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Tom [10]
3 years ago
11

Each week, Marcia travels to the office where she works, the supermarket, and a local fitness center. The three locations repres

ent the vertices of a triangle. Marcia wants to move to an apartment that is equidistant from these three places. Where should her new apartment be located?
Mathematics
2 answers:
ankoles [38]3 years ago
5 0

b is the correct answer

pogonyaev3 years ago
4 0
<span>The choices are:
a.the center of the inscribed circle of the triangle
b.the center of the circumscribed circle of the triangle
c.the point of intersection of the angle bisectors for the triangle
d.the point of intersection of the perpendicular bisectors and the angle bisectors for the triangle

The answer to your question is B. </span>I hope that this is the answer that you were looking for and it has helped you.
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Read 2 more answers
6.6. Using the extended Euclidean algorithm, compute the greatest common divisor and the parameters s,t of 1. 198 and 243 2. 181
Snowcat [4.5K]

Answer:

1) The gcd is 9

9 = 9*243-11*198

2) The gcd is 17

17 = -36*3587+71*1819

Step-by-step explanation:

1) First, we divide the greater number with the smallest:

243/198 = 1.227....

The whole value is 1, and the remainder is243-1*198 = 45

Now we take the second number, 198 and 45 and repeat the same process:

198/45 = 4.4

The whole part is 4

the remainder is

198 - 4*45 = 18

Now we take 45 and 18 and repeat the process

45/18 = 2.5

the whole part is 2, the remainder is 45-2*18 = 9

Now,

18/9 = 2 is a whole number, so we stop in 9, which is the gcd.

How we find s,t?

We have to start from 9 and go upwards, replacing in bigger numbers (used in our algorithm) if possible

9 = 45-2*18

Now, we replace 18, using 18 = 198-4*45

9 = 45-2*18 = 45- 2*(198-4*45) = 9*45 - 2*198

Now, time to replace 45, using 45 = 243-198

9 = 9*45-2*198 = 9*(243-198) - 2*198 = 9*243 - 11*198

If we make the computation 9*243-11*198 = 2187-2178 = 9

Thus, the gcd is 9 and the parameters are 9 for 243 and -11 for 198.

2)

Lets divide 3587 with 1819

3587/1819 = 1.971...

The whole part is 1, the remainder is

3587-1*1819 = 1768

Now, its the turn for 1819 and 1768

clearly, the whole part oof the division will be 1, since ther are similar numbers. The remainder is 1819-1768 = 51

Now, lets continue with 1768 and 51

1768/51 = 34.66666

The whole part is 34, the remainder is

1768-34*51 = 34

Now, between 51 and 34:

The whole part of 51/34 is 1 and the remainder is 51-34 = 17

And between 34 and 17:

34/17 = 2, which is a whole number. So we stop in 17.

The gcd is 17, lets find now the parameters. We start by replacing 17

17 = 51 - 1*34

Now 34: 34 = 1768-34*51

51-34 = 51-(1768-34*51) = 35*51-1768

Now, we replace 51 = 1819-1768:

35*51-1768 = 35*(1819-1768) - 1768 = 35*1819-36*1768

And last, we replace 1768 with 3587-1819

35*1819-36*1768 = 35*1819-36*(3587-1819) = 71*1819 - 36*3587

So, the parameters for 3587 and 1819 are -36 and 71 respectively and the gcd is 17.

Lets check:

-36*3587+71*1819 = -129132+129149 = 17

3 0
4 years ago
Worth 25 points!
MrRissso [65]

Answer:

1) \sqrt{-48}=4\sqrt{3} \ i

2) \sqrt{-63}=3\sqrt{7} \ i

3) \sqrt{-72}=6\sqrt{2} \ i

4) \sqrt{-24}=4\sqrt{6} \ i

5) \sqrt{-84}=2\sqrt{21} \ i

6) \sqrt{-99}=3\sqrt{11} \ i

Step-by-step explanation:

We need to simply the following :

<u>Note: For all questions given we know that </u>\sqrt{-1}=i<u> using it in all the given questions.</u>

1) \sqrt{-48}

Factors of 48 are: 2x2x2x2x3

\sqrt{-48}\\=\sqrt{48}\sqrt{-1}  \\=\sqrt{2\times2\times2\times2\times3}\ i\\=  \sqrt{2^2\times2^2\times3}\ i\\=2\times2\sqrt{3} \ i \\=4\sqrt{3} \ i

2) \sqrt{-63}

Factors of 63 are: 3x3x7

\sqrt{-63}\\=\sqrt{63}\sqrt{-1}  \\=\sqrt{3\times3\times7}\ i\\=  \sqrt{3^2\times7}\ i\\=3\sqrt{7} \ i

3) \sqrt{-72}

Factors of 72 are: 2x2x2x3x3

\sqrt{-72}\\=\sqrt{72}\sqrt{-1}  \\=\sqrt{2\times2\times2\times3\times3}\ i\\=  \sqrt{2^2\times3^2\times2}\ i\\=2\times3\sqrt{2} \ i \\=6\sqrt{2} \ i

4) \sqrt{-24}

Factors of 24 are: 2x2x2x3

\sqrt{-24}\\=\sqrt{24}\sqrt{-1}  \\=\sqrt{2\times2\times2\times3}\ i\\=  \sqrt{2^2\times2\times3}\ i\\=2\sqrt{2\times3} \ i \\=2\sqrt{6} \ i

5) \sqrt{-84}

Factors of 84 are: 2x2x3x7

\sqrt{-84}\\=\sqrt{84}\sqrt{-1}  \\=\sqrt{2\times2\times3\times7}\ i\\=  \sqrt{2^2\times3\times7}\ i\\=2\sqrt{21} \ i

6) \sqrt{-99}\\

Prime factors of 99 are: 3x3x11

\sqrt{-99}\\=\sqrt{99}\sqrt{-1}  \\=\sqrt{3\times3\times11}\ i\\=  \sqrt{3^2\times11}\ i\\=3\sqrt{11} \ i \\=3\sqrt{11} \ i

6 0
3 years ago
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