| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.33 |
| Score | 0% | 67% |
If a rectangle is twice as long as it is wide and has a perimeter of 42 meters, what is the area of the rectangle?
| 98 m2 | |
| 162 m2 | |
| 8 m2 | |
| 18 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 42 meters so the equation becomes: 2w + 2h = 42.
Putting these two equations together and solving for width (w):
2w + 2h = 42
w + h = \( \frac{42}{2} \)
w + h = 21
w = 21 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 21 - 2w
3w = 21
w = \( \frac{21}{3} \)
w = 7
Since h = 2w that makes h = (2 x 7) = 14 and the area = h x w = 7 x 14 = 98 m2
Simplify \( \frac{16}{80} \).
| \( \frac{2}{7} \) | |
| \( \frac{1}{5} \) | |
| \( \frac{5}{6} \) | |
| \( \frac{10}{17} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 16 are [1, 2, 4, 8, 16] and the factors of 80 are [1, 2, 4, 5, 8, 10, 16, 20, 40, 80]. They share 5 factors [1, 2, 4, 8, 16] making 16 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{16}{80} \) = \( \frac{\frac{16}{16}}{\frac{80}{16}} \) = \( \frac{1}{5} \)
What is \( \frac{7}{2} \) + \( \frac{6}{8} \)?
| 4\(\frac{1}{4}\) | |
| 2 \( \frac{1}{8} \) | |
| 2 \( \frac{5}{8} \) | |
| \( \frac{9}{12} \) |
To add 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 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 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{7 x 4}{2 x 4} \) + \( \frac{6 x 1}{8 x 1} \)
\( \frac{28}{8} \) + \( \frac{6}{8} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{28 + 6}{8} \) = \( \frac{34}{8} \) = 4\(\frac{1}{4}\)
Which of the following is not an integer?
\({1 \over 2}\) |
|
1 |
|
-1 |
|
0 |
An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.
What is \( \sqrt{\frac{9}{81}} \)?
| \(\frac{3}{8}\) | |
| \(\frac{5}{9}\) | |
| \(\frac{1}{3}\) | |
| 2\(\frac{1}{3}\) |
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:
\( \sqrt{\frac{9}{81}} \)
\( \frac{\sqrt{9}}{\sqrt{81}} \)
\( \frac{\sqrt{3^2}}{\sqrt{9^2}} \)
\(\frac{1}{3}\)