Find the center and radius of 2x^2 + 2y^2 - 12x + 8y - 24 = 0

Answers

Answer 1

When the equation of the circle is [tex]2x^{2} +2y^{2}-12x+8y-24=0[/tex], then the center of the circle is (3,-2) and the radius of the circle is 6.08 units.

The equation of the circle = [tex]2x^{2} +2y^{2}-12x+8y-24=0[/tex]

The general equation of the circle is [tex]x^{2} +y^{2}+2gx+2fy+c=0[/tex]

Where (-g,-f) is the coordinates of the circle

The equation of the circle = [tex]2x^{2} +2y^{2}-12x+8y-24=0[/tex]

Divide the equation by 2

[tex]x^{2} +y^{2}-6x+4y-12=0[/tex]

Compare the equation with general form

2g= -6

g= -3

2f= 4

f= 2

The center of the circle (-g,-f) = (3,-2)

The radius of the circle = [tex]\sqrt{g^{2}+f^{2}-c }[/tex]

Substitute the values in the equation

r= [tex]\sqrt{(-3)^{2}+2^{2}- (-24) }[/tex]

[tex]=\sqrt{9+4+24} \\=\sqrt{37}[/tex]

=6.08 units

Hence, when the equation of the circle is [tex]2x^{2} +2y^{2}-12x+8y-24=0[/tex], then the center of the circle is (3,-2) and the radius of the circle is 6.08 units.

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Related Questions

in the eight-term sequence $a$, $b$, $c$, $d$, $e$, $f$, $g$, $h$, the value of $c$ is 5 and the sum of any three consecutive terms is 30. what is $a h$?

Answers

The value of A + H is 25 for the given sequence.

What is a series?

A sequence's series is the total number of terms in the sequence.

A series follows some pattern for example if you take data set of natural numbers then there will be a sequence of that data and something will be due to that we can form that series.

Given that sum of any three consecutive terms is 30

Since c = 5

So a + b + c = 30

a + b = 25

⇒ (a+b)+(c+d+e)+(f+g+h)

⇒ 25 + 30 + 30 = 85

Now,

a+b+c+d+e+f+g+h = 85

a + h +(b+c+d)+(e+f+g) = 85

a + h + 30 + 30 = 85

a + h = 25

Hence "The value of A + H is 25 for the given sequence".

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need help !! Please somebody help

Answers

Answer:

The bottom Option

Note:

Due to my sus vibes from your questions, this is the last one I am answering from you. this is basic and easy if you read it.

5. The box plot represents the distribution of the number of points scored by a cross country team at 12 meets.

Answers

Answer:5 teams

Step-by-step explanation:

a clydes dale drinks about 120 gallons of every 4 days at this rate how many gallons of water does a clydsdale drink in 28 days

Answers

The gallons of water that a clydsdale drink in 28 days will be 840 gallons.

How to calculate the gallons?

It should be noted that Clyde's dale drinks about 120 gallons of every 4 days. Therefore, the gallons Frank in a day will be:

= 120 / 4

= 30 gallons

Therefore, the gallons drank for 28 days will be:

= 30 × 28

= 840 gallons.

Therefore, the gallons of water that a clydsdale drink in 28 days will be 840 gallons.

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help with this question please! with show work

Answers

Hi
Check out the attached photo
Let me know in the comments if something isn’t understandable

Charlie, Beth, and Miguel all babysit kids in their neighborhood. The table shows the number of hours and amount each of them earn last night. If each person babysits for five hours next weekend, which person will earn the most money? Use a coordinate plane if needed to solve.

Answers

Answer:

Step-by-step explanation: well first their is int a chart but bye reading the question i think is is Beth.

i hope this helped.

PLEASE PLEASE PLEASE ANSWER !!!

What is the equation of the given line?

x = 0

y = -2

x = -2

y = -1

Answers

Answer:

y = -1

Step-by-step explanation:

→ First determine which axis the line passes through

y

→ Find which point the line passes through

-1

→ Equate both variables

y = -1

If 21% of a number is 3, find 7% of that number.​

Answers

Answer:

7% of the number is 1.

Step-by-step explanation:

21%=3

Divide both sides by 3

7%=1

Answer:

1

Step-by-step explanation:

let x be the number.so.......

if 21%of a number means 21÷100*the number(x)=3

21÷100×X=3 so when we solve this first we have to criss-cross and then 21*X=3*100

then we both divide by 21 in order to get x .so x is going to be 100 divided by 7

then.......

we are asked to get how much percent of 100÷7 is 7% so...let the answer be y

7÷100*X=y

7÷100*100*7 =Y

when calculated the answer will possibly be 1 :)))

large pies cost $5, and small pies cost $2. if 45 pies were sold for $120, how many small pies were sold ?

