| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.32 |
| Score | 0% | 66% |
Convert a-4 to remove the negative exponent.
| \( \frac{-1}{-4a^{4}} \) | |
| \( \frac{1}{a^{-4}} \) | |
| \( \frac{1}{a^4} \) | |
| \( \frac{-1}{a^{-4}} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
What is \( \sqrt{\frac{9}{81}} \)?
| \(\frac{1}{3}\) | |
| 1\(\frac{1}{3}\) | |
| \(\frac{2}{5}\) | |
| \(\frac{3}{7}\) |
To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:
\( \sqrt{\frac{9}{81}} \)
\( \frac{\sqrt{9}}{\sqrt{81}} \)
\( \frac{\sqrt{3^2}}{\sqrt{9^2}} \)
\(\frac{1}{3}\)
What is the greatest common factor of 52 and 36?
| 27 | |
| 29 | |
| 5 | |
| 4 |
The factors of 52 are [1, 2, 4, 13, 26, 52] and the factors of 36 are [1, 2, 3, 4, 6, 9, 12, 18, 36]. They share 3 factors [1, 2, 4] making 4 the greatest factor 52 and 36 have in common.
What is the next number in this sequence: 1, 5, 13, 25, 41, __________ ?
| 61 | |
| 55 | |
| 70 | |
| 63 |
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
If a rectangle is twice as long as it is wide and has a perimeter of 36 meters, what is the area of the rectangle?
| 32 m2 | |
| 2 m2 | |
| 50 m2 | |
| 72 m2 |
The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 36 meters so the equation becomes: 2w + 2h = 36.
Putting these two equations together and solving for width (w):
2w + 2h = 36
w + h = \( \frac{36}{2} \)
w + h = 18
w = 18 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 18 - 2w
3w = 18
w = \( \frac{18}{3} \)
w = 6
Since h = 2w that makes h = (2 x 6) = 12 and the area = h x w = 6 x 12 = 72 m2