Tracy saved her babysitting earnings for a month to buy some souvenirs while on vacation. She promised her three best friends a
2 answers:
The babysitting earnings is an illustration of a linear equation
The total babysitting earnings is $42
<h3>How to determine the babysitting earnings</h3>Represent the earnings with x.
- One third of the earning would be 1/3x
- The hat costs $12
The remaining amount would be:
x - 1/3x - 12
The remaining amount is $4 less than $20.
So, we have:
Collect like terms
Multiply through by 3
Simplify
Divide through by 2
Hence, the total babysitting earnings is $42
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Answer:
3n² + 5n - 2
Step-by-step explanation:
<u>Given sequence</u>:
6, 20, 40, 66, 98, 136, ...
Calculate the <u>first differences</u> between the terms:
As the first differences are not the same, calculate the <u>second differences:</u>
As the <u>second differences are the same</u>, the sequence is quadratic and will contain an n² term.
The <u>coefficient</u> of the n² term is <u>half of the second difference</u>.
Therefore, the n² term is: 3n²
Compare 3n² with the given sequence:
The second operations are different, therefore calculate the differences <em>between</em> the second operations:
As the differences are the same, we need to add 5n as the second operation:
Finally, we can clearly see that the operation to get from 3n² + 5n to the given sequence is to subtract 2.
Therefore, the nth term of the quadratic sequence is:
3n² + 5n - 2