For what value of k does the equation x^2-5x+(k+6)=0 have equal roots?

k = 0.25.

Step-by-step explanation:

For the equation to have equal roots the discriminant b^2 - 4ac = 0.

So for this equation , a = 1, b = -5 and c = (k + 6) so:

(-5)^2 - 4*1*(k + 6) = 0

25 - 4k - 24 = 0

25 - 24 = 4k

4k = 1

k = 1/4

k = 0.25.

(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