What is the center and radius of the circle with the given equation x^2 + y^2 + 14x - 12y +69 = 0

Answers

Answer 1

Answer:

Center is (7,-6)

Our radius is 4

Step-by-step explanation:

Subtract 69 to both sides

Complete the square of the x terms and y terms.

[tex] {x}^{2} + 14x[/tex]

[tex] {y}^{2} - 12y[/tex]

(To complete the square divide the coefficient by 2 and square it).

[tex] (\frac{14}{2} ) {}^{2} = 49[/tex]

[tex]( \frac{ - 12}{2} ) {}^{2} = 36[/tex]

Add those terms to the full equation. Add 36 and 49 to the right side as well

[tex] {x}^{2} + 14x + 49 + {y}^{2} - 12y + 36 = 16[/tex]

Simplify the x and y terms into a binomial.

[tex](x + 7) {}^{2} + (y - 6) {}^{2} = 16[/tex]

Set the left side equal to zero separately to find the center and take the square root of the right side to find the radius.

[tex]x + 7 = 0[/tex]

[tex]x = - 7[/tex]

[tex]y - 6 = 0[/tex]

[tex]y = 6[/tex]

[tex]16 = {x}^{2} [/tex]

[tex]4 = x[/tex]

So our center is (-7,6)

Our radius is 4.


Related Questions

176.625 rounded to the nearest tenth​

Answers

Answer:

176.6

Step-by-step explanation:

Answer:

180 idrk

Step-by-step explanation:

Please help with these math questions I really need it ! Don't just do it for points pls

Answers

Answer:

wouldn't that be 81 but i dont know

Answer:

1. d 2. 43.5 3. 817.5

Step-by-step explanation:

Write and solve equation to answer the question 18 is 32% of what number W? And equation is equal 0.32 the solution is W equal​

Answers

Answer:

W = 56.25

Step-by-step explanation:

Is is equivilent to equals.

Of is equivilent to multiplication.

18 = 0.32 x w

0.32 x W = 0.32w

18 ÷ 0.32 = 56.25

To check it,

56.25 x 0.32 = 18!!

please help:) i would appreciate it lol

Answers

Answer:

subtotal: $65.00

8% sales tax: $5.20

total: $70.20

Step-by-step explanation:

answer quick pls!

Jose wants to plan a skate party for his younger cousin's birthday. Skate Land charges a $65 flat fee and $7.50 per person.
Skate Land uses the equation C = 7.50p + 65 (C = total cost; p = number of people ) to calculate the total cost
based on the number of people attending. Find the total cost, C, of the birthday party if Jose invites 30 friends and family
members.

Answers

Answer:

$290

Step-by-step explanation:

We can use the equation that Skate Land created to find the total cost

C = 7.50p + 65

p = people so if we have 30 people, we have to solve 7.50 x 30

C = 225 + 65

we can now add the flat fee of $65 to get the total cost for the birthday part

C = $290

hope this helps :)

Round up 64,781 to the nearest ten thousand

Answers

64,781

/\

|

60,000

---

hope it helps

Answer:

60,000

Step-by-step explanation:

Hope This Helps ; )

Plz Mark Brainliest

PLEASE HELP ME
If $ 2000 is invested in an account that pays interest compounded continuously, how
long will it take to grow to $ 2800 at 8.25%?

Answers

Answer:

5 years

Step-by-step explanation:

A bottle-filling process has a low specification limit of 1.8 liter and upper specification limit of 2.2 liter. The standard deviation is 0.15 liter, and the mean is 2 liter. The company now wants to reduce its defect probability as 0.0455. To what level would it have to reduce the standard deviation in the process to meet this target

Answers

Answer:

The standard deviation would have to be reduced to 0.1 in the process to meet this target

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

The mean is 2 liter.

This means that [tex]\mu = 2[/tex]

The company now wants to reduce its defect probability as 0.0455.

