In triangle $DEF,$ $\angle D = 30^\circ,$ $\angle F = 60^\circ,$ and $EF = 6.$ Find $DE + DF.$ [asy]
unitsize(2 cm);

pair D, E, F;

D = (0,sqrt(3));
E = (0,0);
F = (1,0);

draw(D--E--F--cycle);

label("$D$", D, N);
label("$E$", E, SW);
label("$F$", F, SE);
label("$6$", (E + F)/2, S);
[/asy]

-4

step-by-step explanation:

(-4+8)=-(4-8)=-8+4=-4

(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

investment b is an ordinary annuity with $3,909.64 in the account after one year.

step-by-step explanation: