For the coefficients to be rational, any complex roots must occur in conjugate pairs. So if
is a root, then so must be
.
Now such a third degree polynomial might be
The only variation to this would be multiplying throughout by some non-zero constant. This doesn't change the roots.
Answer:
20 shares.
Step-by-step explanation:
Starting price paid = 30 * x
Ending price received = 12 * x
Loss = 360
Difference = 30x - 12x = 360
Equation
30x - 12x = 360 Combine the terms on the left
18x = 360 Divide by 18
18x/18 = 360/18 Do the division
x = 20 << Answer
He bought 20 shares of the company originally.
Answer:
We have 40% antifreeze and 70% antifreeze and we need to make 240 liters of 64% antifreeze.
We set up 2 equations where "f" is the 40 % and "s" is the 70%
A) f + s = 240
B) .40f + .70s = (.64 * 240) (or 153.6)
To solve both equations we multiply A) by -.40
A) -.40 f - .40 s = -96.00 then we add this to B)
B) .40f + .70s = 153.60
.30s = 57.6
s = 192
f = 48
48 liters of 40% = 19.20 liters of antifreeze
192 liters of 70% = 134.40 liters of antifreeze
That equals 153.60 liters of antifreeze in a TOTAL liquid amount of 240 liters.
Double Check
153.60 / 240 = 64% antifreeze.
Step-by-step explanation:
Answer:
Step-by-step explanation:
In this question, you would solve for "a".
Solve:
K = 4a + 9ab
Since we have our "a" on the same side, we can factor it out from the variables:
K = a(9b + 4)
To get "a" by itself, we would have to divide both sides by 9b + 4:
K/9b+ 4 = a
Your answer would be K/9b+ 4 = a
It would look like this:
