ANSWER
x = ±1 and y = -4.
Either x = +1 or x = -1 will work
EXPLANATION
If -3 + ix²y and x² + y + 4i are complex conjugates, then one of them can be written in the form a + bi and the other in the form a - bi. In other words, between conjugates, the imaginary parts are same in absolute value but different in sign (b and -b). The real parts are the same
For -3 + ix²y
⇒ real part: -3
⇒ imaginary part: x²y
For x² + y + 4i
⇒ real part: x² + y (since x, y are real numbers)
⇒ imaginary part: 4
Therefore, for the two expressions to be conjugates, we must satisfy the two conditions.
Condition 1: Imaginary parts are same in absolute value but different in sign. We can set the imaginary part of -3 + ix²y to be the negative imaginary part of x² + y + 4i so that the
x²y = -4 ... (I)
Condition 2: Real parts are the same
x² + y = -3 ... (II)
We have a system of equations since both conditions must be satisfied
x²y = -4 ... (I)
x² + y = -3 ... (II)
We can rearrange equation (II) so that we have
y = -3 - x² ... (II)
Substituting into equation (I)
x²y = -4 ... (I)
x²(-3 - x²) = -4
-3x² - x⁴ = -4
x⁴ + 3x² - 4 = 0
(x² + 4)(x² - 1) = 0
(x² + 4)(x-1)(x+1) = 0
Therefore, x = ±1.
Leave alone (x² + 4) as it gives no real solutions.
Solve for y:
y = -3 - x² ... (II)
y = -3 - (±1)²
y = -3 - 1
y = -4
So x = ±1 and y = -4. We can confirm this results in conjugates by substituting into the expressions:
-3 + ix²y
= -3 + i(±1)²(-4)
= -3 - 4i
x² + y + 4i
= (±1)² - 4 + 4i
= 1 - 4 + 4i
= -3 + 4i
They result in conjugates
Answer:
The answer is below
Step-by-step explanation:
There are various tips or suggestions on how others can represent real-life situations using rational functions, one of them is the application of a work problem formula.
By using the work problem formula, one can measure the time it will take different people working at different speeds to complete the work. With the formula w =r*t. Where w = work done, r = rate of work donee, and t = time
Answer: 28.08%
Step-by-step explanation: To find the percent increase, we divide the amount of change by the original number.
The amount of change is the difference between the two numbers which in this case is 561,000 - 438,000 and the original number is 438,000.
561,000 - 438,000 is 123,000 so we are left with 123,000 divided by 438,000 which is 0<em>.</em>2808. Finally, since our problem is asking us for a percent, we write 0<em>.</em>2808 as a percent by moving the decimal point two places to the right to get 28.08%.
So when the population changes from 438,000 to 561,000, it has increased by 28.08%.
Answer: Annette will take 6 hours to do the entire job alone.
Step-by-step explanation:
Given: Time taken by Kelly to do 
of job = 2 hours
i.e. Time for complete job done alone by Kelly =
Rest of work = 
of the job
of the complete job done by both Kelly and Annette in 3 hours
Time would be taken by then to do entire job together = 
Let t be the time taken by Annette to do job alone.
Then, as per situation
hence, Annette will take 6 hours to do the entire job alone.
LIST has 5 lines: L has two, I has 1, T as 2. It has one curve: S.
Therefore LIST = 51
LOAD has 6 lines, 2 curves.
L has 2 lines, A has 3 lines, D has one line (also one curve)
O is one curve, D has one, so LOAD= 62
