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AnnZ [28]
3 years ago
15

Find the circumcenter of the triangle ABC.

Mathematics
1 answer:
mr Goodwill [35]3 years ago
5 0

Answer:

<u>The circumcenter is (-1 , -6.5)</u>

Step-by-step explanation:

the circumcenter is the point where the perpendicular bisectors of a triangle intersects.

See the attached figure

A(-6, - 8), B(4. – 5), C(-6,-5).

As shown at the graph ΔABC is aright triangle at C

The perpendicular bisector of AC is the line y =-6.5

The perpendicular bisector of  BC is the line x = -1

The intersection between y =-6.5 and x = -1 will be the point (-1,-6.5)

<u>So, The circumcenter is (-1 , -6.5)</u>

<u>Another solution:</u>

As the graph represents a right triangle.

The circumcenter of a right triangle lies exactly at the midpoint of the hypotenuse

The hypotenuse is the line segment AB

The midpoint of AB = (A + B)/2 = [(-6, - 8) +(4. – 5)]/2 = (-2,-13)/2 = (-1 , -6.5)

So, <u>The circumcenter is (-1 , -6.5)</u>

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Answer:

1 7/10

Step-by-step explanation:

you can divided them which gives you 1.7 and turn that into a fraction which gives you 1 7/10

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kari74 [83]

Answer:

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Step-by-step explanation:

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(Adding and Subtracting Polynomials)
andrey2020 [161]

Adding and subtracting big polynomials like these are pretty easy. You just need to combine like terms. For example:

1.)

{5x}^{2}  +  {3x}^{2}  =  {8x}^{2}

2.)

({3x}^{2}  + 5xy) + (7xy + 2) =

{3x}^{2} + 12xy + 2

(The 3x^2 and the 2 stay intact while the 5xy and 7xy combine together)

All you have to do is combine the numbers that have the same powers of x and y with each other. x^2 will combine with x^2 and xy^2 wil combine with xy^2 exc. If there is no other number with the same x and y's, then you just leave it as it is in the answer.

Now with the original question, I see a -9xy^3, and thats gonna combine with the 3xy^3 in the second polynomial and the 2xy^3 in the third one.

- 9x {y}^{3}  + 3x {y}^{3}  + 2x {y}^{3} = \\  - 4x {y}^{3}

So far we have -4xy^3, the next term is going to be a -9x^4y^3, and that's gonna combine with the 3x^4y^3 in the third one.

- 9 {x}^{4} {y}^{3}  + 3 {x}^{4}  {y}^{3}  =  - 6{x}^{4}  {y}^{3}

We now finished adding the like terms that were in the first polynomial, we will move onto the second polynomial. The first term in this one is 3xy^3, in which we already added in the first step. At this point, it doesn't look like there are any other terms that have the same x and y behind them. So we can move on and write the final answer:

- 4x {y}^{3} - 6 {x}^{4} {y}^{3}  + 7 {y}^{4}  \\ - 8 {x}^{4} {y}^{4}

(All on the same line of course)

Also, for your second question, the order does not matter in which you write the terms. I could write the 7y^4 behind the -8x^4y^4 and it would still be the same answer.

If you have any other questions let me know :) while I double check my work.

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Answer:

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