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3 years ago

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:

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 n-th term in this sequence by $a_n$ , and denote the given sequence by $\{a_n\}_{n\ge1}$ .

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etc.

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

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and we can easily find the explicit rule:

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and so on, up to

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

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