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Romashka-Z-Leto [24]
3 years ago
11

A 60litres solution of alcohol and water contains 20liters of alcohol .how much alcohol must be added to produce a solution of 5

0% alcohol
Mathematics
1 answer:
iragen [17]3 years ago
7 0
Total quantity of solution containing alcohol and water = 60 liters
Amount of alcohol in the solution = 20 liters
Percentage of alcohol in the solution = (20/60) * 100
                                                           = 100/3
                                                           = 33.33 percent
So
33.33 percent alcohol is = 20 liters
Then
50 percent alcohol = [20/(100/3)] * 50
                               = [(20 * 3)/100] * 50
                               = (60 * 50)/100
                               = 3000/100
                               = 30 liters
So 30 liters of alcohol should be added to make the percentage of alcohol 50% in the solution.
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<span><span> x2-12x-45=0</span> </span>Two solutions were found :<span> x = 15 x = -3</span>

Step by step solution :<span>Step  1  :</span>Skip Ad
Trying to factor by splitting the middle term

<span> 1.1 </span>    Factoring <span> x2-12x-45</span> 

The first term is, <span> <span>x2</span> </span> its coefficient is <span> 1 </span>.
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<span><span>     -45   +   1   =   -44</span><span>     -15   +   3   =   -12   That's it</span></span>


Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -15  and  3 
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Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (x-15)
              Add up the last 2 terms, pulling out common factors :
                    3 • (x-15)
Step-5 : Add up the four terms of step 4 :
                    (x+3)  •  (x-15)
             Which is the desired factorization

<span>Equation at the end of step  1  :</span> (x + 3) • (x - 15) = 0 <span>Step  2  :</span>Theory - Roots of a product :

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Solving a Single Variable Equation :

<span> 2.2 </span>     Solve  :    x+3 = 0<span> 

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Solving a Single Variable Equation :

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Parabola, Graphing Vertex and X-Intercepts :

Root plot for : <span> y = x2-12x-45</span>
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Harrizon [31]

Step-by-step explanation:

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there might (and actually should) be some more direct approaches for "a" out of the other pieces of information, but that was the most straight one right out of my mind, and I don't spend time on finding additional shortcuts, when I have already a working approach.

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