The equation x ^ 2 - 2x + y ^ 2 - 4y = 20 defines a circle in the xy-coordinate plane What is the radius of the circle?

Answers

Answer 1

Answer:

I'll set up the problem and you can do the calculation

Step-by-step explanation:

we need to complete the squares to get the equation in the general form:

[tex] {(x - h)}^{2} + {(y - k) }^{2} = {r}^{2} [/tex]

where h = the x coordinate of the center

k = the y coordinate of the center

r = the radius

so looking at

[tex] {x}^{2} - 2x[/tex]

we can see that if use -1 as the constant we have

[tex] {(x - 1)}^{2} = {x}^{2} - 2x + 1[/tex]

doing the same for y

[tex] {y}^{2} - 4y[/tex]

we can use -2 as the constant (basically you that the s

quare of the y coefficient )

[tex] {(y - 2)}^{2} = {y}^{2} - 4y + 4[/tex]

so now we have to add or subtract the constant on the RHS to see what the square of the radius is according to the general form of the equation at the top

20 +1+4=25

Take the square root and you have the radius


Related Questions

Help me please ASAP

Answers

ans is c it is simple c only meet the need of questions

A farmer uses 1/3 of an acre of land to grow carrots.

The carrots are grown in

There are 15 rows of carrots.

What part of land does each row of carrots take up?

Answers

Answer:

the answer is 1/45

Step-by-step explanation:

just use the proportion method

Perímetro de un círculo de 2.5

Answers

Answer:

La circunferencia del círculo es igual a Pi π veces el diámetro d. Dado que el diámetro d es igual a 2 veces el radio r, la fórmula para la circunferencia que usa el radio es 2πr 2 π r.

Step-by-step explanation:

Jillian and Nikki each filled their cars with gasoline. The graphs below show the amount of gas in each car and the miles driven since filling the tank.

A graph titled Jillian's Car has miles driven on the x-axis, and gallons of gas left on the y-axis. A line goes through (0, 22) and (100, 16). A graph titled Nikki's Car has miles driven on the x-axis and gallons of gas left on the y-axis. A line goes through points (0, 20) and (100, 16).

Which statement is supported by the graphs?

Answers

Answer:

it's AAAAAAAAAAAAAAAAAAA

Answer:

It's A <3

I took the test. ^^

whats 3x+34+23y=
frezz

Answers

Answer:

3x+34+23y, You can not add in this equation as there are no like numbers.

Step-by-step explanation:

Answer:

isnt it 60xy

Step-by-step explanation:

Hiiioo! Can someone please help me out! :)❤️

Answers

Answer:

-2/3

3/2

Step-by-step explanation:

slope is m in the equation y = m*x+b.

3y=-2x-3

y=-2/3x-1

parallel lines have the same slope, so slope of parallel lines is -2/3

perpendicular lines have negative the inverse

so -(-3/2)=3/2

3/2 is the correct answer to your question

Can someone please help I need the answer ASAP

Answers

do you have a clearer picture please? I can help :))

Solve for
20 = 5(x + 1)
X =

Answers

Answer:

x = 3

Step-by-step explanation:

5(x+1) = 20

x+1 = 20/5

or, x+1 = 4

or, x = 4-1

so, x = 3

your answer will be 3 so I’m that case x=3

Find the edge length

Answers

x^3= 125000 m^3

x=50 m

Based on your observations, what conclusion can you draw about the lengths of AB DB AE EC

Answers

Answer:

The ratio of AD to DB is equal to the ratio of AE to EC. In other words, the pairs of lengths are proportional.

Step-by-step explanation:

Sample answer from plato

How do I solve this please? Can SOMEONE please help me this and the ones Iposted on my page.

Answers

Answer: [tex]\dfrac{15}{64}[/tex]

Step-by-step explanation:

Given

Inside radius of figure [tex]r_1=\frac{14}{2}=7\ ft[/tex]

Outside radius of figure [tex]r_2=\frac{16}{2}=8\ ft[/tex]

Area of outside region is [tex]A_1=\pi (8^2)[/tex]

Area of inside region [tex]A_2=\pi (7)^2[/tex]

Area of shaded region [tex]A_1-A_2[/tex]

Probability that point lies inside the shaded region is

[tex]\Rightarrow P=\dfrac{A_1-A_2}{A_1}\\\\\Rightarrow P=\dfrac{\pi (8^2-7^2)}{\pi 8^2}\\\\\Rightarrow P=\dfrac{64-49}{64}\\\\\Rightarrow P=\dfrac{15}{64}[/tex]

Khairul deposited $ 600 in a bank at the end of 2010 and another $ 400 in the same bank at the end of 2011. The bank offers simple interest at a rate of 3% per annum. Find the total amount he has in his bank at the end of 2013.

the answer is 1078 .
(But how ) ​

Answers

Answer:

bat puro math pede history lng

What is the value of [tex]\frac{81^4}{3^5}[/tex]? (Express your answer in exponential form.)

