| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.13 |
| Score | 0% | 63% |
What is the next number in this sequence: 1, 3, 7, 13, 21, __________ ?
| 31 | |
| 32 | |
| 29 | |
| 25 |
The equation for this sequence is:
an = an-1 + 2(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 + 2(6 - 1)
a6 = 21 + 2(5)
a6 = 31
What is \( \frac{-4x^8}{8x^2} \)?
| -2x-6 | |
| -\(\frac{1}{2}\)x16 | |
| -\(\frac{1}{2}\)x\(\frac{1}{4}\) | |
| -\(\frac{1}{2}\)x6 |
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:
\( \frac{-4x^8}{8x^2} \)
\( \frac{-4}{8} \) x(8 - 2)
-\(\frac{1}{2}\)x6
This property states taht the order of addition or multiplication does not mater. For example, 2 + 5 and 5 + 2 are equivalent.
PEDMAS |
|
associative |
|
commutative |
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distributive |
The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.
The total water usage for a city is 5,000 gallons each day. Of that total, 23% is for personal use and 38% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 11,900 | |
| 6,400 | |
| 750 | |
| 5,000 |
38% of the water consumption is industrial use and 23% is personal use so (38% - 23%) = 15% more water is used for industrial purposes. 5,000 gallons are consumed daily so industry consumes \( \frac{15}{100} \) x 5,000 gallons = 750 gallons.
The __________ is the greatest factor that divides two integers.
greatest common multiple |
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greatest common factor |
|
absolute value |
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least common multiple |
The greatest common factor (GCF) is the greatest factor that divides two integers.