According to the Fundamental Theorem of Algebra, which polynomial function has exactly 11 roots?

A ) f(x) = (x - 1)(x + 1)^11

B ) f(x) = (x + 2)^3(x^2 -7x +3)^4

C ) f(x) = (x^5 + 7x + 14)^6

D ) f(x) = 11x^5 + 5x + 25


I originally chose A, but that was incorrect on my quiz.

Answers

Answer 1
B would be the right one

F(x) = (x+2)^3 = the highest power for this type turn out will be x^3
the other part is (x^2 - 7x + 3)^4, the highest power for this part will be x^8
since (x+2)^3(x^2-7x +3)^4 = the highest power of first part x^3 second part x^8
x^3 * x^8 = x^11 that result in 11 roots
This type of math, you don't need to configure the whole problem, you just need to know the basic rules of power of a number. For example, (x^2)^3, then 2*3 = 6 make x^6.
or x^2 * x^3 = x^2 + 3 = x^5.
Answer 2

Answer:

The correct answer is B

Step-by-step explanation:



Related Questions

Write two operations in order that you would use to solve the equation 3x - 2=7 then solve the equation

Answers

Here’s how to solve it:
3x = 7 + 2
3x = 9
x = 9/3
x = 3

3x-2=7

You first subtract 2 from both sides, so 2-2=0 & 7-2=5

3x=5

Then you divide 3 from both sides to get “X” alone, 3x/3= 1x (but the the one is invisible so it equal “X”) and then 5/3= 1.66666..

So the answer to this problem is

X=1.6

Serena paid $194.99 for a game system and then bought two equally-priced games. If she spent a total of $284.97, what is the price, p, of one game? Enter your answer in the box.

Answers

$284.97 - $194.99 = $89.98

$89.98 / 2 = $44.99

Serena bought two equally priced game at a price of $44.99 each and the total money spent in buying all three games is $284.97.

Given information:

The price Serena paid for buying the first game is $194.99

The overall price Serena paid for buying three games is $284.97

Let, the price of one of the two equally priced game is [tex]\bold{P}[/tex]

As, the price of second and third game is equal, we can consider the combined price of second and third game.

Thus , the equation formed according to the information given in the question is:

[tex]\bold{194.99+2P=284.97}[/tex]

Solve, the above equation in order to find the price of one game.

[tex]2P=284.97-194.99\\\2P=89.98}\\{P=44.99}[/tex]

Hence, the price of one game in two equally priced game is $44.99

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Let A = 40. If B is complement of A, and C is a supplmenet of B, what is B+C?


A. 60
B. 150
C. 180
D. 210

Answers

Option C: 180 
Explanation:
 Complementary angles add upto 90 degrees and supplementary angles add to 180 degrees
 Given A=40
 B = Complement of A =90-40 =50
 C = Supplement of B = 180-50 =130
 Therefore B+C = 50 +130 =180.

Four bars of soap cost $1.12. What would you pay for 2 dozen bars? (1 dozen=12)

Answers

4 bars = $1.12
Multiply the above equation by 6.
24 bars = $6.72 . . . . . . the cost for 2 dozen bars.

NEED HELP ASAP

What are the restrictions of:
(n^2 -6) / (n^2 -2)

5 and 2
+/- SQRT5 and +/- SQRT2
5 and -2

Answers

What you should see for this case are the values for which the denominator is NOT defined.
 We have then that in this case the values are:
 (n ^ 2 -2) = 0
 Clearing n we have:
 (n ^ 2) = 2
 n = + / - sqrt (2)
 Answer:
 the restrictions are:
 n = + / - sqrt (2)

The circus is coming to town. Cindy is selling tickets. The first day she sold 8 adult tickets and 5 children tickets for a total of 177.50 in sales. The second day she received $255.00 for 12 adult tickets and 6 children tickets.

Answers

let the price of adult ticket and children ticket be a and c respectively
8a+5c=177.50 -> 24a+15c=532.5
12a+6c=255.00 -> 24a+12c=510

24a+15c-24a-12c=532.5-510
3c=22.5
c=7.5
a=17.5

(02.01 LC) Solve: negative 1 over 2 x + 3 = −x + 7 (5 points) 1 over 2 8 −8 2

Answers

Answer:

2 8 -8 2

Step-by-step explanation:

The correct answer is [tex]-\frac{1}{2}x + 3 = -x + 7$ is $x = 8[/tex].

To solve the equation [tex]-\frac{1}{2}x + 3 = -x + 7[/tex], we can follow these steps:

Step 1: Combine like terms on both sides of the equation.

[tex]-\frac{1}{2}x + 3 = -x + 7[/tex]

[tex]\frac{1}{2}x - 3 = x - 7[/tex]

Step 2: Subtract [tex]x[/tex] from both sides to isolate the terms with [tex]x[/tex].

[tex]\frac{1}{2}x - 3 - x = -7[/tex]

[tex]-\frac{1}{2}x - 3 = -7[/tex]

Step 3: Add 3 to both sides to isolate the term with [tex]x[/tex].

[tex]-\frac{1}{2}x = -4[/tex]

Step 4: Multiply both sides by [tex]-2[/tex] to solve for[tex]x[/tex].

[tex]-2 \left(-\frac{1}{2}x\right) = -2(-4)[/tex]

[tex]x = 8[/tex]

Therefore, the solution to the equation [tex]-\frac{1}{2}x + 3 = -x + 7$ is $x = 8[/tex]

Find the area of the triangle. Round the answer to the nearest tenth.

A.
7.8 square units
B.
8.9 square units
C.
19.3 square units
D.
38.5 square units

Answers

The area of this triangle is 19.25
So the closest answer is C. 19.3

Hope this helps :)

Answer:

19.3 square units .

Step-by-step explanation:

∠D=∠F=52°

Opposite sides of equal angles are equal .

So, DE=EF =6.3

Now sum of all angles of triangle is 180°

So, ∠D+∠F+∠E = 180°

52°+52°+∠E =180°

104°+∠E =180°

∠E =180°-104°

∠E =76°

Now to find the length of DF we will use law of cosines

[tex]c^2=a^2+b^2+2(a)(b) Cos E[/tex]

[tex]DF^2=DE^2+EF^2+2(DE)(EF) Cos E[/tex]

[tex]DF^2=6.3^2+6.3^2+2(6.3)(6.3) Cos 76^{\circ}[/tex]

[tex]DF^2=79.38+79.38 (0.2419)[/tex]

[tex]DF^2=98.582[/tex]

[tex]DF=\sqrt{98.582}[/tex]

[tex]DF=9.9[/tex]

Now we are supposed to find the area of triangle

To calculate the area of given triangle we will use the heron's formula :

[tex]Area = \sqrt{s(s-a)(s-b)(s-c)}[/tex]

Where [tex]s = \frac{a+b+c}{2}[/tex]

a,b,c are the side lengths of triangle  

Now substitute the values :

[tex]s = \frac{6.3+6.3+9.9}{2}[/tex]

[tex]s =11.25[/tex]

[tex]Area = \sqrt{11.25(11.25-6.3)(11.25-6.3)(11.25-9.9)}[/tex]

[tex]Area = 19.2907[/tex]

Hence the area of the triangle is 19.2907 ≈19.3 square units .

Factor x2 – 3x – 28. Identify the values that should be written to complete the X diagram. On the top: On the bottom: On the sides: Rewrite the expression using the numbers on the sides of the X diagram. Use double grouping to factor the four terms. x2 – 3x – 28 =

Answers

x^2 -3x -28
= x^2 -7x +4x -28
= x(x -7) +4(x -7)
= (x +4)(x -7)

-28


-3


-7 and 4

(x-7)(x+4)

1. J. Cole is a successful Hip-Hop recording artist. He has a record contract that pays him $20,000 a month plus an additional $12 for each album that he sells. Last month he earned $24,800. Write an equation to express the money J. Cole earned last month. Let "x" represent the number of albums.

