Pls help me and give steps as to how to do it thank you

Part A: polynomial in Standard form;-

bluef(x) = ax⁴ + bx³ + cx²+ dx + e

Part B: Closure property relates to polynomial;-

The polynomial's closer property for subtraction. When two polynomials of identical degrees with different leading coefficients are subtracted, a polynomial of the same degree is produced.

What is  Polynomial?

A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x2 4x + 7 is an illustration of a polynomial with a single indeterminate x.

A.

Any of the following can be the fourth degree polynomial with two terms:

f1(x) = ax⁴ + bx³

f2(x) = ax⁴ + cx²

f3(x) = ax⁴ + dx

f4(x) = ax⁴ + e

a ≠ 0  in all four instances.

Explanation. Because each of the aforementioned polynomials fi(x)-s can be written in the form of f(x) by setting blue0 equal to (c,d,e), (b,d,e), (b,c,e), and (b,c,d), respectively, each of the aforementioned polynomials is in standard form.

B.

The polynomial's closer property for subtraction. When two polynomials of identical degrees with different leading coefficients are subtracted, a polynomial of the same degree is produced.

Example.

Let r(x) be defined as a₁x³ + a₂x² + a₃x + a₄

s(x) is equal to b₁x³ + b₂x² + b₃x + b₄

where a ≠ 0 ≠ b and a ≠ b both belong to a set of real or complex numbers called ai and bi.

If this is how subtraction is defined, then

r(x) - s(x) = [a₁x³ + a₂x² + a₃x + a₄] - [b₁x³ + b₂x² + b₃x + b₄]

r(x) - s(x) = (a₁ - b₁)x³ + (a₂ - b₂)x² + (a₃ - b₃)x + (a₄ - b₄)

Given that (a₁ - b₁) ≠ 0, r(x) - s(x) is similarly a polynomial of fourth degree in this situation.
To learn more about Polynomial click on the link

https://brainly.com/question/2833285

#SPJ13

The expectation of getting correct option out of total choice of 5 question.

Probability is the ratio of number of favorable outcomes to the total number of outcomes.It can not be more than 1.

we have five question each of them has four choice, two out of them are correct.

Number of correct choice in one question = 2

Total number of choice in a question = 4

probability to get correct option of one question = 2/4 = 0.5.

Then the probability of 5 question = 5(0.5) = 2.5

Thus, the expectation of correct choice is 2.5.

To know more about probability visit:

brainly.com/question/15124899

#SPJ4

Answer:10.75

Step-by-step explanation:

3/4 as a decimal is 0.75. add that to the 10 gives you 10.75

Using the exterior angles theorem, the measures of the named angles are:

m∠PQR = 51°

m∠PRQ = 96°

Based on the exterior angles theorem, the measure of the exterior angle of a triangle has an angle degree that is equal to sum of the interior angles of the triangle.

Therefore, the following equation would be set to find the value of x:

33 + 10x + 1 = 17x - 1

34 + 10x = 17x - 1

Combine like terms

34 + 1 = 17x - 10x

35 = 7x

35/7 = 7x/7

5 = x

x = 5

m∠PQR = 10x + 1 = 10(5) + 1 = 51°

m∠PRQ = 180 - (17x - 1) = 180 - (17(5) - 1) = 96°

Learn more about the exterior angles theorem on:

https://brainly.com/question/24756010

#SPJ1

Answer:

2561.2785

Step-by-step explanation:

All you gotta do is calculate and times 78.93 x 32.45

Answer: m=0

Step-by-step explanation: (-10,17) & (-9, 17) are 2 points away from each other on the x-axis, there is no difference in y. Therefore the answer is zero.

Answer:

-4

Step-by-step explanation:

(-2)^2 + 4(-2) =

= 4 - 8 =

= -4

The number of books bought by the school is 92.

Here it is given that the school spend $925 to buy new books for the library.

The cost of each book is $9.95

So we have to find the number of books that can be bought.

By dividing the total money spent by the cost of each book we get the number of books bought.

Let n be the number of books bought.

n × 9.95 = Total money spend on the books

As we know the total money spend on the books is $925.

So we get:

925 = n × 9.95

n = 925/ 9.95

= 92

Therefore the total number of books bought is 92.

To know more about the cost refer to the link given below:

https://brainly.com/question/2004396

#SPJ4

The value of x are, x = 9, x = -9.

What is undefined expression?

A mathematical expression that consists of a number of variables and arithmetic operations but has no known solution is referred to as an undefined expression. Any expression that has the symbol ∞ in any part of its expression or that has zero in the denominator is regarded as being undefined.

When the denominator is zero, a rational expression cannot be defined. Set the denominator equal to zero and solve the ensuing equation to get the values that render a rational expression undefined.

So, to find the x - values set denominator equal to zero.

[tex]x^2 - 81 = 0\\x^2 = 81\\x = \sqrt{81}[/tex]

x = ± 9

Therefore, the value of x are, x = 9, x = -9.

To know more about the undefined expressions, click on the link

https://brainly.com/question/28033755

#SPJ13

By using algebra properties, the quadratic equation y = x² - 4 contains the roots x = - 2 and x = 2.

In this problem we need to derive the quadratic equation that contains two roots: r₁ = - 2, r₂ = 2. We need to replace all roots in the factor form of the quadratic equation and expand it by algebra properties. First, replace the roots of the factor form of the quadratic equation:

y = (x - r₁) · (x - r₂)

y = (x + 2) · (x - 2)

Second, expand the expression derived in the previous step by algebra properties:

y = (x + 2) · x - (x + 2) · 2

y = x² + 2 · x - 2 · x - 4

y = x² - 4

Third, write the resulting expression:

y = x² - 4

To learn more on quadratic equations: https://brainly.com/question/17177510

#SPJ1

The value of 150/4 to the nearest tenth is 37.50

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. . In a proper fraction, the numerator is less than the denominator. In improper fraction, the denominator is smaller to the numerator.

The value of 150/4 = 75/2= 37 1/2

1/2 in decimal is 0.5

Therefore 150/4= 37+ 0.5= 37.5

learn more about fractions from

https://brainly.com/question/78672

#SPJ1

The absolute value of the difference between the first and second numbers is 5.

Here we have to find the difference between the first and the second numbers.

There are three statements.

Let a, b, and c be the first, second, and third numbers respectively.

The first statement is that the sum of the three number is 96.

The second statement is that the first number is 6 times the third number.

a = 6c

The third statement is that the third number is 40 less than the second number.

c = b - 40

b = c + 40

The sum of the three numbers is 96.

a + b + c = 96

6c + c + 40 + c = 96

8c = 96 - 40

8c = 56

c = 7

As a = 6c and b = c + 40

Now put the value of c as 7 we have:

a = 6 × 7

= 42

b = 7 + 40

= 47

Difference between the first and second numbers= 47 - 42

= 5

Therefore the difference is 5.

To know more about the number refer to the link given below:

https://brainly.com/question/21289653

#SPJ4

The average of aa and bb is 740.

The result of adding together and dividing by the total number of numbers or variables is the arithmetic mean, which is also known as the average or average value. In statistics, the arithmetic mean is significant. Central tendency is measured using the arithmetic mean. By giving each observation the same amount of weight, it enables us to determine the frequency distribution's center for a quantitative variable (in contrast to the weighted arithmetic mean).

Given,

Arithmetic mean = 1515

Total number of values = 5

Formula:

Sum/Total = Arithmetic mean

33 + 55 + 77 + aa + bb/ 5 = 1515

165 + aa + bb = 7575

aa + bb = 7575 - 165

aa + bb= 7410

The average of aa and bb is 740.

To learn more about arithmetic mean, visit:

https://brainly.com/question/13000783

#SPJ4

The required third number will be 12 when numbers are in the A.P.

An arithmetic sequence is defined as an arrangement of numbers that is in a particular order.

The given data as

first number = - 2

fifth number = 26

Assume that the given numbers are in the A.P.

The formula to find the general term of an arithmetic sequence is,

Tₙ = a₁ + (n-1)d  ...(i)

Substitute the value of n = 5 and a₁ = -2 in the above formula

T₅ = a₁ + (5-1)d

26 = -2 + 4d

4d = 28

d = 7

For finding the third term (number):

T₃ = -2 + (3-1)7

T₃ = -2 + (2)7

T₃ = -2 + 14

T₃ = 12

Therefore, the required third number will be 12 when numbers are in the A.P.

Learn more about arithmetic sequence here:

brainly.com/question/21961097

#SPJ1

The record-holder ate 6.205 kilograms of hot dogs.

We are given that 73/10 hotdogs per minute is the record for the most hot dogs eaten and one hot dog and bun has a mass of 85 grams. Also, one kilogram is equal to 1,000 grams. Solving this problem would involve converting units.

