Check the picture below.
notice the solid circle at -4 and 3, since it includes those points.
also notice the dashed line, though the lines keeps on going those ways, is not included in the piece-wise, since it's not part fo the domain or constraints.
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.

Answer:
The solutions are -0.65 and 4.65.
Step-by-step explanation:
3x^2 - 12x = 9
Divide both sides by 3
x^2 - 4x = 3
To make a square with "x^2 - 4x", you need to have a "+ 4" after it so it can be simplified as (x-2)^2. So add 4 to both sides.
x^2 - 4x + 4 = 7
(x-2)^2 = 7
x - 2 = (square root) of 7
x = 2 (+/-) (square root) of 7.
x = {-0.65, 4.65}
The solutions are -0.65 and 4.65.
hope this helps:)sorry if it doesnt
Answer:
1) Bigger sector = 168.8pi
1) Smaller sector = 56.3pi
2) Bigger sector = 529.9
3) Smaller sector = 176.6
Step-by-step explanation:
1) Bigger sector =
×pi×15×15
= 168.75pi
1) Smaller sector =
×pi×15×15
=
×pi×15×15
= 56.25pi
2) Bigger sector =
×3.14×15×15
= 529.875
2) Smaller sector =
×3.14×15×15
=
×3.14×15×15
= 176.625
150 is smaller than 200 so 25 is smaller than 40, but 25, in perspective to the numbers, is much smaller than 40. Ana is faster.
Check:
Takashi: 200 divided by 400 equals 5 yd/sec
Ana: 150 divided by 25 equals 6 yd/sec