Find the remainder when x^100 - x^99 + x^98 − · · · − x + 1 is divided by x + 1.

Answers

Answer 1

Answer:

The remainder is 101.

Step-by-step explanation:

We are dividing:

[tex](x^{100}-x^{99}+x^{98}...-x+1)\div(x+1)[/tex]

By the Polynomial Remainder Theorem, if we are dividing a polynomial P(x) by a binomial in the form (x - a), the our remainder will be P(a).

The divisor is (x + 1). Therefore, our a = -1.

Then the remainder will be:

[tex]P(-1)[/tex]

We can rewrite our polynomial as:

[tex]P(x)=-(x^{99}+x^{97}...+x^3+x)+(x^{100}+x^{98}...+x^2)+1[/tex]

Each of the parentheses contain fifty terms. -1 to any odd power is -1, and -1 to any even power is 1. Therefore:

[tex]P(-1)=-(-50)+(50)+1[/tex]

Evaluate:

[tex]P(-1)=101[/tex]

The remainder is 101.

Answer 2

Answer:

The Answer is 101

Step-by-step explanation:

101 is how much is remaining


Related Questions

A modified roulette wheel has 32 slots. one slot is 0, another is 00, and the others are numbered 1 through 30, respectively. You are placing a bet that the outcome is an odd number. (In roulette, 0 and 00 are neither odd nor even.)<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" />


a. What is your probability of winning ?

The probability of winnign is ?

( type an integer or a simplified fraction)

b. What are the actual odds against winning are ?

c. When you bet that the outcome is an odd number, the payoff odds are 1:1. How much profit do you make if you bet $17 and win ?

If you win, the pay off is ?

d. How much profit should you make on the $17 bet if you could somehow convice the casino to change its payoff odds so that they are the same as the actual odds against winning ?

(rounds to the nearest cent as needed.)Type your question here

Answers

Answer:

0.46875 ; 1.133 ; $17 ;19.27

Step-by-step explanation:

Number of slots = 32

0, 00, {1,.. 30}

Odd outcomes = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29}

1.) probability of winning :

P(winning) = number of odd outcomes / tot possible outcomes

P(winning) = 15 / 32 = 0.46875

2.)

Odds against winning :

Number of losing outcomes / number of winning outcomes

Not odd numbers / odd numbers = 17 /15 = 1.133

C.)

Payoff odd = 1:1

If bet value = $17 ;

Profit made on winning = $17 * 1 = $17

d.)

If Payoff odd = odd against winning = 17 / 15

Profit on $17

17/ 15 * 17

(1.1333333) * 17

= 19.27

;

find the value of each angle.​

Answers

Answer + Explanation:

First, find what the sum of the interior angles must be. You can use the formula 180(n - 2) where n is the number of sides to find this.

n = 5, so 180( 5 - 2) = 180 * 3 = 540 degrees.

Then, you can add up all the interior angles of the pentagon and it will add to 540. This means that:

2x + x + 2x + 90 + 90 = 540

5x + 180 = 540

5x = 360

x = 72

Then you can go through and find the measure of each angle:

S = 90 degrees (given)

T = 2x = 2 * 72 = 144 degrees

U = x = 72 degrees

V = 2x = 72 * 2 = 144 degrees

W = 90 degrees (given)

90° clockwise rotation
Help please

Answers

Answer:

E' (-2,5)

F' (-3,1)

G' (-2,-1)

H' (0,3)

Step-by-step explanation:

The rule for 90 degree clockwise rotation is (h,k) -> (k,-h). This means flip the x-value's sign and then switch x and y's position. For example E (-5,-2), first flip x's sign (5,-2) and then switch x and y's places (-2,5).

The following histogram summarizes the ages of the 25 employees who work for Elon's company. According to the 1.5 IQR wall for outliers how many high outliers are there in the data set

Answers

Answer:

Step-by-step explanation:

1

The number of high outliers in the data set will be 1.

What is the interquartile range?

The interquartile range is a measurement of a data set's "middle fifty." A range is a measurement of where a set's beginning and end are located.

To get the interquartile range, we must know the first and third quartiles. To find those, we need to know the median of the data.

The following histogram summarizes the ages of the 25 employees who work for Elon's company. According to the 1.5 IQR wall for outliers. The number of the high outliers will be 1.

Therefore, the number of high outliers in the data set will be 1.

