determine the equation of the circle graphed below .

( help please )

Determine The Equation Of The Circle Graphed Below .( Help Please )

Answers

Answer 1

Answer:

(x + 5)² + (y - 4)² = 17

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 is the radius

Here (h, k ) = (- 5, 4 ) , then

(x - (- 5) )² + (y - 4)² = r² , that is

(x + 5)² + (y - 4)² = r²

r is the distance from the centre to a point on the circle

Calculate r using the distance formula

r = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (- 5, 4) and (x₂, y₂ ) = (- 1, 5)

r = [tex]\sqrt{(-1+5)^2+(5-4)^2}[/tex]

  = [tex]\sqrt{4^2+1^2}[/tex]

  = [tex]\sqrt{16+1}[/tex]

  = [tex]\sqrt{17}[/tex] ⇒ r² = ([tex]\sqrt{17}[/tex] )² = 17

Then

(x + 5)² + (y - 4)² = 17 ← equation of circle

Answer 2

Answer:

x² + y² + 10x - 8y + 24 = 0

Step-by-step explanation:

equation of a circle :-

equation of a circle :-(x - h)² + (y - k)² = r²

(h, k) is the center of the circle R is the radius of the circle

for this circle :-

h = -5k = 4R = ?

finding radius of the circle

we've been given a point ( -1, 5) that lies on the circle and hence should satisfy the equation of the circle

putting x = -1 and y = 5

=> (-1 - (-5))² + (5 - 4)² = r²

=> (-1 + 5)² + 1² = r²

=> 4² + 1 = r²

=> 17 = r²

[tex] = > r = \sqrt{17} [/tex]

the radius if the circle is √17 units

__________________________________

finding the equation of the circle

=> (x + 5)² + (y - 4)² = (√17)²

=> x² + 25 + 10x + y² + 16 - 8y = 17

as for any two variables a and b, (a + b)² = a² + b² + 2ab

=> x² + y² + 10x - 8y + 24 = 0


Related Questions

Pls help I don’t get it

Answers

Answer:

h = 5/2

Step-by-step explanation:

[tex]\frac{3}{4} *\frac{1}{2} *h=\frac{15}{16} \\\\\frac{3}{8} *h=\frac{15}{16}[/tex]

divide both sides by 3/8

[tex]h=\frac{5}{2}[/tex]

24 : 56 is equivalent to 3 : __

Answers

Answer:

3 : 7

Step-by-step explanation:

24/56 = 3 / 7

Answer:

3:7 helpful answer to your question have a nice evening

Jomar decides that he needs to study for an average of 1 hour and 30 minutes
a day in order to prepare for his French test this Friday. He studies for 2 hours
each day on Saturday through Monday, but is too busy to study on Tuesday
and Wednesday. How long must Jomar study on Thursday to be prepared for
his test?

Answers

Answer:

Jomar needs to study for 3 hours on Thursday to be prepared for his test.

Step-by-step explanation:

If we want to make the average a certain amount of time over a certain number of days, we can first figure out the number of days and total amount needed. Here, we can see that the average is 1 hour and 30 minutes, and there are 6 days (Saturday-Thursday). Therefore, as

average = total / length, we can multiply both sides by length to get

average * length = total

Plugging 1.5 hours in for average and 6 days for length, we get

1.5 * 6 = 9 hours as the total amount needed to get an average of 1.5 hours a day

Our total so far is 2 hours for Saturday, 2 hours for Sunday, and 2 hours for Monday. This adds up to 6 hours, and we need 9. The difference between 9 and 6 is 3, meaning that Jomar needs to study for 3 hours on Thursday to be prepared for his test.

In AHIJ, the measure of ZJ=90°, the measure of ZH=57°, and IJ = 22 feet. Find the
length of HI to the nearest tenth of a foot.
X
22
57°
H

Answers

Answer:

26.2

Step-by-step explanation:

From the given diagram;

Opposite side IJ = 22

Hypotenuse HI = x

Angle of elevation = 57degrees

Using the SOH CAH TOA;

sin theta = opposite/hypotenuse

sin theta = IJ/HI

sin57 = 22/x

x = 22/sin57

x = 22/0.8387

x = 26.2

Hence the legnth of HI is 26.2

Noah wants to buy a skateboard that usually sells for $79.99. All merchandise is discounted by 12%. What is the total cost of the skateboard if Noah has to pay a state sales tax of 6.75%?

