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)

i think it is c, not positive though

step-by-step explanation:

total amount of money that he should pay if he has not used his duty free exemption is $98

step-by-step explanation:

given a united states citizen returning to the states declares the following items at the customs office: 3 shirts at $8.50 each 2 dresses at $27.50 each 1 pair of gold cuff links at $17.50 per pair. we have to find how much he pay

cost of 3 shirts if one cost at $8.50 is

cost of 2 dresses if one cost at $27.50 is  

cost of 1 pair of gold cuff at $17.50

so, total amount of money that he should pay if he has not used his duty free exemption is   $25.5+$55+$17.50=$98