A circle is represented by the equation x2 + 8x + y2 – 12y = –29. Describe the algebraic technique(s) needed to rewrite the equation in standard form. Identify the center and radius of the circle. Show your work

Answers

Answer 1

The equation of the circle can be written in standard form and in a general form

The center of the circle is (-4,6) and the radius is [tex]\sqrt{23[/tex]

How to identify the radius and the center of the circle

The equation of the circle is given as:

[tex]x^2 + 8x + y^2 - 12y = -29[/tex]

Rewrite as:

[tex]x^2 + 8x + k - k + y^2 - 12y + k - k= -29[/tex]

Express k as the square of the half of the coefficients of x and y.

So, we have:

[tex]x^2 + 8x + (4)^2 - (4)^2 + y^2 - 12y + (6)^2 - (6)^2= -29[/tex]

Evaluate the exponents

[tex]x^2 + 8x + 16 - 16 + y^2 - 12y + 36 - 36 = -29[/tex]

Collect like terms

[tex]x^2 + 8x + 16 + y^2 - 12y + 36 = -29 + 16 + 36[/tex]

Express as perfect squares

[tex](x + 4)^2 + (y - 6)^2 = -29 + 16 + 36[/tex]

[tex](x + 4)^2 + (y - 6)^2 = 23[/tex]

The standard equation of a circle is:

[tex](x - a)^2 + (y - b)^2 + r^2[/tex]

Where:

Center = (a,b)

Radius = r

So, we have:

Center = (-4,6)

Radius = [tex]\sqrt{23[/tex]

Hence, the center of the circle is (-4,6) and the radius is [tex]\sqrt{23[/tex]

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Related Questions

What is the most reasonable answer for the following question? There are 1300 students at Eric B. Smith Middle School. Approximately 700 of the students take the bus home. 25% of the rest of the students that do not take the bus get a ride home. Approximately how many students get a ride home?

Answers

Answer:

150 students

Step-by-step explanation:

1300 - 700 = 600

600 x .25 = 150  (25% = 0.25)

Find the value of x.

Answers

The answer would be 2

Find the area of the composite figure.

Answers

Answer:

42cm

Step-by-step explanation:

I'm sry if I'm wrong

Answer:

42 square centimeters

Step-by-step explanation:

We know all the sides of the square is 6 cm.

The side of a square and the triangle on the bottom add to 8 cm.

The bottom part of the triangle must be 2 cm.

The area of the square is 36 square centimeters as we use the formula Area = side x side for a square.

The height of the triangle is 6cm as it is as tall as the square.

The formula of a triangle is 1/2 * base * height.

1/2*(6)*(2) = 6 square centimetes.

Adding the two together,

36 + 6 = 42

BRAINLIEST (will mark) Given that the point $(4,7)$ is on the graph of $y=f(x)$, there is one point that must be on the graph of $2y=3f(4x)+5$. What is the sum of the coordinates of that point?

Answers

Answer: mark me brainliest!!

2y  = 3f(4x) + 5       divide through by  2 y = (3/2) f(4x) + 5/2 

The  "4x"  part  compresses the graph horizontally by a factor of 4The "3/2"  part vertically  stretches the graph by a factor  of 3/2The "5/2"  part  shifts the resulting point up by  5/2 units Applting the first two  to (4,7)  we get  (4*(1/4) , 7* (3/2) ) =  ( 1, 21/2) 

Applying the last one, we arrive at   ( 1, 21/2 + 5/2)  = (1, 26/2)  = ( 1,13) 

The sum of the coordinates  is  1 + 13   = 14

Step-by-step explanation:

If the Lenght of Rectangle is 10 cm and its Breadth is 15 cm . Then find the Area of Rectangle ?​

Answers

Answer:

Given ,

Length of rectangle = 10cm

Breadth of rectangle = 15cm

Now ,

Area of rectangle = length × breadth

‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎= ( 10 × 15 ) cm²

‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎= 150 cm²

[tex]\\[/tex]

hope helpful ~

Question :-

If the Lenght of Rectangle is 10 cm and its Breadth is 15 cm . Then find the Area of Rectangle ?

Answer :-

Area of Rectangle is 150² cm .

[tex] \rule {210pt} {2pt} [/tex]

Given :-

Lenght of Rectangle = 10 cmBreadth of Rectangle = 15 cm

To Find :-

Area of Rectangle = ?

Solution :-

As per the provided information in the given question, we have been given that the Lenght of Rectangle is 10 cm . Breadth of Rectangle is given 15 cm . And, we have been aksed to calculate the Area of Rectangle .

