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:

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

d

step-by-step explanation:

by observation, we can see that the the graph is simply the graph of y = |x| that has been shifted 4 units downwards and 3 units to the left.

we can recognize in choice d :

y = | x + 3 |   - 4 (rewriting in general form)

y = | x - (- 3) |   - 4

the "-4 " term means   that the graph has been shifted by 4 units in the negative y direction

the "-3 " term means   that the graph has been shifted by 3 units in the negative x direction

this matches our observation of the graph described above.

the solution is h=10 because you add 9 to each side of the equation.