Answers

Answer:[tex]3^1^1\\[/tex]

Step-by-step explanation:

[tex]\frac{81^4}{3^5}[/tex]

[tex]\frac{3^1^6}{3^5}[/tex]

The base is same power can be add or subtract

[tex]3^1^6^-^5[/tex]

[tex]3^1^1[/tex]

Plz help ASAP I got 10 mins !!!!!

Answers

Answer:

x=5

Step-by-step explanation:

Since the triangles are similar we can use ratios to solve

4.5     7.5

---- = ------

3            x

Using cross products

4.5x = 3 * 7.5

4.5x = 22.5

Divide each side by 4.5

x = 22.5/4.5

x=5

2. Based on the cash flows shown in the chart below, compute the IRR and MIRR for Project Erie. Suppose that the appropriate cost of capital is 12 percent. Advise the organization about whether it should accept or reject the project.

Project Erie

Time 0 1 2 3 4 5

Cash Flow $12,000 $2,360 $4,390 $1,520 $980 $1,250


Answers

Answer:

IRR = -5.19%

MIRR =  3.33%

The company should reject the project

Step-by-step explanation:

Internal rate of return is the discount rate that equates the after-tax cash flows from an investment to the amount invested

IRR can be calculated with a financial calculator

Cash flow in year 0 = -$12,000

Cash flow in year 1 = $2,360

Cash flow in year 2 =  $4,390

Cash flow in year 3 = $1,520

Cash flow in year 4 = $980

Cash flow in year 5 = $1,250

IRR = 5.19%

The modified internal rate of return is a capital budgeting method used to determine the profitability of an investment. The MIRR assumes that cash inflows are reinvested at the firm's cost of capital and outflows are financed at the firm's financing cost.

MIRR = (Future value of a firm's cash inflow / present value of the firm's cash outflow)^ (1/n)  - 1

n = number of years

present value of the firm's cash outflow = $12,000

Future value of a firm's cash inflow

Future value of year 1's cash flow = $2,360 x (1.12^4) = $3,713.51

Future value of year 2's cash flow =$4,390 x (1.12^3) = $6167.63

Future value of year 3's cash flow =$1,520  x (1.12^2) = $1906.69

Future value of year 4's cash flow = $980 X 1.12 = 1097.60

Future value of year 5's cash flow = 1250

Add the future values together = $14,135.43

($14,135.43 / $12,000)^0.2 - 1 = 3.33%

The project should be rejected because the IRR is negative.  

To find the IRR using a financial calculator:

1. Input the cash flow values by pressing the CF button. After inputting the value, press enter and the arrow facing a downward direction.

2. After inputting all the cash flows, press the IRR button and then press the compute button.  

Find the discriminant and the number of real roots for this equation. x^2 + 2x + 8 = 0
A. -28; no real roots B. 32; one real root C. 32; two real roots D.-28; one real roof​

Answers

Step-by-step explanation:

A is correct option there are no real roots

because discriminant is less than zero

The rectangle has length 4.5cm and width 2.8cm. Work out the area ​

Answers

Answer:

11/1//11/1

Step-by-step explanation:

Area of rectangle= l x b
= 4.5 x 2.8
= 12.6 cm^2

which TWO numbers round to 3 as the nearest whole number?

A. 2.226

B. 2.562

C. 2.332

D. 2.351

E. 1.975

F. 2.864​

, please

Answers

B and F , wish you the best enjoy!

Please answer i will give brainliest

Answers

Answer:

sorry bro......sis

Step-by-step explanation:

don,t know its answer

Radian=degree/57.3 = 26/57.3 = 0.45 rad

Degree= radian x 57.3 = 5π/9 x 57.3 = 100.007 degree

I hope that helps and wish you the best !!


What is the exact area of shaded region of the circle? Show all work.

Answers

Answer:

[tex]A=\frac{513\pi}{8}[/tex]

Step-by-step explanation:

1.Approach

To solve this problem, find the total area of the circle. Then multiply the total area by the fraction of the circle that is shaded.

