Part A: Create an example of a polynomial in standard form. How do you know it is in standard form? (5 points)

Part B: Explain the closure property as it relates to polynomials. Give an example. (5 points)

Answers

Answer 1

Answer:

A)

The "Standard Form" for writing down a polynomial is to put the terms with the highest degree first.

For example, the polynomial f(x)=x5+2x3−x2+2x+1 is in standard form because the highest degree terms are kept first.

B)

The problem 3 + 6 = 9 demonstrates the closure property of real number addition.

Observe that the addends and the sum are real numbers.

The closure property of real number addition states that when we add real numbers to other real numbers the result is also real.

In the example above, 3, 6, and 9 are real numbers  

Answer 2

Part(A),

The standard form of the polynomial is 3x⁴ - 2x³ + 5x² + 7x - 1.

Part(B),

This is another polynomial, so the closure property holds. Similarly, if we subtract or multiply these polynomials, the result is always another polynomial.

2x³ - 4x² - x + 8

What is a polynomial?

A polynomial is a mathematical statement made up of exponents, coefficients, and variables, which are frequently denoted by the symbol x. (numbers that indicate the power to which the variable is raised).

Part A:

An example of a polynomial in standard form is:

3x⁴ - 2x³ + 5x² + 7x - 1

This polynomial is in standard form because the terms are written in descending order of degree, and each term has a coefficient and a variable raised to a power.

Part B:

The closure property of polynomials states that if we add, subtract, or multiply two polynomials, the result is always another polynomial.

For example, consider the polynomials:

f(x) = 2x³- 5x² + 3x + 1

g(x) = x² - 4x + 7

If we add these polynomials, we get:

f(x) + g(x) = 2x³ - 4x² - x + 8

This is another polynomial, so the closure property holds. Similarly, if we subtract or multiply these polynomials, the result is always another polynomial.

The closure property is important in algebra because it ensures that the operations we perform on polynomials are always well-defined and meaningful.

To know more about polynomials follow

https://brainly.com/question/30489746

#SPJ2


Related Questions

1) Red City is 6 cm away from Blue City on a map but the two cities are actually 240 miles
apart in real. What is the scale on the map?

Answers

You divide 240 miles by 6 cm so you can figure out how many miles are in each centimeter. So 240/6=40 miles. The scale is for every one centimeter, that is 40 miles.

pls help me somebody

Answers

Answer:

it is 36 inches

Step-by-step explanation:

What is the positive solution to the equation 2x2 + 3x = 2?

Answers

Answer:

x(2x+3)

Step-by-step explanation:

Answer:

X= -2

2. x = 1/2 = 0.500

Step-by-step explanation:

What would be the new median if 21 was added to the list

Answers

Answer:

52 is the correct answer

Shanna is planning a trip from Dallas, Texas, to San Diego, California. She knows that the distance she will travel is
about 1400 miles. If she looks at a map with a scale of 1 in. = 300 mi, about how far will the trip be on the map?
3
14
in
0 2 in.
in.
WIN
in

Answers

Answer:

4.67 inches

Step-by-step explanation:

Shanna is planning a trip from Dallas, Texas, to San Diego, California.

She will travel about = 1,400 miles

The scale of a map is 300 miles = 1 inches

The trip of 1,400 miles = [tex]\frac{1400}{300}[/tex]

                                    = 4.66666 inches ≈ 4.67 inches

Her trip is 4.67 inches far on the map.

F(x)-mx+ b, f(-2)=3 and f(4)=1 , what is the value of m and b

Answers

Answer: [tex]m=\dfrac{-1}{3}, b=\dfrac{7}{3}[/tex]

Step-by-step explanation:

Given

Function is  [tex]f(x)=mx+b[/tex]

[tex]f(-2)=3[/tex]

[tex]\therefore 3=m(-2)+b\\\Rightarrow b-2m=3\quad \ldots(i)[/tex]

[tex]f(4)=1\\\therefore 1=4m+b\quad \ldots(ii)[/tex]

from (i) and (ii) we get

[tex]m=\dfrac{-1}{3}, b=\dfrac{7}{3}[/tex]

Pls help 10 ptsssssssssssss
NO LINKS

Answers

Answer:

it is actually a very simple question first you add 4+9=13 then you multiply 5 times 13 which gets you the answer of 65

Find the greatest common factor of the following monomials: 20a 46a^2 48a^6​

Answers

60a^5 is the answer to your question

Help me I need this really bad and I need a good grade I’m behind on school

Answers

Answer:

If you share 7 apples equally with 3 people, then there are 2 1/3 apples per person.

