| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.12 |
| Score | 0% | 62% |
Simplify \( \sqrt{75} \)
| 7\( \sqrt{6} \) | |
| 5\( \sqrt{3} \) | |
| 6\( \sqrt{6} \) | |
| 3\( \sqrt{6} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{75} \)
\( \sqrt{25 \times 3} \)
\( \sqrt{5^2 \times 3} \)
5\( \sqrt{3} \)
How many 2\(\frac{1}{2}\) gallon cans worth of fuel would you need to pour into an empty 20 gallon tank to fill it exactly halfway?
| 4 | |
| 7 | |
| 8 | |
| 4 |
To fill a 20 gallon tank exactly halfway you'll need 10 gallons of fuel. Each fuel can holds 2\(\frac{1}{2}\) gallons so:
cans = \( \frac{10 \text{ gallons}}{2\frac{1}{2} \text{ gallons}} \) = 4
Convert 0.0006776 to scientific notation.
| 6.776 x 10-3 | |
| 0.678 x 10-3 | |
| 6.776 x 10-5 | |
| 6.776 x 10-4 |
A number in scientific notation has the format 0.000 x 10exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:
0.0006776 in scientific notation is 6.776 x 10-4
What is the next number in this sequence: 1, 4, 10, 19, 31, __________ ?
| 49 | |
| 46 | |
| 44 | |
| 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
If \(\left|a\right| = 7\), which of the following best describes a?
a = 7 |
|
a = -7 |
|
none of these is correct |
|
a = 7 or a = -7 |
The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).