Question
Find the third degree polynomial function that has an output of 320 when x = 4, and has zeros 2 and
-8i

Answers

Answer 1

Answer:

[tex]f(x)=2(x-2)(x^2+64)[/tex]

Step-by-step explanation:

A standard polynomial in factored form is given by:

[tex]f(x)=a(x-p)(x-q)...[/tex]

Where p and q are the zeros.

We want to find a third-degree polynomial with zeros x = 2 and x = -8i and equals 320 when x = 4.

First, by the Complex Root Theorem, if x = -8i is a root, then x = 8i must also be a root.

Therefore, we acquire:

[tex]f(x)=a(x-(2))(x-(-8i))(x-(8i))[/tex]

Simplify:

[tex]f(x)=a(x-2)(x+8i)(x-8i)[/tex]

Expand the second and third factors:

[tex]=(x+8i)x+(x+8i)(-8i)\\\\=(x^2+8ix)+(-8ix-64i^2)\\\\=(x^2)+(8ix-8ix)+(-64i^2)\\\\=x^2-64(-1)\\\\ =x^2+64[/tex]

Hence, our function is now:

[tex]f(x)=a(x-2)(x^2+64)[/tex]

It equals 320 when x = 4. Therefore:

[tex]320=a(4-2)(4^2+64)[/tex]

Solve for a. Evaluate:

[tex]320=(2)(80)a[/tex]

So:

[tex]320=160a\Rightarrow a=2[/tex]

Our third-degree polynomial equation is:

[tex]f(x)=2(x-2)(x^2+64)[/tex]

Answer 2

Answer:

f(x)=2(x-2)(x^2+64)

Step-by-step explanation:


Related Questions

If the polygon is translated 3 units down and 4 units left, what will the coordinates of the new image be? Use prime notation in expressing the new coordinates.

Answers

Answer:

A' (-2,-4) B' (-3,-7) C' (-1,-8) D' (1,-6)

Step-by-step explanation:

Just take it one point at a time and move each point down 3 and 4 left. Prime notation just means to put this little sign ' so it indicates that this is the new coordinate. So A was (2,-1) and A' (the new one) is (-2,-4)

the ages of six boys are given as 12 years 3 months, 18 years, 13 years 7 months, 17 years 2 months 15 years and 14 years respectively. what is their average age? ​

Answers

Answer:

15 years (180 months)

Step-by-step explanation:

turn it into months first

147

216

163

206

180

168

add them together, then divide by how many there are

1,080/6=180 months

180/12 =15

Paul asked four friends how many hours of tv they watch and their grade on a recent test

Answers

Answer: D

Step-by-step explanation: The answer wouldn't be A because all the information is there, B is out because the question tells you there is a correlation between the two, and C is out because it has a more negative affect than positive.

I have to do a math test what is 8 + (7 + 1) 2 ÷ 4 ⋅

Answers

Answer:

8

Step-by-step explanation:

taking my points back because you answered with spam.

Solve the equation by completing the square.
a2 - 14a - 32 = 0

Answers

Answer:

a=16,-2

Step-by-step explanation:

Use the formula (b/2)^2 in order to create a new term. Solve for a by using this term to complete the square.

What is the area of the triangle in the diagram?

Answers

theres no diagram given

35% of students enrolled in collage are freshmen. if the total enrollment of the collage is 2800, how many of the students are freshmen?

Answers

Answer:

980 students are freshmen.

Step-by-step explanation:

2800*.35=980

Find legit BD

I need help for my assignment

Answers

Answer:

BD = 4

Step-by-step explanation:

∆BAD is congruent to ∆CAD based on the AAS Congruence Theorem.

Therefore:

BD = CD

3x + 1 = 5x - 1 (substitution)

Collect like terms

3x - 5x = -1 - 1

-2x = -2

Divide both sides by -2

x = -2/-2

x = 1

✔️BD = 3x + 1

Plug in the value of x

BD = 3(1) + 1

BD = 3 + 1

BD = 4

WILL GIVE BRAINLIST PLS HELP Find z. Just write the number. Answer should be a whole number.

Answers

Answerz=16

Step-by-step explanation:

Rotational symmetry of 2D shapes
Choose all that apply

Answers

Answer:

B and C

Step-by-step explanation:

I think that this is right.

A pentagon's lines of symmetry go thru an angle and the middle of a side. Every 72 degrees, the pentagon in split into identical halves. Same with 144 because it is basically 2 72 degree rotations.

Answer:

72

Step-by-step explanation:

The order of rotational symmetry of a regular pentagon is 5.

To find the angle of rotation we divide 360 by the number of sides

360/5=72

so the angle of rotation is 72 degrees.

Whoever gets this right gets brainliest note ( ITS 4 FUN ! NOT A GRADE) 2+4x7=?

Answers

It’s 42 lolllllllllllllllll

HELP ME PLEASE ❗❗❗❗
What is the value of Q3 of the data represented by the box plot?



Enter your answer in the box.

