the equation of a circle is x² + y² - 4x + 2y - 31 = 0. what is the center and the radius of the circle? show your work.

centre = (2, - 1), radius = 6

Step-by-step explanation:

Rearrange the equation by placing the x and y terms together and adding 31 to both sides

Given

x² + y² - 4x + 2y - 31 = 0, then

x² - 4x + y² + 2y = 31

Use the method of completing the square

add ( half the coefficient of the x/y term )² to both sides

x² + 2(- 2)x + 4 + y² + 2(1)y + 1 = 31 + 4 + 1

(x - 2)² + (y + 1)² = 36

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r the radius

compare to (x - 2)² + (y + 1)² = 36, then

centre = (2, - 1) and r = = 6

step-by-step explanation:

ok so im not 100% sure but you would start by adding 5.1t and 1.9t beacuse they have the same variable. that is 7t.   then add -3.6 + 1.2 which is -2.4

so then keep that as -2.4 + 7t. i apologize if this is incorrect. best luck on your test < 3

let y equal to

the total fare and x is the mile of taxi ride. so the equation is

y = 0.55x + 1.75

since susie has

$10 to spend for a taxi cab, so he can have

10 = 0.55x +

1.75

x = 15 miles of

taxi ride

so the system of

inequality is

10 < 0.55x +

1.75

x > 2