Answer:
Step-by-step explanation: 252 apex
Answer: a) √50
b) n = 1 + 7i
Step-by-step explanation:
first, the modulus of a complex number z = a + bi is
IzI = √(a^2 + b^2)
The fact that n is complex does not mean that n doesn't has a real part, so we must write our numbers as:
m = 2 + 6i
n = a + bi
Im + nI = 3√10
Im + n I = √(a^2 + b^2 + 2^2 + 6^2)= 3√10
= √(a^2 + b^2 + 40) = 3√10
a^2 + b^2 + 40 = 3^2*10 = 9*10 = 90
a^2 + b^2 = 90 - 40 = 50
√(a^2 + b^2 ) = InI = √50
The modulus of n must be equal to the square root of 50.
now we can find any values a and b such a^2 + b^2 = 50.
for example, a = 1 and b = 7
1^2 + 7^2 = 1 + 49 = 50
Then a possible value for n is:
n = 1 + 7i
Answer:
C) 1/5
Step-by-step explanation:
Answer:
The initial investment is $821.58
Step-by-step explanation:
Giving the following information:
Future Value (FV)= $90,597
Number of periods (n)= 25*12= 300
Interest rate (i)= 1.58% = 0.0158
<u>To calculate the initial investment, we need to use the following present value (PV) formula:</u>
PV= FV/(1+i)^n
PV= 90,597 / (1.0158^300)
PV= $821.58
The initial investment is $821.58
Answer:
(1)
Karen: 
Alice: 
(2): Slope is 2
(3) y intercept
--- For Karen
--- For Alice
(4) They do not intersect
(5) No solution
(6) No
Step-by-step explanation:
Given


Solving (1): Complete the equation.
For Karen:
--- the rate
--- additional spendings
For Alice:
--- the rate
--- additional spendings
The general equation is;

For Karen, it becomes

For Alice, it is:

(2): The slopes.
In (1), we have:
--- the rate (for both Karen and Alice).
This rate implies the slope.
<em>Hence, the slope is 2</em>
(3): The y intercept.
The additional spendings in (1) means the y intercept.
So, we have:
--- For Karen
--- For Alice
(4) Because they have the same slope, they do not intersect
(5) Number of solutions.


Subtract both equations


This means there is no solution
(6) Can they spend the same amount on the same number of loaves
In (5), the equations have no solution
<em>Hence, it is not possible to spend the same amount for the same number of loaves</em>