Answers

Answer:

35 small pies

Step-by-step explanation:

Framing system of linear equations and solving:

  Let the number of large pies be 'l' and

        The number of small pies be 's'.

Total pies sold = 45

⇒  l + s  = 45  ------------(I)

         l = 45 - s  -------(II)

Cost of 45 pies = $120

         Cost of 1 large pie = $5

         Cost of 'l' large pies = 5*l = 5l

    Cost of 1 small pie = $2

   Cost of 's' small pie = 2*s = 2s

         5l + 2s  = 120 --------------(III)

Solving : substitution method

Substitute l = 45 -s in equation (III)

         5*(45 - s) + 2s = 120

       5*45 - 5*s + 2s = 120

        225 - 5s + 2s  = 120   {Combine like terms}

               225 - 3s   = 120

                      -3s     = 120 - 225    {Subtract 225 from both sides}

                           -3s = -105

                              s = -105 ÷ (-3)    {Divide both sides by (-3)}

                             s = 35

Substitute s = 35 in equation (II),

     l = 45 - s

       = 45 - 35

    l = 10

            [tex]\sf \boxed{\text{\bf 35 small pies were sold}}[/tex]

4 ÷ 2/5
Help (( 15 points ))

Answers

[tex]4 \div \frac{2}{5} [/tex]

[tex]4 \times \frac{5}{2} [/tex]

[tex]2 \times 5[/tex]

[tex]10[/tex]

Answer:10

Step-by-step explanation:

first step 4× 5/2
second step 4x5
                       2

third step is to simplify 20/2 which is
10

A hippopotamus can run 6 kilometers in 15 minutes. At this rate, how far can the hippopotamus run in 1 minute? __ kilometer(s) per minute

Answers

Answer:

15 minutes=1km

1 minute=?

(15m:m)×1km

minutes cancel minutes

15×1km=15km

Ginny Brown hoped her crops would get 3 3/4 inches of rain this month. The newspaper said the area received 3.8 inches of rain. Was that more or less than Ginny hoped for? By how much?

Answers

Answer:

More, by 0.05 or [tex]\frac{1}{20}[/tex] inches more.

Explanation:

Find out if the amount of rain was more or less by subtracting the desired outcome from the real outcome. If the answer comes out as positive then the amount of rain was more and if the answer is negative, it was less.

Workout:

[tex]\sf real \ outcome - desired \ outcome[/tex]

[tex]3.8 - 3\dfrac{3}{4}[/tex]

[tex]3.8 - 3.75[/tex]

[tex]0.05[/tex]

Hence, The rain was more than ginny expected by 0.05 inches more.

Using the diagram and the given angle measure to find the other three angle measures

Answers

Solution:

Based on the given.

If [tex]m∠2 = 59°[/tex]

Then, [tex]m∠4 = 59 °[/tex]

(reason: vertically opposite angles are equal)

If [tex]m∠4 = 59 °[/tex]

Then, [tex]m∠1⟹ 180 - 59 = 121 °[/tex]

(reason: angles on a straight line = 180°)

If [tex]m∠1 = 121°[/tex]

Then, [tex]m∠3 = 121°[/tex]

(reason: vertically opposite angles are equal)

Therefore:

[tex]m∠1 = 121°[/tex]

[tex]m∠3 = 121°[/tex]

[tex]m∠4 = 59 °[/tex]

See attached image for the placement of the values.

ASAP!!! PLEASE HELPPP!!Write an equation for the following sentence, then solve for the unknown value.
3 times the difference of a number and 8 is less than 15.

Answers

Answer:
3(x - 8) < 15

Step-by-step explanation:

3(x - 8) < 15

3x - 24 < 15

3x < 39

x < 13

for exercises 17 and 18, find the acute angle between the given lines by using vectors parallel to the lines. y

Answers

Your question was incomplete. Please refer the content below:

For Exercises 17 And 18, Find The Acute Angle Between The Given Lines By Using Vectors Parallel To The Lines.

y = x , y = 2 x + 3

The acute angle between the lines y = x and y = 2 x + 3 is 18.4349°.

We are given the lines:

y = x

y = 2 x + 3

The formula for finding the angles between two vectors is given by:

cos θ = u · v / | u | | v|

We know that (0,0) and (1, 1) lies on the line y = x.

