janessa0502
15.10.2020 •
Mathematics
You have been saving nickels, dimes, and quarters in a jar for about a year. You decide to see how much money you've saved up. When you get everything counted it turns out you have 361 total nickels, dimes, and quarters worth a total of $41.45. You think is is odd that you have exactly twice as many dimes as quarters. Find the number of each coin. Number of Nickels: Number of Dimes: Number of Quarters:
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Ответ:
x = number of nickels = 127
y = number of dimes = 156
z = number of quarters = 78
Step-by-step explanation:
Let
x = number of nickels
y = number of dimes
z = number of quarters
Total worth of the coins = $41.45
Total number of coins = 361
x + y + z = 361 (1)
dime = $0.1,
nickel = $0.05
quarter = $0.25
0.05x + 0.1y + 0.25z = 41.45 (2)
twice as many dimes as quarters.
y = 2z
Substitute y = 2z into (1) and (2)
x + 2z + z = 361
0.05x + 0.1(2z) + 0.25z = 41.45
x + 3z = 361
0.05x + 0.2z + 0.25z = 41.45
x + 3z = 361 (3)
0.05x + 0.45z = 41.45 (4)
Multiply (4) by 20
x + 3z = 361 (3)
x + 9z = 829 (5)
Subtract (3) from (5)
9z - 3z = 829 - 361
6z = 468
Divide both sides by 6
z = 468 / 6
= 78
z= 78
Recall,
y = 2z
= 2(78)
= 156
y = 156
Substitute the value of y and z into
x + y + z = 361
x + 156 + 78 = 361
x + 234 = 361
x = 361 - 234
= 127
x= 127
x = number of nickels = 127
y = number of dimes = 156
z = number of quarters = 78
Ответ:
the correct answer is:
definition of sine in right triangle
explanation:
the ratio for sine is opposite/hypotenuse. this means that for the sine of angle b, we want the side opposite b, which is ae, over the hypotenuse, which is c:
sin b = ae/c
multiply both sides by c:
c sin b = (ae/c)*c
c sin b = ae
this is by definition of sine.
this also applies to step 8.