1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Akimi4 [234]
3 years ago
8

Find an equation of the line containing the centers of the two circles whose equations are given below.

Mathematics
1 answer:
Anna35 [415]3 years ago
5 0

Answer:

<h2><em>3y+x = -5</em></h2>

Step-by-step explanation:

The general equation of a circle is expressed as x²+y²+2gx+2fy+c = 0 with centre at C (-g, -f).

Given the equation of the circles x²+y²−2x+4y+1  =0  and x²+y²+4x+2y+4  =0, to  get the centre of both circles,<em> we will compare both equations with the general form of the equation above as shown;</em>

For the circle with equation x²+y²−2x+4y+1  =0:

2gx = -2x

2g = -2

Divide both sides by 2:

2g/2 = -2/2

g = -1

Also, 2fy = 4y

2f = 4

f = 2

The centre of the circle is (-(-1), -2) = (1, -2)

For the circle with equation x²+y²+4x+2y+4  =0:

2gx = 4x

2g = 4

Divide both sides by 2:

2g/2 = 4/2

g = 2

Also, 2fy = 2y

2f = 2

f = 1

The centre of the circle is (-2, -1)

Next is to find the equation of a line containing the two centres (1, -2) and (-2.-1).

The standard equation of a line is expressed as y = mx+c where;

m is the slope

c is the intercept

Slope m = Δy/Δx = y₂-y₁/x₂-x₁

from both centres, x₁= 1, y₁= -2, x₂ = -2 and y₂ = -1

m = -1-(-2)/-2-1

m = -1+2/-3

m = -1/3

The slope of the line is -1/3

To get the intercept c, we will substitute any of the points and the slope into the equation of the line above.

Substituting the point (-2, -1) and slope of -1/3 into the equation y = mx+c

-1 = -1/3(-2)+c

-1 = 2/3+c

c = -1-2/3

c = -5/3

Finally, we will substitute m = -1/3 and c = 05/3 into the equation y = mx+c.

y = -1/3 x + (-5/3)

y = -x/3-5/3

Multiply through by 3

3y = -x-5

3y+x = -5

<em>Hence the equation of the line containing the centers of the two circles is 3y+x = -5</em>

You might be interested in
Is 0/0x7y³ a positive or negative number
charle [14.2K]

Answer:

A =  0/(0 x 7y³)

Let's see the denominator:  0 x 7y³ = 0

=> Whenever the denominator is 0, A is undefined, neither a positive number or negative number

Hope this helps!

:)

3 0
3 years ago
What’s is the answer to Simplify 3^5 • 3^4
Mariana [72]

3^9

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
What is 5x × 12y - 8xy​
makkiz [27]

Answer:

52xy is the answear. Hope it helps

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
To help consumers assess the risks they are taking, the Food and Drug Administration (FDA) publishes the amount of nicotine foun
QveST [7]

Answer:

We conclude that  the mean nicotine content is less than 31.7 milligrams for this brand of cigarette.

Step-by-step explanation:

We are given the following in the question:  

Population mean, μ = 31.7 milligrams

Sample mean, \bar{x} = 28.5 milligrams

Sample size, n = 9

Alpha, α = 0.05

Sample standard deviation, s =  2.8 milligrams

First, we design the null and the alternate hypothesis

H_{0}: \mu = 31.7\text{ milligrams}\\H_A: \mu < 31.7\text{ milligrams}

We use One-tailed t test to perform this hypothesis.

Formula:

t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }

Putting all the values, we have

t_{stat} = \displaystyle\frac{28.5 - 31.7}{\frac{2.8}{\sqrt{9}} } = -3.429

Now, t_{critical} \text{ at 0.05 level of significance, 8 degree of freedom } = -1.860

Since,                  

t_{stat} < t_{critical}

We fail to accept the null hypothesis and accept the alternate hypothesis. We conclude that  the mean nicotine content is less than 31.7 milligrams for this brand of cigarette.

3 0
3 years ago
What is the value of x? show work
Alona [7]
2x+38=180
2x=142 (or x+x=142 from which 2x=142)
x=71 

The unknown angles are each 71

You know this answer is logical as, since two sides are 21 it hints that we are looking at an equilateral triangle, which means two of its angles will be the same
7 0
3 years ago
Other questions:
  • 10 &lt; –2b or 2b + 3 &gt; 11
    10·1 answer
  • Ava wants to figure out the average speed she is driving. She starts checking her car’s clock at mile marker 0. It takes her 4 m
    11·2 answers
  • Evaluate. [(12−5)⋅12]÷6
    14·1 answer
  • Help please im loss
    13·1 answer
  • Viola took out a $8,470 Stafford loan at the beginning of her four-year college career. The loan has a duration of ten years and
    7·2 answers
  • What is the equation of this line in standard form? (Please explain)
    8·1 answer
  • What is the solution to the following system of equations: 2x + 4y = 8 -2x - 4y = 8 the options are (4, 0),(0, 2) No Solution In
    7·1 answer
  • Which of the following numbers is closest to 11?<br> O A. 7123<br> B. V115<br> O c. 118<br> O D. 120
    5·1 answer
  • How do I solve part c
    12·1 answer
  • Zero and negative exponentswrite in simplest for without zero or negative exponents- 17 ⁰
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!