2.Find the area of the circle

The formula to find the area of a circle is the following,

[tex]A=(\pi)(r^2)[/tex]

Where ([tex]r[/tex]) represents the radius of the circle, that is the distance from the center of the circle to the circumference of the circle (the outer edge). ([tex]\pi[/tex]) represents the numerical value (3.1415..).

Substitute the given values into the formula and solve for the area.

[tex]A=(\pi)(r^2)\\\\A=(\pi)(9^2)\\\\A=(\pi)(81)[/tex]

3.Find the percent of the circle that is shaded

There are a total of (360) degrees in a circle. It is given that (75) degrees are not shaded. To find the fraction of a circle that is shaded, subtract (75) form (360). Then put this value over (360) and simplify.

[tex]360 - 75 = 285[/tex]

Now put this number over (360) to find the fraction of the circle that is shaded.

[tex]\frac{285}{360}[/tex]

[tex]=\frac{19}{24}[/tex]

4.Find the area of the shaded region

Now multiply the total area by the fraction that the shaded region occupies.

[tex](81)(\pi)*(\frac{19}{24})\\\\=\frac{(81)(19)(\pi)}{24}\\\\=\frac{513(\pi)}{8}[/tex]

I'll give brainliest to the best answer if you help me with the image down below!

Includes: an explanation please

Answers

Answer:

3 Pounds

Step-by-step explanation:

2.82 rounded to the nearest whole number is 3.

If we wanted to round 2.82 to 2, it would have to be 2.49 or less

The area of a rectangle is given as x^2+ 5x+6. Which expression represents either the
length or width of the rectangle?
a) (x-3)
b) (x + 6)
c) (x + 1)
d) (x+3)

Answers

Answer:

d) x + 3

Step-by-step explanation:

= x² + 5x + 6

Factorise :-

= x² + 2x + 3x + 6

= x(x + 2) + 3(x + 2)

= (x + 2)(x + 3) [Taking common]

Here we are getting (x + 3) as a factor of x² + 5x + 6 which will be either length or the width


At Appliance Market, a salesperson sells a dishwasher for $569. She gets a commission rate of 18 percent. Which
expression represents how much she will receive in commission from the sale?

Answers


At Appliance Market, a salesperson sells a dishwasher for $569. She gets a commission rate of 18 percent. 569 (0.18) represents how much she will receive in commission from the sale.

Michelle invested $10,000 for one year, part at 8% interest and the rest at 12% annual interest. Her total interest for the year was $944. How much money did she invest at 12% interest?

Step by step please.

Answers

Answer:

Michelle invested $ 6,400 at 8% and $ 3,600 at 12%.

Step-by-step explanation:

Given that Michelle invested $ 10,000 for one year, part at 8% interest and the rest at 12% annual interest, and her total interest for the year was $ 944, to determine how much money did she invest at 12% interest, the following calculation must be done:

10,000 x 0.08 + 0 x 0.12 = 800

8,000 x 0.08 + 2,000 x 0.12 = 880

4,500 x 0.08 + 5,500 x 0.12 = 1,020

6,000 x 0.08 + 4,000 x 0.12 = 960

6,500 x 0.08 + 3,500 x 0.12 = 940

6,400 x 0.08 + 3,600 x 0.12 = 944

Therefore, Michelle invested $ 6,400 at 8% and $ 3,600 at 12%.

What is the area? Bit confused on this one.

Answers

Answer:

A = 9x² + 12x

Step-by-step explanation:

The area (A) of the rectangle is calculated as

A = height × width

  = 3(3x² + 4x) ← distribute parenthesis by 3

   = 9x² + 12x

Answer:

For the blue one:

A1=length*breadth

   =3*3x^2

   =9x^2

For pink:

A2=length*breadth

    =3*4x

    =12x

So the total area is:

A=A1+A2

  =9x^2+12x

Last year, samantha spent $2,478 for natural gas. This year, she decided to use balance billing. What will her monthly payment be this year?

Answers

Answer:

She will need to pay $206.50 per month.