For calculating the Area , we will use Area of Rectangle Formula :-

[tex] \sf {Area \: of \: Rectangle = Lenght \times Breadth} [/tex]

Therefore , by Substituting the given values in the above Formula :-

⇒ Area of Rectangle = Lenght × Breadth

⇒ Area of Rectangle = 10 × 15

⇒ Area of Rectangle = 150

Hence :-

Area of Rectangle = 150² cm

[tex] \underline {\rule {210pt} {4pt}} [/tex]

Additional Information :-

[tex] \begin{gathered}\begin{gathered}\boxed{\begin{array}{c} \\ \underline{ { \textbf {\textsf \red{ \dag \: \: More \: Formulas \: \: \dag}}}} \\ \\ \\ \footnotesize \bigstar \: \bf{Area \: _{Square} = Side \times Side} \\ \\ \\ \footnotesize\bigstar \: \bf{Area \: _{Rectangle} = Lenght \times Breadth} \\ \\ \\ \footnotesize \bigstar \: \bf{Area \: _{Triangle} = \frac{1}{2} \times Base \times Height } \\ \\ \\ \footnotesize \bigstar \: \bf{Area \: _{Parallelogram} = Base \times Height} \\ \\ \\ \footnotesize \bigstar \: \bf{Area \: _{Trapezium} = \frac{1}{2} \times [ \: A + B \: ] \times Height } \\ \\ \\ \footnotesize \bigstar \: \bf {Area \: _{Rhombus} = \frac{1}{2} \times Diagonal \: 1 \times Diagonal \: 2}\end{array}}\end{gathered}\end{gathered} [/tex]

What is -8 +-2 ? Please help

Answers

Answer:

-10

Step-by-step explanation:

-8 + -2

-8 -2

-10

Answer:

-10

Step-by-step explanation:

Larry has a bowl of raspberries and blackberries. There are 2 more raspberries than blackberries, and there are 34 berries in all. How many raspberries does Larry have?

Answers

your equations are:
b+2=r
b+r=34
simplify to get that he has 18 raspberries and 16 blackberries

Line A passes through the points (-3, -1) and (4, 13).


Line B passes through the points (6, -1) and (-4, 19).


Find the point where line A intersects line B

Answers

Answer: (1.5, 8)

Step-by-step explanation:

75% of 120 is what number

Answers

Step-by-step explanation:

75% of 120

[tex] \frac{75}{100} \times 120 [/tex]

[tex] = 15 \times 6[/tex]

[tex] = 90[/tex]

HOPE IT HELPS YOU

Solution:

Let the unknown number be x.

We know that:

The word "of" means multiplication.

This means that:

=> 75% × 120 = x

Step-by step calculations:

=> 75/100 × 120 = x                                                          [75% = 75/100]=> 75/5 × 6 = x=> 15 × 6 = x=> 90 = x

Thus, the number is 90.

Find the error in this And then solve it correctly

Answers

Answer:

m<DCB=34

Step-by-step explanation:

90-56=34

The m<DCA would be 56, not the m<DCB


Homework 4: Trigonometric Ratios &
Finding Missing Sides

solve for x

Answers

Answer:

[tex]\displaystyle 13,834311042... = x[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{x}{13} = csc\:70 \hookrightarrow 13csc\:70 = x \\ \\ 13,834311042... = x[/tex]

OR

[tex]\displaystyle \frac{13}{x} = sin\:70 \hookrightarrow xsin\:70 = 13 \hookrightarrow \frac{13}{sin\:70} = x \\ \\ 13,834311042... = x[/tex]

Information on trigonometric ratios

[tex]\displaystyle \frac{OPPOCITE}{HYPOTENUSE} = sin\:θ \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:θ \\ \frac{OPPOCITE}{ADJACENT} = tan\:θ \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:θ \\ \frac{HYPOTENUSE}{OPPOCITE} = csc\:θ \\ \frac{ADJACENT}{OPPOCITE} = cot\:θ[/tex]

I am joyous to assist you at any time.

Solve for b 6b + 16 = 94

Answers

Answer:

b=13

Step-by-step explanation:

First, subtract 16 from 94. 94-16=78

Then divide 6 into 78. 78/6=13

Therefore, b=13

Answer:

b=13

Step-by-step explanation:

6b+16=94

subtract 16 from both sides

6b=78

divide both sides by 6

b=13

i need to show the work by the way.