2. How many albums did J. Cole sell last month?

Answers

Monthly payment = $20,000
Payment per album = $12
Total earned last month = $24,800

Part (a): Expression for money earned last month
Let x be number of albums last month. Then,
Total earning = Fixed payment + Variable payment

That is,
24,800 = 20,000 + 12*x
24,800 = 20,000 + 12x

Part (b): Number of albums last month
This involves solving for x in the expression derived in part (a) above.
24,800 = 20,000 + 12x
24,800 - 20,000 = 12
12x = 4,800
x = 4,800/12 = 400 albums

Part 1.] Find the value of x in [tex]4,000( 1.5^{x})=25,000[/tex]. Show your work.

Part 2.] Use the domain {½ , 1, 2, 4, 8} to plot the points on the graph for the given equation. The grid marks represent one unit, the horizontal red line represents the x-axis, and the vertical red line represents the y-axis. [tex]y= log_{2} x[/tex]

Answers

Part 1. First we are going to divide both sides of the equation by 4000:
[tex] \frac{4000(1.5^{x}) }{4000} = \frac{25000}{4000} [/tex]
[tex]1.5^{x} = \frac{25}{4} [/tex]
Now we can use logarithms to bring down the variable:
[tex]ln(1.5^{x} )=ln( \frac{25}{4}) [/tex]
[tex]xln(1.5)=ln( \frac{25}{4}) [/tex]
[tex]x= \frac{ln( \frac{25}{4}) }{ln(1.5)} [/tex]
[tex]x=4.52[/tex]

Part 2. Lets use the domain (x values) to find the range (y values):
[tex]log_{2} (\frac{1}{2})=-1 [/tex]
[tex]log_{2} (1)=0 [/tex]
[tex]log_{2} (2)=1 [/tex]
[tex]log_{2} (4)=2 [/tex]
[tex]log_{2} (8)=3 [/tex]

Finale lets put the points together and draw our graph:

Please help if you do not know the answer don’t comment in the answer box just for points

The box plots show the distributions of daily temperatures, in °F, for the month of January for two cities.

Which statements are true about the distributions? Check all that apply.

a. Both distributions are symmetric.

b. Both distributions are skewed right.

c. Both distributions are skewed left.

d. The mean and standard deviation would be the best measures to compare the data.

e. The median and IQR would be the best measures to compare the data.

Answers

I don't know all of them but I can tell you that B and E are answers that you should check.

Hey, the answers are

Both distributions are skewed right.

The median and IQR would be the best measures to compare the data.


That is B and E

Find two consecutive integers whose product is 24 more than three times the first integer

Answers

x= first integer
x+1= second consecutive integer

Product means multiply, so we'll multiply x by x+1. More than means to add and 3 times is multiplication.

x(x + 1)= 3x + 24
use distributive property to multiply x by everything in parentheses
(x*x) + (x*1)= 3x + 24
x^2 + x= 3x + 24
subtract 3x from both sides
x^2 - 2x= 24
subtract 24 from both sides
x^2 - 2x - 24= 0
factor the expression
(x-6)(x+4)= 0
x-6=0
x=6

x+4=0
x=-4

If x= 6 is the first integer, x+1= 7 is the second integer

If x= -4 is the first integer, x+1= -3 is the second integer


Hope this helps! :)

In this activity, you'll calculate a probability and use it to predict the result of repeating a simple chance-based trial many times.

You are in charge of the casino night game area at a fundraising event. In one of the games, called Odd Odds, the player rolls two six-sided dice. The player gets points if the product of the two numbers rolled is odd. So, success in the game depends on the chances of getting an odd number for the result.

