What fraction is equivalent to 80%
2 answers:
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ANSWER
EXPLANATION
The given function is a piecewise defined function.
is the y-value that corresponds to
To determine that y-value, we need to trace from
to where it meets the graph.
We then trace to the y-axis to determine the corresponding y-value as shown in the diagram.
From the graph, we can see that this x-value corresponds to a y-value of
This implies that, when
Therefore
See graph.
EXPLANATION
The given function is a piecewise defined function.
is the y-value that corresponds to
To determine that y-value, we need to trace from
to where it meets the graph.
We then trace to the y-axis to determine the corresponding y-value as shown in the diagram.
From the graph, we can see that this x-value corresponds to a y-value of
This implies that, when
Therefore
See graph.
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