Find the remainder when p(x) = x4 - 27 is divided by x - 4.

Answers

Answer 1

Answer:

229 is the remainder.

Explanation:

In order to find the remainder, insert the value of x in the equation.

Given equation:

[tex]\sf p(x) = x^4 - 27[/tex]

Given x value:

x - 4 = 0x = 4

Find remainder:

[tex]\sf p(4) = 4^4 - 27[/tex]

[tex]\sf p(4) = 256 - 27[/tex]

[tex]\sf p(4) = 229[/tex]

Answer 2

Answer:

229

Step-by-step explanation:

Here we are given a polynomial p(x) and we need to find the remainder when it is divided by (x-4) . As we know that if a polynomial, say [tex]g(x)[/tex] is divided by [tex]x-a[/tex] then the remainder is [tex]g(a)[/tex] .

Firstly equate [tex] x -4[/tex] with 0 , we have;

[tex]\longrightarrow x -4=0\\[/tex]

[tex]\longrightarrow x =0+4\\ [/tex]

[tex]\longrightarrow x = 4 [/tex]

Now substitute [tex] x =4[/tex] in [tex]p(x)[/tex] ,

[tex]\longrightarrow p(x)= x^4-27\\[/tex]

[tex]\longrightarrow p(4)= (4)^4-27\\[/tex]

[tex]\longrightarrow p(4) = 256 - 27 \\[/tex]

[tex]\longrightarrow \underline{\underline{\boldsymbol{ p(4) = 229}}}[/tex]

Hence the remainder is 229 .


Related Questions

In a survey conducted at a pet store, 150 customers were asked if they owned
birds or fish. The survey data are shown in the relative frequency table.
Own a bird
Do not own a
bird
Total
0.04
0.08
Own fish
Do not own fish
Total
0.02
0.86
What percentage of the people surveyed own fish?

Answers

Answer:

12%

Step-by-step explanation:

have faith in me bro :>

12% of the people surveyed own fish.

What is relative frequency?

Relative frequency refers to the percentage or proportion of times that a given value occurs within a set of numbers, such as in the data recorded for a variable in a survey data set.

We get  

Total (own fish) = 0.04 + 0.08 = 0.12

So, own fish = 0.12

= 12%

12% of the people surveyed own fish.

Find out more information about relative frequency here

https://brainly.com/question/16832475

#SPJ2

Write as an equation.

Answers

Answer:

10

Step-by-step explanation:

(5+x=15)☞︎︎︎(Equation)

5-5+x=15-5

X=10

Nahid is payed 200$ a week + 5% of her sales during the week. The equation p=0.05s represents nahids pay for the week. P represents the total pay for week and s represents her total sales. If nahid was payed 290 at the end of the week, use the equation to determine how much did she sold.

Answers

Answer:

She sold $1800 worth.

Step-by-step explanation:

290-200=90

90 x 20 because 100÷5=20

90 x 20 = 1800

$1800

The graph of a function f is shown below find f(-2).

Answers

Answer:

-3

Step-by-step explanation:

when you look at it go to where x is -2 then go down to where the blue line goes on the point

3. Use Structure Shari is drawing a tree diagram
to represent the sample space of rolling a
12-sided game piece and spinning the pointer of
a 4-section spinner. Does it matter if Shari starts
the tree diagram with the game piece outcomes
or the spinner outcomes? Explain.

Answers

The sample space of Shari's tree diagram is the total possible outcomes of rolling the game piece and spinning the pointer.

It doesn't matter if Shari starts with the spinner or the game piece

How to determine the tree diagram

The experiment involves:

Rolling a 12-sided game pieceSpinning the pointer of a 4-section spinner

If Shari starts with the game piece, the sample size (n) would be:

n = 12 * 4

n = 48

If Shari starts with the spinner, the sample size (n) would be:

n = 4 * 12

n = 48

Notice that the sample size remains unchanged irrespective of what he starts with

Hence, it doesn't matter if Shari starts with the spinner or the game piece

Read more about tree diagram at:

https://brainly.com/question/2581880

HELP HELP I NEED HELP ASAP
HELP HELP I NEED HELP ASAP
HELP HELP I NEED HELP ASAP
HELP HELP I NEED HELP ASAP HELP HELP I NEED HELP ASAP
HELP HELP I NEED HELP ASAP

