1.
the equation of a circle is x^2+y^2+10x-4y-12=0. put the equation in standard form. what are the center and radius of the circle? show your work.

Step-by-step explanation:

hello :

an equation of the circle Center at the A(a,b) and ridus : r is :

(x-a)² +(y-b)² = r²

( standard form )

x²+y²+10x-4y-12=0

(x² +10x) + (y²- 4y) -12 = 0

(x² +2(5)(x) +5² -5²) + ( y² -2(2)(y) +2² -2²) -12 = 0

(x + 5)² - 25 + ( y - 2 )² - 4 -12 = 0

(x + 5 )² + ( y - 2 )² = 41 ( standard form )

the center is the point A(-5 ; 2) and   ridus  r = √41

let soccer = x and golf = y

part a

1st equation: x + y = 125

2nd equation: x = y +45

part b

replace x in the 1st equation with the 2nd one:

y + 45 + y = 125

simplify:

2y + 45 = 125

subtract 45 from each side:

2y = 80

divide both sides by 2:

y = 80/2

y = 40

she plays golf for 40 minutes.

part c

no because she plays soccer for 45 minutes longer than golf 40 +45 =   85 minutes, not 80 minutes.