Answers

Answer:

$74.36 sorry all i got

Step-by-step explanation:

First, we need to determine the sales price of the skateboard. The formula for find the discounted prices is:

Where:

is the sales price of the item: what we are solving for in this part of the problem.

is the regular price of the item: $79.16 for this problem.

is the discount rate: 12% for this problem. "Percent" or "%" means "out of 100" or "per 100", Therefore 12% can be written as  

12

100

Substituting and calculating  

gives

79.16

79.16

12

100

79.16

949.92

100

79.16

9.4992

69.6608

69.66

rounded to the nearest cent.

Now we can find the total price of the item with tax included. The formula for this is

#t = p + (p * r)

Where, this time:

is the total price: what we are solving for in this problem.

is the price of the item: it is the sales price of the item for this problem which is $69.66

is the tax rate: 6.75% or, using the same rule as in the formula above:  

6.75

100

Substituting and calculating  

gives:

69.66

69.66

6.75

100

69.66

470.205

100

69.66

4.70205

74.36205

74.36

rounded to the nearest cent.

Noah would pay a total cost (with the discount and after tax) of $74.36

$74.36 should be the answer

Your gross pay is $1,878.96, net income is $1,196.34, and fixed expenses are $1,338.54. What is your discretionary income?

Answers

Answer:

$0

Step-by-step explanation:

This was wrong.. Why?

Answers

Answer:

I think it's 9/22

Step-by-step explanation:

Probability of A given B = (probability of A and B)/probability of B

[tex]\frac{(14/22)(9/22)}{14/22} \\=\frac{9}{22}[/tex]

P(B) = P(1 checked bag) = 14/22

P(A) = P(silver status) = 9/22

P(A ∩ B) = (14/22)(9/22)

solve for x and y in the system of equation
y=x²-4x
2x-y=2
I'll mark brainliest​

Answers

Step-by-step explanation:

[tex]y = {x}^{2} - 4x \\ y = x(x - 4) - - - (a) \\ 2x - y = 2 \\ y = 2x - 2 \\ y = 2(x - 2) - - - (b) \\ (a) = (b) : \\ x(x - 4) = 2(x - 2) \\ {x}^{2} - 4x = 2x - 2 \\ {x}^{2} - 6x + 2 = 0 \\ x = 5.6 \: \: and \: \: 0.4 \\ y = 2(5.6 - 2) \: \: and \: \: 2(0.4 - 2) \\ y = 7.2 \: \: and \: \: - 3.2[/tex]

3. Ruby and Sapphire love strawberries. Ruby starts out with 10 strawberries and finds 3 more
every minute. Sapphire starts out with 30 strawberries and eats 2 every minute. How long will it
take for them to have the same number of strawberries?

PLEASE HELP ME. AND SHOW YOUR WORK. PLEASE IM DYING.

Answers

Answer:

4 minutes

Step-by-step explanation:

Let the time taken for them to have the same number of strawberries be x minutes.

Initially

Ruby: 10 strawberries

Sapphire: 30 strawberries

After x minutes

Ruby: (10 +3x) strawberries

Sapphire: (30 -2x) strawberries

Since we let x minutes be the amount of time that has passed when they have the same amount of strawberries,

10 +3x= 30 -2x

Bring all x terms to one side, constant to the other:

3x +2x= 30 -10

Simplify:

5x= 20

Divide both sides by 5:

x= 20 ÷5

x= 4

∴ It will take 4 minutes.

An author published a book which was being sold online. The first month the author sold 14400 books, but the sales were declining steadily at 5% each month. If this trend continues, how many total books would the author have sold over the first 23 months, to the nearest whole number?

Answers

Answer:

The author sold a total of 30240 books following this trend.

Step-by-step explanation:

Let's find 5% of 14400 first;

14400 * 5%

14400 * 5/100

144 * 5

720 (So now we know that they are decreasing by 720 each month; therefore thats the constant)

=> aₙ = a₁ + r(n - 1)

=> a₂₃ = 14400 + 720(23 - 1)

=> a₂₃ = 14400 + 720(22)

=> a₂₃ = 14400 + 15840

=> a₂₃ = 30240

Hope this helps!