Answers

Answer:For the answer to this It has me stuck between A and B

A statistician takes several random surveys, each of 50 middle school students, to determine the favorite pizza topping of middle school students. The table
shows the mean results from all the surveys.
Pizza Topping Average of Surveys
extra cheese
pepperoni
pineapple
13
17
8
5
sausage
vegetables
7
Which we statements are valid inferences that can be made based on the data collected?
On average, of students prefer pineapple.
On average, tv of students prefer either pineapple or vegetables,
On average, of students prefer either pepperoni or pineapple.
On average, about 10% of students prefer sausage.
On average, about 50% of students prefer elther extra cheese or pepperoni

Answers

Answer:

I'd say On average, about 50% of students prefer elther extra cheese or pepperoni and On average, 1/4 of students prefer pineapple.

Also i tried my hardest to read the picture you took, so im assuming that the pineapple statement is 1/4 correct me if i'm wrong

4. Magnus flips a fair coin once and rolls an ordinary dice once.
a) Write down all the possible outcomes.
b) Find the probability that Magnus gets a head and a 3.

Answers

The possible outcomes of the fair coin and the dice is the sample space

The list of possible outcomes is: {H1,H2,H3,H4,H5,H6,T1,T2,T3,T4,T5,T6}The probability of getting a head and a 3 is 1/12

How to list the possible outcomes

The items are given as:

Coin = 1

Dice = 1

The sample space of both items are:

Coin = {H,T}
Dice = {1,2,3,4,5,6}

So, the list of possible outcomes is: {H1,H2,H3,H4,H5,H6,T1,T2,T3,T4,T5,T6}

The probability of getting a head and a 3

From the above list, there is only one outcome that has a head and a 3 out of 12 possible outcomes

So, the probability of getting a head and a 3 is:

p = 1/12

Hence, the probability of getting a head and a 3 is 1/12

Read more about probability at:

https://brainly.com/question/25870256


Mand N are two points on the circumference of a circle
centre O.
The straight line AMB is the tangent to the circle at M.
Angle MON = y
Prove that angle BMN = 1/2 y

Answers

Explanation:

We can make use of the symmetry of the problem and properties of similar triangles.

Here's a "paragraph proof."

Draw line OP perpendicular to chord MN, such that P lies on line MB. Let the point of intersection of OP with chord MN be designated point Q. Line OP bisects angle MON, so has measure y/2.

Triangles OPM and MPQ are similar (by AA similarity; both right triangles contain angle OPM), so angle QMP ≅ angle MOP. As we observed above, angle MOP has measure y/2, so angle QMP has measure y/2.

Angle BMN is another name for angle QMP, so it has measure y/2.

__

Additional comments

By the HL congruence postulate, the perpendicular bisector of chord MN divides triangle MON into two congruent right triangles. (OM≅ON, MQ≅NQ). That means ∠MOQ≅∠NOQ, so OQ bisects angle MON, as we say above.

__

Another way to come to the desired conclusion is to recognize that for any point X on long arc MN, angle MXN will have measure y/2. (inscribed angle theorem) This remains true in the limit as X approaches M. As X approaches M, secant XM approaches tangent line MB. So, in the limit, angle BMN is y/2.

A colony of 100 bacteria doubles in size every 60 hours. What will the population be 180 hours from now?

Answers

Answer:

600

Step-by-step explanation: [tex]100\times2\times\frac{180}{60}[/tex]

Cross out the common factor

[tex]100\times2\times3[/tex]

Calculate the product or quotient

[tex]200\times3[/tex]
[tex]600\ YOUR\ ANSWER\ which\ can\ also\ be\ written\ as\ 6\times{10}^2\[/tex]

I hope this helps you

:)

If the initial population of the bacteria is 100, then the population of the bacteria after 180 hours will be 800.

What is an exponent?

Exponential notation is the form of mathematical shorthand which allows us to write complicated expressions more succinctly. An exponent is a number or letter is called the base. It indicates that the base is to raise to a certain power. X is the base and n is the power.

A colony of 100 bacteria doubles in size every 60 hours.

The exponential relation will be given below.

[tex]\rm P = 100 \times 2^{t/60}[/tex]

Where t is the number of hours

Then the population of the bacteria after 180 hours will be

[tex]\rm P = 100 \times 2^{t/60} \\\\P = 100 \times 2 ^{180/60}\\\\\rm P = 100 \times 2^{3}\\\\\rm P = 100 \times 8\\\\\rm P = 800[/tex]

More about the exponent link is given below.

https://brainly.com/question/5497425

Please help I will give brainliest.

