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OleMash [197]
3 years ago
8

Mrs. Culland is finding the center of a circle whose equation

Mathematics
1 answer:
Yanka [14]3 years ago
5 0

We have been given that Mrs. Culland is finding the center of a circle whose equation  is x^2+y^2+6x +4y-3 = 0 by completing the square.

Her work is shown.

x^2+6x+y^2 +4y-3 = 0

(x^2+6x)+(y^2 +4y)=3

(x^2+6x+9)+(y^2 +4y+4)=3+9+4.

We can see that Mrs. Culland added half the square of coefficients of x and y terms on both sides to complete the square.

For x term: (\frac{6}{2})^2=3^3=9

For y term: (\frac{2}{2})^2=2^3=4

Our next step is to write the perfect squares in form (a\pm b)^2 as:

(x+3)^2+(y+2)^2=16

We know that standard equation of circle is (x-h)^2+(y-k)^2=r^2, where point (h,k) is center of circle and r is radius of circle.

We can rewrite our equation as:

(x-(-3))^2+(y-(-2))^2=4^2

Therefore, the center of circle is (-3,-2) and equation of circle would be (x+3)^2+(y+2)^2=4^2.

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3 years ago
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Given the distance between (x,1) and (-2,5) is 2 root 7, find the the value of x. Leave your answer in simplified exact form
Neporo4naja [7]

Answer:

Step-by-step explanation:

Distance = the square root of (x2-x1)2 + (y2-y1)2Added:Distance Formula: Given the two points (x1, y1) and (x2, y2), the distance between these points is given by the formula:square root of x2-x1 squared +y2-y1 squared

8 0
3 years ago
-5x + 3y = -8<br> 3x - 7y= -3
AnnZ [28]

Answer:

x = 5/2   y = 3/2

Step-by-step explanation:

You need to write what the question is besides the information in the problem.  I assume the question is to find the values of x and y.

Going on that premise, Let equation (1)   be -5x + 3y = -8 and

equation (2)  be 3x - 7y = -3

Lets multiply (1) by 3 and (2) by 5 and we get equations (4) and (5)

(4)   -15x + 9y = -24    and  (5)    15x - 35y = -15  Now add (4) and (5)

-15x + 9y = -24

<u> 15x - 35y = -15</u>

      -26y = - 39

y = 3/2     Now substitute y = 3/2 in equation (1).  -5x + 3)(3/2) = -8

                                                                                 -5x + 9/2 = -8

                                                                                  -10x + 9 = -16

                                                                                  -10x = -25

                                                                                      x = -25/-10 = 5/2  

x = 5/2   y = 3/2

Check:  Substitute your answers into equation (2) and see if they work.

3(5/2) -7(3/2) = 15/2 - 21/2 = -6/2 = -3   Hooray!  We have the correct values for x and y that makes each equation true  

8 0
3 years ago
V121 + V49 + 4 = 1<br> Answer?
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Answer:

v=1.0046196

Step-by-step explanation:

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Claire and Ashley are soccer players. Throughout the last soccer season, Claire scored three times as many goals as Ashley did.
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The expression could be (1/3)C.

If Claire scored three times as many as Ashley, that means that Ashley scored 1/3 the number that Claire did.

Simply multiply the amount that Claire score by 1/3 and you have the number that Ashley scored.
8 0
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