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3 years ago

F(x) = x4 - x3 - 2x- 4 factor the polynomial function over the complex numbers

Mathematics

1 answer:

olchik [2.2K]3 years ago

8 0

Answer:

Step-by-step explanation:

The given function is f(x) = x⁴ - x³ -2x -4

factor the polynomial function

f(x) = x⁴ - x³ -2x -4 = (x⁴ - 4) - (x³ + 2x ) ⇒ take (-) as a common from (- x³ -2x)

= (x² + 2 ) (x² - 2) - x (x² + 2) ⇒ take (x² + 2) as a common

= (x² + 2 ) ( x² - x - 2)

= (x + √2 i) (x - √2 i) (x -2 ) ( x+1)

Notes: (x⁴ - 4) = (x² + 2 ) (x² - 2)

(x² + 2)= (x + √2 i) (x - √2 i)

( x² - x - 2) = (x -2 ) ( x+1)

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Natalie purchased a used car for $12, 200 and had to pay 83 % sales tax. How much tax did she pay?

Fynjy0 [20]

Answer:

$5,533.33

Step-by-step explanation:

83% sales tax seems a lot, but ok.. anyway...i'm assuming that this is correct.

the final amount that she paid is made up of 2 parts:

100% of the car's price (list price of the car) + 83% of the cars price in taxes

if we add these together, that means she paid

100% + 83% = 183% of the car's price. We are told that this number is $12,200

hence,

183% --------> represents $12,200

1% ------------> represents $(12,200 ÷ 183)

amount in taxes = 83% -------> represents $(12,200 ÷ 183) x 83 = $5,533.33

3 0

3 years ago

I need help with 3 and 4

frosja888 [35]

Answer:

Step-by-step explanation:

3) G

Step-by-step explanation:

Q(-1,-1) R(3,1) S(2,-4)

x+2 y+3 translation then rotation 180 (x,y) be (-x,-y)

Q -1+2 -1+3 (1,2) (-1,-2)

R 3+2 1+3 (5,4) (-5,-4)

S 2+2 -4+3 (4,-1)

4 0

3 years ago

Hannah spent 40% of the money she earned last month. If she spent $50, what was the total amount of money that she earned babysi

gavmur [86]

Let, the amount she earned = x
Then, x * 40% = 50
x * 0.40 = 50
x = 50 / 0.40
x = 125

In short, Your Answer would be Option C

Hope this helps!

8 0

3 years ago

Read 2 more answers

What can be concluded from the pie chart?

QveST [7]

The information that can be concluded from the pie chart is in 2018, more than one-fourth of the revenue collected for state and local governments in Florida came from sales taxes.

A pie chart is a circular graph that is used to show information. The circle is divided into sectors used to represent a numerical proportion. A pie chart adds up to 100%.

The pie chart in this question shows the sources of state and local revenue for Florida in 2018. The circle is divided into seven sectors that represent the sources of revenues.

The following can be deduced from the pie chart:

Excise taxes represent 1.2% of 100% of the circle. This is the smallest source of revenue for the state of Florida. Corporate income taxes represent 2% of the circle. Income from excise tax was less than income from corporate income taxes.

The sector that represents property tax is 13.7% and the sector that represents sales tax is 26.1%. Sales tax was a greater source of revenue when compared with property tax.

The proportion of sales tax to total revenue is 26.1%. This is more than 25%(1/4) of total revenue.

To learn more about pie charts, please check: brainly.com/question/5870339?referrer=searchResults

3 0

2 years ago

Graph the linear equation find three points that solves the equation 2y=5x+11

Julli [10]

Answer:

<h3>Attachment</h3>

Step-by-step explanation:

Convert to the slope-intercept form (<em>y = mx + b</em>):

$2y=5x+11$ <em>divide both sides by 2</em>

$\dfrac{2y}{2}=\dfrac{5x}{2}+\dfrac{11}{2}\\\\y=\dfrac{5}{2}x+\dfrac{11}{2}$

We choose any three x values and calculate the y value:

for x = -1

$y=\dfrac{5}{2}(-1)+\dfrac{11}{2}=-\dfrac{5}{2}+\dfrac{11}{2}=\dfrac{6}{2}=3\to A(-1,\ 3)$

for x = 1

$y=\dfrac{5}{2}(1)+\dfrac{11}{2}=\dfrac{5}{2}+\dfrac{11}{2}=\dfrac{16}{2}=8\to B(1,\ 8)$

for x = -3

$y=\dfrac{5}{2}(-3)+\dfrac{11}{2}=-\dfrac{15}{2}+\dfrac{11}{2}=-\dfrac{4}{2}=-2\to C(-3,\ -2)$

Mark the points on the coordinate plane and draw a line through the given points.

6 0

3 years ago