please answer fast. With full step by step solution.​

Let f(z) = (4z ² + 2z) / (2z ² - 3z + 1).

First, carry out the division:

f(z) = 2 + (8z - 2) / (2z ² - 3z + 1)

Observe that

2z ² - 3z + 1 = (2z - 1) (z - 1)

so you can separate the rational part of f(z) into partial fractions. We have

(8z - 2) / (2z ² - 3z + 1) = a / (2z - 1) + b / (z - 1)

8z - 2 = a (z - 1) + b (2z - 1)

8z - 2 = (a + 2b) z - (a + b)

so that a + 2b = 8 and a + b = 2, yielding a = -4 and b = 6.

So we have

f(z) = 2 - 4 / (2z - 1) + 6 / (z - 1)

or

f(z) = 2 - (2/z) (1 / (1 - 1/(2z))) + (6/z) (1 / (1 - 1/z))

Recall that for |z| < 1, we have

[tex]\displaystyle\frac1{1-z}=\sum_{n=0}^\infty z^n[/tex]

Replace z with 1/z to get

[tex]\displaystyle\frac1{1-\frac1z}=\sum_{n=0}^\infty z^{-n}[/tex]

so that by substitution, we can write

[tex]\displaystyle f(z) = 2 - \frac2z \sum_{n=0}^\infty (2z)^{-n} + \frac6z \sum_{n=0}^\infty z^{-n}[/tex]

Now condense f(z) into one series:

[tex]\displaystyle f(z) = 2 - \sum_{n=0}^\infty 2^{-n+1} z^{-(n+1)} + 6 \sum_{n=0}^\infty z^{-n-1}[/tex]

[tex]\displaystyle f(z) = 2 - \sum_{n=0}^\infty \left(6+2^{-n+1}\right) z^{-(n+1)}[/tex]

[tex]\displaystyle f(z) = 2 - \sum_{n=1}^\infty \left(6+2^{-(n-1)+1}\right) z^{-n}[/tex]

[tex]\displaystyle f(z) = 2 - \sum_{n=1}^\infty \left(6+2^{2-n}\right) z^{-n}[/tex]

So, the inverse Z transform of f(z) is [tex]\boxed{6+2^{2-n}}[/tex].

Multiple Choice
Which option best characterizes Reese's choice of less-than-optimal materials in the following scenario?
Reese has just designed a vándshield for an extremely lightweidot car that can be transported by the military via helicopter. The engineers
wanted to use a specially formulated glass that is lighter than ordinary glass, but the cost was far above the budgeted amount for the
project's materials. Reese decides to use a plastic windshield instead.
Economic considerations should never be placed above safety when designing a model
Economic considerations can endanger the safety of a model.
Economic considerations must be considered vihen designing a model
Economic considerations are the most important factor vihen designing a model

What is the purpose of the graphic language?

Coving is a curved edge between a floor and a wall.
O True
O False

Jamal has Started all season as a safety. Last season,he was making a backup salary, which is 67% of what starters make. If Jamal is able to renegotiate his contract to the starter rate from the $400,000 he's currently making, what will his next salary be?round to the nearest whole number.

Help me with this for brainiest:)

Briefly describe an idea for a new product while thinking mainly about it cost analysis to depict what kinds of direct and indirect cost will be involved in its creation