Answers

Explanation and Answer:

The graph of y=[tex]x^2[/tex] is a parabola (it looks like a u) that intersects the graph at the origin. These are all shifted variations of that graph, so from that you can figure out their formula by visualizing it.

You can also try substituting numbers into the equations and drawing a graph from that.

Graph A is the y=x^2, shifted to the left, so it becomes [tex]y=x^2+x[/tex]. It's +x because now negative numbers can be gotten from the equation, as compared to before when x^2 gives only positive numbers.

Graph B is [tex]y=x^2+3x[/tex] . Similar to graph A, but now it moves down by more units, because of the 3x.

Graph C is [tex]y=-x^2+2[/tex]. Imaging y=x^2 flipped, it changes from looking like a u to n. That's y=[tex]-x^2[/tex]

Graph D is [tex]y= x^2-x[/tex]. The opposite of Graph A.

Help pls get 35pts plsss

Answers

Answer:

above is the solution to the question

Math Question, help please

Answers

Answer: 254.34 yd

Step-by-step explanation:

If the diameter is 18 yd then the radius:

radius = diameter/2

r = 18/2

r = 9 yd

So the area is:

[tex]A = \pi r^2\\= \pi (9)^2\\= (3.14)(81)\\ =254.34 \hspace2yd[/tex]

Therefore, the area of the circle is 254.34 yd

please help me answer these 2

Answers

Answer:

y-2/3x-4

the answer is (0,3)

3x+4y-12

the answer is (0,3)

If ΔRST congruent to ΔNPQ, which of the following is true? A. ∠R congruent to ∠P B. ∠R congruent to ∠Q C. ∠T congruent to ∠P D. ∠T congruent to ∠Q

Answers

Answer:

Step-by-step explanation:

The order of the expression for congruent shapes indicate the

corresponding vertices between the two shapes that are congruent.

The option which is true is D. T = Q.

Reasons:

The given statement is; ΔRST ≅ ΔNPQ

By Corresponding Parts of Congruent Triangle are Congruent, CPCTC, we

have; The sides on ΔRST are congruent to the corresponding sides of ΔNPQ

Therefore;

RS ≅ NP

RT ≅ NQ

ST ≅ PQ

By CPCTC, we have that the angles on ΔRST are congruent to the corresponding angles of ΔNPQ

Therefore;

∠R ≅ ∠N

∠S ≅ ∠P

∠T ≅ ∠Q

Which gives, by definition of congruency;

∠R = ∠N

∠S = ∠P

∠T = ∠Q

Therefore, the true statement is D. T = Q.

give brainliest

NEED HELP ASAP PLEASE EASY 10 to 20 POINTS RN

Answers

Answer:

explicit  definition: [tex]a_n=5n-4[/tex]

recursive definition: [tex]a_n=a_{n-1}+5[/tex]

Step-by-step explanation:

Given arithmetic sequence: 1, 6, 11, 16, 21 ...

Therefore,

first term a = 1common difference d = 5

Using the general form of arithmetic sequence: [tex]a_n=a+(n-1)d[/tex]

[tex]\implies a_n=1+(n-1)5[/tex]

[tex]\implies a_n=1+5n-5[/tex]

[tex]\implies a_n=5n-4[/tex]

or [tex]a_n=a_{n-1}+5[/tex]

What is the measure of ∠A in the image below?

Answers

Answer:

A

Step-by-step explanation:

3x and x + 30 are vertically opposite angles and are congruent , then

3x = x + 30 ( subtract x from both sides )

2x = 30 ( divide both sides by 2 )

x = 15

Then

∠ A = 3x = 3(15) = 45°

See <A and x+30 are opposite angles .

We know that opposite angles are equal

so

3x=x+302x=30x=15

Now

<A=3x=45°

Option A is correct

Simplify the expression below.
–3 X5 X(-9) X (-2)

Answers

Answer:

[tex] - 3 \times 5 \times - 9 \times - 2 \\ - 15 \times + 18 = 3[/tex]

A square and a rectangle have the same area. The square has side length 8 in. The length of the
rectangle is four times its width. What is the length of the rectangle?

Answers

The first step we take is to find the area of the square since the area of the square is equal to the area of the rectangle

       [tex]area-of-rectangle = area- of-square\\area-of-rectangle = 8*8 = 64in^2[/tex]

Another fact we know is that the length of the rectangle is four times the width.

