \( \frac{-6x^9}{5x^2} \)?
| -1\(\frac{1}{5}\)x-7 | |
| -1\(\frac{1}{5}\)x11 | |
| -1\(\frac{1}{5}\)x\(\frac{2}{9}\) | |
| -1\(\frac{1}{5}\)x7 |
To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:
\( \frac{-6x^9}{5x^2} \)
\( \frac{-6}{5} \) x(9 - 2)
-1\(\frac{1}{5}\)x7