To know more about the interquartile range follow

https://brainly.com/question/4102829

#SPJ2

(c)
2x - 3y = 1
3x + y=-5
Solve geographically

Answers

Answer:

1) x=3/2y+1/2

2)x=-1/3y+-5/3

Step-by-step explanation:

1)

Let's solve for x.

2x−3y=1

Step 1: Add 3y to both sides.

102x−3y+3y=1+3y

2x=3y+1

Step 2: Divide both sides by 2.

2x/2

=

3y+1/2

x=3/2y+1/2

25+45+15-31=? what is the anser

Answers

25+45+15-31 equals 54

Round 2,641 to the nearest thousand

Answers

It would be 3,000 as it is the next thousand. Since 2,641 is over 2,500 you can round to the next thousand 3,000

Answer: 2,641⇒3,000

Step-by-step explanation:

      2                       6                     4                 1

Thousand         Hundred            Ten             one

------------------------------------------------------------------

Question:

Round 2,641 to the nearest thousand

Solve:

When the number is less than 5, you move down

When the number is greater or equal to 5, you move up

2 is the thousands place

the number before 2 is 6 on the hundreds place

6 is greater than 5, so you move up

Hope this helps!! :)

Please let me know if you have any questions

4x+14+8x-14=180 find for x

Answers

Answer is x = 15

4x + 14 + 8x -14 = 180

Add/subtract x terms and non x terms

12x = 180

x = 180/12 = 15

Check if answer is right by putting x = 15 back into original equation and seeing if it equals 180

4(15) + 14 + 8(15) -14 = 180

Answer is correct.

the same digits are used for the expression 2^5 and 5^2 explain how to compare the value of the expressions

Answers

the value of 2⁵ is greater than the value of 5² because 2⁵ is equal to 32 then the value of 5² is equal to 25.

HOPE IT'S HELP

#CarryOnLearning

In a financial crisis, the number of bankruptcies will likely be ____ and the company profits will likely be O A. larger; larger O B. smaller; smaller C. smaller; larger O ; D. larger; smaller​

Answers

Answer:larger ,smaller

Step-by-step explanation:

Answer:

larger, smaller

Step-by-step explanation:

on aoex

What is the Y intercept of y=3-4x?​

Answers

Answer:

13

Step-by-step explanation:

PLEASE HELP!!!
The perimeter of a rectangular coffee table is given by the trinomial 2t2+4t+2. The table's length is 2t-3. What is the table's width?

Answers

Answer:

t^2+4

Step-by-step explanation:

The perimeter of the table can be given by the equation 2l+2w, and we know the length is 2t-3, meaning 2(2t-3)+2w=2t^2+4t+2, as we know 2t^2+4t+2 is the perimeter. Simplifying we get:

4t-6+2w=2t^2+4t+2

4t+2w=2t^2+4t+8

2w=2t^2+8

w=t^2+4

This means that the table's width is t^2+4

what is 1/5 + 1/6=
Pls I need help

Answers

Answer:

So the first step would be is to multiply the denominators so you would get this:

6/30 + 5/30

Then you would have 11/30 no simplification needed.

Se image below for more info:

Answer:

11/30

Step-by-step explanation:

To add fractions, you need to find the common denominators

the common denominator for 5 and 6 is 30, because 5*6 = 30

1/5 times (6/6) to get a common denominator of 30. Remember, you have to multiply the numerator by 6 too!

1           6          6

_    x    _    =    _

5         6          30

Now, we just have to multiply 1/6 by (5/5) to get a common denominator of thirty.

1           5          5

_    x    _    =    _

6         5          30

5             6         11

_     +      _    =    _

30          30        30

You final answer should be 11/30

what is the unit rate of paying $15 for 4 people to see a magic show?

Answers

Answer: $3.75

Step-by-step explanation:

Divide 15 by 4

3.75/1 is the answer

The table shows the highest point of elevation of 5 different states. How much higher is the highest point of elevation in Colorado than Texas ?

Answers

Answer:

where is the table

Step-by-step explanation:

27 ÷ 3 and 3 ÷ 27
associative property
Yes, commutative property
Yes, identity property
No, they are not equal
which one is it

Answers

Answer:

No they aren't equal........

No they are not equal

Which of the following is a solution of x2 + 4x + 6? (1 point)

Answers

Answer:

I LOVE ALGEBRA anyways

othe ans is in the picture and the steps how  got the ans

(hope it helps can i plz have brainlist it will make my day :D hehe)

Step-by-step explanation:

Simplify the following expressions and evaluate any numerical expressions.

