You have $6000 to invest in two stock funds. the first fund pays 5% annual interest and the second account pays 9% annual interest. if after a year you have made $380 in interest, how much money did you invest in each account

First fund: $4000

second account: $2000

Step-by-step explanation:

invest x for first fund (A) and y for second fund (B)

interest for A: x * 0.05

interest for B: y * 0.09

0.05 x + 0.09 y = 380 (1)

x + y = 6000 (2)

y = 6000 - x   substitute y in (1)

0.05 x + 0.09 (6000 - x) = 380

0.05x + 540 - 0.09x = 380

0.04 x = 160

x = 4000

y = 6000 -4000 = 2000

check: 4000 x 0.05 + 2000 x 0.09 = 200 + 180 = 380

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step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)

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step-by-step explanation: