| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.35 |
| Score | 0% | 67% |
Convert c-3 to remove the negative exponent.
| \( \frac{1}{c^3} \) | |
| \( \frac{-1}{c^{-3}} \) | |
| \( \frac{3}{c} \) | |
| \( \frac{1}{c^{-3}} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
If \( \left|x - 2\right| \) - 3 = -9, which of these is a possible value for x?
| -10 | |
| -7 | |
| 8 | |
| -8 |
First, solve for \( \left|x - 2\right| \):
\( \left|x - 2\right| \) - 3 = -9
\( \left|x - 2\right| \) = -9 + 3
\( \left|x - 2\right| \) = -6
The value inside the absolute value brackets can be either positive or negative so (x - 2) must equal - 6 or --6 for \( \left|x - 2\right| \) to equal -6:
| x - 2 = -6 x = -6 + 2 x = -4 | x - 2 = 6 x = 6 + 2 x = 8 |
So, x = 8 or x = -4.
What is the next number in this sequence: 1, 4, 10, 19, 31, __________ ?
| 49 | |
| 46 | |
| 51 | |
| 47 |
The equation for this sequence is:
an = an-1 + 3(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 + 3(6 - 1)
a6 = 31 + 3(5)
a6 = 46
A circular logo is enlarged to fit the lid of a jar. The new diameter is 45% larger than the original. By what percentage has the area of the logo increased?
| 22\(\frac{1}{2}\)% | |
| 35% | |
| 27\(\frac{1}{2}\)% | |
| 30% |
The area of a circle is given by the formula A = πr2 where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))2. If the diameter of the logo increases by 45% the radius (and, consequently, the total area) increases by \( \frac{45\text{%}}{2} \) = 22\(\frac{1}{2}\)%
Which of the following is a mixed number?
\({7 \over 5} \) |
|
\({5 \over 7} \) |
|
\({a \over 5} \) |
|
\(1 {2 \over 5} \) |
A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.