In order to find out how many kilograms of hot dogs the record holder ate, we first need to convert 85 grams to kilograms. Since a kilogram is equal to 1,000 grams, 85 grams = 85 / 1,000 = 0.085 kilograms.

Then, we multiply 0.085 by 73 to get 6.205. We can conclude that the record-holder ate 6.205 kilograms of hot dogs.

Find out more about converting units here: brainly.com/question/174910

#SPJ4

The dimension of each corral should be 25 feet in width and 33⅓ feet in length so that the enclosed area will be a maximum.

Adjacent rectengular corral has length and width with area formula as below.

A = L × W

Given:

Because the dimension of adjacent rectangular corrals are the same, so:

W = 4x

L = 3y

3y + 4x = 200

[tex]y = \frac{200 - 4x}{3} [/tex]

There are two adjacent rectangular corrals, so:

A = 2×L×W

[tex]A = 2 \times \frac{200 - 4x}{3} \times \: x [/tex]

A = ⅓(400x–8x²)

We can differentiate to get the maximum area:

⅓×(400x–8x²) = 0

400–16x = 0

16x = 400

x = 25 feet

Substitute x value (width) to get y value (length):

y = (200–4(25)) ÷ 3

y = (200–100) ÷ 3

y = 100 ÷ 3

y = 33⅓ feet

Learn more about area https://brainly.com/question/14742387

#SPJ4

For the given coordinates of the vertices of trapezoid EFGH and E'F'G'H' the following statement is true and explain the relationship correctly :

"Trapezoid EFGH is not congruent to trapezoid E′F′G′H′ because there is no sequence of rigid motions that maps trapezoid EFGH to trapezoid E′F′G′H′.

trapezoid E F G H, is not congruent to , trapezoid E prime F prime G prime H prime, because there is no sequence of rigid motions that maps , trapezoid E F G H, to , trapezoid E prime F prime G prime H prime,"

As given in the question,

Trapezoid EFGH with coordinates of  vertices:

E(−8, 8), F(−4, 12), G(−4, 0), and H(−8, 4).

Trapezoid E'F'G'H' with coordinates of  vertices:

E′(−8, 6), F′(−5, 9), G′(−5, 0), and H′(−8, 3).

First option is not correct as there is no translation.

Third, Fourth, and Fifth options are not correct as both the trapezoids are not congruent.

Only option second describe it correctly which is:

Both the trapezoid are not congruent as there is no sequence of rigid motion that maps EFGH to E'F'G'H'.

Therefore, for the given coordinates of the vertices of trapezoid EFGH and E'F'G'H' the following statement is true and explain the relationship correctly :

"Trapezoid EFGH is not congruent to trapezoid E′F′G′H′ because there is no sequence of rigid motions that maps trapezoid EFGH to trapezoid E′F′G′H′.

trapezoid E F G H, is not congruent to , trapezoid E prime F prime G prime H prime, because there is no sequence of rigid motions that maps , trapezoid E F G H, to , trapezoid E prime F prime G prime H prime,"

Learn more about vertices here

brainly.com/question/27029296

#SPJ1

The inequality for this graph is:

x<2

Answer:

b = (4/3), with rounding

Step-by-step explanation:

Area = A, in cm^2

n = days

A(n) = [tex]A_{0}[/tex][tex]b^{n}[/tex]

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

Data:

n = 2, A = 1.8

A(n) = [tex]A_{0}[/tex][tex]b^{n}[/tex]

1.8 =  [tex]A_{0}[/tex][tex]b^{2}[/tex]

n = 3, A = 2.4

2.4 = [tex]A_{0}[/tex][tex]b^{3}[/tex]

Although we are not given the initial area, we can still make the calculation since we have two data points and each has the same initial area, [tex]A_{0}[/tex].  Lets take the first equation and multiply it by b, in order to bring the [tex]b^{2}[/tex] to [tex]b^{3}[/tex]

1.8 =  [tex]A_{0}[/tex][tex]b^{2}[/tex]

b(1.8 =  [tex]A_{0}[/tex][tex]b^{2}[/tex])

1.8b = [tex]A_{0}[/tex][tex]b^{3}[/tex]

We can know from the second equation that 2.4 = [tex]A_{0}[/tex][tex]b^{3}[/tex] .  We can eliminate this term in the above relationship by substituting 2.4:

1.8b = [tex]A_{0}[/tex][tex]b^{3}[/tex]

