Note: it is not the second answer.

fourth option

Step-by-step explanation:

In a right triangle with legs x ( horizontal leg) and y ( vertical leg) and hypotenuse r, then

sinθ = =

Q=number of quarters
d=number of dimes

total number is 19 so
q+d=19

value of coins is 0.25 for each quarter and 0.1 for each dime
value=valuequarters+valuedimes
4=0.25q+0.1d

the system of equations is
q+d=19
0.25q+0.1d=4
for ease, multily second equation by 10
2.5q+d=40
multiply first equation by -1 and add to this new equation

-q-d=-19
2.5q+d=40 +
1.5q+0d=21

1.5q=21
divide both sides by 1.5
q=14

sub back
q+d=19
14+d=19
mnus 14
d=5

5 dimes
14 quarters