Working simultaneously and independently at an identical constant rate, 4 machines of a certain type can produce a total of x units of product P in 6 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product P in 4 days?

(A) 24
(B) 18
(C) 16
(D) 12
(E) 8

B. 18

Step-by-step explanation:

The 4 machines can produce x units in 6 days. This means they have a daily total rate of x/6 units per day.

Since the machines are similar and that they work at the same rate, this means that the individual rates of each machine would be x/6/4 = x/24 units per day.

Now we are looking at producing 3x units in 4 days. This means that we want to produce 3x/4 units in a single day. Now, since each machine would work at a rate of x/24, we need to know the number of machines we need. To know this number, we simply divide what is to be achieved by the individual rate:

This is 3x/4 divided by x/24. This mathematically means 3x/4 * 24/x = 18 machines

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

-4

step-by-step explanation:

do 6-10=

if u need it to be negative.