Answers

Answer:

30

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

:P

The show has a large display board where visitors are encouraged to pin up their pictures during an even, it measures:
3.6 m
1.8 m

How many 6 cm by 6 cm pictures could fit on the wall?​

Answers

Answer:

3.6m

Step-by-step explanation:

Help Me Please.............................(7)

Answers

Answer:

Step-by-step explanation:

The first step contains the error.

2x - 10 =    22            Add 10 to both sides

   + 10     +10

2x = 32                      Divide by 10

2x/2 = 32/2

x = 16

Tyler has to savings accounts that his grandparents opened for him . One of the accounts Pay 8% annual interest Where as the other pay 10% annual interest. If you have $700 more invested at 10% then you invested at 8%, how much do you have invested in each account If the total amount of interest You earn in a year is $106?

Tyler invested $___at 8%, and $___at 10%

Answers

Thank you hope this helps see photo

6
Solve the inequality. Graph the solution.
11.3 > b /4.3
The solution is

Answers

Step-by-step explanation:

Multiply to remove the fraction, then set equal to

0 and solve.

Inequality Form:

b<48.59

Interval Notation:

(−∞, 48.59)

The solution of the inequality 11.3 > b /4.3 is b< 48.59 along with the number line.

Given Inequality:

11.3 > b /4.3

To solve the inequality 11.3 > b / 4.3,

Multiply both sides of the inequality by 4.3 to eliminate the fraction:

11.3 * 4.3 > (b / 4.3) * 4.3

48.59 > b

The solution to the inequality is b < 48.59.

This means that any value of b that is less than 48.59 will satisfy the inequality.

To graph the solution, indicate that b is less than 48.59 by using an open circle at 48.59 and shading the line to the left of the open circle to represent all the values that satisfy the inequality.

Learn more about Inequality here:

https://brainly.com/question/20383699

#SPJ6

Beryllium is an extremely lightweight metal that is used in many industries, such as aerospace and electronics. Long-term exposure to beryllium can cause people to become sensitized. Once an individual is sensitized, continued exposure can result in chronic beryllium disease, which involves scarring of the lungs. In a study of the effects of exposure to beryllium disease, which involves scarring of the lungs. In a study of the effects of exposure to beryllium, workers were categorized by their duration of exposure (in years) and by their disease status (diseased, sensitized, or normal.) The results were as follows:

Duration of Exposure
< 1 1 to < 5 >= 5
Diseased 12 10 18
Sensitized 14 18 13
Normal 66 142 210

Required:
a. Compute the expected frequencies of diseased workers.
b. Compute the expected frequencies of sensitized workers.
c. How many degrees of freedom are there?

Answers

Answer:

1. Has been answered below

2. Degree of freedom is 4

Step-by-step explanation:

Row 1: 12+10+18 = 40

Row 2: 14+18+13 = 45

Row 3: 66+142+210 = 418

Grand total = 40+45+418 = 503

Column 1 : 12+14+66 = 92

Column 2: 10+18+142 = 170

Column 3: 18+13+210 = 241

Total = 92+170+241 = 503

Expected frequencies of diseased workers

92x40/503 = 7.316

170x40/503 = 13.52

241 x 40/503 = 19.165

Expected frequencies of sensitized workers

92x45/503 = 8.23

170x45/503 = 15.20

241x 45/503 = 21.56

2.

Degree of freedom

= (Number of row -1)(number of column - 1)

= 3-1 * 3-1

= 2x2

= 4


Both questions plssssssss

Answers

Answer: 4 and 1/4

Step-by-step explanation:

1st question is 4-- count the points that fall above the line

2nd question is 2 out of 8, or 1 out of 4

there are only 2 players who played at least 17 matches AND scored about 5000. There are 8 players who played at LEAST 17 matches

Answers:

1. 4

2. ¼

Explanations:

1. the question is asking how many players were awarded more points than the prediction of the line of best fit (trend line), which can be translated to how many dots are above the line on the graph. 4 dots can be counted above the line

2. 8 players played at least 17 tournaments. of these 8 players, only 2 scored more than 5000 ranking points.

thus, to find the probability, we take 2 ÷ 8 = ¼

i hope this helps! :D

The diameter of the circle shown below is 12m. What is the area of the circle

Answers

Answer:

The area of the circle is 113.097

Hope this helped!

Please give brainliest if it helped!

I am very confused on this problem pls help

Answers

Answer:

Step-by-step explanation:

let X be free stickers

let y be number of T-shirts bought

TABLE

X       Y (PUT THIS IN THE BLUE PLACE)

2        1

4         2

6        3

8        4

10       5 (don't have to put this in)

the table :

x y
———
1 2
2 4
3 6
4 8
5 10

Equation: y=2x

explanation the graph goes up by 2 each time meaning the slope is 2

Draw a line through the origin with a slope of 3/2

Answers

Answer:

uhhhh

Step-by-step explanation:

Kenji walks 44 feet in 10 seconds. At this rate, how many miles does Kenji walk in an hour? Show your work. (1 mile 5 5,280 feet) (make it simple)

Answers

Answer:

3 miles

Step-by-step explanation:

1 hour = 3,600 seconds (3,600 ÷ 10 = 360)

360 x 44 = 15,840 Feet

1 mile = 5,280 feet

15,840 feet ÷ 5,280 feet = 3 miles

Kenji walks 3 miles in 1 hour.

