Answer:
see below
Step-by-step explanation:
amount of water w
l liter of pure alcohol = 100% alcohol
solution is 45 % percent alcohol
total amount of fluid is w+l
(w+l)( .45) = l*.100
Distribute
.45w + .45 l = 1l
.45 w = 1l - .45l
.45 w = .55l
w = .55l / .45
w =11/9 l
Let's do this step by step:
Subtract both sides by 7
-2|x-4|= -10
Divide each side by -2
|x-4|= 5
Now since this is an absolute value equation, you will have two answers. This means you make the equation both positive and negative.
X-4= 5and -(x-4)= 5
Solve for x for both
X-4= 5: add four on both sides
X= 9
-x+ 4= 5: subtract 4 and divide by -1
X= -1
So your answer is: X= -1 , 9
500=350(1+0.04/12)^12x
Solve for x
500/350=(1+0.04/12)^12x
X=(Log(500/350)/log(1+0.04/12))/12
X=9 months
Let's solve this by using the quadratic formula:

Note that we only use the coefficients so a=12, b=-14, and c=-6.
Plug values in the quadratic equation:

And so by evaluating those values we obtain:

Now we have two answers which are our factors one where we add another where we subtract and so:
First factor:

Second Factor:

And so your factors are

meaning that those are your roots/x-intercepts.