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MaRussiya [10]
3 years ago
12

Please only answer if you're confident.

Mathematics
2 answers:
Elis [28]3 years ago
8 0

Answer:

∠ B = 70°

Step-by-step explanation:

A and B are alternate exterior angles and congruent, that is

∠ A = ∠ B , substitute values

8x + 6 = 4x + 38 ( subtract 4x from both sides )

4x + 6 = 38 ( subtract 6 from both sides )

4x = 32 ( divide both sides by 4 )

x = 8

Thus

∠ B = 4x + 38 = 4(8) + 38 = 32 + 38 = 70°

lina2011 [118]3 years ago
4 0

Answer:  ∠B=70°

Step-by-step explanation:

It is shown in the diagram that ∠A and ∠B is vertical angles.

  • Vertical angle theorem: opposite angles are congruent.

<u>Solve:</u>

∠A=∠B

8x+6=4x+38

4x=32

x=8

<h2>∠B=4x+38=4(8)+38=32+38=70°</h2>
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An odd number referred to any integer, that is not a fraction, which is not possible to be divided exactly by 2. Therefore, we have:

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B: 2, 4, 6, 8, 10, 11, 13, 15, 17, 20, 22, 24, 26, 28, 29, 31, 33, 35

C: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18

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AUB picks not more than one each of the elements in both A and B without repetition. Therefore, we have:

AUB = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 33, 35

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b. Calculate the probability of A ∩ C  

A∩C picks only the elements that are common to both A and C. Therefore, we have:

A∩C: 1, 3, 5, 7, 9, 11, 13, 15, 17

n(A∩C) = number of elements in A∩C = 9

P(A∩C) = probability of A∩C = n(A∩C) / n(U) = 9 / 38 = 0.236842105263158 = 0.24

c. Calculate the probability of BUC

BUC picks not more than one each of the elements in both B and C without repetition. Therefore, we have:

BUC: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 22, 24, 26, 28, 29, 31, 33, 35

n(BUC) = number of elements in BUC = 27

P(BUC) = probability of A∩C = n(BUC) / n(U) = 27 / 38 = 0.710526315789474 = 0.71

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Bc indicates B component it represents all the elements in the universal set excluding the elements in B. Therefore, we have:

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n(Bc) = number of elements in Bc = 20

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A∩B∩C: 11, 13, 15, 17

n(Bc) = number of elements in A∩B∩C = 4

P(A∩B∩C) = probability of A∩B∩C = n(A∩B∩C) / n(U) = 4 / 38 = 0.105263157894737 = 0.11

Note: All the answers are rounded to 2 decimal places.

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