Use completing the square to find the centre and radius of the circle with equation
x^2-4x+y^2-2y-3=0

Centre: (2,1)

Radius:2^2

Step-by-step explanation:

Circle radius given x^2 - 4x + y^2- 2y - 3 =0        r = 2^2

x^2 - 4x + y^2- 2y - 3 =0

Circle Equation: (x-a)^2+ (y-b)^2=r^2 is the circle equation with a radius, r centered at (a, b)

x^2 - 4x + y^2- 2y - 3 =0 in the form of the standard circle equation

(x-2)^2+(y-1)^2=(2,2^2)^2

Move the loose number to the right side

x^2 - 4x + y^2- 2y - 3 =0

Group x - variables and y - variables together

(x^2 - 4x) + (y^2 -2y) = 3

Convert x to square form

(x^2 - 4x + 4) + (y^2 - 2y) = 3 + 4

Convert to square form

(x -2)^2 + (y^2 - 2y) = 3 + 4

Convert y to square form

(x -2)^2 + (y^2 - 2y + 1) = 3 + 4 + 1

Convert to square form

(x-2)^2 + (y - 1)^2 = 3 + 4 + 1

Refine 3 + 4 + 1

(x-2)^2+(y-1)^2=8

Rewrite the standard form

(x-2)^2 + (y - 1)^2 = (2^2)^2

Therefore the circle properties are

(a, b) = (2,1), r = 2^2

And the radius is

2^2

CENTRE:

Move the loose number to the right

X^2-4x+y^2-2y = 3

Group x- variables and y- variables together

(x^2 - 4x) + (y^2 - 2y) = 3

Convert x to square form

(x^2 - 4x + 4) + (y^2 - 2y) = 3 + 4

Convert to square form

(x -2)^2 + (y^2 - 2y) = 3 + 4

Convert y to square form

(x -2)^2 + (y^2 - 2y + 1) = 3 + 4 + 1

Convert to square form

(x -2)^2 + (y - 1) = 3 + 4

Refine 3 + 4 + 1

(x- 2)^2 + (y - 1)^2 = 8

Rewrite in standard form

(x-2)^2 + (y - 1)^2 = (2^2)^2

Therefore the circle properties are:

(a, b) = (2, 1), r+2^2

And the center is:

(2, 1)

step-by-step explanation:

always plug in x. in this case, x equals 4.

i'm going to first solve 4(2+3x)

1) 4(2+3(4)) use pemdas to solve.

i'm going to multiply whats in the parenthesis first, so 3 times 4=12.

2)4 (2+12) i'm then going to multiply 4 by both numbers in the parenthesis (because multiplying comes before adding)

4 times 2= 8.   4 times 12= 48

4) (8+48)= 56 (answer)

i'm then going to solve 8+12x and plug in 4 for x.

1) 8 +12(4)

multiplying comes before adding, so i'm gonna multiply 12 and 4.

12 times 4= 48.

2) 8+48=56

both equal the same!

(w – 2.5)(w + 2.5)

(–4v – 9)(–4v + 9)

step-by-step explanation: