given FH with coordinates F(4,-5) and H(-8,19), if G lies on FH such that that the ratio of FG to FH is 1:6, find the coordinates of G

  G = (2, -1)

Step-by-step explanation:

You want ...

  FG/FH = 1/6 = (G -F)/(H -F)

  H -F = 6(G -F)

  H +5F = 6G . . . . . . add 6F, simplify

  G = (H +5F)/6 . . . . .divide by 6

Substituting the given coordinates, we get ...

  G = ((-8, 19) +5(4, -5))/6 = (-8+20, 19 -25)/6 = (12, -6)/6

  G = (2, -1)

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet

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