Select the correct answer PLEASE HELP

Select The Correct Answer PLEASE HELP

Answers

Answer 1

The required answer is the statement mAB x mBC = -1 is proved.

Given that AB is perpendicular to BC

To find the slope of AB, we use the formula:

mAB = (y2 - y1) / (x2 - x1)

Assuming point A is (0, 0) and point B is (1, d):

mAB = (d - 0) / (1 - 0) = d

Assuming point B is (1, d) and point C is (0,0):

mBC = (e - d) / (1 - 0) = e.

Since BC is perpendicular to AB, the slopes of AB and BC are negative reciprocals of each other.

Taking the reciprocal of mAB and changing its sign, gives:

e = (-1/d)

Consider mAB x mBC = d x e

mAB x mBC = d x (-1/d)

mAB x mBC = -1

Therefore, (-1/d) x d = -1.

Hence, the statement mAB * mBC = -1 is proved.

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Related Questions

Question 10 of 10
The Vaughns make $58,000 a year and live in Florida, which has a median
annual income of $47,778. If their monthly expenses amount to $4600 per
month, do they qualify for Chapter 7 bankruptcy?

Answers

No, the Vaughns do not qualify for Chapter 7 bankruptcy.

Do the Vaughns qualify for Chapter 7 bankruptcy in Florida?

Filing petition under chapter 7 stops most collection actions against the debtor or the debtor's property.

In the field of bankruptcy, the means test is used to determine whether an individual or family qualifies for Chapter 7 bankruptcy. This test compares the debtor's income to the median income in their state.

In this case, the Vaughns make $58,000 a year which is above Florida's median annual income of $47,778. Therefore, this stipulates they are not eligible for Chapter 7 bankruptcy.

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itaimle fentan' th the yen +1 Mime chose Sowe Mitide chices asccereiond pls: * attonach 7= Which of the liliswing in a cintical ritik to the wocest of yod tritivees plan? Mrryin Dreite hisculte ievitor: porinumalike Q.wide Orete be Connie decides to open "Connie's Corner Cafe" and finds the ideal location for her venture. However, it appears that Connie will have to approach investors or bankers for financial backing. When she talks to her local bank manager. Mr. Johnson, he immediately asks for Connie's business plan. Connie is in trouble because she does not know what a business plan looks like. Which of the following plans is most useful for demonstrating a new technology or service or to reach a market that is widely spread out? Mutiple Choice an irvertion plan a proof-of-concept website an operational plan a screening plan Connie decides to open "Connie's Corner Cafe" and finds the ideal location for her venture. However, it appears that Connie will have to approach investors or bankers for financial backing. When she talks to her local bank manager, Mr. Johnson, he immediately asks for Connie's business plan Connie is in trouble because she does not know what a business plan looks like. Which of the following statements about the market section of the classic business plan is not true? Muniple Choice The market section bullds on material you may have developed in the IDEO, business model canvas, and feasibility analyses done eatilier, Marketing plans remain the same across any multiple target audiences; Target audiences are aiso ealled custamer segments. Some people prefer to relocate the compettion and competilve advantage section from the market section to the industry section. Connie decides to open "Connie's Corner Café" and finds the ideal location for her venture. However, it appears that Connie will have to approach investors or bankers for financial backing. When she talks to her local bank manager, Mr. Johnson, he immediately asks for Connie's business plan. Connie is in trouble because she does not know what a business plan looks like. Which of the following is a critical risk to the success of your business plan? Mulitiple Choice overlooked competition assumptions given for the financials adequate paybock direct customer connection Connie decides to open "Connie's Corner Café" and finds the ideal location for her venture. However, it appears that Connie will have to approach investors or bankers for financial backing. When she talks to her local bank manager, Mr. Johnson, he immediately asks for Connie's business plan. Connie is in trouble because she does not know what a business plan looks like. Which of the following pitch deck categories is sometimes given in the form of a user's experience? Multiple Cholce product sides problem slide solution slide introductory slide Connie decides to open "Connie's Corner Cafe" and finds the ideal location for her venture. However, it appears that Connie will have to approach investors or bankers for financial backing. When she talks to her local bank manager, Mr. Johnson, he immediately asks for Connie's business plan. Connie is in trouble because she does not know what a business plan looks like. There are two goals you can seek in the "ask" of your elevator pitch. One is to build your network and the other is get the listener Multiple Choice to make a micro-commitment. provide feedback look at your invention plan, to piedge money Connie decides to open "Connie's Corner Cafe" and finds the ideal location for her venture. However, it appears that Connie will have to approach Investors or bankers for financial backing. When she talks to her local bank manager, Mr. Johnson, he immediately asks for Connie's business plan. Connie is in trouble because she does not know what a business plan looks llike. A good marketing strategy is most likely to focus on Multiple Choice productiservice description. key activities and operations: value proposition. the longerterm competitive plan.

