Solve the system y = -x + 7 and y = 0.5(x - 3)^2
show all work.

x=-1, y=8

or

x=5, y=2

Step-by-step explanation:

if you rewrite the first as x = 7-y (bring x to the left, y to the right) you can substitute it in the second:

y = 0.5(7-y-3)²

then work out the quadratic factor:

y = 0.5(4² -8y + y²)

2y = y² - 8y + 16

y² - 10y + 16 = 0

(y-8)(y-2) = 0

y=8 or y=2

using x = 7-y you can match the x with that:

y=8 => x = 7-8 = -1

y=2 => x = 7-2 = 5

hope it you

step-by-step explanation:

sin(7pi/6 - pi/3)  

= sin(7pi/6 - 2pi/6)  

= sin(5pi/6)  

= sin(pi - pi/6)  

= sin(pi/6)  

= 1/2  

sin 7pi/6 - sin pi/3  

= sin (pi + pi/6) - sin pi/3  

= -sin pi/6 - sin pi/3  

= -1/2 - sqrt(3)/2  

= -(1+sqrt(3))2

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step-by-step explanation:

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