Now, vector u for the line y = x will be:

u = (1,1) - (0,0) = {1, 1}

(0,3 ) and (1, 5) lies on the line y = 2 x + 3

Similarly, vector v will be equal to:

v = (1, 5) - (0, 3) = {1, 2}

cos θ = {1, 1} · {1, 2} / √1 + 1 √1 + 4

cos θ = 1 + 2 / √10

cos θ = 3 / √10

θ = cos⁻¹ ( 3 / √10)

θ = 18.4349°

Therefore, the acute angle between the lines y = x and y = 2 x + 3 is 18.4349°.

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the area of a certain state is 840000 square miles. what is this area in scientific notation?
1. 8.4x10.-4
2. 84x10.-3
3. 84x10.3
4. 8.4x10.5
please help

Answers

Answer:

4. 8.4×10^5

Step-by-step explanation:

The exponent of ×10 is the amount of places that you move the decimal. When the exponent is negative, you move the decimal to the left and when it is positive, you move it to the right. Number 1 and 2 are wrong right away because they move the decimal to the left which is not what we want. Number 3 is wrong because there are not enough 0's when we move the decimal. So, option 4 is correct. I hope this helps!

Ted is a freshman attending a 4-year college. He has been approved for an $8.000 subsidized federal loan at 4.29% for 10 years. How much will the U.S. Department of
Education subsidize in interest costs during his 4.5-year non-payment period?

Answers

Answer:

12.17634

Step-by-step explanation:

Answer: $1,544.40

Step-by-step explanation: It just is

Members of a softball team raised $1943.50 to go to a tournament. they rented a bus for $1148.50 and budgeted $53 per player for meals. write and solve an equation which can be used to determine x, the number of players the team can bring to the tournament.

Answers

The number of players the team can bring to the tournament are 15

Firstly we need to form the equation. The components of equation based on given information are as follows -

Total amount raised by softball team = Cost of bus + Cost of meal × number of players

Let the number of players be represented with x.

1943.50 = 1148.50 + 53×x

Rewriting the equation

53x = 1943.50 - 1148.50

Performing subtraction to Right Hand Side of the equation

53x = 795

Shifting 75 to Right Hand Side of the equation

x = 795 ÷ 53

Performing division at Right Hand Side of the equation

x = 15

Hence, 15 players the team can bring to the tournament.

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let v = (2, 3, 1), w = (1, 1, 1), and 3u + 2v 4w = (1, 2, 3). find (a) the vector u (b) the linear combination: 2u 3v + 5w

Answers

The vector u is  [tex]\frac{-7}{3} i -\frac{8}{3}j -k[/tex].

The linear combination 2u + 3v + 5w  is 19/3 i + 17/3 j + 6k.

According to the given question.

v = (2, 3, 1)

w = (1, 1, 1)

And

3u + 2v + 4w = (1, 2, 3)

From,

v = (2, 3, 1)

⇒ v = 2i + 3j + 1k

w = (1, 1, 1)

⇒ w = i + j + j

a). Let vector u be xi + yj + zk

Here,

3u + 2v + 4w = (1, 2, 3)

⇒ 3u + 2v + 4w = i + 2j + 3k

⇒ 3(xi + yj + zk) + 2(2i + 3j + k) + 4(i + j +k) = i + 2j + 3k

⇒ 3xi + 3yj + 3zk + 4i + 6j + 2k + 4i + 4j + 4k = i + 2j + 3k

⇒3xi + 3yj + 3zk + 8i + 10j + 6k = i + 2j + 3k

⇒ 3xi + 3yj + 3zk  = i + 2j + 3k - 8i -10j -6k

⇒ 3xi + 3yj + 3zk = -7i -8j -3k

⇒ xi + yj + zk = (1/3)(-7i -8j-3k)

⇒ xi + yj + zk = [tex]\frac{-7}{3} i -\frac{8}{3}j -k[/tex]

b). The linear combination

2u + 3v + 5w

= 2(-7/3i -8/3j - k ) + 3(2i + 3j + k) + 5(i + j + k)

= -14/3 i -16/3j -2k + 6i + 6j + 3k + 5i + 5j + 5k

= -14/3 i -16/3j -2k  + 11i + 11j + 8k

= 19/3 i + 17/3 j + 6k

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I don’t really understand how to get this one :/

Answers

in function notation, we get that the transformed function is:

g(x) = -2*f(x - 10) + 800

How to identify the transformation?

Here the parent function is:

f(x) = x^2

And the transformed function is the one graphed in the lower right side of the given image.

Notice that the y-intercept of the transformed function is y = 600.

