Answer:
The expression that shows how long the two machines will operate simultaneously is:

Step-by-step explanation:
We know that:
x: hours to manufacture a deck of cards for machine A
y: hours to manufacture a deck of cards for machine B
z: hours that machine A operates alone
The number of decks manufactured only by machine A is:

So, the remaining decks are given by:

Then, the combined rate of machines A and B would be:

The work-rate formula is:

Hence, the time that the two machines work simultaneously is:


Well it depends on where the number is at. So you have to estimate to the closest number on the answers.
Ok?
Answer:
r = 40/π exact answer
r = 12.7 decimal approximation
Step-by-step explanation:
arc length formula
s = (∅/360) * 2πr
s = (∅/180) * πr
--------------------------------
Plug in the givens
10 = (45/180) * πr
10 = .25πr
Divide both sides by .25
40 = πr
divide both sides by π
40/π = r
r = 40/π exact answer
r = 40/3.14
r = 12.7 decimal approximation