1.8b = 2.4

b =  1.3333

       or (4/3)

Check:

Does the value of (4/3) for b work for both data points?  To check this, we do need to assume an initial starting area.  Lets assume the starting area, [tex]A_{0}[/tex] = 1.

n = 2, A = 1.8, b = (4/3)

A(n) = [tex]A_{0}[/tex][tex]b^{n}[/tex]

1.8 =  1*[tex](4/3)^{n}[/tex]

1.8 =  1.78  Close enough?

n = 3, A = 2.4, b = (4/3)

2.4 = [tex]A_{0}[/tex][tex](4/3)^{n}[/tex]

2.4 = 1*[tex](4/3)^{3}[/tex]

2.4 = 2.37 Close enough?

z = 134 (number of mezzanine units sold)

b = 834 (number of balconies sold)

m = 1120 (number of main floor sales)

Equations:

60m + 42b + 40z = 107,588

m = b + z + 152

b = 3z + 432

Substitute for "b" to get m = 4z + 584

------

Substitute for m and b and solve for "z"::

60(4z+584) + 42(3z+432) + 40z = 107588

240z + 35040 + 126z + 18144 + 40z = 107588

406z + 53184 = 107588

406z = 54404

z = 134 (# of mezzanine sold)

Solve for "b" and for "m" using z = 134

b = 3(134) + 432

b = 834 (# of balcony sold)

m = 834 + 134 + 152

m = 1120 (# of main floor sold)

learn more about equations here:

https://brainly.com/question/10413253

#SPJ4

In linear equation, 275 hamburgers were sold on Wednesday​ .

What in mathematics is a linear equation?

Let x = the number of hamburgers sold

Let x - 67 = the number of cheeseburgers sold

x + x - 67 = 483

2x = 483 + 67

2x = 550

x = 275

x = 275 hamburgers

Learn more about linear equation

brainly.com/question/11897796

#SPJ13

Answer:

146 degrees

Step-by-step explanation:

Sum of all triangle angles equal 180 degrees

We know 2

56 and 90 so we add them

90+56=146

Now we subtract to 180 to find the third angle of the triangle

180-146=34

To find x we gotta subtract 34 from 180 since it’s on a flat plane

180-34=146

angle x=146 degrees

hopes this helps please mark brainliest

Length of the line AB is 1.414 units and midpoint of AB is (3.5,5.5).

Given in the graph,

A(4,6)  and B(3,5)

Distance formula = [tex]\sqrt{(x1-x2)^{2} +(y1-y2)^{2} }[/tex]

                      AB =  [tex]\sqrt{(4-3)^{2} +(6-5)^{2} }[/tex]

                            = [tex]\sqrt{1^{2} +1^{2} }[/tex]

                            = [tex]\sqrt{2}[/tex]

                            = 1.414 units

Midpoint = [tex](\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]

Let midpoint of AB be C(x,y)

C = (x,y) = [tex](\frac{4+3}{2},\frac{6+5}{2})[/tex]

             = [tex](\frac{7}{2},\frac{11}{2})[/tex]

             = (3.5,5.5)

Hence, length is 1.414 units and midpoint is (3.5,5.5).

To learn more about length here:

https://brainly.com/question/8552546

#SPJ1

The sum of the reciprocal of the two numbers is 44.

Let a and b be the two number

It is given that the sum of the number is equal to 44 times their product.

So from this, we get an equation:

a + b = 44 ab -------(1)

Now we have to find the sum of the reciprocal of the two numbers.

1/a + 1/b = b + a/ ab

            = a + b / ab -------(2)

As from equation (1) we have

a + b/ ab = 44

Now put this value in equation (2) we get

1/a + 1/ b = 44

Therefore the sum of the reciprocal of the two numbers is 44.

To know more about the reciprocal refer to the link given below:

https://brainly.com/question/27590585

#SPJ4

The expressions 25x−(6x+12) and (25x−6x)+12 are equivalent expressions.

In this question we have been given two expressions 25x−(6x+12) and (25x−6x)+12

We know that the associative property of addition.

For any real numbers a, b, c

a + (b + c) = (a + b) + c

Consider an expression,

25x − (6x + 12)

= (25x - 6x) + 12                   ..........(Associative property)

Therefore, the expressions 25x−(6x+12) and (25x−6x)+12 are equivalent expressions.

Learn more about an expression here:

https://brainly.com/question/1859113

#SPJ1