| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.19 |
| Score | 0% | 64% |
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?
| 25% | |
| 20% | |
| 17\(\frac{1}{2}\)% | |
| 22\(\frac{1}{2}\)% |
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\(\frac{1}{2}\)%
What is the next number in this sequence: 1, 4, 10, 19, 31, __________ ?
| 50 | |
| 45 | |
| 47 | |
| 46 |
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
What is -3c7 - 9c7?
| -12c7 | |
| 6c7 | |
| -12c-7 | |
| 12c-7 |
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:
-3c7 - 9c7
(-3 - 9)c7
-12c7
The __________ is the greatest factor that divides two integers.
absolute value |
|
greatest common multiple |
|
least common multiple |
|
greatest common factor |
The greatest common factor (GCF) is the greatest factor that divides two integers.
If \( \left|b - 1\right| \) - 5 = 4, which of these is a possible value for b?
| 10 | |
| 4 | |
| 18 | |
| -11 |
First, solve for \( \left|b - 1\right| \):
\( \left|b - 1\right| \) - 5 = 4
\( \left|b - 1\right| \) = 4 + 5
\( \left|b - 1\right| \) = 9
The value inside the absolute value brackets can be either positive or negative so (b - 1) must equal + 9 or -9 for \( \left|b - 1\right| \) to equal 9:
| b - 1 = 9 b = 9 + 1 b = 10 | b - 1 = -9 b = -9 + 1 b = -8 |
So, b = -8 or b = 10.