Answer:
The value of annuity is
Step-by-step explanation:
From the question we are told that
The periodic payment is
The interest rate is
Frequency at which it occurs in a year is n = 2 (semi-annually )
The number of years is
The value of the annuity is mathematically represented as
(reference EDUCBA website)
substituting values
Answer:
Option D.
Step-by-step explanation:
The given system of equations is
...(1)
...(2)
On simplifying the second equation, we get
On dividing by -1, we get
...(3)
It is clear that equation (1) and (3) are same equations. It means equation (1) and (2) represent the equivalent equation.
So, the given system of equations has infinitely many solutions.
Therefore, the correct option is D.
Answer:
Step-by-step explanation:
This is a third degree polynomial because we are given three roots to multiply together to get it. Even though we only see "2 + i" the conjugate rule tells us that 2 - i MUST also be a root. Thus, the 3 roots are x = -4, x = 2 + i, x = 2 - i.
Setting those up as factors looks like this (keep in mind that the standard form for the imaginary unit in factor form is ALWAYS "x -"):
If x = -4, then the factor is (x + 4)
If x = 2 + i, then the factor is (x - (2 + i)) which simplifies to (x - 2 - i)
If x = 2 - i, then the factor is (x - (2 - i)) which simplifies to (x - 2 + i)
Now we can FOIL all three of those together, starting with the 2 imaginary factors first (it's just easier that way!):
(x - 2 - i)(x - 2 + i) =
Combining like terms and canceling out the things that cancel out leaves us with:
Remembr that , so we can rewrite that as
and
That's the product of the 2 imaginary factors. Now we need to FOIL in the real factor:
That product is
which simplifies down to
And there you go!