(50 - x) is the amount of the 15% Alcohol solution to use. If you solve for x first.
<span>0.10x + 0.15(50 – x) = 0.12(50)
0.10x - 0.15x + 7.5 = 6
-0.05x + 7.5 = 6
7.5 - 6 = 0.05x
1.5 = 0.05x
1.5/0.05 = x
30 mL = x
Then the 15% solution: 50 - 30 = 20 mL
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A = 6
x^2 + 6x is equal to x(x+6)
b=2
Denominator and numerator of the first term are multiplied by x.
c=6
Second term is multiplied by (x-6)/(x-6)
d=2
Now that they have the same denominator, the two terms are combined. 2 is the coefficient of the first term
e=6
In the same way as d is carried over from b, e is carried over from c.
f = 6
2x - x + 6 = x + 6
g = 1
We factor out the (x+6) from the numerator and denominator
We know the triangle is an isosceles triangle. So, we use the Pythagorean Theorem.
a^2+b^2=c^2
The c would be 22, because it's the longest edge. Now find a or b. They are the same, that is how you find the two sides of the triangle for part A.
To find the area of the triangle, the forumla is a=hb/2
Plug in the numbers for that formula and the answer would be found for part B.
I hope I helped.
Common ratio = second term / first term = 12 / 8 = 1.5
