Answer:
Step-by-step explanation:
Given the following complex numbers, we are to expressed them in the form of a+bi where a is the real part and b is the imaginary part of the complex number.
1) (2-6i)+(4+2i)
open the parenthesis
= 2-6i+4+2i
collect like terms
= 2+4-6i+2i
= 6-4i
2) (6+5i)(9-2i)
= 6(9)-6(2i)+9(5i)-5i(2i)
= 54-12i+45i-10i²
= 54+33i-10i²
In complex number i² = -1
= 54+33i-10(-1)
= 54+33i+10
= 54+10+33i
= 64+33i
3) For the complex number 2/(3-9i), we will rationalize by multiplying by the conjugate of the denominator i.e 3+9i
= 2/3-9i*3+9i/3+9i
=2(3+9i)/(3-9i)(3+9i)
= 6+18i/9-27i+27i-81i²
= 6+18i/9-81(-1)
= 6+18i/9+81
= 6+18i/90
= 6/90 + 18i/90
= 1/15+1/5 i
4) For (3 − 5i)(7 − 2i)
open the parenthesis
= 3(7)-3(2i)-7(5i)-5i(-2i)
= 21-6i-35i+10i²
= 21-6i-35i+10(-1)
= 21-41i-10
= 11-41i
The correct answer is B. x is greater than -2.
1 cartons of juice = $4.20
3 single cartons = 4.20 * 3 = $12.60
1 pack = $9.45
He saved 12.60 - 9.45 = $3.15
So, he saved $3.15, compared to the total ($12.60)
To calculate the percentage, we will do a proportion:
3.15 (money saved) : 12.60 (total of 3 single cartons) = x (how much percentage) : 100 (total)
3.15 : 12.6 = x : 100
To calculate x, we will moltiplicate the ends (where we have known numbers) than divide all per 12.6
So
x = (3.15 * 100) / 12.60 = 315 / 12.6 = 25
So the percentage saving is 25%
Well... looking at how to question is defining things.....i think this is a multiple choice question.....
Given:
"y" represents the population
"x" represents the number of years
duration = 2000 - 1990 = 10 years
population increase = 2700 - 1200 = 1500
Now,
<u></u><u>It says linear equation........</u><u>, So, we have to assume that every ten years the population increases by a fixed </u><u>amount that is 1500 people every 10 years.</u><u />
Now,
Every 10 years, the population increases by 1500
Every 1 year , the population increases by 1500 / 10
= 150
Now,
The equation in determining the population is:
y = 150x + 1200
<u />
Answer:
The minimum unit cost is equal to $15,339
Step-by-step explanation:
Let
x ----> the number of engines
C ---> the cost in dollars to make each airplane engine
we have
This is a vertical parabola open upward (the leading coefficient is positive)
The vertex represent the minimum of the parabola
The minimum unit cost is equal to the y-coordinate of the vertex
Convert the quadratic equation into vertex form
Factor 0.5
Complete the square. Remember to balance the equation by adding the same constants to each side
Rewrite as perfect squares
----> equation into vertex form
The vertex is the point (100,15,339)
The y-coordinate of the vertex is 15,339
therefore
The minimum unit cost is equal to $15,339
