X+2y=-1 and 4x-4y=20 solve by substitution
1 answer:
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Answer:
(x) = 2(1/6)^x
Step-by-step explanation:
To easily solve this problem, we can graph each option using a graphing calculator, or any equation plotting tool.
Case 1
f(x) = 2(6)^x
Case 2
f(x) = 1/2*(6)^x
Case 3
f(x) = 2(1/6)^x
Case 4
f(x) = 1/2*(1/6)^x
By looking at the pictures below, we can tell that the correct option is
Case 3
f(x) = 2(1/6)^x
Since the stretch is done by a factor of 2
When the initial input is equal to 15 and the final output is -6, the machines should be stacked in this order:
- Fourth machine (y₄ = -2x + 34)
- Second machine (y₂ = (x - 2)²)
- First machine (y₁ = -|3x|)
- Third machine (y₃ = -x/3 - 10)
When the initial input is equal to 8 and the final output is 2, the machines should be stacked in this order:
- First machine (y₁ = -|3x|)
- Third machine (y₃ = -x/3 - 10)
- Second machine (y₂ = (x - 2)²)
- Fourth machine (y₄ = -2x + 34)
From the information provided, we know that the initial input is equal to 15 and the final output is -6. Thus, we would solve the puzzle as follows:
For the fourth machine, we have;
y₄ = -2x + 34
y₄ = -2(15) + 34
y₄ = -30 + 34
y₄ = 4.
Therefore, the output is equal to 4.
For the second machine, we have:
y₂ = (x - 2)²
y₂ = (4 - 2)²
y₂ = 2²
y₂ = 4
Therefore, the output is equal to 4.
For the first machine, we have:
y₁ = -|3x|
y₁ = -|3 × 4|
y₁ = -12.
Therefore, the output is equal to -12.
For the third machine, we have:
y₃ = -x/3 - 10
y₃ = -(-12)/3 - 10
y₃ = 12/3 -10
y₃ = 4 - 10
y₃ = -6
Therefore, the output is equal to -6.
In conclusion, we can logically deduce that the machines should be stacked in this order:
- Fourth machine (y₄ = -2x + 34)
- Second machine (y₂ = (x - 2)²)
- First machine (y₁ = -|3x|)
- Third machine (y₃ = -x/3 - 10)
When the initial input is equal to 8 and the final output is 2. Thus, we would solve the puzzle as follows:
y₁ = -|3x|
y₁ = -|3 × 8|
y₁ = -24.
For the third machine, we have:
y₃ = -x/3 - 10
y₃ = -(-24)/3 - 10
y₃ = 24/3 -10
y₃ = 8 - 10
y₃ = -2.
For the second machine, we have:
y₂ = (x - 2)²
y₂ = (-2 - 2)²
y₂ = 4²
y₂ = 16
For the fourth machine, we have;
y₄ = -2x + 34
y₄ = -2(16) + 34
y₄ = -32 + 34
y₄ = 2.
When the initial input is equal to 8 and the final output is 2, the machines should be stacked in this order:
- First machine (y₁ = -|3x|)
- Third machine (y₃ = -x/3 - 10)
- Second machine (y₂ = (x - 2)²)
- Fourth machine (y₄ = -2x + 34)
Read more on final outputs here: brainly.com/question/17670171
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Complete Question:
1. In what order should you stack the machines so that when 15 is dropped into the first machine, and all four machines have had their effect, the last machine’s output is -6?
2. When the initial input is 8 in what order should the machines be arranged so that the final output is 2?