This means that:

P(X < 1.8) = 0.0455/2 = 0.02275

P(X < 2.2) = 0.0455/2 = 0.02275

This means that the pvalue of Z when X = 1.8 is 0.02275. This means that when [tex]X = 1.8, Z = -2[/tex]. We use this to find the new standard deviation [tex]\sigma[/tex]. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-2 = \frac{1.8 - 2}{\sigma}[/tex]

[tex]-2\sigma = -0.2[/tex]

[tex]\sigma = \frac{0.2}{2}[/tex]

[tex]\sigma = 0.1[/tex]

The standard deviation would have to be reduced to 0.1 in the process to meet this target

Another friend's distance d from you (in feet) after t seconds is given by
d = |80 - 5t|. What does the 80 in the equation represent? What does the 5 in the equation represent? At what times is she 60 ft from you?

Answers

I think the 80 represents how far away they initially start from you

And the 5 is their speed

d=|80-5t|
60=|80-5t| |square both sides
60² = (80-5t)(80-5t)
3600 = 6400-400t-400t +25²
25t²-800t +6400 =3600
25t² -800t + 2800=0
5t² -160t +560=0
(ax²+bx+c=0)
(a=+5 b=-160 c=+560)
Sub into -b formula
x=(-b±√(b²-4ac))/(2a)
t= (-(-160)±√((-160)²-4(5)(560))/(2(5)) .


Should get t=4 seconds and t=28 seconds
sub both values back in to make sure

d=|80-5(4)|
d=|80-20|
d=60ft

d=|80-5(28)|
d=|80-140||
d=60ft

Out of a group of 30 volunteers, 17 people are chosen to participate in a survey about the number of phone calls they make each week. What is the sample in this situation?​

Answers

Answer:

i dont know

Step-by-step explanation:

cool

Answer:

I know you properly don't need it anymore but other people might so here you go!

Step-by-step explanation:

need help on question 22 and 23 , ill give extra points

Answers

22. Republic
23. Veto
22) republic
23) veto


Work out the gradient of the line joining the points (2, 3) and (5,7)

Answers

Answer:

The gradient of the line joining the points [tex]P(x,y) = (2,3)[/tex] and [tex]Q(x,y) = (5,7)[/tex] is [tex]\frac{4}{3}[/tex].

Step-by-step explanation:

The gradient of the line joining two distinct point on a plane is represented by the slope of a secant line ([tex]m_{PQ}[/tex]), that is:

[tex]m_{PQ} = \frac{y_{Q}-y_{P}}{x_{Q}-x_{P}}[/tex] (1)

If we know that [tex]P(x,y) = (2,3)[/tex] and [tex]Q(x,y) = (5,7)[/tex], then the gradient of the line is:

[tex]m_{PQ} = \frac{7-3}{5-2}[/tex]

[tex]m_{PQ} = \frac{4}{3}[/tex]

The gradient of the line joining the points [tex]P(x,y) = (2,3)[/tex] and [tex]Q(x,y) = (5,7)[/tex] is [tex]\frac{4}{3}[/tex].

Find the lettered angles.

Answers

It’s 59 bro it’s easy

Burger Queen a popular fast food restaurant among college students has undertaken a study to determine the weights of the hamburgers served in its new location in San Marcos, TX. Half pounders should weigh at least 8 ounces. The weight is assumed to be normally distributed. A sample of 500 hamburgers reveals the average precooked weight to be 8.02 ounces, with a standard deviation of .4 ounce.
1. What is the probability that a hamburger selected at random will weigh between 7.76 and 8.02 ounces?
2. What is the probability that a hamburger selected at random with less than 7.52 ounces?

Answers

Answer:

1. 0.2422 = 24.22% probability that a hamburger selected at random will weigh between 7.76 and 8.02 ounces

2. 0.1056 = 10.56% probability that a hamburger selected at random with less than 7.52 ounces.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

A sample of 500 hamburgers reveals the average precooked weight to be 8.02 ounces, with a standard deviation of .4 ounce.

