Can someone please please tell me what the general form for (x-6)^2+(y-3)^2=16 is. I would really appreciate the help!

Answers

Answer 1

Answer:

x² + y² - 12x - 6y + 29 = 0

Step-by-step explanation:

Simplifying the equation using (a + b)² = a² + 2ab + b²:

(x - 6)² + (y - 3)² = 16

⇒ [x² - 2(x)(6) + 6²] + [y² - 2(y)(3) + 3²] = 16

⇒ [x² - 12x + 36] + [y² - 6y + 9] = 16

⇒ x² - 12x + 36 + y² - 6y + 9 = 16

General form of a circle = x² + y² + Cx + Dy + E = 0

Before we reorganize the equation in general form, we need to have the R.H.S as 0. For that, we need to subtract 16 both sides.

Subtract 16 both sides:

⇒ x² - 12x + 36 + y² - 6y + 9 = 16

⇒ x² - 12x + 36 + y² - 6y + 9 - 16 = 16 - 16

⇒ x² - 12x + 20 + y² - 6y + 9 = 0

Reorganizing the equation in general form:

x² - 12x + 20 + y² - 6y + 9 = 0

⇒ x² - 12x + 20 + y² - 6y + 9 = 0

⇒ x² + y² - 12x + 20 - 6y + 9 = 0

⇒ x² + y² - 12x + 20 - 6y + 9 = 0

⇒ x² + y² - 12x - 6y + 20 + 9 = 0

x² + y² - 12x - 6y + 29 = 0

Thus, the equation in general form is x² + y² - 12x - 6y + 29 = 0.


Related Questions

What is the circumference

Answers

25.1 yards
multiply the radius by 2 and multiply that number with pi and you get your answer of 25.1 yards

Please answer ASAP! I am very confused. Please explain steps if possible.

Answers

Answer:

943 exponent 14

Step-by-step explanation:

The question deals with indices(exponents). Therefore,all laws of indices related to the question must be applied to clearly solve and understand the question.

so,(943 exponent 78 · 943 exponent 1)/943 exponent 65

· means multiplication so simply,(943 exponent 78 × 943 exponent 1)/943 exponent 65

The laws of indices clearly state that, when two indices of the same base are multiplying, you add their exponents and when dividing,you subtract their exponents.

As all the indices have the same base which is "943", we can quickly add & subtract the exponents.

(Leaving base out of calculation now to make it easier to directly deal with exponents)

(78+1)-65(From the rules)

79-65=14,which means 943 exponent 14

∴The answer is 943 exponent 14

Can someone solve this?

Answers

Step-by-step explanation:

First box =25

Second Box = 0.25

What is the area and circumference of the circle? diameter = 12 cm​

Answers

Answer:

Circumference = 7.68 cm

Area = 113.04 cm²

Step-by-step explanation:

First, let us find the radius of the given circle.

d = 2r

r = d / 2

r = 12 / 2

r = 6 cm

And now, let us find the circumference of the circle using the below formula.

C = 2 π r

C = 2 × 3.14 × 6

C = 37.68 cm

And now let us find the area of the circle using the below formula.

A = π r²

A = 3.14 × 6 × 6

A = 113.04 cm²

help please :) help ​

Answers

Answer:

6

Step-by-step explanation:

4 time one is 1

plug in 1 for m

and you got 4 - -2

witch both negatives make a positive

Mike is building storage boxes. Each box will have a length of 5 feet, a width of 412 feet, and a height of 312 feet. A pint of paint covers 50 square feet.

How many pints of paint does Mike need to buy in order to paint 4 boxes?

9 pints
7 pints
6 pints
5 pints

Answers

The pints of paint that Mike needs to buy in order to paint 4 boxes is 9 pints.



How many pints is needed?


The first step is determine the total surface area of a box.


Total surface area of a cuboid = 2 (lw + wh + lh)


where:
l = length
w = width
h = height


2 x[ (5 x 9/2) + (9/2 x 7/2) + (5 x 7/2) ]
2 x ( 45/2 + 63/4 + 35/2) = 111.5ft


The second step is to determine the total surface area of 4 boxes:


111.5 x 4 = 446


Now, divide 446 by 50


446 / 50 = 9 pints

Answer:

Step-by-step explanation:

The question contains typos as I believe the boxes should be 5x4.2x3.2 in dimensions instead.

Assuming that and all 6 faces of each storage boxes will be painted, the surface area of each box is:

= (5*4.2*2) + (4.2*3.2*2) + (3.2*5*2)

= 100.88 square feet

4 boxes will have a total surface area of

100.88*4

= 403.52 square feet

Each pint of paint covers 50 square feet so a total of

403.52/50 = 8.07 or

9 pints is needed.

