| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.51 |
| Score | 0% | 70% |
Simplify \( \sqrt{12} \)
| 5\( \sqrt{3} \) | |
| 8\( \sqrt{6} \) | |
| 3\( \sqrt{3} \) | |
| 2\( \sqrt{3} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{12} \)
\( \sqrt{4 \times 3} \)
\( \sqrt{2^2 \times 3} \)
2\( \sqrt{3} \)
The total water usage for a city is 5,000 gallons each day. Of that total, 26% is for personal use and 37% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 550 | |
| 13,500 | |
| 10,350 | |
| 2,600 |
37% of the water consumption is industrial use and 26% is personal use so (37% - 26%) = 11% more water is used for industrial purposes. 5,000 gallons are consumed daily so industry consumes \( \frac{11}{100} \) x 5,000 gallons = 550 gallons.
What is \( \frac{1}{6} \) ÷ \( \frac{1}{5} \)?
| \(\frac{1}{5}\) | |
| \(\frac{1}{18}\) | |
| \(\frac{5}{6}\) | |
| \(\frac{1}{56}\) |
To divide fractions, invert the second fraction and then multiply:
\( \frac{1}{6} \) ÷ \( \frac{1}{5} \) = \( \frac{1}{6} \) x \( \frac{5}{1} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{1}{6} \) x \( \frac{5}{1} \) = \( \frac{1 x 5}{6 x 1} \) = \( \frac{5}{6} \) = \(\frac{5}{6}\)
What is the next number in this sequence: 1, 2, 3, 4, 5, __________ ?
| 12 | |
| 14 | |
| -2 | |
| 6 |
The equation for this sequence is:
an = an-1 + 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 + 1
a6 = 5 + 1
a6 = 6
What is -4a6 - 8a6?
| -12a6 | |
| 4a-12 | |
| 12a-6 | |
| -12a-6 |
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:
-4a6 - 8a6
(-4 - 8)a6
-12a6