1)Find the number of outcomes in the sample space, n(S), of the trial of this game.

2)List and count all the outcomes for event E, in which the product of the two numbers rolled is odd.

3)Find the probability of getting an odd number. In this case, you will calculate the probability, P(E), of event E, in which the product of the two numbers rolled is odd. Write the probability as a fraction reduced to lowest terms and as a decimal correct to two places.

Answers

Answer:


Step-by-step explanation:

They are saying the player gets points if the PRODUCT of the two numbers rolled is odd not the SUM  So the answer should be

(1,3) (1,5) (3,1) (3,3) (3,5) (5,1)(5,3)(5,5)  which is 9 out of 36 which would be 1/4 or 0.25

Final answer:

In this activity, the student needs to calculate the number of outcomes in the sample space, list and count the outcomes for event E, and find the probability of getting an odd number.

P(E) = 9/36 = 1/4 = 0.25.

Explanation:

To find the number of outcomes in the sample space (n(S)) of the trial, we need to consider all the possible combinations of rolling two six-sided dice. Since each die has six sides, the total number of outcomes for each die is 6. To find the total outcomes in the sample space, we multiply the outcomes for each die: n(S) = 6 * 6 = 36.

In this game, we are interested in the outcomes where the product of the two numbers rolled is odd. To list and count these outcomes, we need to consider the combinations where one or both of the numbers rolled is odd. By listing all the possible outcomes, we have: (1, 1), (1, 3), (1, 5), (3, 1), (3, 3), (3, 5), (5, 1), (5, 3), (5, 5). There are 9 outcomes for event E.

To find the probability of getting an odd number, we need to divide the number of outcomes for event E by the total number of outcomes in the sample space. P(E) = 9/36 = 1/4 = 0.25.

WILL GIVE BRAINLIEST ANSWER!!! PLEASE HELP!!! 12 POINTS!!!!!!!

The formula for the volume, V, of a right rectangular pyramid is one-third its base length, l, times its base width, w, times its height, h. Which of the equations below are equivalent to the formula described?

-----Note: more than one must be used-----

ANSWER OPTIONS:

* l = V over 3hw

* w = V over 3lh

* l = 3V over wh

* h = 3Vl over w

* w = 3V over lh

* h = V over 3lw

Answers

V = 1/3 h l w

h l w = 3V

l = 3V / w h    Which is the third choice.

h = 3V / l w

w = 3V / h l - which is the fifth choice

The third and fifth are equivalent to the formula described.

Jordan is 4 feet 8 inches tall, her mother is 5 ft 10 inches tall, how much taller is Jordan's mother than Jordan? Give your answer in feet and inches.

Answers

since it takes 4 in to get to 5 ft from 4ft 8in and another 10 inches to get to 5ft 10in, that give you a total of 14 inches. And there are 12 inches in a foot, So the answer is 1ft 2in.
Jordan's mom is I foot and 2 inches taller than Jordan

What is the relation between the graphs of f(x)=x^2 and g(x)=x^2+6?

a.
the graph of g(x) is a translation of the graph of f(x) up 6 units
c.
the graph of g(x) is a translation of the graph of f(x) right 6 units
b.
the graph of g(x) is a translation of the graph of f(x) left 6 units
d.
the graph of g(x) is a translation of the graph of f(x) down 6 units

Answers

The answer is letter a

Answer:

I think it is the first one

Step-by-step explanation:

Please give brainliest

Sandra got a 3/27 balloon mortgage and her initial payments were $945. She decided to refinance her balloon payment with a 30-year mortgage and her new payments were $937. What is the total financed cost she paid for her house?

Answers

371,340 (APEX) hope this helps.

Sandra got a 3/27 balloon mortgage and her initial payments were $945.

This means Sandra paid $945 per month for 3 years. Total payment made in 3 years = 945*3*12 = $34,020

Later, she decided to refinance her balloon payment with a 30-year mortgage. Her new payments were $937.

