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zysi [14]
3 years ago
8

Delaney would like to make a 5 lb nut mixture that is 60% peanuts and 40% almonds. She has several pounds of peanuts and several

pounds of a mixture that is 20% peanuts and 80% almonds. Let p represent the number of pounds of peanuts needed to make the new mixture, and let m represent the number of pounds of the 80% almond-20% peanut mixture.
(a) What is the system that models this situation?
(b) Which of the following is a solution to the system: 2 lb peanuts and 3 lb mixture; 2.5 lb peanuts and 2.5 lb mixture; 4 lb peanuts and 1 lb mixture? Show your work.
Mathematics
1 answer:
jonny [76]3 years ago
4 0

A) A ratio system

B) The 4 lb peanuts and the 1 lb mixture because the 4lb added to the 1lb of mixture give the correct percentages.

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G(5) for the sequence g = <span>{(6,3), (-4,2), (5,0)} is 0</span>
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If you have a cubic polynomial of the form y = ax^3 + bx^2 + cx + d and lets say it passes through the points (2,28), (-1, -5),
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Step-by-step explanation:

<u>Step 1:  Solve using the first point</u>

<em>(2, 28)</em>

28 = a(2)^3 + b(2)^2 + c(2) + d

28 = 8a + 4b + 2c + d

<u>Step 2:  Solve using the second point</u>

<em>(-1, -5)</em>

-5 = a(-1)^3 + b(-1)^2 + c(-1) + d

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<u>Step 3:  Solve using the third point</u>

<em>(4, 220)</em>

220 = a(4)^3 + b(4)^2 + c(4) + d

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<u>Step 4:  Solve using the fourth point</u>

<em>(-2, -20)</em>

-20 = a(-2)^3 + b(-2)^2 + c(-2) + d

-20 = -8a + 4b - 2c + d

<u>Step 5:  Combine the first and fourth equations</u>

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8 = 8b + 2d

8 - 8b = 8b - 8b + 2d

(8 -8b)/2 = 2d/2

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<u>Step 6:  Solve for c in the second equation</u>

-5 + 5 = -a + b - c + d + 5

0 + c = -a + b - c + c + d + 5

c = -a + b + d + 5

<u>Step 7:  Substitute d with the stuff we got in step 5</u>

c = -a + b + (4 - 4b) + 5

c = -a + b + 4 - 4b + 5

c = -a - 3b + 9

<u>Step 8:  Substitute d and c into the first equation</u>

<u />28 = 8a + 4b + 2(-a - 3b + 9) + (4 - 4b)

28 = 8a + 4b - 2a - 6b + 18 + 4 - 4b

28 - 22 = 6a - 6b + 22 - 22

6 / 6 = (6a - 6b) / 6

1 + b = a - b + b

1 + b = a

<u>Step 9:  Substitute a, b, and c into the third equation</u>

220 = 64(1 + b) + 16b + 4(-(1 + b) - 3b + 9) + (4 - 4b)

220 = 64 + 64b + 16b + 4(-1 - b - 3b + 9) + 4 - 4b

220 - 100 = 60b + 100 - 100

120 / 60 = 60b / 60

2 = b

<u>Step 10:  Find a using b = 2</u>

a = b + 1

a = (2) + 1

a = 3

<u>Step 11:  Find c using a = 3 and b = 2</u>

c = -a - 3b + 9

c = -(3) - 3(2) + 9

c = -3 - 6 + 9

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<u>Step 12:  Find d using b = 2</u>

d = 4 - 4b

d = 4 - 4(2)

d = 4 - 8

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Answer:  a = 3, b = 2, c = 0,d = -4

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2 years ago
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Answer:

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JulijaS [17]

Answer:

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end up with: (1/3)y + 14 = (1/2)y

2) multiply both sides of your equation by 2 to cancel out the (1/2)

end up with: (2/3)y + 28 = y

3) subtract (2/3)y from both sides of the equation to cancel out the positive (2/3)y

end up with: 28 = (1/3)y

4) multiply both sides of the equation by 3 to cancel out the (1/3)

end up with: 84 = y

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kirill [66]

Answer:

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Bus A takes 30 minutes to complete its route once

Bus B takes 40 minutes to complete its route once.

We solve this finding the Lowest Common Multiple of the minutes each bus uses to complete it's route

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= 3 × 4 × 10

= 120 minutes

120 minutes after 9 am is

60 minutes = 1 hour

60 minutes = 1 hour

= 2 hours.

9am + 2 hours

= 11 am.

Therefore, they be back at the bus depot together at 11 am

4 0
3 years ago
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