Step-by-step explanation:

Divide the total cost ($2,478) by the number of months (12 mos) to obtain Sam's monthly payment:

 $2,478

---------------- = $206.50/month

12 months

She will need to pay $206.50 per month.

small question will mark brainly “A cube has edges all of 6cm. A cuboid with the same volume has a side of 4cm and a side of 6cm. As one side is 2cm shorter than one of the sides of the cube, to keep the volume the same the other side must be made 2cm longer. how much is the total?? and please explain

Answers

Answer:

Volume of cube = 216

Dimesnions of cuboid = 4 * 6 * x

x = 216 / 24x

x = 9cm

Step-by-step explanation:

Hope this helps... pls vote as brainliest

in a class 3/5 of the pupils are boys. If there are 24 girls,how many boys are there in the class ?​

Answers

Answer:

36 boys

Step-by-step explanation:

let x be the number of pupils in the class , then

[tex]\frac{3}{5}[/tex] x + 24 = x ( multiply through by 5 to clear the fraction )

3x + 120 = 5x ( subtract 3x from both sides )

120 = 2x ( divide both sides by 2 )

60 = x

Then

number of boys = [tex]\frac{3}{5}[/tex] × 60 = 3 × 12 = 36

In a right angle triangle , the two shorter sides are 6cm and 8cm in length . What is the length of the longest side

Answers

Answer:

10 cm

Step-by-step explanation:

In a right triangle, there are three sides, A, B, and C.

A and B are the short sides, while C is the long side.

So we know that A = 6 cm, and B = 8 cm.

We can then use the Pythagorean theorem which states that

[tex]C=\sqrt{(A^2)+(B^2)[/tex]

Once we plug in the numbers we get

[tex]C=\sqrt{6^2+8^2}[/tex]

[tex]C=\sqrt{36+64}[/tex]

[tex]C=\sqrt{100}[/tex]

C=10 cm

I need help fast please!!!!

Answers

Answer:

f translates right 2 units to get g. sorry about my English

Other Questions
Find the sum of the first 5 terms of the following geometric series.512 - 256 + 128 +... Which statement best describes the meter Which function's graph has a period of 2?O A. y = cos -y = cos(x - 22O B. y = 2 sinaxO C. y = 3cosxO D. y = -4 sin 2x If a tree cast a 3.5 foot shadow at the same time is 6 foot tall women cast a shadow measuring 13.8 feet what would be the height of the tree the diagram below shows a triangular metal plate with sides 4.5cm,6cm and 7.5cm. it has three small circular holes of radius 4mm.calculate the area of the plate to the nearest square centimeters. Read the sentence from the passage.The suggestion that we might find a measure of solace in the very machines responsible for our battered minds will seemImplausible to some.What is the best meaning of the word solace as it is used in the passage?OA inspirationOB. Sympathy.encouragementOD. relief the right of man was a book written by thomas paine during whatA)the American revolution B)the French Revolution C) his time in French jail If 12 muffins cost $27, how much would 2 muffins cost? Use the calculator to evaluate each expression. Round your answers to the nearest hundredth.(GIVING BRAINLEST TO BEST ANSWER) Help Im stuck!!!! Solve the equation below for x. Enter your answer as a fraction in lowesterms, using the slash mark (/) as the fraction bar. 4/21 + 2/9X= The triangle below has a perimeter of 27\text{ cm}27 cm27, start text, space, c, m, end text.What is the length of one side of the triangle?All 333 sides are the same length. The author of a humorous story has purposely made some ideas and events seem less important than they really are. Which literary device is the writer using?paradoxironyhyperbole HELP WITH MY MATH PLEASEEE Discuss 2 issues that the Workers Rights faced WILL MARK YOU IF YOU HELP ME !!!! Which of the following is not a possible pollutant?a carbon dioxideb. pesticidesc.fertilizerd.all are possible pollutants Difference Quotient. Correct answer is shown. It says multiply by conjugate but I dont understand what that is and how they did it. TIA Yes, she had changed her mind after sixty years and she would like to see George. I want you to find George. Find him and be sure to tell him I forgot him. I want him to know I had my husband just the same and my children and my house like any other woman. A good house too and a good husband that I loved and fine children out of him. Better than I had hoped for even. Tell him I was given back everything he took away and more.Question:Which two themes does this passage most clearly develop?Choices:A. The past can give us hope; those who wait will be rewarded.B. The mind can play tricks on you; you must determine your own self-worth.C. One person's trash is another's treasure; seeking revenge leads to disaster.D. The past influences the present what has been lost can be regained. HELP ME PLSSS!The graph below have a same shape what is the equation of the red graph?A) g(x)=(3-x)2B) g(x)=3-x2C) g(x)=2-x2D) g(x)=(2-x)2 HELP ASAP PLS 10 points AND BRAINLEST