The x-intercepts are x = -10 and x = 30

Then the polynomial is something like:

y = a*(x + 10)*(x - 30)

Using the fact that the y-intercept is y = 600, then:

600 = a*(0 + 10)*(0 - 30) = a*-300

600/-300 = a = -2

The transformed function is:

g(x) = -2*(x + 10)*(x - 30)

Expanding that:

g(x) = -2( x^2 + 10x - 30x - 300)

Completing squares we get:

g(x) = -2*(  x^2 - 20x - 300)

      = -2*(x^2 - 2*10*x - 300)

Now we can add and subtract 100, so we get:

-2*(x^2 - 2*10*x - 300 + 100 - 100)

-2*(  (x - 10)^2 - 400)

Finally, expanding that:

g(x) = -2*(x - 10)^2 + 800

Writing it in function notation, we get that the transformed function is:

g(x) = -2*f(x - 10) + 800

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Sebastian started watching a movie at 17:30 (5:30 pm).
The movie was 1 hour and 54 minutes but partway through he paused it for 15 minutes.

What was the time when he finished the movie?
Give your answer using the 24 hour clock.

Answers

The answer is 7:39 or 19:39.

7/4 to 4 is the same as x to 32

Answers

Answer:

14

Step-by-step explanation:

7/4:4 = x:32

x = 32(7/4) / 4 = 14

An item costs $480 before tax, and the sales tax is $14.40.
Find the sales tax rate. Write your answer as a percentage.

Answers

sales % =14.40*100/480
sales =3% ans

Is this answer correct?

Answers

Answer:

yes this is correct

Step-by-step explanation:

this is correct because angle gqh is adjacent to mqk, meaning they are the same degree which would mean kqg and hqm are adjacent

I need help with this question!

Answers

the angle measures less than 90°, thus, the correct classification is acute.

Which is the correct classification for the angle ∠JML?

First, let's define the possible angles that we have here:

Obtuse: With a measure larger than 90° and smaller than 180°Acute: With a measure between 0° and 90°Right: With a measure of 90°Straight: With a measure of 180°.

Notice that the angles HML and LMK should add up to 180°, then we can write:

HML + LMK = 180°

132° + LMK = 180°

LMK = 180° - 132° = 48°

Now we can see that:

∠JML = ∠JMK + ∠LMK

∠JML = 41° + 48° = 89°

So the angle measures less than 90°, thus, the correct classification is acute.

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a consumer affairs investigator records the repair cost for 1010 randomly selected vcrs. a sample mean of $72.82$⁢72.82 and standard deviation of $24.17$⁢24.17 are subsequently computed. determine the 90�% confidence interval for the mean repair cost for the vcrs. assume the population is approximately normal. step 1 of 2 : find the critical value that should be used in constructing the confidence interval. round your answer to three decimal places.

Answers

Your question was incomplete. Please refer the content below:

Consumer affairs investigator records the repair cost for 10 randomly selected VCRs. A sample mean of $72.82 and standard deviation of $24.17 are subsequently computed. Determine the 90% confidence interval for the mean repair cost for the VCRs. Assume the population is approximately normal. Construct the 90% confidence interval. Round your answer to two decimal places.

We get that the critical value of the 90 % confidence interval is 1.833 and the interval is (58.81, 86.83).

We are given that the number of VCRs are 10.

So, we get that:

Sample size = n = 10

Now, we get the degree of freedom as:

d o f = n - 1

d o f = 10 - 1

d o f = 9

For 90% confidence interval , critical value will be:

t (0.10, 9) = 1.833

Lower limit of 90% confidence interval will be:

Lower interval  = Mean - t (0.10,9) × s / √n

= 72.82-1.833 × 24.17 /√10

= 58.81

Upper limit of 90% confidence interval will be:

Upper interval = Mean + t (0.10,9) × s /√n

= 72.82 + 1.833 × 24.17/√10

= 86.83

Therefore, we get that the critical value of the 90 % confidence interval is 1.833 and the interval is (58.81, 86.83).

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Julio is paid 1.3 times his normal hourly rate for each hour he works over 29 hours in a week. last week he worked 44 hours and earned $456.32

Answers

The hourly rate is $9.40 per hour.

How to calculate the hourly rate?

It should be noted that in this case, Julio works for 44 hours which mean 15 hours more than 29 hours.

He gets 1.3 times rate for this 15 hours and normal rate for the first 29 hours. Then the salary he would get should be: 29x + 1.3x(15)= 29x + 19.5x= 48.5x

Julio gets $456.32 which was 48.5 times of his hourly rate. The hourly rate would be:

= $456.32 /48.5

= $9.40/hour

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Julio is paid 1.3 times his normal hourly rate for each hour he works over 29 hours in a week. last week he worked 44 hours and earned $456.32.

Calculate the hourly rate.

