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Viktor [21]
3 years ago
10

Please look at the attached picture.

Mathematics
2 answers:
ludmilkaskok [199]3 years ago
8 0

Answer:

m<B is the answer

all work is shown

Reptile [31]3 years ago
7 0

Answer:

B

Step-by-step explanation:

we know that sum of all angles = 180°

A + B + C = 180°

(2x+7) + (4x-10) + ( 7x-25) = 180°

2x + 7 + 4x - 10 + 7x -25 = 180°

2x + 4x + 7x +7 -10 - 25 = 180°

13x - 28 = 180

13x = 180+ 28

13x = 208

x = 208/13

x = 16

∠B = (4x - 10) = 4(16) - 10

= 64 - 10 = 54

∠B = 54°

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The easy thing to do is notice that 1^4 = 1, 2^4 = 16, 3^4 = 81, and so on, so the sequence follows the rule n^4+1. The next number would then be fourth power of 7 plus 1, or 2402.

And the harder way: Denote the <em>n</em>-th term in this sequence by a_n, and denote the given sequence by \{a_n\}_{n\ge1}.

Let b_n denote the <em>n</em>-th term in the sequence of forward differences of \{a_n\}, defined by

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Next, let c_n denote the <em>n</em>-th term of the differences of \{b_n\}, i.e. for <em>n</em> ≥ 1,

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One more time: let e_n denote the <em>n</em>-th difference of \{d_n\}:

e_n=d_{n+1}-d_n

e_1=d_2-d_1=24

e_2=24

etc.

The fact that these last differences are constant is a good sign that e_n=24 for all <em>n</em> ≥ 1. Assuming this, we would see that \{d_n\} is an arithmetic sequence given recursively by

\begin{cases}d_1=60\\d_{n+1}=d_n+24&\text{for }n>1\end{cases}

and we can easily find the explicit rule:

d_2=d_1+24

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d_4=d_3+24=d_1+24\cdot3

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Use the same strategy to find a closed form for \{c_n\}, then for \{b_n\}, and finally \{a_n\}.

\begin{cases}c_1=50\\c_{n+1}=c_n+24n+36&\text{for }n>1\end{cases}

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c_4=c_3+24\cdot3+36=c_1+24(1+2+3)+36\cdot3

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b_3=b_2+12\cdot2^2+24\cdot2+14=b_1+12(1^2+2^2)+24(1+2)+14\cdot2

b_4=b_3+12\cdot3^2+24\cdot3+14=b_1+12(1^2+2^2+3^2)+24(1+2+3)+14\cdot3

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