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


Here is the equation of a circle: x2 + y2 + 12x + 2y + 12 = 0
Find the center and radius of the circle.

Answers

Answer:

centre = (- 6, - 1 ) , radius = 5

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

Given

x² + y² + 12x + 2y + 12= 0

Collect the x- terms and the y- terms together and subtract 12 from both sides

x² + 12x + y² + 2y = - 12

Using the method of completing the square

add ( half the coefficient of the x / y coefficients )² to both sides

x² + 2(6)x + 36 + y² + 2(1)y + 1 = - 12 + 36 + 1

(x + 6)² + (y + 1)² = 25 ← in standard form

with (h, k ) = - 6, - 1 ) as centre and r = [tex]\sqrt{25}[/tex] = 5

the size of the angles of a quadrilateral are in the ratio 1:2:3:3. calculate the size of each angle???​

Answers

The size of the angles of a quadrilateral are in the ratio 1:2:3:3. Calculate the size of each angle. Explanation. Verified. Step 1. 1 of 2.

One angle in a triangle is 4 times the size of another angle.The third angle 90, and three angles of tue triangle add up to 180.How big are the two unknown anges?

Answers

Answer:

30 degrees and 60 degrees

What is 0.27 as a percent?
A)0.27%
B)27%
C)2.7%
D)270%

Answers

Answer:

B.

Step-by-step explanation:

to turn a decimal into a percentile you have to move the decimal point over two spaces to the right.

Answer:

B

Step-by-step explanation:

Move the decimal 2 places to the left to find a percent.

Lalit got 50% in Hindi,75% in English and 90 marks in maths. The maximum marks in each subject were 100,140 and 160 respectively. Find his aggregate percentage

Answers

Answer:

61%

Step-by-step explanation:

     MARKS  

        %    Max   Actual  

Hindi 50%    100 50  

English 75%     140 105  

Math              160 90  

   400 245       61%

(245/400)

Given: 3(7x-9)-19x=-15
Prove: x=6

Answers

Step-by-step explanation:

3(7x-9)-19x = -15

21x-27-19x = -15

2x-27 = -15

2x = -15+27

2x = 12

x = 6

prove x = 6

Substitute x=6 into the equation.

3(7(6)-9)-19(6) = -15

3(42-9)-114 = -15

3(33)-114 = -15

99-114 = -15

-15 = -15 True✓

what are the zeros of the function of y=x^2-3x+2​

Answers

Answer:

1 and 2

Step-by-step explanation:

Zeros of the function is where the function intersect with x-axis (or in other way the zeros of function is x value when y = 0 )

y=x^2-3x+2​

(we substitute y with zero)

0 = x^2-3x+2​

or in other way

x^2-3x+2​ = 0

Then we factor out the function by using the grouping method

(When we should give two numbers that there sum is equal -3 and if we multiply them we get 2)

and these two numbers are -2 and -1

x^2-3x+2​ = 0

*Substitute the middle term with -x-2x

x^2-x-2x+2​ = 0

*factor out x , then factor out -2

x(x-1)-2(x-1) = 0

*factor out x-2

(x-2)(x-1)=0

Either

x-2 = 0

So

x = 2

Or

x-1 = 0

So

x = 1

in conclusion the zeros of this function is 1,2

There is a line that includes the point (8,3) and has a slope of 1. What is its equation in slope-intercept form?

Answers

Answer:

y=x-5

Step-by-step explanation:

y-y1=m(x-x1)

y-3=1(x-8)

y-3=x-8

y=x-8+3

y=x-5

If
f (x) = -3x + 15
find:
f (x)
-6

Answers

Answer:

33

Step-by-step explanation:

f(-6) = -3(-6) + 15

       = 18 + 15

       = 33

BRAINLIEST
Please do one or more questions

Answers

Answer:

12. ⇒ 218 °

13. ⇒ 282 °

Step-by-step explanation:

Problem 12:

Given - MK = 10 m

JK = 52 °

Since ∠LNJ = 90 °

Then LKJ = 90 °

So, KL = 90 ° - 52 ° = 38 °

Now, MK = 180 °

= MKL = MK + KL

= 180 ° + 38 °

= 218 °

Problem 13:

VYX = 360° - (YW + 15°)

YW = 180° - 117° = 63°

VYX = 360° - (63° + 15°) = 360° - 78° = 282°

Answer:

Step-by-step explanation:

what is the right answer
giving out brainliest

Answers

The answer is QT bisects VS

because according to the image you can see by the markings that both sides of VS are congruent being divide by QT

Hope this helps!
Brain is much appreciated!

Simplify completely quantity x squared plus 12 x plus 35 all over 3 x plus 15 . (1 point)


quantity of x squared plus 21 over 3

quantity of x squared plus 11 over 3

quantity x plus 7 over 3

quantity of x plus 5 over 3

Answers

Answer:

  (c)  (x +7)/3

Step-by-step explanation:

Factor each expression and cancel common factors.