Help please! For highschool algebra! You will get 20 points and no links please :)

Answers

Answer: a. 12x+19

b. 67

Step-by-step explanation:

a. P=a+b+c+d

P=x+7+2x+2+8x+x+10

P=x+2x+8x+x+7+2+10

P=3x+9x+19

P=12x+19

b. P=12(4)+19

P=48+19

P=67

now we’ll look at what happens when we take the average of four normal draws (sample size is 4), and do that 100 times (number of trials is 100), so we get 100 means of four normals. first consider the theoretical quantities. question 6: for the sampling distribution of the mean of four standard normals, what are its theoretical mean and its standard deviation?

Answers

The theoretical mean and standard deviation is 22 and 38 respectively

np>5 and n(1-p)>5 for normal approximation

p=0.77

np>5  n×0.77>5=6.49

n(1=0.77)>5

n>5/0.23

n=21.7

The standard error of the mean for a sample size of 153 is 25 . In quest to reduce the SE of the mean in half(to 12.5 )

Standard error of sample maean is se=sd/sqrt n

se=sd/sqrt 153

Taking four times of sample size we get 4×153=612

The required sample size is 612

The mean of an infinite population is 73 and a standard deviation of 38 . The sample size of 121 is taken randomly from the given population. The SE of the sample mean equals:

standard error of the sample mean =38/sqrt121=3.4545

A concise measure of the deviations of each observation from the mean is the standard deviation.

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Sebastian has 100$ he spits it to four of his friends how much does sebastian give?

Answers

Answer: $25 to each friend

Step-by-step explanation: 100 divided by 4 = 25

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If state A has more countiesthan state B, how many counties does each state have? Which part of the plotstructure does the followingsection of Stephen Crane's "AGreat Mistake" fall under?"For a time he was a simpleworshipper at this goldenshrine. Then tumultuousdesires began to shake him.His dreams were of conquest."A. falling actionB. rising actionC. resolutionResources Help me on my question please A proton has a charge ofa. -1 and is smaller in size than an electron b. +1 and is smaller in size then an electron c. -1 and is larger in size then an electron d. + and is larger in size then an electron Destruction causes development. Justify Bob is a self-employed lawyer and is required to take a week of continuing legal education every year to maintain his license. This year he paid $1,295 in course fees for his continuing legal education in a different city. He also paid $467 for airfare and a hotel room and paid $250 for meals, all of which were provided by the hotels restaurant. Bob also purchased a $6 bag of snacks from a newsstand while waiting for his plane in the airport because he missed lunch.What is the total amount he can deduct on his Schedule C related to these expenses? Your goal in this section is to take a closer look at some aspects of the topic finding solutions ofquadratic equations. You are going to think deeper and test further your understanding about solvingquadratic equations using any of the four methods discussed.1. Sheryl says that the solutions of the quadratic equations w = 49 andw +49 = 0 are the same. Do you agree with Sheryl? Justify your answer.2. Patricia says that it's more appropriate to use the method of factoringthan extracting square roots in solving the quadratic equation4x - 9 = 0. Do you agree with Patricia? Explain your answer.3. If you are to choose between completing the square and factoring infinding the solutions of each of the following equations, which would youchoose? Explain and solve the equation using your preferred method.b. x + 7x + 12 = 0a. 4x - 20x = 114. The values of a, b, and e of a quadratic equation written in standard formare -2, 8, and 3, respectively. Another quadratic equation has 2, -8, and-3 as the values of a, b, and c, respectively. Do you agree that the twoequations have the same solutions? Justify your answer."pa answer po please".. Match The Following:1.Aristotle a. They believed the Earth to be flat2.Kepler b. Thought that the Earth did not move3.Egyptians c. How the planets move around the Sun4.Ellipse d. Suggested the modern model of the Solar System long-term visual outcomes after release from protocol in patients who participated in the inhibition of vegf in age-related choroidal neovascularisation (ivan) trial Which of the following describes the cerebral prefrontal cortex? A. grows rapidly just before puberty B. governs the ability to draw and dance C.governs the ability to reason, plan, remember, and regulate mood D. grows fast just after and before puberty E. grows rapidly just after puberty the excitement was evident, it was the first time they performed for such a large audience. a. singers several studies state that long commuting times have a negative impact on job satisfaction. test if job satisfaction is correlated to distance to work. what is the correlation coefficient? should ibm offer additional incentives to employees who live far from work? one of the reasons marketers emphasize nonprice differences in their competitive strategies is because A very important concept of succession is facilitation, where the successes of one community typechange the environment gradually so as to not favor their own (or their children's) continueddominance, but rather favor the success of some new, different community members. Why do you thinkorganisms would facilitate the success of other organisms when it would be at the expense of their ownsuccess? (10 points)1