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Mila [183]
3 years ago
13

I’m confused on the type of angles these are and how to solve them . (Parallel lines and Transversals)

Mathematics
1 answer:
svp [43]3 years ago
4 0

Answer:

7) 49°

8) 77°

9) 87°

10) 135°

Step-by-step explanation:

7) The angles are between the parallel lines, so are "interior." They are on opposite sides of the transversal, so are "opposite interior" angles. Such angles are congruent, so ...

... ? ≅ 49°

8) The angles are adjacent interior angles, so are supplementary.

... ? + 103° = 180°

... ? = 77°

9) The angles are outside the parallel lines, so are "exterior." They are on opposite sides of the transversal, so are "opposite exterior" angles. Such angles are congruent.

... ? ≅ 87°

10) These are vertical angles, so are congruent. (The other parallel line is irrelevant and doesn't need to be there for this relationship to be true.)

... ? ≅ 135°

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Levart [38]

The next term is double the previous term, so that the n-th term is given recursively by

\begin{cases}a_1=1\\a_n=2a_{n-1}&\text{for }n>1\end{cases}

This rule tells us that

a_2=2a_1

a_3=2a_2=2^2a_1

a_4=2a_3=2^3a_1

and so on, with the explicit rule

a_n=2^{n-1}a_1=2^{n-1}

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If 512 is the k-th term in the sequence, then

512=2^{k-1}\implies\log_2512=\log_22^9=\log_22^{k-1}\implies9=k-1\implies k=10

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3 years ago
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Yuliya22 [10]
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use the three given points to find the three unknown constants a, b, and c:
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Answer:

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Step-by-step explanation:

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I hope this helps!

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