| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.32 |
| Score | 0% | 66% |
What is \( \frac{5y^7}{3y^4} \)?
| 1\(\frac{2}{3}\)y\(\frac{4}{7}\) | |
| 1\(\frac{2}{3}\)y3 | |
| \(\frac{3}{5}\)y3 | |
| 1\(\frac{2}{3}\)y1\(\frac{3}{4}\) |
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:
\( \frac{5y^7}{3y^4} \)
\( \frac{5}{3} \) y(7 - 4)
1\(\frac{2}{3}\)y3
Convert a-4 to remove the negative exponent.
| \( \frac{1}{a^4} \) | |
| \( \frac{1}{a^{-4}} \) | |
| \( \frac{-4}{a} \) | |
| \( \frac{-1}{-4a} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
Which of the following is a mixed number?
\({5 \over 7} \) |
|
\(1 {2 \over 5} \) |
|
\({7 \over 5} \) |
|
\({a \over 5} \) |
A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.
What is the next number in this sequence: 1, 4, 10, 19, 31, __________ ?
| 37 | |
| 46 | |
| 51 | |
| 43 |
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
How many 2 gallon cans worth of fuel would you need to pour into an empty 8 gallon tank to fill it exactly halfway?
| 4 | |
| 2 | |
| 9 | |
| 7 |
To fill a 8 gallon tank exactly halfway you'll need 4 gallons of fuel. Each fuel can holds 2 gallons so:
cans = \( \frac{4 \text{ gallons}}{2 \text{ gallons}} \) = 2