It is given that AB CD Identify the postulate that proves the triangles are congruent

Answers

Answer:

i can't see the multiple choice

Step-by-step explanation:

angle c and b are equal

angle a and d are equal

and you have a common angle o

and ab = cd

The triangles ΔAOB and ΔDOC are congruent to each other by SSS and SAS postulates. Then the correct option is A.

What is the triangle?

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

It is given that AB || CD. The side AB is congruent to the side CD.

The line AD and BC intersect at the mid-point. Then the line segment AO and OD will be congruent and the line segment CO and OB will be congruent.

And the angle ∠AOB and ∠COD will be congruent because they are vertically opposite angles.

The triangles ΔAOB and ΔDOC are congruent to each other by SSS and SAS postulates. Then the correct option is A.

More about the triangle link is given below.

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Model this equation using a visual model.
4x + 8.46 = 2x + 15.62

Answers

I will clarify you
Soln:-
Or,4x-2x=15.62-8.46
Or,2x=7.16
Or,x=7.16/2
Or,x=3.58

Here are the endpoints of the segments BC, FG, and JK.
B, −67

Answers

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ B(\stackrel{x_1}{-6}~,~\stackrel{y_1}{7})\qquad C(\stackrel{x_2}{-4}~,~\stackrel{y_2}{4})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ BC=\sqrt{[-4 - (-6)]^2 + [4 - 7]^2}\implies BC=\sqrt{(-4+6)^2+(-3)^2} \\\\\\ BC=\sqrt{2^2+(-3)^2}\implies \boxed{BC=\sqrt{13}} \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~~~~~~~\textit{distance between 2 points}[/tex]

[tex]F(\stackrel{x_1}{-2}~,~\stackrel{y_1}{-4})\qquad G(\stackrel{x_2}{1}~,~\stackrel{y_2}{-2})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ FG=\sqrt{[1 - (-2)]^2 + [-2 - (-4)]^2}\implies FG=\sqrt{(1+2)^2+(-2+4)^2} \\\\\\ FG=\sqrt{9+4}\implies \boxed{FG=\sqrt{13}} \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ J(\stackrel{x_1}{4}~,~\stackrel{y_1}{2})\qquad K(\stackrel{x_2}{5}~,~\stackrel{y_2}{-2})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}[/tex]

[tex]JK=\sqrt{[5 - 4]^2 + [-2 - 2]^2}\implies JK=\sqrt{1^2+(-4)^2}\implies \boxed{JK=\sqrt{17}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \overline{BC}\cong \overline{FG}~\hfill[/tex]

Toni typed 600 words in 1hour, 250 words in 20 minutes and 480 words in 40minutes. How many words did Toni typed in 2 hours?


a 1 113 words

b 3 113 words

c 1 330 words

d 1 130 words

Answers

1hour=600

2hour=600+600

=1200words

What is the center and radius of the circle given by x2 + y2 - 10x - 12y + 24 = 0?​

Answers

Answer:

centre (5, 6 ) , r = [tex]\sqrt{37}[/tex]

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r the radius

given

x² + y² - 10x - 12y + 24 = 0 ( collect x and y terms together and subtract 24 from both sides )

x² - 10x + y² - 12y = - 24

using the method of completing the square

add ( half the coefficient of the x / y terms)² to both sides

x² + 2(- 5)x + 25 + y² + 2(- 6)y + 36 = - 24 + 25 + 36

(x - 5)² + (y - 6)² = 37 ← in standard form

with centre (h, k ) = (5, 6 ) and r = [tex]\sqrt{37}[/tex]

What is the area of the quadrilateral

Answers

Answer:

Or you could also find the area of 2 triangles and one rectangle.

Area of a triangle = bh/2

1st triangle = 6 x 2 = 12

12 ÷2 = 6

2nd triangle = 6x2= 12 ÷ 2 = 6

Area of a rectangle

A=bh

b = 4

h= 6

6x4=24

Now add all the areas to find out the area of the shape, so

6+6+24 =

[tex]36 {ft}^{2} [/tex]

2,7, 12, ...
Find the 46th term.

Answers

Given is an A.P. in which -

First term,a = 2Common difference = Second term - First term

[tex]\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad = a_2-a_1[/tex]

[tex]\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad = 7-2 [/tex]

[tex]\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad = 5[/tex]

Solution:-

nth term of an A.P ,is given by-

[tex]\green{ \underline { \boxed{ \sf{a_n =a+(n-1)d }}}}[/tex]

where

[tex]a_n = nth \;term[/tex]a = first termn = number of termd = common difference

Putting n = 46

[tex]\begin{gathered}\\\implies \sf a_{46}= 2 + (46-1)\times 5 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies \sf a_{46}= 2 + 45\times 5 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies \sf a_{46}= 2 + 225 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies \sf a_{46}= 227 \\\end{gathered} [/tex]

[tex]\longrightarrow[/tex]Therefore, the 46th term is 227

Hence, the [tex]46th[/tex] term is [tex]227[/tex].

