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marta [7]
3 years ago
15

What are the measures of Angles a, b, and c? Show your work and explain your answers. (10 points)

Mathematics
1 answer:
Rus_ich [418]3 years ago
7 0

Answer:

The measure of angle a is 35 degrees, b is 55 degrees and c is 110 degrees.

∡a has an angle of 40°. Vertical angles are always congruent.

∡b is the 3rd angle in a triangle, the other two are 40° and 90° all of the interior angles in a triangle add up to 180°.

∡c is a linear angle, linear angles always add up to 180°.

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Find the missing length, simplify completely
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What value of x is in the solution set of 4x - 12 = 16 + 8x?<br><br> -10<br> -9<br> -8<br> -7
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Step-by-step explanation:

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Given the statement 11^(n -6) is divisible by 5 for every positive integer n. What must be shown in the induction step?
Lilit [14]

Answer:

Proved

Step-by-step explanation:

The given data is:

11^n - 6 not 11^{n - 6

Required

Prove by induction that it is divisible by 5

Assume n = k

So, we have:

11^k - 6 = 5p where p is a positive digit

Rewrite as:

11^k = 5p + 6

To solve further, we have to prove that 11^k - 6 is true for n=k+1

So, we have:

11^{k+1} - 6

11^{k+1} - 6 = 11^k * 11 - 6

Add 0

11^{k+1} - 6 = 11^k * 11 - 6 + 0

Replace 0 with -5 +5

11^{k+1} - 6 = 11^k * 11 - 6 - 5 + 5

11^{k+1} - 6 = 11^k * 11 - 11- 5

Factorize

11^{k+1} - 6 = 11 (11^k - 1)- 5

Substitute 11^k = 5p + 6

11^{k+1} - 6 = 11 (5p + 6- 1)- 5

11^{k+1} - 6 = 11 (5p + 5)- 5

Factorize

11^{k+1} - 6 = 11 *5(p + 1)- 5

Factorize

11^{k+1} - 6 = 5[11(p + 1)- 1]

<em>The 5 outside the bracket implies that it is divisible by 5</em>

3 0
3 years ago
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