| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.17 |
| Score | 0% | 63% |
\({b + c \over a} = {b \over a} + {c \over a}\) defines which of the following?
distributive property for division |
|
commutative property for division |
|
distributive property for multiplication |
|
commutative property for multiplication |
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, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).
On average, the center for a basketball team hits 30% of his shots while a guard on the same team hits 45% of his shots. If the guard takes 10 shots during a game, how many shots will the center have to take to score as many points as the guard assuming each shot is worth the same number of points?
| 13 | |
| 8 | |
| 9 | |
| 7 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 10 x \( \frac{45}{100} \) = \( \frac{45 x 10}{100} \) = \( \frac{450}{100} \) = 4 shots
The center makes 30% of his shots so he'll have to take:
shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)
to make as many shots as the guard. Plugging in values for the center gives us:
center shots taken = \( \frac{4}{\frac{30}{100}} \) = 4 x \( \frac{100}{30} \) = \( \frac{4 x 100}{30} \) = \( \frac{400}{30} \) = 13 shots
to make the same number of shots as the guard and thus score the same number of points.
Simplify \( \sqrt{48} \)
| 4\( \sqrt{3} \) | |
| 2\( \sqrt{3} \) | |
| 8\( \sqrt{6} \) | |
| 4\( \sqrt{6} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{48} \)
\( \sqrt{16 \times 3} \)
\( \sqrt{4^2 \times 3} \)
4\( \sqrt{3} \)
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 35% off." If Alex buys two shirts, each with a regular price of $24, how much money will he save?
| $4.80 | |
| $12.00 | |
| $9.60 | |
| $8.40 |
By buying two shirts, Alex will save $24 x \( \frac{35}{100} \) = \( \frac{$24 x 35}{100} \) = \( \frac{$840}{100} \) = $8.40 on the second shirt.
What is the distance in miles of a trip that takes 7 hours at an average speed of 35 miles per hour?
| 390 miles | |
| 330 miles | |
| 245 miles | |
| 165 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 = \( 35mph \times 7h \)
245 miles