 [tex]\dfrac{x^2+12x+35}{3x+15}=\dfrac{(x+7)(x+5)}{3(x+5)}=\boxed{\dfrac{x+7}{3}}[/tex]

Answer:

C

Step-by-step explanation:

passed the quiz

Determine the intercepts of the line

Answers

Answer:

25, -55

Step-by-step explanation:

Intercepts are where the line crosses the x and y axis

x intercept = 25

y intercept = -55

-2,75 is greater or less than -2.5

Answers

Answer: less than s less than -2.5

Step-by-step explanation:

Answer:

-2.75 < -2.5

-2.75 is less than -2.5

Step-by-step explanation:

If we were to plot these numbers on a number line, it would look like the this:

<--- (-3) --- (-2.75) --- (-2.5) --- (-2.25) --- (-2) --->

When it comes to negative numbers, the "smaller" number is actually greater.

Therefore, -2.75 is less than -2.5.

What value(s) of x will make x2 = 25 true?
A. 5 and -5
B. 5
C. 5
D. 12.5 and -12.5


Answers

x^2 = 25

x = -5, 5

Check your work!

(-5)^2 = 25

(5)^2 = 25

Hope this helps! :)

6.True or False.
A numeral, such as 22 is called a constant.

Answers

Answer:

True

Step-by-step explanation:

The term with no variable attached to it is the constant

Answer:

te voy a devolver el susto me diste 9 veces peor

Step-by-step explanation:

Which frequency table is consistent with the histogram of weights of 86 different students, below?

Answers

Answer:

 B

Step-by-step explanation:

The incorrect tables each have at least one flaw that makes it not match the histogram.

A. The relative frequency associated with 4 of 86 is about 0.047, not 0.055. The relative frequencies are incorrect.

B. this table matches the histogram

C. The "bins" are not of uniform width, nor are they centered on the same values as shown in the histogram.

D. The values in a cumulative frequency table should be non-decreasing. The table value of 24 should be 54.

If the triangles are similar, which must be true? StartFraction R Y Over Y S EndFraction = StartFraction R X Over X T EndFraction = StartFraction X Y Over T S EndFraction StartFraction R Y Over R S EndFraction = StartFraction R X Over R T EndFraction = StartFraction X Y Over T S EndFraction StartFraction R Y Over R S EndFraction = StartFraction R X Over R T EndFraction = StartFraction R S Over R Y EndFraction StartFraction R Y Over R X EndFraction = StartFraction R S Over R T EndFraction = StartFraction X Y Over T S EndFraction.

Answers

The correct relation between the triangles if the triangles are similar is, [tex]\dfrac{RY}{RS} = \dfrac{RX}{RT} = \dfrac{XY}{TS}[/tex].

Given that,

Consider [tex]\rm \triangle RST[/tex] and [tex]\rm \triangle RYX[/tex].

Triangle RST is shown.

Line XY is drawn parallel to side ST within triangle RST to form a triangle [tex]\rm \triangle RYX[/tex].

We have to determine,

If the triangles are similar, which must be true?

According to the question,

Consider [tex]\rm \triangle RST[/tex] and [tex]\rm \triangle RYX[/tex].

Triangle RST is shown.

The relationship between the triangles is line XY is drawn parallel to side ST within triangle RST to form [tex]\rm \triangle RYX[/tex].

The point X on side RT and point Y on side RS in [tex]\rm \triangle RYX[/tex].

Then,

The [tex]\rm \triangle RST[/tex] is similar to [tex]\rm \triangle RYX[/tex], the corresponding ratio of their sides are equal,

[tex]\dfrac{RY}{RS} = \dfrac{RX}{RT} = \dfrac{XY}{TS}[/tex]

Hence, The correct relation between the triangles if the triangles are similar is, [tex]\dfrac{RY}{RS} = \dfrac{RX}{RT} = \dfrac{XY}{TS}[/tex].

For more details about Triangle refer to the link given below.

https://brainly.com/question/13858149

Answer:

B.

Step-by-step explanation:

Edge 2022

pls pls pls help meeeee

Answers

Answer:

What do you need help with?

Step-by-step explanation:

Which value of x makes the equation true 3x-6/3 7x-3/6 ?A. -11 B. -9 C. -3 D. 3

Answers

Answer:im pretty sure its d

Step-by-step explanation:

Suppose y varies directly with x where y=21 when x=7 find y when x = 15

Answers

Golfkrieg ist die ganze Woche im Auto oder ist das 56357

Which number sentence is true?
OA) 5.6 > |-8.91
OB) |-5.6] < |-8.91
OC) -5.6 > 1-8.91
OD 15.6] > 1-8.91

Answers

The first one (when simplify) is

5.6>8.91

Which is not true if you plot it on a number line

The second one (when simplify) is

5.6<-8.91

which is not true because it is the same thing as number 1

The third one (when simplify) is

-5.6>8.91

which is obviously not true since negatives are way smaller than positives

So that leaves us the last one

Thefore the answer is OD.