Payment made under mortgage = 937 * 30 * 12 = $337,320

The total financed cost she paid for her house = $34020 + $ 337320 = $371340

Hope this helps..!!

Thank you :)

Which of the following situations models a geometric sequence? Select all that apply.

Answers

Answer:

Options 1, 3, 4.

Step-by-step explanation:

We will check each and every option given here.

1) Amount of cell phone users increases by 33% every year.

Its a geometric sequence because the number of users are increasing exponentially every year.

2) Amount of cakes in bake sale increases by 3 each year the fundraiser is held.

amount of cakes is increasing with a common difference of 3 so it's an arithmetic sequence.

3).Uranium loses half of its weight every 415 years.

Exponential decay in every 415 years. So geometric sequence with a common ratio of 1/2.

4).A family of rabbits doubles in size every 3 months.

Exponential series again so geometric sequence with a common ratio of 2.

5).Car drives at a constant speed of 58 mph.

Its a linear function representing an arithmetic sequence with a common difference of 58 mph.

6). Number of students increases by 122 every year.

An arithmetic sequence with a common difference of 122.

7). Number of pieces of chalk in a class room decreases by 10 throughout the school year.

It's an arithmetic sequence having common difference of 10.

Amount of cell phone users increase by 33% every year. Uranium loses half of its weight every 415 years. A family of rabbits doubles in size every 3 months. Then the correct options are A, C, and D.

What is a geometric sequence and how to find its nth terms?

Suppose the initial term of a geometric sequence is a and the term by which we multiply the previous term to get the next term is r.

Then the sequence would look like

a, ar, ar², ar³,.....   (till the terms to which it is defined)

Amount of cell phone users increase by 33% every year.

It's a geometric sequence because the number of users is increasing exponentially every year.

Uranium loses half of its weight every 415 years.

Exponential decay every 415 years. So geometric sequence with a common ratio of 1/2.

A family of rabbits doubles in size every 3 months.

Exponential series again so geometric sequence with a common ratio of 2.

Then the correct options are A, C, and D.

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John bought 6 dumplings for $3.00.

Let x represent the number of dumplings purchased, and let y represent the total cost.

Graph the line that represents the proportional relationship.

Answers

just make the slope as 1/2 remember rise over run and start at 0

Average Monthly Temperature Month Temperature January 45 degrees February 42 degrees March 54 degrees April 62 degrees May 78 degrees June 85 degrees July 92 degrees August 94 degrees September 89 degrees October 78 degrees November 65 degrees December 54 degrees The average monthly temperatures for the city of Mathville are given in the chart above. One year was particularly warm, and the average temperature each month increased by 5°. What did this do to the average yearly temperature? A) The average remained the same. B) The average increased by 5°. C) The average decreased by 5°. D) The average increased by 60°.

Answers

Let 
x------------> the average yearly temperature

if One year was particularly warm, and the average temperature each month increased by 5°
in one year the temperature increased------->5*12-----> 60°
so
[the new average yearly temperature]=x+(60)*12-------> x+5°

therefore 

the answer is the option
B) The average increased by 5°. 

f(x)=9x^3+2x^2-5x+4 and g(x)=5x^3-7x+4 what isf(x)-g(x)

Answers

Answer:
f(x) - g(x) = 4x³ + 2x² + 2x

Explanation:
We are given that:
f(x) = 9x³ + 2x² - 5x + 4
g(x) = 5x³ - 7x + 4

We want to get the value of f(x) - g(x). This means that we will simply subtract g(x) from f(x) as follows:
f(x) - g(x) = 9x³ + 2x² - 5x + 4 - (5x³ - 7x + 4)
f(x) - g(x) = 9x³ + 2x² - 5x + 4 - 5x³ + 7x - 4
f(x) - g(x) = 9x³ - 5x³ + 2x² - 5x + 7x + 4 - 4
f(x) - g(x) = 4x³ + 2x² + 2x

Hope this helps :)

You are working on a proof. You know that A and B are on the perpendicular bisector of CD. What can you conclude? A) AC = BD B) CB = AD C) AC = AD D) AB = CD

Answers

You can only conclude that AC = AD  

Its C

Which graph shows a proportional relationship? help!!

