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
lubasha [3.4K]
3 years ago
12

What is the standard form of 3x^2+3y^2+12x+18y-15=0

Mathematics
1 answer:
vichka [17]3 years ago
6 0

Answer:

(x + 2)^2 + (y + 3)^2 = 18

Step-by-step explanation:

To write this equation in the standard form i.e. (x - h)^2 + (y - k)^2 = R^2, we need to complete the squares on the left side.

For completing the squares, put variables on one side and constants on the other side:

3x^2 + 3y^2 + 12x + 18y - 15 = 0

3x^2 + 3y^2 + 12x + 18y  = 15

Rearrange the like terms together:

3x^2 + 12x + 3y^2 + 18y  = 15

Since the coefficients of x^2 and y^2 terms are the same, divide both the sides by this coefficient i.e. 3 to get:

x^2 + 4x + y^2 + 6y  = 5

Now, square the 1/2 of coefficients for x and y and add them to both sides of the equation:

square of 1/2 of coefficient for x = (4/2)^2 = 4; and

square the 1/2 of coefficient for y = (6/2)^2 = 9

x^2 + 4x + 4 + y^2 + 6y + 9 = 5 + 4 + 9

x^2 + 4x + 4 + y^2 + 6y + 9 = 18

Rewriting this as perfect squares:

(x + 2)^2 + (y + 3)^2 = 18

You might be interested in
How to write 15,409 in word form
Papessa [141]
Fifteen thousand, four hundred and nine
5 0
3 years ago
Read 2 more answers
If the price for 12 cookies is 42 dollars how much would if cost for 1 cookie
Andrews [41]

Answer:

$3.50

Step-by-step explanation:

42 divided by 12 is the price of one cookie.

42 divided by 12 = $3.50

hope this helps :)

7 0
3 years ago
Need helpppppppppp please
aleksley [76]
Adding the two equations
3x + 6y + 3x - 6y = 36+0
6x = 36
x = 6
.
subtracting second equation from first
(3x + 6y ) - (3x-6y) =36 -0
12y = 36
y = 3
.
therefore
x = 6 and y = 3
(6,3)
8 0
2 years ago
Read 2 more answers
To download movies off the internet you must pay 1.99 per movie, plus onetime fee of 5.50. Write an expression to show the total
solmaris [256]
T=total cost m=number of movies t=1.99m+5.50. I hope this helped.
6 0
3 years ago
Determine whether the pair of equations represent parallel lines, perpendicular lines, or neither.
Ivahew [28]

Answer:

Parallel

Step-by-step explanation:

Parallel lines have the same slope but different y-intercepts. If you multiply the top equation by 2, you get:

2(12x + 4y = 16)

24x + 8y = 32

This shows that both lines have the same slope, but then you find the y-intercepts, they are different:

1st equation y-int = 4

2nd equation y-int = 9/2 or 4.5

6 0
3 years ago
Other questions:
  • A text message plan costs ​$3 per month plus ​$0.37 per text. Find the monthly cost for x text messages
    12·2 answers
  • you buy butter 4.13 a pound one portion of onion requires 1.7 oz of butter how much dose the butter for one portion cost
    11·1 answer
  • ¿Cuánto es $ 3.57 redondeado al dólar más cercano?
    7·1 answer
  • What is 972 written in standard form
    5·2 answers
  • ‼️Someone help please.. <br> Find the missing term in each sequence
    9·1 answer
  • Help please <br> What is the answer?
    7·1 answer
  • The table below records the low winter temperatures for four cities.
    7·1 answer
  • Help me please<br> 8. Match each angle pair with the corresponding drawing. Choose the best answer!
    9·1 answer
  • Thanks for the answer
    7·1 answer
  • What is 75.6 divided by 4
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!