| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.96 |
| Score | 0% | 59% |
What is \( 2 \)\( \sqrt{20} \) - \( 5 \)\( \sqrt{5} \)
| -3\( \sqrt{100} \) | |
| -3\( \sqrt{20} \) | |
| 10\( \sqrt{4} \) | |
| -1\( \sqrt{5} \) |
To subtract these radicals together their radicands must be the same:
2\( \sqrt{20} \) - 5\( \sqrt{5} \)
2\( \sqrt{4 \times 5} \) - 5\( \sqrt{5} \)
2\( \sqrt{2^2 \times 5} \) - 5\( \sqrt{5} \)
(2)(2)\( \sqrt{5} \) - 5\( \sqrt{5} \)
4\( \sqrt{5} \) - 5\( \sqrt{5} \)
Now that the radicands are identical, you can subtract them:
4\( \sqrt{5} \) - 5\( \sqrt{5} \)On average, the center for a basketball team hits 35% of his shots while a guard on the same team hits 45% of his shots. If the guard takes 30 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?
| 24 | |
| 26 | |
| 46 | |
| 37 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 30 x \( \frac{45}{100} \) = \( \frac{45 x 30}{100} \) = \( \frac{1350}{100} \) = 13 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 = \( \frac{13}{\frac{35}{100}} \) = 13 x \( \frac{100}{35} \) = \( \frac{13 x 100}{35} \) = \( \frac{1300}{35} \) = 37 shots
to make the same number of shots as the guard and thus score the same number of points.
What is \( \frac{7}{8} \) - \( \frac{9}{12} \)?
| 2 \( \frac{2}{5} \) | |
| \(\frac{1}{8}\) | |
| 1 \( \frac{1}{7} \) | |
| \( \frac{9}{24} \) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [24, 48, 72, 96] making 24 the smallest multiple 8 and 12 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{7 x 3}{8 x 3} \) - \( \frac{9 x 2}{12 x 2} \)
\( \frac{21}{24} \) - \( \frac{18}{24} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{21 - 18}{24} \) = \( \frac{3}{24} \) = \(\frac{1}{8}\)
What is the least common multiple of 2 and 8?
| 12 | |
| 8 | |
| 11 | |
| 1 |
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 have in common.
Simplify \( \frac{28}{72} \).
| \( \frac{7}{18} \) | |
| \( \frac{3}{7} \) | |
| \( \frac{5}{14} \) | |
| \( \frac{10}{19} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 28 are [1, 2, 4, 7, 14, 28] and the factors of 72 are [1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{28}{72} \) = \( \frac{\frac{28}{4}}{\frac{72}{4}} \) = \( \frac{7}{18} \)