The number 2 represents the number of whole apples each individual gets.

The denominatior, 3, represents how many times an apple will have to be split to divide equally

The numerator, 1, represents how many 3rds each person gets.

A news report states that the 90% confidence interval for the mean number of daily calories consumed by participants in a medical study is (1920, 2140). Assume the population distribution for daily calories consumed is normally distributed and that the confidence interval was based on a simple random sample of 22 observations. Calculate the sample mean, the margin of error, and the sample standard deviation based on the stated confidence interval and the given sample size. Use the t distribution in any calculations and round non-integer results to 4 decimal places.
1. What is the sample mean?
2. What is the margin of error?
3. What is the sample standard deviation?

Answers

Answer:

ddXvffggf

Step-by-step explanation:

vvzgsgygsv gdhvsysgvs gsvysvvs6sg he's) v gateways tsgsyysgd Yacc subs USB GA t gsd

how do i find the polar form of
1-2i

Answers

Answer:

9

Step-by-step explanation:

Riley's grandparents drive from city A to city B every spring. It takes them several days. Each day they use the expression 2+ distance over 54 to figure out how many hours they will be on the road. The first day they were on the road for 7 hours. How far did they travel on the first day?

Answers

9514 1404 393

Answer:

  270 miles

Step-by-step explanation:

For h hours of driving the distance d is covered:

  h = 2 +d/54

Solving for d, we find the distance covered in h hours is ...

  d = 54(h -2)

In 7 hours, the distance they traveled is ...

  d = 54(7 -2) = 270 . . . miles

They traveled 270 miles on the first day.

Using the same scenario as above, but now you do not know the population variance. You collect a random sample of n = 21 cereal boxes and find the sample mean is 12.8 and the sample standard deviation to be 0.5. Test the null hypothesis H0: µ = 13 against the alternative hypothesis HA: µ < 13 at level of significance α = 0.01.

Required:
a. Find the test statistic.
b. Using the rejection region, do you reject or not reject the null hypothesis?
c. Find the p-value.
d. Using the p-value, do you reject or not reject the null hypothesis?
e. In context of your problem, what is your conclusion about the ounces contained in cereal boxes?

Answers

Answer:

-1.833 ; we do not reject the Null.

Pvalue = 0.0409 ; We do not reject the Null

There is no significant evidence to conclude that the number of ounces contained in the cereal boxes is less than 13

Step-by-step explanation:

H0 : μ = 13

HA : μ < 13

Test statistic :

(xbar - μ) ÷ s/sqrt(n)

(12.8 - 13) ÷ 0.5/sqrt(21)

-0.2 / 0.1091089

= - 1.833

The critical value at α = 0.01 ; df = 21 - 1 = 20 = 2.528

-1.833 > - 2. 528 (left tailed test) ; Hence we do not reject the Null.

Test statistic :

Pvalue from Test statistic at DF = 20 ; α = 0.01

Pvalue = 0.0409

Pvalue > α

0.0409 > 0.01 ; Hence, we do not reject H0.

There is no significant evidence to conclude that the number of ounces contained in the cereal boxes is less than 13

(1 point) An open-top box is to be constructed from a 8 \ \mbox{in} by 14 \ \mbox{in} rectangular sheet of tin by cutting out squares of equal size at each corner, then folding up the resulting flaps. Let x denote the length of the side of each cut-out square. Assume negligible thickness. (a) Find a formula for the volume, V, of the box as a function of x. \ \ V(x)

Answers

Answer:

Volume=[tex]4x^3-44x^2+112x[/tex]

Step-by-step explanation:

Let x denotes the length of the side of each cut

After Cutting square length will be=8-2x (where 2x for 2 squares as on each side two corners are there thus 2 squares will be cut down)

After cutting square width will be=14-2x (where 2x for 2 squares as on each side two corners are there thus 2 squares will be cut down)

Height = x

Volume=Length*width*Height

Volume=(8-2x)*(14-2x)*x

On solving we will get:

Volume=[tex]4x^3-44x^2+112x[/tex]

PLEASE HELP, anything is very appreciated

Answers

Answer:

117.8097 [tex]in^{2}[/tex]

Step-by-step explanation:

Depending on how you're math is going there are two ways to solve this,  find the are by the arc or just figure out the whole cookie and divide by 6.   Let's try the latter is seems easier to say.    I mean easier for me to say.  