What is the sequence?

A sequence is a list of objects, typically numbers, in which order matters, repetition is allowed, and the same elements can appear multiple times at different positions in the sequence.

Here given sequence is

[tex]2,7, 12,...[/tex]

Here,

[tex]a=2[/tex]

[tex]d=a_2-a_1\\d=7-2\\d=5[/tex]

The general formula of the sequence is

[tex]a_n=a+(n-1)d[/tex]

where,

[tex]a_n=[/tex] nth term

[tex]a[/tex] is the first term

[tex]d[/tex] is the common difference

[tex]n[/tex] is the number of terms

Now substituting the values in general formula is

[tex]a_{46}=2+(46-1)5\\\\a_{46}=2+(45)5\\\\a_{46}=2+225\\\\a_{46}=227\\[/tex]

Hence, the [tex]46th[/tex] term is [tex]227[/tex].

To know more about the sequence

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Triangle PQR is shown, what is the value of x?

Answers

Answer:X = 13

Step-by-step explanation:

An exterior angle is equal to the sum of the two opposite interior angle

⇒95=4x+3 + 3x+ 1

95=4x + 3x + 3 + 1

95=7x + 4

95-4=7x

91=7x

91/7=x

13=x

This implies that X= 13

jimmy has 27 apples and there are 9 houses. he feeds the same number of apples to each horses. how many apples dose jimmy feed to each horse?

Answers

-------------------------------------------------------------------------------------------------------------

Answer:

The answer is, Jimmy, fed the horses 3 apples each.

27 apples divided into the 9 horses

27 ÷ 9 = 3

If you had 27 seven apples and you individually gave one apple to each of the 9 horses each horse would end up having 3.
-------------------------------------------------------------------------------------------------------------

please help me i need to solve for x

Answers

Answer:

1.732i (complex form)

its weird, at high-school level complex shouldn't come, its considered mistake in the question. But the mathematically its all correct

Step-by-step explanation:

Find the measure of the arc or angle indicated

Answers

Answer:

D) 130

Step-by-step explanation:

So there are three arc sections in this problem,

The first one is given: 158

To find the arc between S and R, you can use the angle of point T and double it.

So:

36 * 2 = 72

The second arc is 72

Now for the one that they want you to find, you have to add the two arcs that you have and substract it from 360, which is the angle of a whole circle

Like so:

360 - (158 + 72) = 130

Answer:

130

Step-by-step explanation:

NEED ANSWERS QUICKLY! CORRECT ANSWER GETS BRAINLIEST
Write a division problem such that the quotient is the same as 3/7 divided by 5/14


.

Answers

Answer:

6 6

---- ÷ ---

16 10

Step-by-step explanation:

equals 5/8

The are 3 blue marbles, 4 red marbles and 2 yellow marbles. Find the ratio of blue marbles to red and yellow marbles.

Question 2 options:

4:3


3:4


3:2

1:2

Answers

Step-by-step explanation:

3 blue

4 red

2 yellow

in total 9 marbles.

when looking at the 3 blue marbles that leaves 9-3 = 6 others (red and yellow).

so, the ratio is

3:6 = 1:2

remember, a ratio is a fraction and follows the same rules of calculation, simplification, ...

Hi I have been working on this for hours and I still can't figure out what 23x3 is I would really be thankful if you can help me.
Thanks!

Answers

The answer to your question is 69

what is the answer for this also?

Answers

Answer:

64 cm^3

Step-by-step explanation:

V = lwh

V = 4 x 4 x 4

V = 64 cm^3

Hope this helps!

[tex] \huge\fbox\orange{ANSWER} [/tex]

[tex] \mathsf \purple{volume \: of \: square = {x}^{3} }[/tex]

[tex] \mathsf \pink{v = {4}^{3} }[/tex]

[tex] \mathsf \purple{v = {64cm}^{3} }[/tex]

Determine the solution to each linear system by using the substitution method
3x+y=8
6x+2y=10

Answers

Answer:

No solution.

Step-by-step explanation:

Isolate the term of x and y from one side of the equation.

3x+y=8 and 6x+2y=10

3x+y=8

x=8-y/3

Solve.

Rewrite the problem down.

6*8-y/3+2y=10

Then, solve.