(−3x)2

Select one:

−9x4


−9x2


9x4


9x2

Answers

Answer:

-6x

Step-by-step explanation:

Why is it 9? Cuz its not 3(3)

At an ice cream shop, 16 of the last 72 cones sold had pistachio ice cream. What is the
experimental probability that the next cone sold will have pistachio ice cream?

Answers

Answer:

2/9

Step-by-step explanation:

Total cones sild= 72

Pistachio ice cream sild= 16

p= 16/72

p=2/9

PLEASE MARK ME AS BRAINLIEST!!!!

Researchers make a one-sample z interval to estimate the proportion of adults who would say they learned
something new in the past month. Previous studies have suggested that about 40% would answer "yes" to this
question. The researchers plan on using a confidence level of 95%, and they want the margin of error to be no
more than 25%.

Answers

Answer:369

Step-by-step explanation:

Distribute and solve
(p + 24) = 9

Answers

Answer:

p+24=9

p=-15

Step-by-step explanation:

plz make me brainliest

(p+24) = 9
p + 24 = 9
-24 = -24
p = -15

A book sold 39,900 copies in its first month of release. Suppose this represents 8.2% of the number of copies sold to date. How many copies have been sold to date?

Answers

Answer:

486,585

Step-by-step explanation:

x = total number of books sold

0.082 x x = 39,900

to find x divide both sides by 0.082

x = 486,585

Someone help me with this??

Answers

Answer:

w = 215 degrees

Step-by-step explanation:

A  circle = 360 degrees total. So, 145 + w should equal 360.

145 + w = 360

145 + w -145 = 360 - 145

w = 215

Hope this helps :)

Maybe brainliest?

Can someone help please?

Answers

Answer:

16

Step-by-step explanation:

since he needs 32 points to get to 75 points,

soo you just dividi the points you need by the points you get by every question since it's 2 for every question you just need half of the question needed to get to 32 points soo divide it by 2 and the answer you get is 16.

A city council organized a marathon race to promote good health. There were 3 times as many female participants as male participants in the marathon. If the total number of participants was 812, how many participants were male

Answers

Answer:

609 males

Step-by-step explanation:

A city council organized a marathon race to promote good health.

Let the number of

Females = x

Males = y

There were 3 times as many female participants as male participants in the marathon.

3x = y

If the total number of participants was 812,

x + y = 812..... Equation 1

We substitute 3x for y in Equation 1

x + 3x = 812

4x = 812

x= 812/4

x = 203 females

3x = y

Solving for y

3(203) = 609 males

The number of males participants = 609

Calculate the quotient.
A. 3/4 divided by 5 1/5 is?
B. 3/7 divided by 2 1/2 is?
C. 5/8 divided by 6 5/6 is?
D. 8 3/10 divided by 5/8 is?

Answers

A) 3/4 ÷ 5 1/5.

Answer:

[tex] \frac{15}{104} [/tex]

B) 3/7 ÷ 2 1/2.

Answer:

[tex] \frac{6}{35} [/tex]

C) 5/8 ÷ 6 5/6.

Answer:

[tex] \frac{15}{164} [/tex]

D) 8 3/10 ÷ 5/8.

Answer:

[tex]13 \frac{7}{25} [/tex]

PLEASE HELP WILL GIVE BRAINLIEST TO CORRECT ANSWER

Answers

Answer:

Step-by-step explanation:

h(x) = 7 - x - 2x^5

h(-1) = 7 + 1 - 2(-1)^5

h(-1) = 7 + 1 + 2

h(-1) = 10

Now differentiate h(x)

h'(x) = -1 - 2*5*x^4

h'(x) = -1 - 10x^4

h'(x) = -1 - 10(x)^4

h'(x) = -1 - 10 (x)^4

h'(-1) = -1 - 10(10000)

h'(-1) = -1 - 100000

h'(-1) = - 99999

Evaluate the expression.
-8.x – 3y if x = 4 and y = -2

Answers

Answer:

-8.4 + 6 hope this helped!

Step-by-step explanation:

Answer:

-38

Step-by-step explanation:

-8.x – 3y

x = 4

y = -2

Since we have the value for x and y we can use that and substitute it into the expression

-8(4) - 3 (-2)

-32 - 6

When you add 2 negative numbers (or subtract them) they will give you a bigger number so think of it as adding 2 positive numeber, but then putting a negative sign in the beginning of it.

