| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.62 |
| Score | 0% | 72% |
Simplify \( \sqrt{45} \)
| 5\( \sqrt{5} \) | |
| 3\( \sqrt{5} \) | |
| 4\( \sqrt{10} \) | |
| 9\( \sqrt{10} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{45} \)
\( \sqrt{9 \times 5} \)
\( \sqrt{3^2 \times 5} \)
3\( \sqrt{5} \)
What is -3y4 x 6y4?
| 3y16 | |
| -18y8 | |
| -18y0 | |
| -18y16 |
To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:
-3y4 x 6y4
(-3 x 6)y(4 + 4)
-18y8
What is (c5)2?
| 5c2 | |
| c-3 | |
| 2c5 | |
| c10 |
To raise a term with an exponent to another exponent, retain the base and multiply the exponents:
(c5)2A circular logo is enlarged to fit the lid of a jar. The new diameter is 40% larger than the original. By what percentage has the area of the logo increased?
| 20% | |
| 32\(\frac{1}{2}\)% | |
| 30% | |
| 17\(\frac{1}{2}\)% |
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 40% the radius (and, consequently, the total area) increases by \( \frac{40\text{%}}{2} \) = 20%
What is the next number in this sequence: 1, 4, 7, 10, 13, __________ ?
| 8 | |
| 13 | |
| 16 | |
| 17 |
The equation for this sequence is:
an = an-1 + 3
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
a6 = 13 + 3
a6 = 16