Let x = amount of 45% antifreezeLet y = amount of 70% antifreeze EQUATION 1: x + y = 150 (total of 150 gallons mixed) EQUATION 2: .45x + .75y = .55(x + y) Simplify and solve the system of equations Multiply second equation by 100 on both sides to remove the decimals 45x + 75y = 55(x + y) Combine like terms 45x + 75y = 55x + 55y 45x - 55x + 75y - 55y = 0 -10x + 20y = 0 Now we have the following system of equations: x + y = 150 -10x + 20y = 0 Multiply the first equation by -10 to get opposite coefficients for x; add the equations to eliminate x 10x + 10y = 1500 -10x + 20y = 0 ------------------------------ 30y = 1500 Solve for y 30y = 1500 y = 50 Since the total mixed gallons is 150, x = 150 - 50 = 100 So we need 100 gallons of the 45% antifreeze and 50 gallons of the 70% antifreeze
Answer:
x = 9 or x = 0 or x = -2
Step-by-step explanation:
Solve for x:
3 x^3 - 21 x^2 - 54 x = 0
The left hand side factors into a product with four terms:
3 x (x - 9) (x + 2) = 0
Divide both sides by 3:
x (x - 9) (x + 2) = 0
Split into three equations:
x - 9 = 0 or x = 0 or x + 2 = 0
Add 9 to both sides:
x = 9 or x = 0 or x + 2 = 0
Subtract 2 from both sides:
Answer: x = 9 or x = 0 or x = -2
So to find a percent of increase you have to put the current number minus previous number(in this case 20-16) over the previous number(16 in this case) and multiply by 100.
So we have 20-16/16 multiplied by 100.
Since 4/16= 0.25,multiplying It by 100 gives you 25.
So the answer is 25%
Answer:
k=-1
Step-by-step explanation:
-18-6k=6(1+3k)
-18-6k=6+18k
+6k +6k
-18=6+24k
-6 -6
-24=24k
/24 /24
k=-1
