| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.84 |
| Score | 0% | 57% |
A 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?
| 17\(\frac{1}{2}\)% | |
| 22\(\frac{1}{2}\)% | |
| 27\(\frac{1}{2}\)% | |
| 20% |
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%
Which of the following statements about exponents is false?
b1 = 1 |
|
all of these are false |
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b0 = 1 |
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b1 = b |
A number with an exponent (be) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b1 = b) and a base with an exponent of 0 equals 1 ( (b0 = 1).
Simplify \( \sqrt{75} \)
| 4\( \sqrt{3} \) | |
| 9\( \sqrt{3} \) | |
| 5\( \sqrt{3} \) | |
| 2\( \sqrt{3} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{75} \)
\( \sqrt{25 \times 3} \)
\( \sqrt{5^2 \times 3} \)
5\( \sqrt{3} \)
What is 2a7 + a7?
| a-7 | |
| a7 | |
| 3a7 | |
| 3a-14 |
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:
2a7 + 1a7
(2 + 1)a7
3a7
What is \( \frac{2x^6}{9x^4} \)?
| \(\frac{2}{9}\)x24 | |
| \(\frac{2}{9}\)x1\(\frac{1}{2}\) | |
| \(\frac{2}{9}\)x2 | |
| 4\(\frac{1}{2}\)x10 |
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:
\( \frac{2x^6}{9x^4} \)
\( \frac{2}{9} \) x(6 - 4)
\(\frac{2}{9}\)x2