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
