| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.57 |
| Score | 0% | 71% |
What is \( \frac{14\sqrt{35}}{2\sqrt{5}} \)?
| \(\frac{1}{7}\) \( \sqrt{\frac{1}{7}} \) | |
| 7 \( \sqrt{7} \) | |
| 7 \( \sqrt{\frac{1}{7}} \) | |
| \(\frac{1}{7}\) \( \sqrt{7} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{14\sqrt{35}}{2\sqrt{5}} \)
\( \frac{14}{2} \) \( \sqrt{\frac{35}{5}} \)
7 \( \sqrt{7} \)
What is \( \frac{3}{8} \) x \( \frac{2}{8} \)?
| \(\frac{3}{40}\) | |
| \(\frac{3}{32}\) | |
| \(\frac{4}{27}\) | |
| \(\frac{8}{63}\) |
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{3}{8} \) x \( \frac{2}{8} \) = \( \frac{3 x 2}{8 x 8} \) = \( \frac{6}{64} \) = \(\frac{3}{32}\)
What is the next number in this sequence: 1, 5, 13, 25, 41, __________ ?
| 61 | |
| 53 | |
| 58 | |
| 59 |
The equation for this sequence is:
an = an-1 + 4(n - 1)
where n is the term's order in the sequence, an is the value of the term, and an-1 is the value of the term before an. This makes the next number:
a6 = a5 + 4(6 - 1)
a6 = 41 + 4(5)
a6 = 61
Simplify \( \frac{28}{68} \).
| \( \frac{9}{14} \) | |
| \( \frac{7}{17} \) | |
| \( \frac{9}{16} \) | |
| \( \frac{4}{9} \) |
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 68 are [1, 2, 4, 17, 34, 68]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{28}{68} \) = \( \frac{\frac{28}{4}}{\frac{68}{4}} \) = \( \frac{7}{17} \)
Which of these numbers is a factor of 40?
| 4 | |
| 14 | |
| 16 | |
| 5 |
The factors of a number are all positive integers that divide evenly into the number. The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40.