If the polynomial
[tex] {x}^{19} + {x}^{17} + {x}^{13} + {x}^{11} + {x}^{7} + {x}^{5} + {x}^{3} [/tex]
is divided by (x² + 1), then the remainder is:
(a) 1
(b) x² + 4
(c) -x
(d) x

Please solve this for me. Spam free answer required. Thank you.​

Answers

Answer 1

Answer:

(C) - x

Step-by-step explanation:

Given polynomial:

x¹⁹ + x¹⁷ + x¹³ + x⁷ + x⁵ + x³

Group as follows:

(x¹⁹ + x¹⁷) + (x¹³ + x¹¹) + (x⁷ + x⁵) + (x³ + x) - x = x¹⁷(x² + 1) + x¹¹(x² + 1) + x¹⁵(x² + 1) + x(x² + 1) - x

As we see all terms have (x² + 1) as factor apart from the last one.

It means the remainder is - x

Correct choice is C


Related Questions

The price of a pair of shoes increases from $54 to $68. What is the percent increase to the nearest percent? [The percent increase is ___%]​

Answers

Step-by-step explanation:

[tex]68 - 54[/tex]

[tex]14 \div 68 \times 100[/tex]

after doing that calculation you will get the percent increase

Can someone help me please

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Answer:

the equation is linear, the equation is y=9.8x

Step-by-step explanation:

Please help me !!


Nine more than eight times a number (x) is at least forty-nine

What’s the inequality & the solution to the inequality is ..

Answers

Answer:

x = 5.

Sorry if you didn't mean find x and I have no idea about the inequality stuff.

Step-by-step explanation:

We can do a reverse equation in steps. So the first thing we'll do is..

49 - 9 which equals 40.

Then we should do a division since the opposite of multiplication is division.

40 divided by 8 = 5.

To check that we do 5 x 8 = 40 + 9.

Hope that helps. x

Answer:

See below

Step-by-step explanation:

9 + 8x [tex]\geq[/tex] 49

Subtract 9 from both sides

8x [tex]\geq[/tex] 40

Divide by 8

x [tex]\geq[/tex] 5

Mr. Cooper determined functions to represent his distance traveled in miles, d, in terms of the number of hours, 1, of driving on two types of
highways. He found that on a state highway the function was d = 45t, and on a U.S. highway, the function was d = 601.
If Mr. Cooper drove for 1.5 hours on each type of highway, how much farther did he drive on the U.S. highway than on the state highway?
Enter the answer in the box.

Answers

Answer:

105t1

Step-by-step explanation:

por qué los sumas te da

algebric expressions formula​

Answers

Answer:

a2 – b2 = (a – b)(a + b)

(a + b)2 = a2 + 2ab + b

a2 + b2 = (a + b)2 – 2ab

(a – b)2 = a2 – 2ab + b

That's all i know- rip TvT

When solving a system of equations graphically, when would you need to estimate the solution? Explain.

Answers

Answer:

25

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

PLEASE HELP MEE i dont really understand this

4(p+1.25)=7 2/5

Answers

Answer:

p=0.6

Step-by-step explanation:

The regular price of a ladder is $250. If a customer uses the coupon, what percent will the customer save?

Answers

How much does the coupon take off of the original price?

Which number is closest to 1/2

Answers

Answer:

0.56

it's basically the number closest to 50. Don't get tricked by the 0.05 because that's only 5% not 50%

Can someone help me on this question? The question is down below...

Answers

Answer:12m

Step-by-step explanation:

Because you are given that this is a right angled triangle, you can apply the pythagoras theorem where a^2 = b^2 + c^2

15^2 = 9^2 + x^2

225-81 = x^2

144 = x^2

x = 12m

the length of a is 12 m

​Justin completed 85% of a book when he read the first 170 pages. How many pages are in the book?

