| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.04 |
| Score | 0% | 61% |
What is \( 5 \)\( \sqrt{50} \) - \( 8 \)\( \sqrt{2} \)
| -3\( \sqrt{25} \) | |
| -3\( \sqrt{-21} \) | |
| 17\( \sqrt{2} \) | |
| -3\( \sqrt{2} \) |
To subtract these radicals together their radicands must be the same:
5\( \sqrt{50} \) - 8\( \sqrt{2} \)
5\( \sqrt{25 \times 2} \) - 8\( \sqrt{2} \)
5\( \sqrt{5^2 \times 2} \) - 8\( \sqrt{2} \)
(5)(5)\( \sqrt{2} \) - 8\( \sqrt{2} \)
25\( \sqrt{2} \) - 8\( \sqrt{2} \)
Now that the radicands are identical, you can subtract them:
25\( \sqrt{2} \) - 8\( \sqrt{2} \)What is \( \frac{9}{5} \) - \( \frac{7}{9} \)?
| 2 \( \frac{7}{15} \) | |
| \( \frac{8}{45} \) | |
| \( \frac{5}{45} \) | |
| 1\(\frac{1}{45}\) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50] and the first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 5 and 9 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{9 x 9}{5 x 9} \) - \( \frac{7 x 5}{9 x 5} \)
\( \frac{81}{45} \) - \( \frac{35}{45} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{81 - 35}{45} \) = \( \frac{46}{45} \) = 1\(\frac{1}{45}\)
A tiger in a zoo has consumed 72 pounds of food in 12 days. If the tiger continues to eat at the same rate, in how many more days will its total food consumtion be 90 pounds?
| 6 | |
| 5 | |
| 3 | |
| 2 |
If the tiger has consumed 72 pounds of food in 12 days that's \( \frac{72}{12} \) = 6 pounds of food per day. The tiger needs to consume 90 - 72 = 18 more pounds of food to reach 90 pounds total. At 6 pounds of food per day that's \( \frac{18}{6} \) = 3 more days.
Simplify \( \frac{28}{44} \).
| \( \frac{7}{15} \) | |
| \( \frac{7}{19} \) | |
| \( \frac{5}{13} \) | |
| \( \frac{7}{11} \) |
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 44 are [1, 2, 4, 11, 22, 44]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{28}{44} \) = \( \frac{\frac{28}{4}}{\frac{44}{4}} \) = \( \frac{7}{11} \)
A triathlon course includes a 500m swim, a 20.1km bike ride, and a 9.0km run. What is the total length of the race course?
| 29.6km | |
| 62.5km | |
| 37.3km | |
| 37.4km |
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 + 20.1km + 9.0km
total distance = 29.6km