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

(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

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

the factor is 2

step-by-step explanation:

let f(x)=8(3^(x−2)+2)

to stretch a graph by 3, it would be 3f(x)

g(x) =3f(x)

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

x     −2     0     2     4     6

f(x) 1/64 1/16   1/4     1     4

1/64 * z * z = 1/16

i multiplies by z twice because it its 2 steps from -2 to 0

1/64 z^2 = 1/16

multiply by 64 to clear the fraction on the left side

1/4 * 64 z^2 =1/16 *64

z^2 = 4

take the square root of each side

sqrt(z^2) = ±sqrt(4)

z = ±2  

we are multiplying by 2 each time.