The author sold a total of 30240 books following this trend.

Let's find 5% of 14400 first;

[tex]14400 * 5\%\\14400 * 5/100\\144 * 5=720[/tex]

What is an arithmetic progression?

A, is a type of numerical sequence studied by Mathematics, where each term or element counting from the second is equal to the sum of the previous term with a constant.

So using the arithmetic progression we have:

[tex]a_n = a_1 + r(n - 1)\\a_{23} = 14400 + 720(23 - 1)\\ a_{23} = 14400 + 720(22)\\ a_{23} = 14400 + 15840\\a_{23} = 30240[/tex]

See more about arithmetic progression at brainly.com/question/20385181

How will she know if 5(3x – 6) is equivalent to 15x – 30?

Answers

Answer:

By distributing the parenthesis

Step-by-step explanation:

Given

5(3x - 6) ← multiply each term in the parenthesis by 5

= 15x - 30 ← as required

32% of a number is 64 what is the number

Answers

Answer:

If you take 32 percent of a number and get 64, then what is that number? In other words, you know that 32 percent of a number is 64 and you want to know what that initial number is. Therefore, the answer to "64 is 32 percent of what number?" is 200, and you can also derive that 32 percent of 200 equals 64.

Step-by-step explanation:

200

Step-by-step explanation:

32% x = 64

(32/100)x= 64

0.32x=64

x=64÷0.32

x=200

Math help please urgent

Answers

Answer:

area of circle is 2πr²

= 2 x 3.14 x 8 x 8

= 402 cm

In a class, 60% of the students are girls. There are 18 girls in the class.

a. How many students are in the class?

b.How many boys are in the class?

Answers

Answer:

a. Total of 45 students.

b. 18 Boys.

Answer:

There are 45 students and 18 boys in the class

Aidan is saving money to buy a new computer. He made a scatter plot and a linear model for the amount of money he has saved over the past eight weeks. The equation of the line is y = 17.63x + 27.52 . Use the model to predict how much aidan saved over five weeks

Answers

Answer:

Aidan saved 115.67 over five weeks.

Step-by-step explanation:

After x weeks:

The amount of money saved by Aidan is given by:

[tex]y(x) = 17.63x + 27.52[/tex]

How much aidan saved over five weeks?

This is y when x = 5. So

[tex]y(x) = 17.63x + 27.52[/tex]

[tex]y(5) = 17.63*5 + 27.52 = 115.67[/tex]

Aidan saved 115.67 over five weeks.

Can someone help me with this question please

Answers

Answer:

A. Conditional Statement

Step-by-step explanation:

In a conditional statement, A would be the premise, and B would be the conclusion.

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Have a great summer :)

The evolutionary pathways of ten different species are represented in the diagram below. SA Which two species are the most closely related?

E and I
G and J
A and F
O and D​

Answers

Answer:

I don't see an O in the picture at all.

but here's how you solve it: just count the nodes between the species, the fewer the closer

I would go for E and I, only one step between them

The ratio of coloured papers to wight papers is 3:8.If there are 48 wight papers, how many coloured papers are there?

Answers

Answer:  The total number of colored papers is 18.

Step-by-step explanation:

Given: The ratio of coloured papers to wight papers is 3:8.

Let total number of colored papers = 3x

and total number of wight papers = 8x

Since, there are 48 wight papers , then

[tex]8x=48[/tex]

[tex]\Rightarrow\ x=6[/tex]

Now , number of colored papers = 3(6)=18

Hence, the total number of colored papers is 18.

can you please find the range of these numbers? 18, 16, 19, 15, 17. I will give 16 points​

Answers

Answer: Hi the Range is 4

Step-by-step explanation: The range of a data set in statistics is the difference between the largest and the smallest values. While range does have different meanings within different areas of statistics and mathematics, this is its most basic definition, and is what is used by the provided calculator. Using the same example:

18, 16, 19, 15, 17

19,18,17,16,15

19-15= 4

find the equation of a line that passes through (3 1) and ia parallel to y=1-2x leave your answer in the form of y=mx+c

Answers

Answer:

y = -2x+7

Step-by-step explanation:

Parallel lines have the same slope

y = 1-2x has a slope of -2

So the new line has a slope of -2

We have a slope of -2 and a point of (3,1)

y = mx+c

1 = -2(3)+c

1 = -6+c

Add 6 to each side

1+6 =c

7 =c

y = -2x+7

Luis wants to change companies for his phone service. Company SaveMore charges $16 for the initial service plus $0.20 for every 1 text of use.Write an equation that represents the cost of the service, with the cost of the constant number of text, t added After how many texts will the two companies be the same charge for the service?

