Answer: 1 5/9 (one and five-ninths)
Where is the picture? If you could add your picture I’d be glad to help you!! :)
the assumption being that the first machine is the one on the left-hand-side and the second is the one on the right-hand-side.
the input goes to the 1st machine and the output of that goes to the 2nd machine.
a)
if she uses and input of 6 on the 2nd one, the result will be 6² - 6 = 30, if we feed that to the 1st one the result will be √( 30 - 5) = √25 = 5, so, simply having the machines swap places will work to get a final output of 5.
b)
clearly we can never get an output of -5 from a square root, however we can from the quadratic one, the 2nd machine/equation.
let's check something, we need a -5 on the 2nd, so

so if we use a "1" as the output on the first machine, we should be able to find out what input we need, let's do that.

so if we use an input of 6 on the first machine, we should be able to get a -5 as final output from the 2nd machine.

Step-by-step explanation:
- In the first parabola it opens on the left and the equation of parabola can be expressed as,
in vertical component <u>(y)² = (-) a (x-h)² + k</u>
cause the parabola is horizontal and it opens on the left.
2. In the second parabola the vertex opens on the right and hence the equation cane be given as,
in vertical component <u>(y)² = a (x-h)² + k</u>
cause the parabola is horizontal and opens on the right.
3. the third equation is given as,
in horizontal component<u> (x²) =</u> <u> (-) a (x-h)² + k</u>
since the parabola is vertical and opens down.
4. the fourth equation is given as,
in the horizontal component <u>(x)² = a (x-h)² + k</u>
since the parabola is vertical and opens up.