Answer:
(3 ± √23 * i) /4
Step-by-step explanation:
To solve this, we can apply the Quadratic Equation.
In an equation of form ax²+bx+c = 0, we can solve for x by applying the Quadratic Equation, or x = (-b ± √(b²-4ac))/(2a)
Matching up values, a is what's multiplied by x², b is what's multiplied by x, and c is the constant, so a = 2, b = -3, and c = 4
Plugging these values into our equation, we get
x = (-b ± √(b²-4ac))/(2a)
x = (-(-3) ± √(3²-4(2)(4)))/(2(2))
= (3 ± √(9-32))/4
= (3 ± √(-23))/4
= (3 ± √23 * i) /4
With amounts measured in gallons, let
x = amount of 65% antifreeze
y = amount of 90% antifreeze
1 gal of the 65% brand contains 0.65 gal of pure antifreeze; x gal would contain 0.65x gal. Similarly, y gal of the 90% brand contains 0.90y gal of pure antifreeze.
To obtain 120 gal of 80% antifreeze solution (which contains 0.80•120 = 96 gal of pure antifreeze), we must have
x + y = 120 … … … … … [total volume of antifreeze solution]
0.65x + 0.90y = 96 … [total volume of pure antifreeze]
Solve the first equation for y :
y = 120 - x
Substitute this into the second equation and solve for x :
0.65x + 0.90 (120 - x) = 96
0.65x + 108 - 0.90x = 96
0.25x = 12
x = 48
Solve for y :
y = 120 - 48
y = 72
Answer:
31.
Step-by-step explanation:
1. Write out the problem.
6w-19 + k; w=8 and k=2
2. Figure out the first part of the problem.
So, if w=8 and 6 and w are next to each other, we should multiply 6*8, which is 48. Next, it says to subtract 19. 48-19=29.
3. Find out what the last part of the problem is.
Since the first part of the problem is 29 and k=2, we should add 29+2=31, which is the final answer.
Hope this helped :)
9.81784090317
I added more just in case if a teacher needs the whole answer for some reason.
The total number of cups of sugar needed will be given by:
Total amount=(number of bottles)×(number of cups of sugar per box)
number of bottles to be made is 5 bottles
number of cups per box is 3/4
thus the total number of cups required will be:
Total amount=3/4×5=3 3/4 cups