Answers

Answer:

A) 61º

Step-by-step explanation:

since the line is straight that means that it is a 180º angle.

 7 10

180

-119

061

What mixed number is the arrow pointing to?'

1. 12 4/5
2. 12
3. 12 1/2
4. 12 2/3

Answers

Answer:

4. 12 2/3

Step-by-step explanation:

You count the number of intervals between it takes to get from 12 to 13.

It takes 6 times.

We see that the arrow is at the 4th interval.

So out of 6 intervals, the arrow is at the 4th interval

So 4th interval / 6th interval = 4/6

We reduce 4/6 to 2/3 because dividing both top and bottom by 2 gets us 2/3.

4/6 =  2/3

We have

12 2/3

tate whether the following ratios are proportional.

1) 2:3 and 4:6

2) 1:4 and 6:18

3) 3:5 and 1:3

4) 2:5 and 8:20

5) 4:9 and 12:27

6) 6:15 and 2:5

Answers

Answer:

4÷2=2

6÷2 =3

2:3 this is 4:6 in its simplest form

they are proportional or equal

Step-by-step explanation:

multiple are numbers a divide with and not get

a remainder

example 8÷4=2

8÷3=2 remainder 1 meaning that 3 in not a multiple

2) they are not proportional

6÷2=3

18÷2=9

3:9

6÷3=2

18÷3=4=6

6÷6=1

18÷6=3

1:3

this ratios are all not equal or proportional to1:4

Which equation illustrates the Associative Property of Multiplication? WILL MARK BRAINLEIST IF ANSWERED
3(x + 2) = 3x + 6
2xy = yx3
3x = 0
(3x)y = 3(xy)

Answers

Answer:

3(x+2)=3x+6

Step-by-step explanation:

i hope it helps

if its wrong let me know so i can change it or something or just remove my comment

Find the common difference of the arithmetic sequence 14, 8, 2,.

Answers

Answer:

-6

Step-by-step explanation:

9 8/12 - 4 9/12

Simplest form please

Answers

59/12 if you want to simplify more 4 11/12

Answer:

1/3

Step-by-step explanation:

were going to subtract the wholes so what is 9-9=? it =0

2. Now we know we have 0 wholes. Next what is 8 -4=? 8 -4=4

3. Now our fraction is 4/12 now since 4 x 3 =12 then that means it's the first number besides 3 so what I mean about that is it is 1/3 but if the fraction were 8/12 then it would be 2/3 but it is 4/12 so it is 1/3.

4. That is our answer and were finished the final answer is 1/3 or 33.333

5.Hope this helps have a awesome day:)

Find the magnitude and direction of the
vectors:-
A) which displaces A(√3,1)to B(2√3,2)

Answers

Magnitude is distance between points

[tex]\\ \rm{:}\dashrightarrow AB=\sqrt{(2\sqrt{3}-\sqrt{3})^2+(2-1)^2}=\sqrt{3+1}=2units [/tex]

Direction is slope

[tex]\\ \rm{:}\dashrightarrow \alpha=tan^{-1}(\dfrac{2-1}{\sqrt{3}})[/tex]

[tex]\\ \rm{:}\dashrightarrow \alpha=tan^{-1}(\dfrac{1}{\sqrt{3}})[/tex]

[tex]\\ \rm{:}\dashrightarrow \alpha=\dfrac{\pi}{6}[/tex]

A grocery store sells a bag of 4 oranges for $3. 64. How much would it cost for 6 oranges?

Answers

Answer:

$5.46

Step-by-step explanation:

4 / 3.64 = 6 / x

A local craft store is selling different kinds of craft paint for $2, $3,
$2, $15, and $2. When placing an ad in the local paper, which
measure of central tendency should it use to advertise?

Answers

The measure of the central tendency of the local paper can be mean, median or mode

The local paper should use the median as the measure of the central tendency

How to determine the measure of central tendency

The dataset is given as:

$2, $3, $2, $15, and $2

Rearrange the dataset

$2, $2, $2, $3, $15

In the above dataset, $15 is relatively larger than the other dataset

This means that:

$15 is an outlier of the dataset

Median is not affected by outlier, while mean is affected by outliers

Hence, the local paper should use the median as the measure of the central tendency

Read more about central tendency at:

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A rectangle’s width is one-fourth of its length. Its area is 9 square units. The equation l(l) = 9 can be used to find l, the length of the rectangle. What is the length of the rectangle? 0. 75 units 1. 5 units 3 units 6 units.

