Regular hexagon ABCDEF is inscribed in circle X and has an apothem that is 6√3 inches long. Use the length of the apothem to cal
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X+y=32
xy=-80
x+y=32
minus x both sides
y=32-x
sub for y
x(32-x)=-80
32x-x^2=-80
times both sides by -1
x^2-32x=80
minus 80 both sides
x^2-32x-80=0
use quadratic formula
where
ax^2+bx+c=0
x=
a=1
b=-32
c=-80
x=
x=
x=
x=
x=16+/-4√21
the numbers are
16+4√21 and 16-4√21
xy=-80
x+y=32
minus x both sides
y=32-x
sub for y
x(32-x)=-80
32x-x^2=-80
times both sides by -1
x^2-32x=80
minus 80 both sides
x^2-32x-80=0
use quadratic formula
where
ax^2+bx+c=0
x=
a=1
b=-32
c=-80
x=
x=
x=
x=
x=16+/-4√21
the numbers are
16+4√21 and 16-4√21