I hope this helped!!

86,400 seconds into day.please ​

Answers

[tex]\underline\mathtt\colorbox{gold}{1 day}[/tex]

Step-by-step explanation:

1440 minutes, 24 hours or 1 day

Its easy to check - - - Divide 86400 by 60(to make into minutes) =1440 minFurther. Divide 1440 by 60 (to make into hours) =24 hrsNow who doesn't know that 24 hours is 1 day?

SOCCER Four soccer players are practicing a drill. Goalie A is facing Player B
to receive the ball. Goalie Athen turns tº to face Player A to pass her the ball. If
Goalie B is facing Player A to receive the ball, then through what angle
measure should Goalie B turn to pass the ball to Player B?

Answers

Answer:

x

Step-by-step explanation:

In a parallelogram opposite angles are equal, so if Goalie A angle is x, also Goalie B's will be x

The angle measure for Goalie B turn to pass the ball to Player B is given by the parallelogram and the angle is B = x°

What is a Parallelogram?

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The four types are parallelograms, squares, rectangles, and rhombuses

Properties of Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent.

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

Given data ,

Let the parallelogram be represented as ABCD

Now , the measure of Goalie A = x°

And , for a parallelogram

Opposite angles are congruent

So , the angle of Goalie B = angle of Goalie A

Substituting the values in the equation , we get

The angle for Goalie B = x°

Therefore , the value of B = x°

Hence , the opposite angle of parallelogram is x°

To learn more about parallelogram click :

https://brainly.com/question/23488153

#SPJ2

Find the slope of this line.​

Answers

Answer:

5/2

Step-by-step explanation:

To find a slope you use rise over run.

The graph shows that you rise 5 for every 2 right.

I need help with this Graph!

Graph a right triangle with the two points forming the hypotenuse. Using the sides, find the distance between the two points, to the nearest tenth (if necessary). (-6,3) and (3, -9)

find leg number 1 and leg number 2 and the distance​

Answers

Answer:

Step-by-step explanation:

The distance between two points (-6, 3) and (3, -9) is 10.81 units.

We have a graph a right triangle with the two points A(-6,3) and B(3, -9) forming the hypotenuse.

We have find the distance between the two points using only the sides of the right triangle.

What is the formula to find the distance between the two points on Cartesian plane ?

The distance between two points -

[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]

According to the question, we have -

Coordinates of Point A = (- 6, 3)

Coordinates of Point C = (3, -9)

Now -

Coordinates of Point B will be (- 6, -9) [formed by the intersection of sides].

Distance AB -

[tex]AB = \sqrt {\left( {-6 - (-6) } \right)^2 + \left( {3 - (-9 } \right)^2 }[/tex]  = 6 units

Distance BC -

[tex]BC = \sqrt {\left( {-6 - 3 } \right)^2 + \left( {-9 - (-9 } \right)^2 }[/tex] = 9 units

Using the Pythagoras theorem -

[tex](AC)^{2} =(AB)^{2} +(BC)^{2}[/tex]

[tex](AC)^{2} =[/tex] 36 + 81

AC = [tex]\sqrt{117}[/tex] = 10.81

Hence, the distance between two points (-6, 3) and (3, -9) is 10.81 units.

To solve more questions on Distance formula, visit the link below -

brainly.com/question/12662141

#SPJ6

Can someone help me with this question?

Answers

Answer:

radius, center, chord, diameter

Step-by-step explanation:

a. radius

b. center

c. chord

d. diameter

Radius,center,chord,diameter

Pls help me 15 points total

Answers

It’s 738 text me if you need anything else

PLS HELP WILL GIVE BRAINLYEST

Answers

131° is the right answer

Step-by-step explanation:

the supplementary angle to 139° (left of that angle, still under the red l line) is 180 - 139 = 41°.

therefore,

A = 180 - 90 - 41 = 49°.

B is the supplementary angle to A.

B = 180 - 49 = 131°

remember, the sum of all angles around one point on one side of a line is 180° (that is called supplementary angles).

and the sum of all angles in a triangle is always 180° too.

Use your knowledge of isosceles and equilateral triangle‘s to find the requested information.

Find m

Answers

Answer:

48 degrees

Step-by-step explanation:

6y=8y-16

y=8

8(8)-16= ?

64-16=

Answer:

∠ P = 48°

Step-by-step explanation:

Since NM = PM then the triangle is isosceles with base angles being congruent, then

∠ P = ∠ N , that is

8y - 16 = 6y ( subtract 6y from both sides )

2y - 16 = 0 ( add 16 to both sides )

2y = 16 ( divide both sides by 2 )

y = 8

Then

∠ P = 8y - 16 = 8(8) - 16 = 64 - 16 = 48°

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