This means that [tex]\mu = 8.02, \sigma = 0.4[/tex]

1. What is the probability that a hamburger selected at random will weigh between 7.76 and 8.02 ounces?

This is the pvalue of Z when X = 8.02 subtracted by the pvalue of Z when X = 7.76. So

X = 8.02

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{8.02 - 8.02}{0.4}[/tex]

[tex]Z = 0[/tex]

[tex]Z = 0[/tex] has a pvalue of 0.5

X = 7.76

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{7.76 - 8.02}{0.4}[/tex]

[tex]Z = -0.65[/tex]

[tex]Z = -0.65[/tex] has a pvalue of 0.2578

0.5 - 0.2578 = 0.2422

0.2422 = 24.22% probability that a hamburger selected at random will weigh between 7.76 and 8.02 ounces.

2. What is the probability that a hamburger selected at random with less than 7.52 ounces?

This is the pvalue of Z when X = 7.52. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{7.52 - 8.02}{0.4}[/tex]

[tex]Z = -1.25[/tex]

[tex]Z = -1.25[/tex] has a pvalue of 0.1056

0.1056 = 10.56% probability that a hamburger selected at random with less than 7.52 ounces.

Can someone
Please
Help me

Answers

Answer:

First let's calculate the area of the bottom part

diameter is 34 m

so the radius (r) is 1/2 * 34 m = 17 m

bottom part is 1/2 of a circle

circle surface area formula is πr²

so surface area of our bottom part is 1/2 * πr²

1/2 * πr² = 1/2 * 3,14 * 17² = 453,73

so it's 453,73 m²

Triangle part consists of 2 smaller rectangular triangles

surface area for rectangular triangle is 1/2 * a * h

in our case a = r = 17 m and h = 30m

so one smaller rectangular triangle is 1/2 * r * h = 1/2 * 17 * 30 = 255

so it's 255 m²

and because our entire triangle part consists of 2 smaller rectangular triangles it's area is 2 * 255 m² = 510 m²

Surface area of the entire figure is a sum of 510 m² and  453,73 m²

510 m² +  453,73 m² =  963,73 m²

I need help!!!! I’m stuck!!!

Answers

Answer:

66.3

Step-by-step explanation:

Find the measure of 46.
6
620
6.6
{
66 = [?]
2003 - 2021 Stellus Corporation. All Rights Reserved.

Answers

?=118°

Answer:

<6+62=180 co interior angle

<6=180-62=118°

Carl hits the target 50% pf the time he throws a ball at it. Carl uses a coin to simulate his next three pitches. The assigns H for a hit and T for a miss. The results of the 12 trials are shown below. Based on the results, what is the probability that cael will hit the next the Target with exactly two of his next three throws

Answers

Answer:

I have that same problem but im trying to figure out the answer

Step-by-step explanation:

A package of gift cards has a length of
8 inches, a width of 4 inches and a
volume of 64 inches cubed. What is
the height of the box?
A) 6
B) 8.
C) 4
D) 2.
D) 2.
8x4=32
64/32=2

Answers

Answer:

8x(4) = 64

8x = 16

h = 2 inches

Helpp!
Find the value of x. ​

Answers

Answer:

the answer is C

Step-by-step explanation:

Please someone if you know how to do this I need help 10. And 11 please.

Answers

Answer:

10.

bag a is lighter than bag b

bag b is lighter than bag c

so bag a is lighter that bag c

Step-by-step explanation:

... sorry i dont know #11, but hope this helps

Answer:

10.

Bag A is LIGHTER than Bag B

Bag B is LIGHTER than Bag C

So, Bag A is LIGHTER than Bag C

11.

pear is the heaviest, and the strawberry is the lightest

Step-by-step explanation:

This is really simple! Looking at the weight scale, the heavier object always goes lower than the lighter object. Knowing this, we can figure out which is heavier and which is lighter.

10.

Bag A is LIGHTER than Bag B

Bag B is LIGHTER than Bag C

Looking at these we can infer that bag c is heavier than both.

