If you covert it to 18/30 then it is much simpler yet if you still need help then read on
4/30
Answer:
(i) = 3
(ii) = 20
Step-by-step explanation:
x = 1
y = -2
z = -1
(i) 4x - 3y + 7z
4(1) - 3(-2) + 7(-1)
4 + 6 - 7 = 3
(ii) 2x³ - 6y²z + 3xyz²
2(1)³ - 6(-2)²(-1) + 3(1)(-2)(-1)²
2 + 24 - 6 = 20
5/4 - square root of 3 = -0.48
Check the picture below.
let's notice the "white" ∡1 is an inscribed angle with an intercepted arc of (x-32), and the "green" ∡5 is also an inscribed angle with an intercepted arc of (2x).
the ∡6 and ∡2 are both external angles, however they intercepted two arcs, a "far arc" and a "near arc", thus we'll use the far arc - near arc formula, as you see in the picture, and we'll use the inscribed angle theorem for the other two.
![\bf \measuredangle 1=\cfrac{x-32}{2}\implies \measuredangle 1 =\cfrac{32}{2}\implies \measuredangle 1 = 16 \\\\[-0.35em] ~\dotfill\\\\ \measuredangle 5 =\cfrac{2x}{2}\implies \measuredangle 5 = x\implies \measuredangle 5 = 64 \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cbf%20%5Cmeasuredangle%201%3D%5Ccfrac%7Bx-32%7D%7B2%7D%5Cimplies%20%5Cmeasuredangle%201%20%3D%5Ccfrac%7B32%7D%7B2%7D%5Cimplies%20%5Cmeasuredangle%201%20%3D%2016%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cmeasuredangle%205%20%3D%5Ccfrac%7B2x%7D%7B2%7D%5Cimplies%20%5Cmeasuredangle%205%20%3D%20x%5Cimplies%20%5Cmeasuredangle%205%20%3D%2064%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
![\bf \measuredangle 2 = \cfrac{(2x+8)~~-~~(x-32)}{2}\implies \measuredangle 2=\cfrac{2x+8-x+32}{2} \\\\\\ \measuredangle 2=\cfrac{x+40}{2}\implies \measuredangle 2=\cfrac{104}{2}\implies \measuredangle 2=52 \\\\[-0.35em] ~\dotfill\\\\ \measuredangle 6=\cfrac{[(2x+8)+(x)]~~-~~(2x)}{2}\implies \measuredangle 6=\cfrac{3x+8-2x}{2}\implies \measuredangle 6=\cfrac{x+8}{2} \\\\\\ \measuredangle 6=\cfrac{72}{2}\implies \measuredangle 6=36](https://tex.z-dn.net/?f=%5Cbf%20%5Cmeasuredangle%202%20%3D%20%5Ccfrac%7B%282x%2B8%29~~-~~%28x-32%29%7D%7B2%7D%5Cimplies%20%5Cmeasuredangle%202%3D%5Ccfrac%7B2x%2B8-x%2B32%7D%7B2%7D%20%5C%5C%5C%5C%5C%5C%20%5Cmeasuredangle%202%3D%5Ccfrac%7Bx%2B40%7D%7B2%7D%5Cimplies%20%5Cmeasuredangle%202%3D%5Ccfrac%7B104%7D%7B2%7D%5Cimplies%20%5Cmeasuredangle%202%3D52%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cmeasuredangle%206%3D%5Ccfrac%7B%5B%282x%2B8%29%2B%28x%29%5D~~-~~%282x%29%7D%7B2%7D%5Cimplies%20%5Cmeasuredangle%206%3D%5Ccfrac%7B3x%2B8-2x%7D%7B2%7D%5Cimplies%20%5Cmeasuredangle%206%3D%5Ccfrac%7Bx%2B8%7D%7B2%7D%20%5C%5C%5C%5C%5C%5C%20%5Cmeasuredangle%206%3D%5Ccfrac%7B72%7D%7B2%7D%5Cimplies%20%5Cmeasuredangle%206%3D36)