| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.84 |
| Score | 0% | 57% |
If \( \left|a - 8\right| \) + 2 = -4, which of these is a possible value for a?
| -7 | |
| -8 | |
| 2 | |
| -13 |
First, solve for \( \left|a - 8\right| \):
\( \left|a - 8\right| \) + 2 = -4
\( \left|a - 8\right| \) = -4 - 2
\( \left|a - 8\right| \) = -6
The value inside the absolute value brackets can be either positive or negative so (a - 8) must equal - 6 or --6 for \( \left|a - 8\right| \) to equal -6:
| a - 8 = -6 a = -6 + 8 a = 2 | a - 8 = 6 a = 6 + 8 a = 14 |
So, a = 14 or a = 2.
If a rectangle is twice as long as it is wide and has a perimeter of 18 meters, what is the area of the rectangle?
| 72 m2 | |
| 18 m2 | |
| 2 m2 | |
| 98 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 18 meters so the equation becomes: 2w + 2h = 18.
Putting these two equations together and solving for width (w):
2w + 2h = 18
w + h = \( \frac{18}{2} \)
w + h = 9
w = 9 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 9 - 2w
3w = 9
w = \( \frac{9}{3} \)
w = 3
Since h = 2w that makes h = (2 x 3) = 6 and the area = h x w = 3 x 6 = 18 m2
Which of these numbers is a factor of 48?
| 18 | |
| 30 | |
| 4 | |
| 46 |
The factors of a number are all positive integers that divide evenly into the number. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
In a class of 18 students, 5 are taking German and 6 are taking Spanish. Of the students studying German or Spanish, 3 are taking both courses. How many students are not enrolled in either course?
| 17 | |
| 12 | |
| 10 | |
| 13 |
The number of students taking German or Spanish is 5 + 6 = 11. Of that group of 11, 3 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 11 - 3 = 8 who are taking at least one language. 18 - 8 = 10 students who are not taking either language.
What is 4\( \sqrt{6} \) x 2\( \sqrt{4} \)?
| 6\( \sqrt{24} \) | |
| 8\( \sqrt{6} \) | |
| 16\( \sqrt{6} \) | |
| 6\( \sqrt{4} \) |
To multiply terms with radicals, multiply the coefficients and radicands separately:
4\( \sqrt{6} \) x 2\( \sqrt{4} \)
(4 x 2)\( \sqrt{6 \times 4} \)
8\( \sqrt{24} \)
Now we need to simplify the radical:
8\( \sqrt{24} \)
8\( \sqrt{6 \times 4} \)
8\( \sqrt{6 \times 2^2} \)
(8)(2)\( \sqrt{6} \)
16\( \sqrt{6} \)