Amachine can stamp 40 envelopes in 8 minutes. how many of these machines, working simultaneously, are required or needed to stamp 120 envelopes per minute?

The number of machines, working simultaneously, that are required or needed to stamp 120 envelopes per minute is 3 machines.

Given the following data:

To find how many machines, working simultaneously, are required or needed to stamp 120 envelopes per minute:

In order to solve this mathematical problem, we would use direct proportion.

By direct proportion:

40 envelopes = 8 minutes

120 envelopes = X minutes

Cross-multiplying, we have:

X = 24 minutes

For the number of machines:

Machine = 3 machines

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Divide 40 by 8 minutes to find the quantity per minute for one machine:

40 / 8 = 5 per minute.

One machine does 5 envelopes per minute.

Now divide 120 by 5 to find the number of machines needed:

120 / 5 = 24

24 machines would be needed.

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.