It would be: 6/10 & 12/20
Step One
Find z
All triangles have 180 degrees. No exceptions.
z + 47 + 90 = 180 combine like terms on the left.
z + 137 = 180 subtract 137 from both sides
z = 180 - 137
z = 43 degrees.
Step Two
Use the sine function to find y
Sin(43) = opposite side / hypotenuse
opposite side = 35
sin(43) = 35 / hypotenuse
hypotenuse = 35 / sin(43)
y = 35/0.6820
y = 51.32
Solve using cos(x)
Note this problem could have been done in a shorter way.
Cos(47) = adjacent / hypotenuse.
hypotenuse = adjacent / cos(47)
y = 35 / cos(47)
y = 35 / 0.6820
y = 51.32 Both answers agree. It is a good thing to know how to do this question both ways.
Represent the unknows with n and d.
Then n+d = 44 (# of coins)
and
$0.05n + $0.10d = $3.10 (value of coins)
Solving the first equation for n, we get n = 44-d. Subst. 44-d for n in the 2nd equation:
0.05(44-d) + 0.10d = 3.10
Then 2.20 - 0.05d + 0.10d = 3.10, or
2.20 + 0.05d = 3.10, or 0.05d = 0.90. Solving for d,
0.90
d = -------- = 18
0.05
There are 18 dimes and 44-18 nickels. How many nickels is that? ;)
30 divided by 60 is 1/2
1/2 miles per minute
10 x 1/2 = 5
5 miles in 10 minutes
Hope this helped
