See in the explanation
<h2>
Explanation:</h2>
In this exercise, <em>we have the following points:</em>

And <em>the following linear equations:</em>

When plotting these graphs, we find the following facts:
<h3>For (1):</h3>
We see the graph in the first figure below. The graph only passes through the point (0, 8)
<h3>For (2):</h3>
This is the second graph below. The graph passes neither through point (0, 8) nor (6, 4)
<h3>For (3):</h3>
This is the third graph below. The graph passes neither through point (0, 8) nor (6, 4)
<h3>For (4):</h3>
This is the fourth graph below. The graph only passes through the point (0, 8)
So, <em>there is no any equation of the line that passes through the points (0.8) and (6.4) at the same time.</em>
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Answer:
3 batches
Step-by-step explanation:
We have been given that a sports drink recipe calls for 5/3 tablespoons of powered drink mix for every 12 ounces of water.
We need to find out how many batches can be made with 5 tablespoons of drink mix and 36 ounces of water.
So, from the given information we see that to make 1 batch of sports drink we need 5/3 tablespoons of powdered drink mix for every 12 ounces of water.
So, we have 36 ounces of water. But we know that for 1 batch of sports drink we need to 12 ounces. So with 36 ounces of water we can make
= 3 batches
Therefore, we can make 3 batches of sports drink from 5 tablespoons of powdered drink mix and 36 ounces of water.
We know that
The mixture in Tank A is 5/(5+10) = 1/3 pure alcohol.
The mixture in Tank B is 3/(3+12) = 1/5 pure alcohol.
We want to combine these to make a mixture that is 25% = 1/4 pure alcohol.
Let
x------------------> the volume in gallons of solution taken from Tank A.
y------------------>the volume in gallons of solution taken from Tank B
Then
the volume taken from Tank B will be y=(8 -x)
remember that we are making a total of 8 gallons of solutions.
The alcohol content of the mixture is(1/3)x +(1/5)(8 -x) = (1/4)*85x + 3(8 -x) = 30 ----------> 5x+24-3x=30----------> 5x-3x=30-24
2x = 6 ----------------> x=3
y=8-x--------> y=8-3-----> y=5
the answer is
3 gallons should be taken from Tank A;
5 gallons should be taken from Tank B