Answers

there are 200 pages

Answer:

200 BooksStep-by-step explanation:

I need helppp
It’s for math and I’m clueless

Answers

Answer:

14

Step-by-step explanation:

x=4 y=1

Substitute them into the equation 3x-4yy+6

3(4)-4(1)+6

12-4+6

HELLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLPPPPPPPPPPPPPPPPP

Answers

Answer:

a, h and k have values 1, -5 and -10 respectively

The image below represents a Function. Describe what is happening in this "machine".

Answers

Answer:

The input is being multiplied by 10.

This can be represented with the function x * 10 = y with x representing the input and y representing the output.

Step-by-step explanation:

what the vertical height of a hemisphere

Answers

Answer:

V= (2/3) π r³

hope this helps :>

how to sovle
(x+1/x)^2

Answers

[tex] (\frac{x + 1}{x} ) ^{2} \\ = \frac{ {(x + 1)}^{2} }{ {x}^{2} } \\ = \frac{ (x + 1)(x + 1) }{ {x}^{2} } \\ = \frac{ {x}^{2} + 2x + 1}{ {x}^{2} } [/tex]

Hope you could get an idea from here.

Doubt clarification- use comment section.

3y-2x-4x+5x+7
please help meeeeeeeeeeee

Answers

Answer:

3y-2x-4x+5x+7

please help meeeeeeeeeeee

[tex]3y-2x-4x+5x+7\\\\=3y-x+7[/tex]

Records show that Oliver is typically 10–30 minutes late for his shift at work. The distribution for the minutes he is late forms a consistent pattern, which can be graphed as the given uniform density curve.

A uniform density curve is at y = StartFraction 1 Over 20 EndFraction.

Company policy requires employees to be less than 12 minutes late for work. What percentage of the time will Oliver meet company policy?

6.7%
10%
60%
90%

Answers

Based on the information given, the percentage of time that'll be required to meet the policy will be 10%.

From the complete information, the probability distribution will be:

= 1/(b - a) = 1/(30 - 10) = 1/20

Since the company policy requires employees to be less than 12 minutes late for work, the percentage of the time that Oliver will meet company policy will be:

= (12 - 10) × 1/20

= 2 × 1/20

= 1/10

= 10%

In conclusion, the correct option is 10%.

Learn more about percentage on:

https://brainly.com/question/24304697

find the slope of the line that passes through (3,1) (4,9)

Answers

Answer:

+8

Step-by-step explanation:

The slope here would be 8 using rise over run formula which puts y/x and gives you 8

Hi!! So I am doing test corrections for a test that I did bad on but I need to know what is the equation for this??

Answers

Answer:

u can use fraction calculator

Step-by-step explanation:

just go and search 'fraction calculator'

May I please receive help?

Answers

Are you looking for a acute angle?

Answer:

Its right angel

Step-by-step explanation:

Sorry if m wrong

WILL GIVE BRAINLY,5 STARS, THANKS


4,800/60 = 480 tens / 6 tens = ___

Answers

Answer:

80

Step-by-step explanation:

Answer:

800 = 80 tens

Step-by-step explanation:

4800 / 60 = 800

the monthly income of a family is rs 2500 the ratio of the expenditure and saving is 3:2 find amount of saving.​

Answers

Answer:

The amount of saving is Rs.1000.

Step-by-step explanation:

Solution :

Let the,

>> Expenditure = 3x>> Saving = 2x

So, solving for x.

[tex]{\dashrightarrow{\tt{Expenditure + Saving = 2500}}}[/tex]

[tex]{\dashrightarrow{\tt{3x + 2x = 2500}}}[/tex]

[tex]{\dashrightarrow{\tt{5x = 2500}}}[/tex]

[tex]{\dashrightarrow{\tt{x = 2500 \div 5}}}[/tex]

[tex]{\dashrightarrow{\tt{x = \dfrac{2500}{5}}}}[/tex]

[tex]{\dashrightarrow{\tt{x = \cancel{\dfrac{2500}{5}}}}}[/tex]

[tex]{\dashrightarrow{\tt{x =500}}}[/tex]

[tex]{\star{\underline{\boxed{\tt{\red{x =500}}}}}}[/tex]

Hence, the value of x is 500.

