In a factory, a certain machine needs 10 min to warm up. it takes 15 min for the machine to run a cycle. the machine can operate for as long as 6 h per day including warm up time. draw a graph showing the total time the machine operates during 1 day as a function of the number of cycles it runs. -what domain and range are reasonable? -is the function a linear function?

Step-by-step explanation:

The machine always takes 10 minutes (or 1/6 hours) to warm up and performs each cycle in 15 minutes, or 0.25 hours.

The maximum amount of daily hours that the machine can work is 6 hours.

Therefore we can represent this situation by means of an equation of the form:

Where

y = daily amount of hours the machine works.

x = number of daily cycles performed.

This equation is a linear function.  Because it has the form y = ax where a is a real number

The graph of this equation is shown in the attached image, where the gray shaded area represents the domain of the function.

The domain of the function is:

(because you can not perform less than zero cycles a day)

. Because the machine can not exceed 6 hours per day, then it can not do more than 23.33 cycles.

So:

The range of the function is:

(because you can not work less than 0 hours a day)

(because the machine can not work more than 6 hours a day)

So

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1

the answer is simply just 6n add the two together as they have an n