What two numbers add up to -14 and multiply out to -240
2 answers:
So x+y=-14
xy=-240
x+y=-14
subtract y from both sides
x=-14-y
subsitute for x in second equation
(-14-y)y=-240
multiply
-y^2-14y=-240
add y^2+14y to both sides
0=y^2+14y-240
use quadratic equation to solve which is
if you have ax^2+bx+c so
a=1
b=14
c=-240
subsitute and get
(+/- means that there are 2 equations exg 2+/-8=2+8 and 2-8)
the numbers are 10 and -24
xy=-240
x+y=-14
subtract y from both sides
x=-14-y
subsitute for x in second equation
(-14-y)y=-240
multiply
-y^2-14y=-240
add y^2+14y to both sides
0=y^2+14y-240
use quadratic equation to solve which is
a=1
b=14
c=-240
subsitute and get
the numbers are 10 and -24
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Answer:
r = 10 , centre = (6, - 2 )
Step-by-step explanation:
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 is the radius
given
x² - 12x - 60 = - y² - 4y ( add y² + 4y to both sides )
x² - 12x + y² + 4y - 60 = 0 ( add 60 to both sides )
x² - 12x + y² + 4y = 60
using the method of completing the square
add ( half the coefficient of the x and y terms )² to both sides
x² + 2(- 6)x + 36 + y² + 2(2)y + 4 = 60 + 36 + 4
(x - 6)² + (y + 2)² = 100 ← in standard form
with centre = (6, - 2 ) and r = = 10