area of a circle is pi * r^2

the diameter is 30 inches so the radius is half of that or 15 inches

then the whole cookie is

pi*15^2 = 706.858 [tex]in^{2}[/tex]

now divide by 6 or each piece

706.858 [tex]in^{2}[/tex] / 6 = 117.8097 [tex]in^{2}[/tex]

now eat your cookie  :p  

A triangle flower bed has a perimeter of 15cm the drawing has a scale of 1:200. What is the perimeter of the actual flower bed

Answers

Answer:

300cm

Step-by-step explanation:

scale 1:200 means 1cm on drawing represent 200cm on ground so 15cm will be 15×200 which is 3000cm

100Points! show work

Answers

Using angle sum property

[tex]\\ \sf\longmapsto x+43+73+70=180[/tex]

[tex]\\ \sf\longmapsto x+43+143=180[/tex]

[tex]\\ \sf\longmapsto x+186=180[/tex]

[tex]\\ \sf\longmapsto x=180-186[/tex]

[tex]\\ \sf\longmapsto x=-6[/tex]

Option C is correct

Sum of angles of any triangle is 180°

x+43+73+70=180x+186=180x=180-186x=-6

Option C

someone pls help I'm genuinely confused

I've literally been trying to figure out all three of these for like two hours now but I can't figure it out

Answers

Answer:

the area is 50

Step-by-step explanation:

Answer:

its 0.09637 but round it by urself . please like my answer and brainliest me hshsshhs

¿cuales tienen solo un eje de simetría?


English:Which have only one axis of symmetry?​

Answers

Answer:

if your looking for a shape it would be a kite if your looking for a line it would be a parabolas.

si buscas una forma sería una cometa, si buscas una línea sería una parábola.

Step-by-step explanation:

Suppose 10 tosses of a coin were all heads, and you switch to a new coin. What is the probability of tossing this new coin and getting another head?​

Answers

Answer:

50% or 1/2 Could be 100% but i think it is 50%

Step-by-step explanation:

Because Changing the coin will make no difference.

The probability of getting heads is same as the probability of tails which is [tex]\frac{1}{2}[/tex].

What is the probability?

The concept of probability is used to assign a numerical description to the likelihood of occurrence of an event.

Probability can be defined as the number of favorable outcomes divided by the total number of possible outcomes of an event.

Here given that,

The [tex]10[/tex] tosses of a coin were all heads, and you switch to a new coin.

So, the probability of getting all heads is [tex]2^{-n}[/tex]

And we have [tex]n=10[/tex],

Then, the probability of getting the heads is

[tex](^{n}C_k)(\frac{1}{2})^k(\frac{1}{2})^{n-k}=2^{-n}(^nC_k)[/tex]

Hence, the probability of getting heads is same as the probability of tails which is [tex]\frac{1}{2}[/tex].

To know more about the probability

https://brainly.com/question/26257968

#SPJ2

Please help me btw if I see links I’ll report

Answers

Answer:

bro that is easy its 15*1/2

Step-by-step explanation:

g(x) = 2x – 4
h(x)=x²-3
Find (g.h)(5)

Answers

Answer:

40

Step-by-step explanation:

This is asking you to plug in the value of h(5) into g(x). First solve for h(5)

x^2-3 = h(x)

5^2-3= 22

h(5) = 22

h(5) is 22. So now, plug that into g(x).

g(h(5)) = 2(22)-4

44-4=40

(g.h)(5) is 40.

For the following right triangle, find the side length x, Round your answer to the nearest hundredth.
12
x
6

Answers

Answer:

x=12

Step-by-step explanation:

which is a true statement about the two rectangular prism shown below

Answers

can you show a picture of the prism?

can someone help me with this please

Answers

9514 1404 393

Answer:

  1. attendance (y), time (x)

  2. 1,2: increasing; 3: constant; 4: decreasing

  3. attendance increases, remains constant, then decreases

  4. increasing; pre-heating the oven

Step-by-step explanation:

It is always difficult to read the mind of the author of questions like these. Usually, specific wording is expected. If your curriculum material has examples you can copy from, you should do that.

__

1. The variables and what they stand for are listed on the axes of the graph. The y-variable stands for attendance. The x-variable stands for time. It isn't clear whether the desired answer is "y and x" or "attendance and time".

__

2. The graph slopes upward in intervals 1 and 2. It can be described as "increasing."

The graph remains level in interval 3. It can be described as "constant."

The graph slopes downward in interval 4. It can be described as "decreasing."

__

3. The attendance is adequately described in question 2. Attendance increases, remains constant, then decreases. It isn't clear how general or specific the answer is supposed to be.

