Which dilation is shown by the graph?

D. D₂ (∆XYZ)

Step-by-step explanation:

Dₙ = (x,y) → ((n)x, (n)y)

X = (-1, 2).

Y = (2, -1).

Z = (-2, -1).

Dₙ ∆XYZ:

X(-1, 2) → X'(-2, 4)

Y(2, -1) → Y'(4, -2)

Z(-2, -1) → Z'(-4, -2)

-2 / -1 = 2, 4 / 2 = 2.

4 / 2 = 2, -2 / -1 = 2.

-4 / -2 = 2, -2 / -1 = 2.

D₂ = (x,y) → ((2)x, (2)y).

X(-1, 2) → ((2)(-1), (2)(2)) = X'(-2, 4)

Y(2, -1) → ((2)(2), (2)(-1)) = Y'(4, -2)

Z(-2, -1) → ((2)(-2), (2)(-1)) = Z'(-4, -2)

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