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likoan [24]
3 years ago
5

The general form of the equation of a circle is x^2+y^2−8x+6y+21=0.

Mathematics
2 answers:
densk [106]3 years ago
7 0

Answer:

The coordinates of the center of the circle are (4,-3).

Step-by-step explanation:

The general form of the equation of a circle is

x^2+y^2-8x+6y+21=0

It can be written as

(x^2-8x)+(y^2+6y)+21=0

Add and subtract (\frac{-b}{2a})^2 in each parenthesis, to make perfect squares.

For first parenthesis,

(\frac{-b}{2a})^2=(frac{8}{2(1)})^2=(4)^2=16

For second parenthesis,

(\frac{-b}{2a})^2=(frac{-6}{2(1)})^2=(-3)^2=9

(x^2-8x+16-16)+(y^2+6y+9-9)+21=0

(x^2-8x+16)+(y^2+6y+9)+21-16-9=0

(x-4)^2+(y+3)^2-4=0

(x-4)^2+(y+3)^2=4                  .... (1)

The standard form of a circle is

(x-h)^2+(y+k)^2=r^2              .... (2)

Where, (h,k) is center of the circle and r is radius.

On comparing (1) and (2) we get,

h=4,k=-3,r=2

Therefore the coordinates of the center of the circle are (4,-3).

Minchanka [31]3 years ago
5 0
The anwser is (4,-3)
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Roseanne is making chocolate chip cookies for dessert the recipe for one batch of chocolate chip cookies calls for 2 1/2 cups of
umka21 [38]

Answer:

8 3/4 cups of sugar

Step-by-step explanation:

1 batch of chocolate chip cookies ↔ 2 1/2 cups of sugar

3 1/2 batch of chocolate chip cookies ↔ 3 1/2 * 2 1/2 cups of sugar

3 1/2 * 2 1/2 = 7/2 * 5/2 = 35/4 = 8 3/4 = 8.75

4 0
3 years ago
the sum of three numbers is 79. The second number is 5 times the first, while the third is 16 more than the first. Find the Numb
faust18 [17]
Let the 1st number be x; 2nd number be y; 3rd number be z.

x + y + z = 79

x = number we are looking for.
y = x * 5 ==> 5 times the first
z = x + 16 ==> 16 more than the first

Therefor,

x + (x * 5) + (x+16) = 79

1st step, multiply the 2nd number: x * 5 = 5x

x + 5x + x + 16 = 79

Add all like numbers:

7x + 16 = 79

To get x, transfer 16 to the other side and change its sign from positive to negative.

7x = 79 - 16
7x = 63

To get x, divide both sides by 7

7x/7 = 63/7
x = 9

To check. Substitute x by 9.

x + (x * 5) + (x+16) = 79

9 + (9 * 5) + (9 + 16) = 79
9 + 45 + 25 = 79
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4 0
3 years ago
Read 2 more answers
Find the coordinates of the point 7/10 of the way from A to B. a=(-3,-6) b=(12,4)
Artemon [7]

Answer:

The coordinates of M are x = \frac{15}{2} and y = 1.

Step-by-step explanation:

Let be A = (-3,-6) and B = (12, 4) endpoints of segment AB and M a point located 7/10 the way from A to B. Vectorially, we get this formula:

\overrightarrow {AM} = \frac{7}{10}\cdot \overrightarrow {AB}

\vec M - \vec A = \frac{7}{10}\cdot (\vec B - \vec A)

By Linear Algebra we get the location of M:

\vec M = \vec A + \frac{7}{10}\cdot (\vec B - \vec A)

\vec M = \vec A +\frac{7}{10}\cdot \vec B - \frac{7}{10}\cdot \vec A

\vec M = \frac{3}{10}\cdot \vec A + \frac{7}{10}\cdot  \vec B

If we know that \vec A = (-3,-6) and \vec B = (12, 4), then:

\vec M = \frac{3}{10}\cdot (-3,-6)+\frac{7}{10}\cdot (12,4)

\vec M = \left(-\frac{9}{10},-\frac{9}{5}  \right)+\left(\frac{42}{5} ,\frac{14}{5} \right)

\vec M =\left(-\frac{9}{10}+\frac{42}{5} ,-\frac{9}{5}+\frac{14}{5}   \right)

\vec M = \left(\frac{15}{2} ,1\right)

The coordinates of M are x = \frac{15}{2} and y = 1.

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Darina [25.2K]
Answer: 5x3 + x2 - 2x + 5

Make sure to combine like terms and watch out for if it’s subtraction or addition.
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3 years ago
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