X = amount of 50% solution
y = total amount after mixing
Note that the amount of alcohol in the 20% solution is 80 (0.2) = 16 oz.
We have 2 unknowns, so we need 2 equations:
first, we can write the equation for the total volume:
y = x + 80
next, apply the percentages to get an equation for the amount of alcohol:
0.4 y = 0.5 x + 16
Finally, solve the pair of equations (in this case, by substitution of the 1st into the second:
0.4 (x + 80) = 0.5x + 16
0.4 x + 32 = 0.5X + 16
rearrange and combine like terms:
0.1x = 16
x = 160
from the 1st equation:
y = 160 + 80 = 240
Answer: 1/6
because there are 6 side to a cube and you can only have a outcome of 1 so therefore, the answer is 1/6
Answer:
18x + 13y = 60
6x + 2y = 6 ---> 6x = -2y +6 ---> 18x = -6y+18
Substitution
(-6y +18)+13y =60
-18 -18
--------------------------
7y = 42 so y=6
Then, 6x + 2(6) =6, which you will get x = -1
(-1, 6)
Answer: the lines are not parallel.
Explanation: if you isolate the x in 3x^2-4y=-1, the equation is y=3/4x^2+1/4
So, they are not parallel because the slope is not the same.
Answer:
D)The equation is f(x)=3x^2−9x+3, and the parabola opens upward.