Answers

Answer:

[tex]y = 16 + 0.2t[/tex] --- the equation of SaveMore company

Step-by-step explanation:

Given

SaveMore

[tex]Initial = 16[/tex]

[tex]Additional\ Rate = 0.20[/tex]

Required

Determine the equation

Let

[tex]y \to cost[/tex]

[tex]t \to texts[/tex]

So, we have:

[tex]y = Initial + Additional\ Rate * t[/tex]

[tex]y = 16 + 0.20 * t[/tex]

[tex]y = 16 + 0.2t[/tex]

The equation for the second company is not given. So, the (b) part cannot be correctly answered.

A general solution to the (b) part is:

Assume the equation is:

[tex]y = 10 + 0.4t[/tex]

Next, we equate both

i.e.

[tex]y = y[/tex]

This gives:

[tex]16 + 0.2t = 10 + 0.4t[/tex]

Collect like terms

[tex]0.4t - 0.2t = 16 - 10[/tex]

[tex]0.2t = 6[/tex]

Divide by 0.2

[tex]t = 30[/tex]

Hence, the charges will be the same after 30 texts

Given m||n, find the value of x.

(7x-4)
(3x+28)º

Answers

Answer:

8

Step-by-step explanation:

7 x 8 = 56 56 - 4 = 52.

3 x 8 = 24 24 + 28 = 52

The 12 pair pack of socks includes 4 pairs of Polo, 5 pairs of plain white socks, and a few grey pairs. What is the Possibility of pulling a pair of grey sock two times in a row? The first pair is not to be returned.

Answers

Answer:

2/11

Step-by-step explanation:

12-4-5=3

So now we know that we have:

4 pairs of polo socks

5 pairs of plain white socks

3 pairs of grey socks

To pull a grey sock one time is 3/12 since there are 12 total socks and 3 pairs of grey socks but since we remove a sock, in the second time, the probability would be 2/11.

Hope this helps! Brainliest?

*Brainliest* What is the value of X?

or how do I solve this equation?

Answers

Answer:

x = 6

Step-by-step explanation:

The sum of the angles of a quadrilateral is 360

69+111+12x-3 +111 = 360

Combine like terms

12x+288=360

Subtract 288 from each side

12x+288-288 = 360-288

12x = 72

Divide by 12

12x/12 = 72/12

x = 6

Answer:

x = 6

Step-by-step explanation:

All angles together equal 360

Us this to set up your formula

360 = 111 + 111 + 69 + 12x-3

360 = 288 + 12 x

360 - 288 = 12x

72 = 12x

72/12 = x

6 = x

You could also use the fact that angle t and r are equal to set your formula up as

69 = 12x-3

69+3=12x

72=12x

72/12=x

6=x

Find the perimeter of the window to the nearest hundredth perimeter: about ft

Answers

Answer:

I would answer but I have no numbers to give the answer

What is the polar form of Negative 9 StartRoot 3 EndRoot + 9 i?

Answers

Answer:

Step-by-step explanation:

In the rectangular complex number -9√3 + 9i, which has a standard form a + bi, the a = -9√3 and the b = 9. We need this in polar form (r, θ) where

[tex]r=\sqrt{a^2+b^2}[/tex] and filling in:

[tex]r=\sqrt{(-9\sqrt{3})^2+(9)^2 }[/tex] (notice we do not put the i in there with the 9).

