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
Artyom0805 [142]
3 years ago
15

Using the method of completing the square, put each circle into the form

Mathematics
1 answer:
tatiyna3 years ago
3 0

Answer:

Standard form: (x-\frac{1}{2})^2 + (y-0)^2 = 15

Center: (\frac{1}{2}, 0)

Radius: r =\sqrt{15}

Step-by-step explanation:

The equation of a circle in the standard form is

(x-h)^{2} + (y-k)^{2} = r^{2}

Where the point (h, k) is the center of the circle

To transform this equation 4x^{2} -4x + 4y^{2} - 59 = 0 this equation  in the standard form we use the method of square.

First, we group similar variables

(4x^{2} -4x) + (4y^{2}) - 59 = 0

Divide both sides of equality by 4

(x^{2} -x) + (y^{2}) - 14.75 = 0

Now we complete square for variable x.

Take the coefficient "b" that accompanies the variable x and divide by 2. Then, elevate the result to the square:

b =-1\\\\\frac{b}{2}= \frac{-1}{2}= -\frac{1}{2}\\\\(\frac{b}{2})^2=  (-\frac{1}{2})^2 = \frac{1}{4}

Now add (\frac{b}{2})^2 on both sides of the equality

(x^{2} -x +\frac{1}{4}) + (y^{2}) - 14.75 = (\frac{1}{4})

Factor the expression and simplify the independent terms

(x-\frac{1}{2})^2 + (y^{2}) = 15

(x-\frac{1}{2})^2 + (y-0)^2 = 15

Then

h =\frac{1}{2}\\\\k=0

and the center is (\frac{1}{2}, 0)

radius r =\sqrt{15}

You might be interested in
A store sells the basic model of a phone for $60 and the upgraded model for $200. It costs the store $10 to buy each basic model
ivolga24 [154]

Answer:

6

Step-by-step explanation:

(6*200)+(10*60)=1800

(6*50)+(10*10)=400

5 0
2 years ago
PLEASE HELP ASAP!!!!!
sveta [45]
Accute hope this helps
8 0
3 years ago
Read 2 more answers
In Europe, gasoline efficiency is measured in km/L. If your car's gas mileage is 31.0mi/gal , how many liters of gasoline would
maw [93]
We need to convert the mileage from mi/gal units into to km/L units using the conversion factors.

(31.0 mi/gal) x (1 km / 0.6214 mi) x (1 gal / 3.78 L) = 13.20 km/L

Next, we divide the distance by the mileage. 
(142 km) / (13.20 km/L) = 10.79 L

<span>Therefore, you need 10.79 liters of gasoline.</span>
7 0
3 years ago
Read 2 more answers
Which is the smallest number in this set of numbers? <br> A. √8<br> B. 14/5<br> C. 2.28<br> D. 2.288
-Dominant- [34]

Answer:

B.

Step-by-step explanation:

a = 2.828

b = 2.800

c = 2.288

d = 2.288

8 0
3 years ago
Read 2 more answers
A line intersects the point (6,9) and (7,4). What is the slope intercept equation for this line?
BartSMP [9]

Answer:

im kind of rusty on this math but i think the equation would be y=-5x+b  i forgot how to find b tho :( im sorry

6 0
3 years ago
Other questions:
  • University Theater sold 556 tickets for a play. Tickets cost $22 per adultand $12 per senior citizen. If total receipts were $84
    6·1 answer
  • What reason explains why the m∠Q = 115°? A) diagonals of a parallelogram bisect each other B) opposite sides of a parallelogram
    7·2 answers
  • Solve the equation by using the Square Root Property.<br><br><br><br> 16x2 + 16x + 4 = 81
    8·1 answer
  • (20 points) geometry
    11·1 answer
  • What is the value of x?<br> 39° (3x)°
    5·2 answers
  • What is the ratio of dogs to cats? <br><br><br>What is the ratio of cats to dogs?
    6·1 answer
  • Can anyone help me please?
    13·2 answers
  • Hello, my friend had his account deleted recently and i need my bro back, he goes by co oper, if you dont know the guy then help
    6·2 answers
  • Maria earns $40 washing 5 cars. At this rate, how much does Maria earn washing 6 cars?​
    5·1 answer
  • An art gallery wants to display 4 pieces of art in the front window. If there are 8 pieces to choose from, how many distinct dis
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!