      L = 4W

L: Length's lengthW: Width's length

Now let's put the variables, found above, into the format to find the area of the rectangle

  [tex]area-of-rectangle = L * W, (L = 4W)\\area-of-rectangle = 4W * W\\\\64 = 4W^2\\16 = W^2\\\\W^2 = 16\\\\W = 4[/tex]

Since the Width is 4, L = 4 * W = 4 * 4 = 16 in.

So the length is 16 inches

Hope that helps!

   

The equation for a circle is shown x ^ 2 + y ^ 2 = 9 Which statement best explains why the equation does not describe a function?

Answers

x2+y2=9 is not a function

In order for an equation to represent a function any single value of x must have at most one corresponding value of y which satisfies the equation.

For

x

2

+

y

2

=

9

XXXX

if (for example)

x=0XXXX there are two values for y (namely +3 and −3) which satisfy the equation

A cylinder has a height of 17 centimeters and a diameter of 18 centimeters. What is its
volume? Use a * 3.14 and round your answer to the nearest hundredth.

Answers

Answer:4323.78cm^3

Step-by-step explanation:

A random sample of 30 professional tennis players is selected. For each tennis player, their first serve percentage and their second serve percentage are recorded. A 95% confidence interval for the mean difference (first – second) in serve percentages is found to be 0.10 to 0.18. A tennis coach claims that there is no difference in first and second serve percentages among professional tennis players. Is this claim supported by the confidence interval?

No, the confidence interval does not contain the value of 0.
Yes, the confidence interval does not contain the value of 0.
No, the confidence interval does not contain negative numbers.
Yes, the confidence interval consists entirely of positive numbers.

Answers

No, the confidence interval does not contain the value of 0

ANSWER QUICKLY PLEASE!!!!!!

Answers

Answer:

See below

Step-by-step explanation:

1

Use similarity ΔPQS ~ ΔRQS

Use the ratio of corresponding sides:

PS/QS=QS/SRPS*SR = QS²PS*20 = 8²20PS = 64PS = 64/20PS = 3.22

Find PS

PS = PR - RS = 72 - 54 = 18

Use similarity ΔPQS ~ ΔPRQ

Ratio of corresponding sides:

PQ/PR=PS/PQPQ² = PR*PSPQ² = 72*18 = 4*18*18 = (2*18)² = 36²PQ = 363

Use similarity ΔPQS ~ ΔPRQ

Ratio of corresponding sides:

PQ/PR=PS/PQPS=PQ²/PRPS = 14²/28 = 7

Find RS:

RS = PR - PS = 28 - 7 = 214

Answer options

a) ΔRPQ ~ ΔRQS - correctb) ΔRQS ~ ΔQPS - correctc) ΔRPQ ~ ΔQPS - correctd) ΔRPQ ~ ΔRQS ~ ΔQPS - most correct as combines all above choices

Today only, a suit is being sold at a 67% discount. The sale price is $270.60.
What was the price yesterday?

Answers

Answer:

$820.00

Step-by-step explanation:

x = price yesterday (initital price)

If it is 67% off, then the price is 33% of the initial.

x(.33) = 270.60

divide .37 on both sides

x = 820.00

The price of the suit yesterday is $820.00.

Anotha oneee, irrelevant answers will be deleted. Thank you so much!!​

Answers

Answer:

k = 5/7; y = 5vw/(7z)w = 18/5; y = 10vw/zy = 3/2; k = 96v = 5/6; k = 8y = 168/5; y = 6vw/z

Step-by-step explanation:

As with other forms of direct and inverse variation, the "constant of variation" (k) is the constant multiplier in the equation. "Varies directly" means the independent variable is in the numerator. "Varies inversely" means the independent variable is in the denominator. The variation equation can be solved for missing values of constants or variables.

The equation for "varies directly with v and w, and inversely with z" means the equation is of the form ...

  y = k·v·w/z

Then the values of v or w are ...

  v = y·z/(k·w)

  w = y·z/(k·v)

__

a)

  k = y·z/(v·w) = 5·24/(12·14) = 5/7; the equation is y = 5·v·w/(7·z)

b)

  w = y·z/(k·v) = 18·8/(10·4) = 18/5; the equation is y = 10·v·w/z

c)

  k = 3/2 (read from the equation); y = (3/2)v·w/z = 3·16·24/(2·6) = 96

d)

  k = 8 (read from the equation); v = y·z/(k·w) = 20·2/(8·6) = 5/6

e)

  y = k·v·w/z = 6·12·7/15 = 168/5; the equation is y = 6·v·w/z

helppp pls ASAP first correct answer gets brainleist​

Answers

[tex]\tt \dfrac{3}{8}\times 28.7=10.7625=10.76~kg[/tex]

to solve m + 9 = 45, should you add or subtract 9 from both sides of the equation

Answers

Answer:

subtract 9 from both sides

Step-by-step explanation:

m + 9 = 45 ( subtract 9 from both sides )

m = 36

Answer:

Subtract

Step-by-step explanation:

You should subtract since the equation says to add.

