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notsponge [240]
2 years ago
14

If mAD=85 degrees and mBC=31 degrees find the value

Mathematics
1 answer:
Eddi Din [679]2 years ago
7 0
Answer: x = 11

To start, we know that a whole circle equals 360 degrees. If we subtract the 2 arcs we know, 85 and 31, we have 244 degrees left for the 2 congruent arcs. Dividing that by 2 gives us 122 for each arc.

Now, write the equation:  122 = 13x - 21

Solve this, to find the x = 11.
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Two non-simultaneous events have an equal likelihood of occurring (50%). If the events are independent of each other, what is th
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2 years ago
The first term of a finite geometric series is 6 and the last term is 4374. The sum of all the term os 6558. find the common rat
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A geometric series is written as ar^n, where a is the first term of the series and r is the common ratio.

In other words, to compute the next term in the series you have to multiply the previous one by r.

Since we know that the first time is 6 (but we don't know the common ratio), the first terms are

6, 6r, 6r^2, 6r^3, 6r^4, 6r^5, \ldots.

Let's use the other information, since the last term is 4374 > 6, we know that r>1, otherwise the terms would be bigger and bigger.

The information about the sum tells us that

\displaystyle \sum_{i=0}^n 6r^i = 6\sum_{i=0}^n r^i = 6558

We have a formula to compute the sum of the powers of a certain variable, namely

\displaystyle \sum_{i=0}^n r^i = \cfrac{r^{n+1}-1}{r-1}

So, the equation becomes

6\cfrac{r^{n+1}-1}{r-1} = 6558

The only integer solution to this expression is n=6, r=3.

If you want to check the result, we have

6+6*3+6*3^2+6*3^3+6*3^4+6*3^5+6*3^6 = 6558

and the last term is

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2 years ago
The area of a right triangle is 210 square inches. The height of the right triangle is 35 inches.
deff fn [24]
35 squared + 35 squared
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35 rad 2
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2 years ago
Read 2 more answers
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