Answer:
She uses 200 milliliters of solution B
Step-by-step explanation:
Notice that there are two unknowns in this problem: 1) the amount of solution A that is being used, and 2) the amount of solution B being used. We can name such unknowns with letters to facilitate our work:
Amount of solution A to be used = A
Amount of solution B to be used = B
So, since we need to find two unknowns, we need to create a system of two equations to solve them.
Our first equation can be obtained from the sentence: "She uses twice as much Solution A as Solution B," which written in mathematical form is:
A = 2 B
The second equation we can build from the information of the amount of alcohol in each solution that combined will add up to 104 milliliters of alcohol in the mixture. Knowing the percent of alcohol in each solution, we can write an equation for the amount of alcohol:
0.19 A + 0.14 B = 104
Now we can use our first equation to substitute A in terms of B in the second equation:
0.19 (2 B) + 0.14 B = 104
0.38 B + 0.14 B = 104
0.52 B = 104
B = 104 / 0.52
B = 200 milliliters
A could be 2 while B could be 3, so -2a+3b turns into -4+9, which equals 5.
From what I know you can't really solve a a single equation with two-variables so it's just a matter of trial and error.
Just try plugging in a small number like 2 for a just to try it and you get 8b^2=72.
Divide everything by 8 to isolate b and you get that b^2=9.
Square root everything and you'll find that b=3. This is just one possible combination, I'm sure there are many more but this is obviously the one that was intended to be found.
Now that we know that a=2 and b=3 just plug them into the equation.
-2(2)+3(3)=?
-4+9=?
5
Sorry about having to use this ^ symbol, the equation maker is not working.
To convert the angle in radian measure to degree measure, multiply it by 180/π.
The given angle in radian measure is 257π/360 . Multiply it by 180/π to get the angle in degrees.
So,
The angle in degrees = 257π/360 x 180/π = 257/2 = 128.5 degrees
3.45 rounded to the nearest whole number would be 3 because 5 or more let it soar 4 or less let it rest