[tex]r=\sqrt{243+81}[/tex] so

r = 18. Now let's move on to the angle, which is a little more difficult. The angle is found in the inverse tangent ratio:

[tex]tan^{-1}(\frac{b}{a})[/tex] so filling that in, we have:

[tex]tan^{-1}(\frac{9}{-9\sqrt{3} })=\frac{1}{-\sqrt{3} }[/tex] Since tangent is the side opposite over the side adjacent, y is positive and x is negative in the second quadrant. This is a 30 degree angle in QII, which has a reference angle of 150 degrees. This angle in radians is [tex]\frac{5\pi}6}[/tex], so the polar form of that number is (18, [tex]\frac{5\pi}{6}[/tex])

Answer:

its d

Step-by-step explanation:

i guessed lol

Pls help me with this i don’t really get it pls

Answers

Answer:

a y intercept (0,8)

Flat rate 8

b  slope is 4

c  3.5 hours

Step-by-step explanation:

The y intercept is where it crosses the y axis, which is (0,8)

The flat rate is the y intercept which is 8

The rate per hour is the slope

m = ( y2-y1)/(x2 -x1)

Using 2 point ( 1,12) and ( 2,16)

    = (16 -12)/(2-1)

     = 4/1

    = 4

The equation is

y = mx+b

y = 4x+8

Let y = 22

22 = 4x+8

Subtract 8 from each side

22-8 = 4x+8-8

14 = 4x

Divide by 4

14/4 = 4x/4

3.5 = x

3.5 hours

Problem and answer:

a) what is the y intercept?

(0,8) is the y intercept because it crosses the y axis.

What is the flat rate?

We can see that the flat rate is 8, which is the y intercept.

b) Find the slope and write an equation for the line.

[tex] \quad\quad\quad\boxed{ \tt{m = \frac{rise}{run} = \frac{ y \tiny{2} \: \small{ - } \: y \tiny{1}}{x \tiny{2} \: \small{ - } \: x \tiny{1}} }}[/tex]

We will use the first 2 points in the graph which is (1,12) and (2,16).

[tex]\quad\quad\quad\boxed{ \tt{m = \frac{16 - 12}{2 - 1} }}[/tex]

[tex]\quad\quad\quad\boxed{ \tt{m = \frac{4}{1} }}[/tex]

[tex] \quad\quad\quad\boxed{ \color{green}\tt{m = 4}}[/tex]

The equation is:

[tex] \quad \quad \quad \boxed{ \tt{y = mx + b}}[/tex]

c) Jack has $22 for how many hours can he rent an e-bike?

Let's use the equation as formula:

[tex] \quad \quad \quad \boxed{ \tt{y = mx + b}}[/tex]

Let's y = 22, mx = 4 and b = 8.

[tex] \quad \quad \quad \boxed{ \tt{22 =4x + 8}}[/tex]

Let's subtract 8 from each side.

[tex] \quad \quad \quad \boxed{ \tt{22 - 8 = 4x + 8 - 8}}[/tex]

[tex] \quad \quad \quad \boxed{ \tt{14 = 4x \: \:\cancel{ \color{red}+ 8 - 8}}}[/tex]

Let's devide it by 4 to cancel out the number 4.

[tex]\quad \quad \quad \boxed{ \tt{ \frac{14 = \cancel4x}{ \cancel{4} }}}[/tex]

[tex]\quad \quad \quad \boxed{ \color{green} \tt{3.5 = x}}[/tex]

Hence the answer for this is 3.5 hours or 3h50m. It is approximately 4 hours.

_________

#LetsStudy

#HikariSquad

What is the first step in solving the equation 4.2y-5.2=18.5

Answers

Add 5.2 then divide

Jennifer can clean the house by herself in 3 hours. Her little brother Andy helps her clean and it takes them 2
hours working together. How long would it have taken Andy to clean the house if he had worked alone?
a. hours
b. 3 hours
c. 6 hours
d. 1 hour

Answers

Answer:

c

Step-by-step explanation:

If he could clean the house alone in one hour, then it wouldve taken him and his sister less than that. if he could clean it in 3 hours, it wouldve tkane him and his sister 1.5 hours.

Answer:

Step-by-step explanation:

c. 6 hours

Can someone help me with this, Thx!

Answers

Answer:

x = 45

Step-by-step explanation:

x = 20 + 25

as x is vertically opposite to GED

and vertically opposite angles are equal

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