| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.07 |
| Score | 0% | 61% |
What is \( 7 \)\( \sqrt{112} \) - \( 9 \)\( \sqrt{7} \)
| 63\( \sqrt{16} \) | |
| 63\( \sqrt{112} \) | |
| 63\( \sqrt{7} \) | |
| 19\( \sqrt{7} \) |
To subtract these radicals together their radicands must be the same:
7\( \sqrt{112} \) - 9\( \sqrt{7} \)
7\( \sqrt{16 \times 7} \) - 9\( \sqrt{7} \)
7\( \sqrt{4^2 \times 7} \) - 9\( \sqrt{7} \)
(7)(4)\( \sqrt{7} \) - 9\( \sqrt{7} \)
28\( \sqrt{7} \) - 9\( \sqrt{7} \)
Now that the radicands are identical, you can subtract them:
28\( \sqrt{7} \) - 9\( \sqrt{7} \)What is (b2)2?
| 64 | |
| b4 | |
| 2b2 | |
| b0 |
To raise a term with an exponent to another exponent, retain the base and multiply the exponents:
(b2)2What is \( \frac{2}{8} \) x \( \frac{2}{8} \)?
| \(\frac{4}{49}\) | |
| \(\frac{1}{24}\) | |
| \(\frac{1}{10}\) | |
| \(\frac{1}{16}\) |
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{2}{8} \) x \( \frac{2}{8} \) = \( \frac{2 x 2}{8 x 8} \) = \( \frac{4}{64} \) = \(\frac{1}{16}\)
On average, the center for a basketball team hits 35% of his shots while a guard on the same team hits 50% of his shots. If the guard takes 15 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?
| 28 | |
| 20 | |
| 15 | |
| 26 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 15 x \( \frac{50}{100} \) = \( \frac{50 x 15}{100} \) = \( \frac{750}{100} \) = 7 shots
The center makes 35% 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 = \( \frac{7}{\frac{35}{100}} \) = 7 x \( \frac{100}{35} \) = \( \frac{7 x 100}{35} \) = \( \frac{700}{35} \) = 20 shots
to make the same number of shots as the guard and thus score the same number of points.
Which of the following is an improper fraction?
\({7 \over 5} \) |
|
\(1 {2 \over 5} \) |
|
\({a \over 5} \) |
|
\({2 \over 5} \) |
A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.