Thus,

>> Expenditure = 3 × 500 = Rs.1500>> Saving = 2 × 500 = Rs.1000

[tex] \rule{300}{1.5}[/tex]

3. Rich has t dollars in his checking account. On June 3, he deposited
w, h, and v dollars, and cashed a check for k dollars. Write an alge-
braic expression that represents the amount of money in his account
after the transactions.

Answers

b=(t-whv)+k
b = his end total after the transactions

A CBS News/New York Times opinion poll asked 1,190 adults whether they would prefer balancing the federal budget over cutting taxes; 59% of those asked said "yes." Suppose that in fact 62% of all adults favor balancing the budget over cutting taxes. If this poll was not biased, what is the probability you would get p^=0.59 or less?

Answers

Using the normal distribution and the central limit theorem, it is found that there is a 0.0166 = 1.66% probability of a sample proportion of 0.59 or less.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

It measures how many standard deviations the measure is from the mean.  After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X. By the Central Limit Theorem, the sampling distribution of sampling proportions of a proportion p in a sample of size n has mean [tex]\mu = p[/tex] and standard error [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex]

In this problem:

1,190 adults were asked, hence [tex]n = 1190[/tex]In fact 62% of all adults favor balancing the budget over cutting taxes, hence [tex]p = 0.62[/tex].

The mean and the standard error are given by:

[tex]\mu = p = 0.62[/tex]

[tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.62(0.38)}{1190}} = 0.0141[/tex]

The probability of a sample proportion of 0.59 or less is the p-value of Z when X = 0.59, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.59 - 0.62}{0.0141}[/tex]

[tex]Z = -2.13[/tex]

[tex]Z = -2.13[/tex] has a p-value of 0.0166.

0.0166 = 1.66% probability of a sample proportion of 0.59 or less.

You can learn more about the normal distribution and the central limit theorem at https://brainly.com/question/24663213

Simplify for x: 2/3 = x-1/5

Answers

Answer:

x=13/15

Step-by-step explanation:

2/3=x-1/5

find LCD=15

10/15=x-3/15

add 3/15 to both sides

13/15=x

Find the solution set of each inequality below, and then determine which inequalities have the same
solution set as -(-8x – 3) < 23. Select all that apply.

A
1
(8x + 3) < -23
B
(10x =
- 20) >-44
1
(8x + 3) >-23
(10
(10x +20) >44
E
(8x + 3) < 23
F-crx
(10x +20) < -44
+

Answers

Answer:

(8x+3)<23 is the same as -(-8x-3)<23

Step-by-step explanation:

-(-8x-3)<23  Original equation

(8x+3)<23   [Remove the parentheses]

It is the same equation as the chosen answer: (8x+3)<23

Answer:

Choice E.

Step-by-step explanation:

-(-8x – 3) < 23

-8x - 3 >  -23

-8x > -20

x < 20/8

x < 2.5.

E:-

(8x + 3) < 23

8x < 20

x < 2.5.

find 4/5 x 1 2/3?? please help!

Answers

0.2 is the correct answer because you simplify then solve

Which is the last step when creating and analyzing a scatterplot from a table of values?

Plot the ordered pairs of the independent variable and the dependent variable on the coordinate plane.
Draw or obtain a blank coordinate plane.
Identify if there is a relationship between the independent and dependent variables.
Label the axes of the coordinate plane according to the input and output variables.

Answers

Answer:

A quadratic equation. ax2 +bx+c=0 has exactly one real solution if ∆=b2-4ac=0. We check the answers. In (A) ∆=1 ; in (B) ∆ =25: in (C) ∆=0; in (D)∆=1 . (C) is the correct answer.

Answer:

C. Identify if there is a relationship between the independent and dependent variables.

Step-by-step explanation:

Solve the system of linear equations y= 2x -3Y= x + 6

Answers

Answer:

x=9, y=15. (9, 15).

Step-by-step explanation:

y=2x-3

y=x+6

----------

2x-3=x+6

2x-x-3=6

x-3=6

x=6+3

x=9

y=9+6=15

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