| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.68 |
| Score | 0% | 74% |
What is the next number in this sequence: 1, 7, 13, 19, 25, __________ ?
| 31 | |
| 27 | |
| 40 | |
| 24 |
The equation for this sequence is:
an = an-1 + 6
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 + 6
a6 = 25 + 6
a6 = 31
What is the greatest common factor of 16 and 56?
| 8 | |
| 10 | |
| 6 | |
| 16 |
The factors of 16 are [1, 2, 4, 8, 16] and the factors of 56 are [1, 2, 4, 7, 8, 14, 28, 56]. They share 4 factors [1, 2, 4, 8] making 8 the greatest factor 16 and 56 have in common.
What is \( \frac{6}{2} \) - \( \frac{4}{10} \)?
| 2 \( \frac{6}{10} \) | |
| 2\(\frac{3}{5}\) | |
| 1 \( \frac{3}{10} \) | |
| 2 \( \frac{8}{10} \) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [10, 20, 30, 40, 50] making 10 the smallest multiple 2 and 10 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{6 x 5}{2 x 5} \) - \( \frac{4 x 1}{10 x 1} \)
\( \frac{30}{10} \) - \( \frac{4}{10} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{30 - 4}{10} \) = \( \frac{26}{10} \) = 2\(\frac{3}{5}\)
What is \( \frac{-8x^9}{5x^2} \)?
| -1\(\frac{3}{5}\)x11 | |
| -\(\frac{5}{8}\)x7 | |
| -\(\frac{5}{8}\)x-7 | |
| -1\(\frac{3}{5}\)x7 |
To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:
\( \frac{-8x^9}{5x^2} \)
\( \frac{-8}{5} \) x(9 - 2)
-1\(\frac{3}{5}\)x7
A factor is a positive __________ that divides evenly into a given number.
integer |
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fraction |
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mixed number |
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improper fraction |
A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.