Hopefully this helps :3 sorry if wrong :( plz mark brainiest if correct :D Your bootiful/handsome! Have a great day luv <3

-Bee~

I WILL GIVE BRAINLIEST !!!What is the product of 4 and 7?
7
O
o
8 9
14
9
14
7
8

Answers

The product of 4 and 7 would be 28!
When someone says the product of x means they are looking to multiply!

Answer:

8? I think I'm not quite sure. lmk

Solve the following question:
 
Q1: A family has booked a long holiday in Skragness, where the probability of rain on any particular day is 0.3. 
a) Find the probability that the first day to rain will be on the third day of their holiday.
b) Find the probability chance that it will not rain for the first 2 weeks of their holiday.
 
[hint:  X~Geo(0.3)  a) P(X=__), b) P(X<__)]
 
Q2: If G~B(42, 7/12)
a) Find E(G) and Var(G) giving your answer as a fraction or mixed number
 
b*) Find P(G=20) correct to 3 significant figures.

Answers

Answer is in the photo. I can only upload it to a file hosting service. link below!

tinyurl.com/wpazsebu

If an object with a volume of 400 is dilated by 1/2, what is the new volume?

Answers

^ pls don’t click the link y’all it’s a hacker

MULTIPLE CHOICE QUESTION A car travels 120 miles in 2 hours. It goes an average of South East direction. What is its velocity? 60 mph south east 45 mph 45 mph south east 60 mph​

Answers

Answer:

60 miles per hour southeast.

Step-by-step explanation:

We are told that the car is moving southeasternly, so that answers the question right off the bat. The car is moving 120 miles per 2 hours. We need to know how much it moves in one hour though, so we must divide hours and miles by 2. We ger 60 miles per hour.

Velocity will be 60 mph southeast.

What is the difference between velocity and speed?

The distance that an item travels in a unit of time is referred to as its speed. It merely takes into account the size of the item and ignores its orientation. Speed is referred to as a scalar quantity in this way. When referring to velocity, however, it is said that velocity is the rate at which displacement changes. A vector quantity, that is.

Given distance traveled by car is 120 miles in 2 hours. Since speed is distance divided by time.

Speed = 60 mph

Also, there is a given direction which is southeast.

Therefore, the velocity of the car will be 60 mph southeast.

Learn more about velocity here:

https://brainly.com/question/18084516

#SPJ2

please help
85-v=213
solve for v

Answers

Step-by-step explanation:

subtract the whole equation by 85 on both sides to get v by itself on the left side

85-85-v=213-85

-v=128

Now we divide the whole equation by negative 1

-1v/-1=128/-1

v=-128

Hope that helps :)

WILL MARK BRAINLIEST!! Just help me out with number 2 please. :)

Here is an inequality: -2x > 10.
1. List some values for x that would make this inequality true.
Answer: Any negative number above -5, like -6, -7, etc.

2. How are the solutions to the inequality -2x ≥ 10 different from the solutions to
-2x > 10? Explain your reasoning.

Answers

9514 1404 393

Answer:

  -5 is included in the solution set of the first, but not the second

Step-by-step explanation:

The solution to -2 ≥ 10 is x ≤ -5. The solution to -2x > 10 is x < -5. The difference is that x = -5 is included in the solution set of the first inequality, but is not included in the solution set of the second inequality.

When plotted on a number line, the former inequality has a solid dot at -5, indicating that point is included. The latter inequality has an open dot (circle) at -5, indicating that point is not included. (Both plots are shaded to the left of the dot.)

Dan is randomly selecting an outfit to wear to school. He can choose from 3 shirts: blue striped, red striped, or white. He
can choose from 3 pairs of shorts: tan, blue, or plaid.
Determine whether each statement is true or false.
Select True or False for each statement.
The probability that Dan chooses a striped shirt and a pair of tan shorts is
O True
o
False
There are 6 possible outcomes in the sample space.
O
True
O
False
The probability that Dan chooses a striped shirt and a pair of blue shorts is
o
True
O False
There are 2 ways to choose a red striped shirt and a pair of tan shorts.
O True
O False

Answers

Answer:i dont know :(

Step-by-step explanation:

im sorry :(

Answer:

1. true

2. false

3. false

4. false

Step-by-step explanation:

hope this helps

please mark brainiest

please give 5 stars

thank you

The sum of the ages of two brothers is 38. in four years ago the age of the elder brother was the square of the younger brother. Find their ages

Answers

Answer:

Elder brother: 25

Younger brother: 5

Step-by-step explanation:

38 - (4+4)= 30

Now trial all square numbers

e.g 2 + 4 = 6 (does not work)

5 + (5x5)= 30

The elder brother is 25 years old and the younger brother is 5 years old.
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