Amoure0723
Answered

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Leila puts an integer into the "In" box of each machine.
She finds that the answer that appears in the "Out" box of Machine A is the same as the
answer that appears in the "Out" box of Machine B.
What was the answer produced by both machines?
Show how you figured it out

Sagot :

MrRoyal

The machines represent equivalent expressions.

The output produced by both machines is 372

The equation represented on machine A is:

[tex]\mathbf{y = 2(5x + 3) - 24}[/tex]

The equation represented on machine B is:

[tex]\mathbf{y = 4(2(x + 11) - 7)}[/tex]

Where: x and y represent the inputs and the outputs, respectively

When the outputs are the same, it means:

[tex]\mathbf{y = y}[/tex]

So, we have:

[tex]\mathbf{2(5x + 3) - 24 = 4(2(x + 11) - 7)}[/tex]

Open brackets

[tex]\mathbf{10x + 6 - 24 = 8x + 88 - 28}[/tex]

[tex]\mathbf{10x - 18 = 8x + 60}[/tex]

Collect like terms

[tex]\mathbf{10x - 8x = 18 + 60}[/tex]

[tex]\mathbf{2x = 78 }[/tex]

Divide both sides by 2

[tex]\mathbf{x = 39 }[/tex]

Substitute 39 for x in [tex]\mathbf{y = 2(5x + 3) - 24}[/tex]

[tex]\mathbf{y = 2 \times (5 \times 39 + 3) - 24}[/tex]

[tex]\mathbf{y = 372}[/tex]

Hence, the output produced by both machines is 372

Read more about equivalent expressions at:

https://brainly.com/question/15715866

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