-32 - 6

-38

Hope this helped!

Have a supercalifragilisticexpialidocious day!

What is equation of the line graphed below?

Answers

using the parent function y = mx + b,
y = -3x
slope is m- so rise over run -3/1 = -3
where the line crosses the y axis is b- 0 (origin)
ExplanationFind the slope by using rise over run with two coordinate points.

[tex](0,0) \longrightarrow \sf{part \: \: of \: \: the \: \: graph} \\ (1, - 3)\longrightarrow \sf{given \: \:coordinate \: \: point}[/tex]

[tex]m = \frac{dy}{dx} = \frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute these coordinate values in.

[tex]m = \frac{0 - ( - 3)}{0 - 1} \\ m = \frac{3}{ - 1} \\ m = - 3[/tex]

Hence, the slope is -3.

Find the y-intercept.

From the graph, the line passes through the origin point. Therefore, the y-intercept is (0,0).

Slope-Intercept form

[tex]y = mx + b \\ \begin{cases} \sf{m = slope} \\ \sf{b = y - intercept} \end{cases}[/tex]

Substitute both m and b in the slope-intercept form.

[tex]y = - 3x + 0 \\ y = - 3x[/tex]

Hence the answer is y = -3x.

Answer

[tex] \large \boxed{y = - 3x}[/tex]

help with rounding off!!please

Answers

Answer:

Step-by-step explanation:

A.0.4821 ( 3 d.p)=0.482

B.0.595 (2 d.p)= 0.60

C.0.0346(3 d.p)=0.03

D.2.94999(1 d.p)=2.9

Mark me as a brainliest

0.482
0.60
0.03
2.9
those are the answers
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The speaker of "The World IsToo Much with Us" believes that if he were a pagan, he would be? "The six sides of a cube are labeled 1, 2, 3, 4, 5 and 6. You flip a coin and roll the number cube. What is the theoretical probability that the coin lands on tails and you roll a number less than 3? Write your answer as a fraction. Show your work."my answer is "1/4" _____________|H or T | 3||H | 3 ||T | 3 |thats my work its a chart i think Which of the following actions explains why Britain officially entered World War II? (5 points) Which of the following is true of personification? Select all that apply.Personification gives life to inanimate objectsPersonification allows objects to speak that normally could notPersonification helps you get to know a personPersonification is the imitation of another person Plss HELP I need the answers to the 5 questions at the bottom I will mark brainliest want Brain-lest then this is the probably gonna be the second one i am sending so for for like the lats 2 so please give me real answers. thanks :) 2. Emma knows that her mix of 5 cups of orange juice to 2 cups of gingerale will create enough drink for 7 people. If she is looking to createenough drinks for 28 people, how many cups of orange juice will sheneed? * An area of a wall is 50 in. wide and 35 in. high. Will a mirror with a 62 in. diagonal fit in it? Identify the correct explanation. PLEASE HELP ON #3 ASAP! plz help! What are the main 6 belief or practices of Buddhism Can someone solve this please Can I get some help on this pls What does g =??? 2/5g = 5 Put the following 3 fictional plants in order from earliest to most recent according to their characteristics:A. The Terpad Plant: This plant reproduces using spores and has proper leaves and vascular tissue. B. The Feltris Plant: The Feltris plant lives in moist environments since it doesn't have any vascular tissue to maintain hydration throughout the plant. This plant has no roots either but has small root-like structures called rhizoids which help anchor them to the ground. Water is also required in order for fertilization.C. The Lancelot Plant: This plant can grow in either moist or dry environments, has true roots, stems and leaves and reproduces via seeds which develop within an ovary. someone pls factorise step by step x^2 + 5x - 24 matematikte terim nedir Microscopic examination of amniotic fluid How can the Senate check the actions of the President? Group of answer choices by ruling that a law is unconstitutional by vetoing a proposed bill by refusing to confirm a Presidential nominee by issuing a pardon I. find the distance the two given points 4 What is the relationship between Domains and Kingdoms? (1 Point) -Domains are further broken down into Kingdoms.- Kingdoms include the prokaryotic cells and Domains do not. -Kingdoms are larger groups of organisms and contain Domians -Domains are specific to Genus of living things and Kingdoms are Species of living things.