Mathematics College

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

Please help me with this and explain how you got the answer thank you

Answers

The answer would be 4. All you need to do is multiply the 2/3 by the 6.

Find the value of x

Answers

Answer:

it's 60

Step-by-step explanation:

carry out the following divisions.

Answers

Answer:

9a²b²c²

Step-by-step explanation:

72a³b⁴c⁵ / 8ab²c³

= 9a²b²c²

Find the errors and correct the following mathematical sentences.

Answers

Answer:

Step-by-step explanation:

18). 3x + 2 ÷ 3x = [tex]\frac{2}{3x}[/tex]

Since, 3x + 2 ÷ 3x = 3x + [tex]\frac{2}{3x}[/tex]

Therefore, right hand side of the equation will be = 3x + [tex]\frac{2}{3x}[/tex]

20). [tex]\frac{4x+3}{3}=x+1[/tex]

Since, [tex]\frac{4x+3}{3}=\frac{4x}{3}+\frac{3}{3}[/tex]

= [tex]\frac{4}{3}x+1[/tex]

Therefore, right hand side of the equation should be [tex]\frac{4}{3}x+1[/tex].

What is x in 1/150/1/200x2=x

Answers

Answer:

6.66666667E-5

hope this helped a bit!

pls help asap
AABC ~ ADEF B. Х 8 А 'C E 3 6. D ' x = [?] Enter

Answers

Answer:

[tex] \boxed{ \tt{x = 4}}[/tex]

Step-by-step explanation:

[tex] \frac{3}{x} = \frac{6}{8} \\ 6x = 24 \\ x = 4[/tex]

city workers recorded the number of squirrels in a park over a period of time. At the first count, there were
30 total squirrels. After 1 year, the city workers recorded a total of 60 squirrels, and after 2 years there were
120
a. Write a function that represents the population of squirrels recorded over x number of years,
b. Assuming the same growth rate and no squirrel dies, what will the squirrel population be in 6 years?
Justify your answer mathematically

Answers

Function:

A. x times 60 = the amount of squirrels in that year

Answer

B. 6 X 60 = 360

Step-by-step explanation

Years | Squirrels

______________

1 | 60

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

2 | 120

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

3 | 180

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

4 | 240

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

5 | 300

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

6 | 360

Which conic section is represented by the following equation?

5x2 – x + 5y2 – 3y + 4 = 0

Circle
Ellipse
Parabola
Hyperbola

Answers

Answer:

A. circle

Step-by-step explanation:

Answer:

A: Circle!

Step-by-step explanation:

Edge 2022

Half of a number is equal to 14

Answers

28 is the answer

Half of 28 is 14

Story Problem:
Avery purchased 4 tacos and 2 burritos and her total cost was $21. Sasha purchased 4 tacos and 3 burritos
and her total cost was $26.50. What is the price of one burrito?

Answers

Answer:

Step-by-step explanation:

Let tacos be x and burritos be y

So, Avery purchased 4x+2y = 21

Sasha purchased 4x+3y = 26.5

Solving the 2 eqns:

4x+2y=21

-4x-3y=-26.5

-y=-5.5

The cost of one burrito is $5.5

5 books cost $15. How much do 7 books cost?

Answers

5 / 15 = 3

So 3 x 7 = 21

ANSWER:
$21

STEP BY STEP:
Each book is 3 dollars, so we multiply 7 by 3, and you get 21.

hope this helps

how many 5 digits numbers can be created using digits 1,2,3,7, and 6 without repeating any digits within that 5-digit number?

Answers

There are 5 numbers that can be used.

The first digit can be 1 of 5

The second digit can be 1 of 4

The third digit is 1 of 3

The fourth digit is 1 of 2

The fifth digit is 1 of 1

Total digits that can be created = 5 x 4 x 3 x 2 x1 = 120

Please help! :( If AJKL = ARST, which congruences are true by CPCTC? Check all that apply.
A. ZL ZR
B. KL: ST
C. KZS
D. JK = RS
E. JL - RS
F. LJ2S

Answers

Step-by-step explanation:

I just got it on a pex. JK=RS. KL=ST. K=S. those are the answers

The congruences that are true by CPCTC are:

∠L = ∠R

KL ≅ ST

What is a triangle?

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

If ΔJKL = ΔRST, then the corresponding parts of the triangles are congruent.

CPCTC stands for "corresponding parts of congruent triangles are congruent,"

So we can use this property to determine which congruences are true.

∠L = ∠R:

This is true by CPCTC because they are corresponding angles in congruent triangles.

JK ≅ RS:

This is not true by CPCTC because they are not corresponding sides in congruent triangles.

KL ≅ ST:

This is true by CPCTC because they are corresponding sides in congruent triangles.

JL ≅ RS:

This is not true by CPCTC because they are not corresponding sides in congruent triangles.

∠L = ∠S:

This is not necessarily true just by the fact that ΔJKL = ΔRST.

