Solve each system of equations
x^2+y^2+18x+29=0
x+y=1

two solutions : (-3;4)  and (-5;6)

Step-by-step explanation:

hello :

X²+y²+18x+29=0    ..(1)

X+y=1 ...(2)

by (2) : y = 1 - x

put this value in (1) : x² +(1-x)² +18x+29 = 0

x² +1 +x² -2x+18x +29 =0

2x²+16x +30 = 0

x²+8x+15 =0

delta = b²-4ac     a=1   b=8   c = 15

delta = (8)²-4(1)(15)=64-60 =4 = 2²

X1=(-8+2)/2 = - 3

X2=(-8-2)/2 = - 5

case 1 : x = -3    y = 1 - (-3) = 4

case 2 : x = -5    y = 1 - (-5) = 6

(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180 

same as (2x + 16) + (x) = 180