You basically do the opposite of what it says.

For example, if it was m - 9 = 45 you would add 9 on both sides, but in this case, you would subtract since its m + 9 = 45

m + 9 = 45

subtract nine by 9 and 45:

m = 36

36 + 9 = 45

tan7A - tan4A - tan3A = tan7A*tan4A*tan3A​

Answers

what kind of question

answer is tan 7 a 4 a tan4a

Use substitution to solve the system of equations​



y=x+1.75 4x-2y = 4

Answers

Answer:

y=x+1.75

4x-2y = 4

The answer is (3. 75, 5.5)

Step-by-step explanation:

If you plot the two equations on Desmos' Graphing Calculator, you will see that the solution is intersected at (3.75, 5.5).

are these similar

(the second one)

Answers

Problem 2

Answer: Not similar

Why not? Well it's because the angles do not match up perfectly.

The triangle on the left is a 30-60-90 triangle; while the triangle on the right is a 40-50-90 triangle. The numbers mentioned are the angle values.

Only the "90"s match up, but everything else does not. We need to have three pairs of congruent angles to be able to use the angle angle (AA) similarity theorem.

Other Questions
The purpose of cache memory is to keep handy the most recently accessed data and instructions so that the CPU can access them repeatedly without wasting time. This purpose is similar to that of the ____ of a Web browser. Which description is true about the organization of an ecosystem? A bag of marbles contains five red marbles three green marbles and six yellow marbles what is the probability of randomly choosing a marble that is green Blossom corporation recently reported an EBITDA of $29. 3 million and net income of $9. 7 million. The company had $6. 9 million interest expense, and it's average corporate income tax rate is 35 percent. What is it's deprecriation and amortorization expense? 15. If two complementary angles measures (2x+10and (x + 20. Find the value of x? A. 500 B. 40 C.300 D. 20 PLEASE HELP QUICKIs this triangle acute, right, or obtuse?acute right obtuse The parties have to depend largely on what for their campaign funding. Find the radius of the cylinder with the given volume WILL GIVE BRAINLIEST Marbury v. Madison established the principle of ______ review. According to _____ review, the ________ Court determines if laws and executive acts are unconstitutional. 8The word "citizen" means someone who is a member of a country or community with its duties, rights, and privileges. Therefore, aU.S. citizen is a member of the United States. There are three possible ways to become a U.S. citizen.1.Be born on U.S. soil2.Have parents who are U.S. citizens3.What is the third way to become a citizen?OA. Become naturalizedOB. Renounce citizenship in another countryOC. Get a job in the United StatesOD. Start paying taxesResetSubmit I need help ASAP!!!!!I need to do speaking and I need tips and important things about these topics"Myself", "My Family", "My house","My best friend" and etc.I appreciate your answers and Thank you very much. The sides of a triangle measure 31 inches, 22 inches, and 17 inches. What is the area of the triangle? Round intermediate results to 3 decimal places and the final answer to 1 decimal place. The area of the triangle is? help pls pls pls pls pls Suppose you are saving money to buy a digital video camera that costs $340. You have already saved $120 and plan to save $20 each week. How many weeks will you need to save? Which type of energy is stored in chemical compounds and released in chemical reactions?potentialkineticchemicalelectrical Look at VSW and ZTSW in the image below.Which of the following is the best description for this pair of angles?O complementaryO supplementaryO acuteO straight Cohn's disease is characterized by bouts of remission and ______.A. InfectionB. DehydrationC. Exacerbation D. Constipation Which feature is part of the criteria for judging both persuasive and analytical writing? a well-organized plot objective, neutral language use of original figures of speech a well-written claim statement MDMA increases the levels of all of the following except:MDMA increases the levels of all of the following except:a)Serotoninb)Dopaminec)GABAd)Norepinephrine 2 CaliphateThe Abbasid Caliphate and ?