It could be true in some cases, but it is not guaranteed by CPCTC.

Therefore,

The congruences that are true by CPCTC are:

∠L = ∠R

KL ≅ ST

Learn more about triangles here:

https://brainly.com/question/25950519

#SPJ7

Mr. Conway is leaning a ladder against the side of his house to repair the roof. The top of the ladder reaches the
roof, which is 20 feet high. The base of the ladder is 15 feet away from the house, where Mr. Conway's son is
holding it steady. How long is the ladder? Draw a picture and show your work.

Answers

I am pretty sure the answer is 300 but I cannot draw a picture to show you because I cannot draw on here

The question is in the graph. Please help.

Answers

Answer:

A I think

Step-by-step explanation:

because if you add them up.

Answer:

Aprox. 216 days

Step-by-step explanation:

Add the counts of the green bar(5-10mm) and the brown bar (0-5mm).

The brown is roughly 130 and the green is roughly 80, which is approx 216 days.

If i helped, a brainliest answer would be greatly appreciated!

I think the answer is nine but I’m not sure how to explain how I got my answer

Answers

Answer:

ur answer is right it is 9

Step-by-step explanation:

NOTE: divide the number 36 with 4 and u will get 9

GOOD JOB

Please mark as brainliest

Have a great day, be safe and healthy

Thank u

Please help! Thank you.

Answers

Answer:

2.478x10^7

Step-by-step explanation:

They give you each radius, so you just add them together.

15,300,000+9,480,000=24,780,000 = 2.478x10^7

(or)

1.53x10^7+0.948x10^7= 2.478x10^7

a number rounded to the nearest thousand is 47000 which number could be the number that was rounded?

Answers

Answer:

46900

Step-by-step explanation:

46900 or 46800 or 46700 or 46600

Consider the figure shown below. What is the value of the angle x?

x = _______ degree.

Answers

X=66 degrees. Because of corresponding alternate interior angles. Interior angles of triangle is 180 degrees

Find the equation of this line.
Simplify the fractions.

Answers

Answer:

Step-by-step explanation:

Where's the line?

It cost $5.25 for a bottle of 150 vitamins. if the cost varies directly with the number of vitamins in the bottle, what should a bottle of 250 vitamins cost?
what is the equation o the situation?
Could you please give me the equation and show me how you got it please so I could understand... thanks.

Answers

Answer: $8.75 for 250 vitamins.

Step-by-step explanation:

To find how much each vitamin costs we can divide $5.25 by 150.

5.25/150 = 0.035. So each vitamin is equal to $0.035.

We can then multiply the cost of 1 vitamin by 250.

0.035 x 250 = 8.75 or $8.75.

We can also make an equation for this problem. Let the total cost be equal to y and each vitamin equal to x.

y = 0.035x

So the equation above states that the total cost, y, is the amount of vitamins that are bought.

During the football game, Justin caught three passes. One was for a touchdown and went 52 yards.
The other was for a first down and was for 17 yards. The other was on a screen pass that did not
work so well and ended up a gain of -10 yards. What was the total yardage gained by Justin on the
pass plays?

Answers

Answer:

Step-by-step explanation:

52+17-10=59

What is the rectangular form of Theta = StartFraction 3 pi Over 4 EndFraction?

Answers

Answer:

Step-by-step explanation:

edge

Answer:

C or x+y=0

Step-by-step explanation:

edg

8increase by 3 times a number (t).

Answers

Answer:

8 + 3n

Step-by-step explanation:

Answer:

8 + 3t

Explanation:

Question 7 (5 points)
(06.04 LC)
The equation of the line of best fit of a scatter plot is y = 8x - 1. What is the slope of
the equation? (5 points)
1)-8
2-1
3) 1
4) 8

Answers

Answer:

4) 8

Step-by-step explanation:

In the formula y = mx + b, m is the slope and b is the y-intercept

m = 8

b = -1

If m = 8 and m is the slope, then the slope is 8

Please guys, can someone help me out?

Answers

Center point= 8 , 3
radius =7 Good luck!

Luis walked for 16 minutes. Natalie walked for w minutes. Luis walked twice as long as Natalie. How long did Natalie walk?

Answers

Answer:

Natalie walked for 4 minutes because 16 divided by 2 is 4

Answer:

Step-by-step explanation:

16/2=8

Help please!!!
I’m failing math and I need help

Answers

Answer:

vertically opposite angles ,

= 30°

4. 50° +30°+2x = 180°

80°+2x=180°

2x=180°-80°

2x=100°

Clara went to a music store and brought some CDs and DVDs. She paid $14 for each CD and $17 for each DVD. Let x represent the number of CDs that she purchased and y represent the number of DVDs.

Answers

14x+17y= total spent

Six more than five times a number

Answers

Answer:

? = 5n + 6

Explanation:

Answer:

5x + 6

Step-by-step explanation:

Let the number = x. 5 times x = 5x. So, the equation 5x + 6.

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