Pennies (P) = 24
Nickels = 1/2P
Dimes = 1/2P + 5
Quarters = (1/2P + 5) -6
Therefore...
Nickels = 1/2P = 1/2(24)= 12
Dimes = 12 + 5 = 17
Quarters = 17 - 6 = 11
Let`s assume that points M, N and P are the touching points of those 3 circles:Then:Y M + M Z = 14,Z N + N X = 20X P + P Y = 18And also: M Z = ZN, Y M = P Y and N X = X P.Now we have a system of 3 equations ( Y M, M Z and X P are the radii of each circle ):Y M + M Z = 14M Z + X P = 20X P + Y M = 18 Y M - M Z = - 14+X P + Y M = 18 X P - M Z = 4Y M - M Z = - 14+M Z + X P = 20 X P - Y M = 6 /* ( - 1 )X P - M Z = 4 X P + Y M = - 6 X P - M Z = 4 Y M - M Z = - 2 Y M + M Z = 14 2 Y M = 12 => Y M = 6M Z - 6 = 2 => M Z = 8X P + 6 = 18
X P = 12
Radii of the circles are: 12, 8 and 6.
Let c represents the cost of a candy apple and b represents the cost of a bag of peanuts.
Darius can purchase 3 candy apples and 4 bags of peanuts. So his total cost would be 3c + 4b. Darius can buy 3 candy apples and 4 bags of peanuts in $11.33,so we can write the equation as:
3c + 4b = 11.33 (1)
Darius can purchase 9 candy apples and 5 bags of peanuts. So his total cost would be 9c + 5b. Darius can buy 9 candy apples and 5 bags of peanuts in $23.56,so we can write the equation as:
9c + 5b = 23.56 (2)
<span>Darius decides to purchase 2 candy apples and 3 bags of peanuts. The total cost in this case will be 2c + 3b. To find this first we need to find the cost of each candy apple and bag of peanuts by solving the above two equations.
Multiplying equation 1 by three and subtracting equation 2 from it, we get:
3(3c + 4b) - (9c + 5b) = 3(11.33) - 23.56
9c + 12b - 9c - 5b = 10.43
7b = 10.43
b = $1.49
Using the value of b in equation 1, we get:
3c + 4(1.49) = 11.33
3c = 5.37
c = $ 1.79
Thus, cost of one candy apple is $1.79 and cost of one bag of peanuts is $1.49.
So, 2c + 3b = 2(1.79) + 3(1.49) = $ 8.05
Therefore, Darius can buy 2 candy apples and 3 bags of peanuts in $8.05</span>
Answer: 1 over 20
Step-by-step explanation: If the spinner has 5 parts to it at purple is one of those parts then the spinner has a 1/5 chance of it landing there.
If there are 4 cards and 1 of them are pink then there is a 1/4 chance of picking pink(if done randomly)
So if we mutiply 1/4 and 1/5, we get 1/20
That is how I arrived at my answer of 1 over 20
Answer:
(2, 13)
(-7, -5)
Step-by-step explanation:
Easiest and fastest way to do this is to graph the systems of equations and analyze the graph where the 2 graphs intersects.
