| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.09 |
| Score | 0% | 62% |
What is the least common multiple of 5 and 7?
| 1 | |
| 35 | |
| 34 | |
| 11 |
The first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50] and the first few multiples of 7 are [7, 14, 21, 28, 35, 42, 49, 56, 63, 70]. The first few multiples they share are [35, 70] making 35 the smallest multiple 5 and 7 have in common.
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?
| 72 m2 | |
| 162 m2 | |
| 2 m2 | |
| 32 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
If \(\left|a\right| = 7\), which of the following best describes a?
a = -7 |
|
none of these is correct |
|
a = 7 or a = -7 |
|
a = 7 |
The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).
What is \( \frac{6}{6} \) + \( \frac{3}{14} \)?
| 2 \( \frac{3}{8} \) | |
| 2 \( \frac{5}{42} \) | |
| 2 \( \frac{8}{42} \) | |
| 1\(\frac{3}{14}\) |
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 14 are [14, 28, 42, 56, 70, 84, 98]. The first few multiples they share are [42, 84] making 42 the smallest multiple 6 and 14 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{6 x 7}{6 x 7} \) + \( \frac{3 x 3}{14 x 3} \)
\( \frac{42}{42} \) + \( \frac{9}{42} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{42 + 9}{42} \) = \( \frac{51}{42} \) = 1\(\frac{3}{14}\)
If \( \left|b + 4\right| \) + 1 = -1, which of these is a possible value for b?
| -6 | |
| -4 | |
| -9 | |
| 9 |
First, solve for \( \left|b + 4\right| \):
\( \left|b + 4\right| \) + 1 = -1
\( \left|b + 4\right| \) = -1 - 1
\( \left|b + 4\right| \) = -2
The value inside the absolute value brackets can be either positive or negative so (b + 4) must equal - 2 or --2 for \( \left|b + 4\right| \) to equal -2:
| b + 4 = -2 b = -2 - 4 b = -6 | b + 4 = 2 b = 2 - 4 b = -2 |
So, b = -2 or b = -6.