Answer:
See the attached image below for the filled out chart.
- First box = 0.1
- Second box = 0.1
- Third box = 4
- Fourth box = -3
- Fifth box = 3
- Sixth box = -1
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Explanation:
Part 1
Pick any term and subtract off its previous term
So for instance 4.2 - 4.1 = 0.1
Or you could say 4.3-4.2 = 0.1
Whichever pair you pick, you should find that the common difference is 0.1
This means we add 0.1 to each term to get the next term. Therefore, the recursive rule is 
which says "add 0.1 to the (n-1)th term to get the nth term". The (n-1)th term is the term just before the nth term.
The first term is 
as shown in the given sequence 4, 4.1, 4.2, ...
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Part 2
We'll follow the same idea as part 1.
Subtract any two adjacent terms
-10-(-7) = -10+7 = -3
We add -3 to each term to get the next. This is the same as subtracting 3 from each term, which is reflected in 
The first term is 
Everything is summarized in the diagram below.
Answer:
first one is simnple cross multiply and divide
12*7=4x
84=4x
x=21
2nd same process but more steps
7x=5(x+8)
7x=5x+40
7x-5x=40
2x=40
x=20
Step-by-step explanation:
Answer:
Assuming that the circle bissects the triangles equal sides at their midpoints, the ratio of the larger to smaller triangle should be close to 1/3
Evaluating the given sequence, it is evident that the next number is twice the number prior to it. Thus, the given is a geometric sequence with first term (a1) equal to 1 and common ratio of 2. The geometric series may be calculated by the equation,
Sn = a1 x (1 - r^n) / (1 - r)
where Sn is the sum of n terms in this case, n = 11.
Substituting the known values,
<span> Sn = 1 x (1 - 2^11) / (1 - 2) = 2047
</span>
Thus, S11 is 2047.