__

4. The graph of the function is "increasing." We don't know if the indicated temperature is the temperature of the bread, the oven, or the room containing the oven. If we assume the indicated temperature is that of the oven, we expect an increase during the oven pre-heat interval.

If the indicated temperature is that of the bread, then the increase would be following insertion of the bread into the oven.

Determine the missing factor in ■ × 4.2 = 16.8.

Answers

4 is the missing factor!

Answer this and I’ll give you a sticker

Answers

B is the correct answer because they all equal -0.6

Find the area of the shape shown below. 2 4 1. 2 2 2 2 units​

Answers

9514 1404 393

Answer:

  10 square units

Step-by-step explanation:

The shape is a trapezoid with bases of 2 units and 8 units. Its height is 2 units, so its area is ...

  A = 1/2(b1 +b2)h

  A = (1/2)(2 +8)(2) = 10

The area of the shape is 10 square units.

A cold water tap can fill a tub in 6 minutes, and a hot water tap can fill the tub in 8 minutes. A drain can empty a full tub in 10 minutes. If both taps are on and the drai is open, how long will it take to fill the tub? It will take
how many minutes?

Answers

Answer:

12 minutes

Step-by-step explanation:

The Hot tap fills 1/30th of the bath in 1 minute. The cold tap fills 1/20th of the bath in one minute. In one minute both taps together will fill (1/30 + 1/20) of the bath, which is 5/60ths or 1/12th of the bath. Since it takes one minute to fill 1/12th of the bath, it’ll take 12 minutes to fill the bath

If x varies inversely as y and x=16 when y=5, find x when y=20.

Answers

9514 1404 393

Answer:

  x = 4

Step-by-step explanation:

The inverse variation means that when y goes up by a factor of 20/5 = 4, the value of x goes down by the same factor.

  x = 16/4

  x = 4

Other Questions
How many countries speak Portuguese in South America? For what purpose does the government use the taxes it collects from the public? for each photograph below, identify the plant as a monocot or dicot. give as many reasons as you can for each answer What is the factor of 42? celia was obtaining a conventional loan, and she put $50,000 down as a down payment. why might her lender also require her to obtain private mortgage insurance? which of the following is false about probability distributions? O point the probabilities must total O. each probability should be greater than or equal to O. each probability should be positive, less than or equal to O. the outcomes listed must be independent. The following molecular equation represents the reaction that occurs when aqueous solutions of lead(II) nitrate and barium bromide are combined.Pb(NO2)3(aq)+BaBr2(aq) = PbBr2(s)+Ba(NO3)2(aq)Write the balanced net ionic equation for the reaction. A bag contains 3 gold marbles, 7 silver marbles, and28 black marbles. Someone offers to play this game:You randomly select one marble from the bag. If itis gold, you win $3. If it is silver, you win $2. If it isblack, you lose $1.What is your expected value if you play this game? Explaining cause and effects why was that important to many Americans that the constitution including bill of rights Cloning of plants from cuttings demonstrates that ________.A) an individual plant cell cannot de-differentiate and then re-differentiateB) differentiated plant cells may contain embryonic mRNAsC) plants lose genetic information in the differentiation processD) mature plant cells retain the full genetic information needed to carry out the developmental processes to produce a new individual plant Match the following types of prokaryotic control of gene regulation with their example.Transcriptional , Translational, and Post Translational1. mRNA is quickly degraded by an enzyme in the cells cytoplasm before a protein can be made.2. RNA polymerase needs additional proteins to tightly bind a genes promoter.3. A protein needs to have a phosphate group added to its structure before it can perform its function. If a football quarterback runs into and tackles another player by grabbing onto them, what type of collision would this technically be? a. Elastic b. InelasticWhich of the following would be an example of a closed system? a. A person pushing a refrigerator box across a rough floor b. A water bucket being pulled up by rope from a well c. A rolling oil drum across a smooth, frictionless marble floor d. A large moving rock slowing down while ploughing through loose sand Why did the government sue New York Times? 7. Sketch a model to represent the equation2x + 2 = 12. Then, solve the equation. true or false, gravity only acts on heavy objects URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!! What are the 15 categories of Scope 3 emissions? What do entrepreneurs do what is the first step of their process? What's the inverse of 2? Regarding therapeutic drug monitoring, which of the following statements is correct when collecting a specimen for a peak level Peak level is the point at which the drug is lowest in the patient's body Peak level is the point at which the drug is highest in the patient's body Peak level is tested on a blood sample that is collected immediately prior to when the next dose of the drug is given None of the above choices are correct