| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.79 |
| Score | 0% | 56% |
If \( \left|x - 2\right| \) + 7 = -5, which of these is a possible value for x?
| -16 | |
| -12 | |
| 14 | |
| 3 |
First, solve for \( \left|x - 2\right| \):
\( \left|x - 2\right| \) + 7 = -5
\( \left|x - 2\right| \) = -5 - 7
\( \left|x - 2\right| \) = -12
The value inside the absolute value brackets can be either positive or negative so (x - 2) must equal - 12 or --12 for \( \left|x - 2\right| \) to equal -12:
| x - 2 = -12 x = -12 + 2 x = -10 | x - 2 = 12 x = 12 + 2 x = 14 |
So, x = 14 or x = -10.
What is \( \frac{2a^7}{7a^2} \)?
| \(\frac{2}{7}\)a-5 | |
| \(\frac{2}{7}\)a\(\frac{2}{7}\) | |
| \(\frac{2}{7}\)a14 | |
| \(\frac{2}{7}\)a5 |
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:
\( \frac{2a^7}{7a^2} \)
\( \frac{2}{7} \) a(7 - 2)
\(\frac{2}{7}\)a5
What is the next number in this sequence: 1, 5, 13, 25, 41, __________ ?
| 61 | |
| 65 | |
| 64 | |
| 67 |
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
Cooks are needed to prepare for a large party. Each cook can bake either 2 large cakes or 16 small cakes per hour. The kitchen is available for 4 hours and 34 large cakes and 390 small cakes need to be baked.
How many cooks are required to bake the required number of cakes during the time the kitchen is available?
| 10 | |
| 9 | |
| 7 | |
| 12 |
If a single cook can bake 2 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 2 x 4 = 8 large cakes during that time. 34 large cakes are needed for the party so \( \frac{34}{8} \) = 4\(\frac{1}{4}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 16 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 16 x 4 = 64 small cakes during that time. 390 small cakes are needed for the party so \( \frac{390}{64} \) = 6\(\frac{3}{32}\) cooks are needed to bake the required number of small cakes.
Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 5 + 7 = 12 cooks.
If a rectangle is twice as long as it is wide and has a perimeter of 12 meters, what is the area of the rectangle?
| 8 m2 | |
| 72 m2 | |
| 162 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 12 meters so the equation becomes: 2w + 2h = 12.
Putting these two equations together and solving for width (w):
2w + 2h = 12
w + h = \( \frac{12}{2} \)
w + h = 6
w = 6 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 6 - 2w
3w = 6
w = \( \frac{6}{3} \)
w = 2
Since h = 2w that makes h = (2 x 2) = 4 and the area = h x w = 2 x 4 = 8 m2