16=10

Therefore, the final answer is no solution.

I hope this helps you! Let me know if my answer is wrong or not.

help me!!Write a function using correct notation that models the value of each car.

Answers

Answer:

[tex]f(x) = 2000 * 1.05^x[/tex]

Step-by-step explanation:

The key to this question is interpreting the graph and then modelling it into an exponential function.

You are given 2 key characteristics of this graph. 1 characteristic being that it intercepts the y-axis at (0,2000), and another characteristic being that it goes through the point (1,2100)

Now refer to the standard form of an exponential function.

[tex]y = a * b^x[/tex]

Since you know that when x = 0, y = 2000, a must be 2000. Because [tex]b^0 = 1[/tex], 2000 * 1 = 2000

So you got your a value. Sub it into the equation and now you got.

[tex]y = 2000 * b^x[/tex]

You still need to solve for b, so this is where you do some algebra. Pick your key point, (1,2100), sub in those values for x and y, and solve for b.

[tex]2100 = 2000 * b^1\\\frac{2100}{2000} = b\\ 1.05 = b[/tex]

Now you have your a and b values. Now you can express using a function:

[tex]f(x) = 2000 * 1.05^x[/tex]

Luz borrowed
money from her bank for home repairs, the principal was $25,000, the rate
was 15% the time was 6 years. How
much interest will she pay and what is the total amount she will have to
pay back? (Principal and interest).

Answers

The total amount accrued, principal plus interest, from simple interest on a principal of $25,000.00 at a rate of 15% per year for 6 years is $47,500.00.

Answer:

I =  $22,500.00

A = $47,500.00

Simple interest

Given Data

Principal = $25000

Rate = 15%

Time = 6 years

Equation:

A = P(1 + rt)

Calculation:

First, converting R percent to r a decimal

r = R/100 = 15%/100 = 0.15 per year.

Solving our equation:

A = 25000(1 + (0.15 × 6)) = 47500

A = $47,500.00

I = A - P = $22,500.00

Learn more about simple interest here:

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Which property can be used to solve the equation?

5 d = 75
addition property of equality
subtraction property of equality
multiplication property of equality
division property of equality

Answers

Answer:

Division property of equality

Step-by-step explanation:

If you have an equation with the variable not equal to one you want it to equal one so you would divide to get the variable to 1 so 5/5 and then you would do the same to the other side(75/5) d=15.

Answer:Division property of equality

Step-by-step explanation:If you have an equation with the variable not equal to one you want it to equal one so you would divide to get the variable to 1 so 5/5 and then you would do the same to the other side(75/5) d=15.

There are 19 students in the class today 14 are absent. How many students are in class total? Draw a tape diagram that would represent this scenario. Solve X

Answers

Answer:

5

Step-by-step explanation:

19-14=5

for the Tape diagram just make 19 boxes and fill in 5.

In which quadrant does θ lie given that sinθ < 0 and cosθ < 0? Thank You!

Quadrant I

Quadrant II

Quadrant III

Quadrant IV

Answers

Answer:

Quadrant III.

Step-by-step explanation:

u said the answer :3

The quadrant that θ lies given that sinθ < 0 and cosθ > 0 will be Quadrant IV

What are trigonometric identities?

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

we need to first know the signs of the trigonometric functions in each of the 4 quadrants going in an anti-clockwise direction.

In the first quadrant, the cot, sin, cos and tan are all positive.

In the second quadrant going anti-clockwise, only sine is positive.

In the third quadrant going anti-clockwise, only tangent is positive.

In the fourth quadrant going anti-clockwise, only cosine is positive.

We are told that the

sinθ < 0 and cos θ > 0.

This means that sine is negative and cosine is positive.

Looking at the rule, it is clear that the angle is in the fourth quadrant.

Read more about quadrant signs of trigonometric functions at;

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Why didn't the physics teacher marry the biology teacher

Answers

Answer: There wasn't chemistry in them?

XD I dunno ._.       >w<

John drove 737 miles in 11 hours At the same rate, how many miles would he drive in 5 hours?

Answers

Answer:

Step-by-step explanation: 737/ 11= 67

sooooo 67 x 5= 335

What is 3/5 1/2 because my answer is 7/10 and my teacher said it's wrong

Answers

Answer:

If you want to multiply then,

3/5 × 1/2 = 3/10 or 0.3

If you want to Add then,

3/5 + 1/2 = 6 + 5/5 × 2 = 11/10 or 1.1

If you want to subtract then,

3/5 – 1/2 = 6 – 5/5 × 2 = 1/10 or 0.1

If you want to Divide then,

3/5 ÷ 1/2 = 3/5 × 2/1 = 6/5

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