James must mix 60 millilitres of 10% solution and 40 millilitres of 50% solution.
Given that, James needs to mix a 10% acid solution with a 50% acid solution to create 100 millilitres of a 26% solution.
Let the acid solution needs to mix with 10% be <em>x</em> ml and the acid solution needs to mix with 50% will be 100 - <em>x</em> ml.
Now,
10% x + 50% ( 100 - <em>x</em> ) = 26% ×100
⇒
⇒10<em>x</em> + 50( 100 - <em>x</em> ) = 2600
⇒10 <em>x</em> + 5000 - 50<em>x</em> = 2600
⇒10 <em>x</em> - 50 <em>x</em> = 2600-5000
⇒-40 <em>x</em> = -2400
⇒<em>x</em>=60
Therefore, James must mix 60 millilitres of 10% solution and 40 millilitres of 50% solution.
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You haven't provided the required roots, but I can tell you how to do this kind of exercises in general.
If the
coefficient is 1, i.e. the equation is written like
, then you can say the following about the coefficients b and c:
is the opposite of the sum of the roots
is the multiplication of the roots.
So, for example, if we want an equation whose roots are 4 and -2, we have:
So, the equation is 
If your roots are rational, you can work like this: suppose you want an equation with roots 3/4 and 1/2. You have:
And so the equation is

In order to have integer coefficients, you can multiply both sides of the equation by 8:

To solve this function, all we need to do is substitute -4.3 in for wherever "x" appears and then simplify.
f(x) = 7.45x + 33.7; x = -4.3
f(-4.3) = 7.45(-4.3) + 33.7
f(-4.3) = -32.035 + 33.7
f(-4.3) = 1.665
This means that, when x = -4.3, f(x) = 1.665.
Note: It may help to remember that, in a function such as this, f(x) can be thought of as the "y" value that corresponds to the given "x" value (in fact, when writing it out with words, f(x) is the same as "function of x"). And, if you are given a value for f(x), then the opposite is true. Just substitute in the value given for f(x) and solve for x.
Hope this helps!