| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.64 |
| Score | 0% | 73% |
\({b + c \over a} = {b \over a} + {c \over a}\) defines which of the following?
distributive property for multiplication |
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commutative property for multiplication |
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distributive property for division |
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commutative property for division |
The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).
Convert z-2 to remove the negative exponent.
| \( \frac{2}{z} \) | |
| \( \frac{1}{z^{-2}} \) | |
| \( \frac{-1}{-2z} \) | |
| \( \frac{1}{z^2} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
A triathlon course includes a 500m swim, a 30.9km bike ride, and a 9.100000000000001km run. What is the total length of the race course?
| 38.9km | |
| 40.5km | |
| 45.4km | |
| 64.1km |
To add these distances, they must share the same unit so first you need to first convert the swim distance from meters (m) to kilometers (km) before adding it to the bike and run distances which are already in km. To convert 500 meters to kilometers, divide the distance by 1000 to get 0.5km then add the remaining distances:
total distance = swim + bike + run
total distance = 0.5km + 30.9km + 9.100000000000001km
total distance = 40.5km
If a car travels 675 miles in 9 hours, what is the average speed?
| 35 mph | |
| 75 mph | |
| 20 mph | |
| 60 mph |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)What is the distance in miles of a trip that takes 8 hours at an average speed of 20 miles per hour?
| 175 miles | |
| 280 miles | |
| 330 miles | |
| 160 miles |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)Solving for distance:
distance = \( \text{speed} \times \text{time} \)
distance = \( 20mph \times 8h \)
160 miles