Answers

Graph C and D because they make sense

Triangle ABC is similar to triangle FGH. Angle A measures 42 degrees. Angle B measures 19 degrees. Find the measure of angle H.

42

19

119

29

Answers

IF triangle ABC is similar to triangle FGH, then angles of this triangles are equal.
Let's find the angle C:
∠C=180-42-19=119
Then ∠H=119
Answer: 119 degrees

The perimeter of an isosceles triangle is 14 cm. One of its sides is twice longer than another of its sides. Find all sides of the triangle.

Answers

An isosceles triangle has 2 equal sides so the 3 sides = a a and b
The side that is twice longer than another side make it equal 2*a.
So the total of the 3 sides would equal 14
4a = 14
So 2 sides = 3.5 and the third side = 7.
3.5 + 3.5 + 7 = 14


Answer:

Step-by-step explanation:

2.8, 5.6, 5.6

Melina has 4 sheets of wacky face sticker individually from the sheet. She then divides them evenly into 3 piles to give to friends. How many stickers are in each pile?

Answers

I FOUND YOUR COMPLETE QUESTION IN ANOTHER SOURCE.
 SEE THE ATTACHED IMAGE.

 For this case what we must do is first find the total number of stickers.
 We have then:
 (4) * (24) = 96
 Then, we must organize the stickers in three piles.
 We have then:
 (96) / (3) = 32
 Answer:
 in each pile are 32 stickers

The answer explains how to divide 4 stickers into 3 piles, resulting in 1 sticker each.

To find out how many stickers are in each pile:

Count the total number of stickers = 4 sheets x 1 sticker per sheet = 4 stickers.Divide the total number of stickers evenly into 3 piles: 4 stickers ÷ 3 piles = 1 sticker in each pile.

Which example best represents balanced forces

Answers

The forces are equal and opposite, the book remains at rest, representing a state of balanced forces.

Balanced forces occur when the net force acting on an object is zero, meaning that the forces are equal in magnitude and opposite in direction. As a result, the object remains in a state of equilibrium and does not accelerate.

One example that best represents balanced forces is:

A book resting on a table.

When a book is placed on a table, it doesn't move because the force of gravity pulling it down (its weight) is balanced by the normal force exerted by the table, pushing the book upward.

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What is the value of y in the parallelogram below?

Answers

Answer:

The answer is the option B

[tex]23\°[/tex]

Step-by-step explanation:

we know that

In a parallelogram consecutive angles are supplementary

so

In this problem

[tex]5y\°+65\°=180\°[/tex]

Solve for y

[tex]5y\°=180\°-65\°[/tex]

[tex]y=115\°/5=23\°[/tex]

Answer:

23

Step-by-step explanation:

just took the test

What is the area of this triangle A=bh2

Answers

Area of a triangle = 1/2 b h
 where b is the base and h is the height
base = 6 in and height = 8 in
 Area = 1/2 ×6×8
         =  24 square inches
Therefore, the area of the triangle is 24 square inches
◆ TRIANGLES ◆

[tex]we \: know \: that \: \: , \\ \\ area \: of \: triangle \: = \frac{1}{2} \times base \times height \\ \\ or \: ,area \: of \: triangle \: = \frac{1}{2} \times base \times perpendicular \\ \\ here \: , \\ base = 6 \: in \\ perpendicular = 8 \: in \\ hypotenuse = 10 \: in \: \\ \\ therefore \: \: , \: \\ area \: of \: triangle \: = \frac{1}{2} \times 6 \times 8 \\ \\ = 24 \: {in}^{2} \: \: \: \: \: ans.[/tex]
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