Find the slope intercept equation that passes through (-3,8) and is perpendicular to the line with the equation: x-7y=12
a: y=1/7x+ 59/7
b: y=-7x - 13
c: y=7x +29
d: y= -1/7x+ 53/7

C.  y = 7x + 29 .

Step-by-step explanation:

First find the slope of the given line:

x - 7y = 12

7y = x - 12

y = 1/7 x - 12/7

The slope = 1/7 so the slope of the line perpendicular to this line is

- 1 / -1/7 = 7.

Finding the equation of the  required line:

y - y1 = m(x - x1)

y1 = 8 , m = 7 and x1 = -3:

y - 8 = 7(x + 3)

y = 7x + 21 + 8

y = 7x + 29  answer.

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47