Answers

By using the given condition, the length of the rectangle is 6 units.

It is given that

Area of the rectangle = 9 square units

Width of the rectangle = 1/4 of length

What is the area of a rectangle?

The area of a rectangle is the multiplication of its length to width.

Let us take the length of the rectangle as l

So, the width of the rectangle will be l/4

Area of the rectangle,

[tex]l*\frac{l}{4} = 9(given)[/tex]

[tex]l^{2} = 36\\l = 6[/tex]

Therefore, the length of the given rectangle is 6 units,

To get more about rectangles, visit:

https://brainly.com/question/25292087

Answer: 6 units or D.

Step-by-step explanation:

What is the domain of the function y- +4?
-00 O 45x<00
O 0SX <0
O 45x<00

Answers

Answer:

I think its A. I might be wrong tho so sorry if i am

Step-by-step explanation:

Lmk if its correct :)

Please help me


Several points appear on the number line, which shows numbers from 0 through 1. On the number line, point M represents 0.25. What fraction does point M also represent on the number line?

Answers
A= 1/5
B= 1/3
C= 1/4
D= 1/25

Answers

Answer:

1/4

Step-by-step explanation?

Keep in mind that fractions are technically division problems.

Divide 1 by 4 and you will end up with 0.25

Next time try to answer the problem on your own :)

Review the graph of
Which point lies outside of the solution set? (y+4)^2/9-(x+1)^2/9>1

Answers

The point outside the solution set are the false values of the inequality

The point outside the solution set of (y+4)^2/9-(x+1)^2/9>1 is (-1,-1)

How to determine the point outside the solution set

The inequality of the graph is given as:

[tex]\frac{(y+4)^2}{9}-\frac{(x+1)^2}{9} > 1[/tex]

Next, we test the options

Option A. (-2,4)

This gives

[tex]\frac{(4+4)^2}{9}-\frac{(-2+1)^2}{9} > 1[/tex]

[tex]\frac{64}{9}-\frac{1}{9} > 1[/tex]

Evaluate the difference

[tex]7 > 1[/tex] -- this is true

Option B. (2,-12)

This gives

[tex]\frac{(-12+4)^2}{9}-\frac{(2+1)^2}{9} > 1[/tex]

[tex]6.1 > 1[/tex]  -- this is true

Option C. (-1,-1)

This gives

[tex]\frac{(-1+4)^2}{9}-\frac{(-1+1)^2}{9} > 1[/tex]

[tex]1 > 1[/tex]  -- this is false

Hence, the point outside the solution set of (y+4)^2/9-(x+1)^2/9>1 is (-1,-1)

Read more about solution sets at:

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Answer: it is C (-1, -1)

Step-by-step explanation:

A university has 29,370 students. In a random sample of 210 students, 14 speak three or more languages. Predict the number of students at the university who speak three or more languages.

Answers

Answer:

ok so out of 210 14 speak 3 or more so that is a ratio of

210:14

so lets find out how many times 210 goes into the whole populaiton

29370/210=139.857142857

then lets multiply the 14 by that amount

14*139.857142857=1958(exact)

so out of the 29370 1958 speak 3 or more launges

Hope This Helps!!!

Write the ratio of 2 oranges to 3 apples in three different ways

Answers

Answer:

2:3

3:2

2/3

Step-by-step explanation:

Answer:

2:3

2 to 3

2/3

If you are comparing one data point (A) to another data point (B), your formula would be A/B. This means you are dividing information A by information B. For example, if A is five and B is 10, your ratio will be 5/10. Solve the equation.

The ice cream truck has a jar containing a slip of paper for each of the flavors . Shaun chooses three slips of paper without looking . What is the probability that Shaun's triple scoop cone contains two of his five favorite flavors ?

Answers

Answer: 5/31

explanation: there are 31 flavors in all. 5 are his favorite. Therefore, the answer is 5/31

solve for y in terms of x (rewrite each equation so that it starts with "y=")

a. 6x + 5y = 20

b. 4x - 8y = 16

thanks!

Answers

answers:

a. y = -6/5x + 4

b. y = 1/2x - 2

Step-by-step explanation:

a.

5y = 20 - 6x

y = 20/5 - 6/5x

y = -6/5x + 4

b.

-8y = -4x + 16

y = -4/-8x + 16/-8

y = 1/2x -2

Find the surface area of the prism.round to the nearest whole number
And working out

Answers

I'm not entirely sure if this is what you're looking for, but I'm going to try to help anyways.

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