So, Bag A is LIGHTER than Bag C

11. The pear falls lower than the apple, meaning it is heavier. The apple falls lower, meaning is it heavier than the apple. We can infer that the pear is the heaviest, and the strawberry is the lightest

Hope this helps!!

-Ketifa

Graph the line with slope 6 and y intercept -3

Answers

Answer:

Step-by-step explanation:

Find the measure of 46.
t
56°/1249
46
te
s6 = [?]

Answers

Answer:

56°

Step-by-step explanation:

1st reason= alternate angles.

2nd reason= 124 and angle 6 is co-interior angles which means that little are shoudk adds up to 180.

180-124=56

A flagpole casts a shadow that is 23 feet long. Jorge is 5.25 feet tall, and
while standing near the flagpole he casts a shadow that is 3 feet long. How
tall is the flagpole?

Answers

Answer:

5.5

7.5 =

h

23.5

7.5h = 129.25

h = 17.2

3

The flagpole is 17.2 feet long.

The measure of height of flagpole is 40.25 feet.

Given that, a flagpole casts a shadow that is 23 feet long.

What are heights and distances?

Heights and Distances is a study about the applications of Trigonometry. It has many real-life applications, such as measuring the object’s height, depth of the object, the distance between two celestial objects etc. The formulas and the ratios of trigonometry are helpful in the study of heights and distances.

Jorge is 5.25 feet tall, and while standing near the flagpole he casts a shadow that is 3 feet long.

Let the height of the flagpole be x.

Now, tan θ=5.25/3 -------(I)

and tan θ=x/23 -------(II)

Equation (I)=(II), we get

5.25/3 = x/23

⇒ 3x=5.25×23

⇒ 3x=120.75

⇒ x=120.75/3

⇒ x=40.25 feet

Therefore, the measure of height of flagpole is 40.25 feet.

To learn more about the heights and distance visit:

brainly.com/question/24271007.

#SPJ2

A cube is a special right rectangular prism with congruent sides. If a block of cheese is shaped like a cube with a length of 5 inches, find the volume of the block of cheese.

A) 25 cubic inches B) 100 cubic inches Eliminate C) 125 cubic inches D) 175 cubic inches

Answers

Answer:

125 cubic inches

Step-by-step explanation:

Hey There!

We can easily find the volume of a cube by cubing the side length

[tex]5^3\\5*5=25\\25*5=125[/tex]

so we can conclude that the volume of the block of cheese is 125 cubic inches

The series converges by the Limit Comparison Test. Each term is less than that of a convergent geometric series. The series converges by the Limit Comparison Test. The limit of the ratio of its terms and a convergent p-series is greater than 0. The series diverges by the Limit Comparison Test. Each term is greater than that of the divergent p-series. The series diverges by the Limit Comparison Test. The limit of the ratio of its terms and the harmonic series is greater than 0.

Answers

Answer:

hello your question has some missing information attached below is the complete question

answer : The series diverges by the Limit Comparison Test. The limit of the ratio of its terms and the harmonic series is greater than 0.

Step-by-step explanation:

steps to determine if the series converges

step 1 : apply series limit comparison test

step 2 : consider Cauchy's convergence condition ; which states that ∑an converges if and only if for every ∈ > 0 there is a natural number N

attached below is the detailed solution

A culture of bacteria has an initial population of 790 bacteria and doubles every 4
hours. Using the formula P+ = Po.2, where P is the population after t hours, Po
is the initial population, t is the time in hours and d is the doubling time, what is the
population of bacteria in the culture after 11 hours, to the nearest whole number?

Answers

Answer:5314.4563≈5314

Step-by-step explanation:

HELPPP!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

try the last one on your own then check answer

Prove that: cotθ - tanθ = 2cos²θ - 1/sinθcosθ

Need help, fast!​

Answers

See attachment to get your answer. Thanks.

What expression is equivalent to 1/3x + 1/4 - 2/3x
Show work please

Answers

Answer:

1/12 * (-4x+3)

Step-by-step explanation:

1/3x + 1/4 - 2/3x

1/12 * (4x+3-8x)

1/12 * (-4x+3)

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