Select the correct answer which type of function best models the data?
1 answer:
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Answer:
-0.9090... can be written as .
Explanation:
Any <em>repeating </em>decimal can be written as a fraction by dividing the section of the pattern to be repeated <em>by </em>9's.
We can start by listing out
0.909090... = 9/10 + 0/100 + 9/1000 + 0/10000 + 9/100000 + 0/1000000 + ...
Now. we let this series be equal to x, that is
= 9/10 + 0/100 + 9/1000 + 0/10000 + 9/100000 + 0/1000000 + ...
Now, we'll multiply both sides by 100 .
= 90 + 0 + 9/10 + 0/100 + 9/1000 + 0/10000 + ...
Then, subtract the 1st equation from the second like so:
= 90 + 0 + 9/10 + 0/100 + 9/1000 + 0/10000 + 9/100000 + 0/1000000 + ...
= - 9/10 - 0/100 - 9/1000 - 0/10000 - 9/100000 - 0/1000000 - ...
And we end up with this:
Finally, we divide both sides by 99 in order to isolate x and get the fraction we're looking for.
Which can be reduced and simplified to
Hope this helps!
Answer:
A
Step-by-step explanation:
using the rule : =
+ 7
sequence A with a₁ = 11
a₂ = a₁ + 7 = 11 + 7 = 18
a₃ = a₂ + 7 = 18 + 7 = 25
a₄ = a₃ + 7 = 25 + 7 = 32
sequence A is generated using the rule
sequence B with a₁ = 17
a₂ = a₁ + 7 = 17 + 7 = 24
a₃ = a₂ + 7 = 24 + 7 = 31
a₄ = a₃ + 7 = 31 + 7 = 38
sequence B is not generated using the rule
sequence C with a₁ = - 15
a₂ = - 15 + 7 = - 8
a₃ = a₂ + 7 = - 8 + 7 = - 1
a₄ = a₃ + 7 = - 1 + 7 = 6
sequence C is not generated using the rule
sequence D with a₁ = - 9
a₂ = a₁ + 7 = - 9 + 7 = - 2
a₃ = a₂ + 7 = - 2 + 7 = 5
a₄ = a₃ + 7 = 5 + 7 = 12
sequence D is not generated using the rule