Answers

The plan that is most useful for demonstrating a new technology or service or to reach a market that is widely spread out is a proof-of-concept website

How to explain the information

The statement about the market section of the classic business plan that is not true is that some people prefer to relocate the competition and competitive advantage section from the market section to the industry section.

A critical risk to the success of your business plan is Overlooked competition.

The pitch deck categories that is sometimes given in the form of a user's experience is Problem slide.

There are two goals you can seek in the "ask" of your elevator pitch. One is to build your network and the other is to get the listener to Make a micro-commitment

A good marketing strategy is most likely to focus on the longer-term competitive plan.

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how do you do it please help me with this problem

Answers

Step-by-step explanation:

with which problem....not visible

Answer:

What is the problem?

For the following equation, determine the values of the missing entries. Reduce all fractions to lowest terms.
6x - 4y = 18
Note: Each column in the table represents an ordered pair. If multiple solutions exist, you only need to identify one.
Answer

For the following equation, determine the values of the missing entries. Reduce all fractions to lowest

Answers

answer: first x is 3, fourth is 5 2/3
second y is -4.5, third is is -1 1/2

work:
solve for y:

6x-4y=18
-6x -6x

-4y=-6x+18
divide whole equation by -4

y=3/2x-4.5

solve for x:

6x-4y=18
+4y +4y

6x=4y+18
divide whole equation by 6

x=2/3y+3

Determine the value for j in the equation 17 over 20 equals j plus 11 over 20. 3 over 20 6 over 20 6 over 40 28 over 40
FLVS MATH MIDDLE

Answers

On solving the provided question, we get the following linear equation as the , that is  j = 6/20.

What is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

How do you identify a linear equation?

A mathematical equation is said to be linear if it has the formula y=mx+b, where m denotes the slope and b the y-intercept.

Why is it called linear equation?

An algebraic equation is said to be linear if each term has an exponent of 1, and if the equation is graphed, it always produces a straight line. This is the basis for its designation as a "linear equation."

the linear equation:

\(17/20 = j + 11/20\\ 17/20 - 11/20 = j + 11/20 - 11/20\\ (17 - 11)/20 = j\\ 6/20 = j\)

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please hurry and answer <33 !!!

please hurry and answer &lt;33 !!!

Answers

Answer:

-17, -8

Step-by-step explanation:

if it reflects over the x-axes it only changes the y into positive or negative

What is 212 tens / 10

What is 212 tens / 10

Answers

212 tens divided by 10 = - 4442962

Answer:

212 ones

Explaination:

If you have 212 tens and trade them all for ones, hence the ÷10, you'll get 212 ones.

I need some help... I am very confused.

I need some help... I am very confused.

Answers

The base of the triangle shown is 12 millimeters

What is an equation?

An equation is an expression that can be used to show the relationship between numbers and variables.

Given that:

A is the area of the triangleb is the base of the triangleh is the height

b = 2A/h

For the triangle, A = 36 mm², h = 6 mm

Substituting:

b = 2(36)/6

Simplifying gives:

b = 12 mm

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a context level data flow diagram includes many detailed processes representing the computer programs within the system.true or false?

Answers

The claim that "a context level data flow diagram includes many detailed processes representing the computer programmes within the system" is false.

A context level data flow diagram (DFD) is a particular kind of diagram that shows how various system components interact with one another. The main objective of building a DFD is to visually depict the data flow and system activities.

The highest-level diagram that shows the system's overall operation without going into specifics about particular processes or data stores is a context level DFD, also referred to as a Level 0 DFD.

The statement that "a context level data flow diagram includes many detailed processes representing the computer programmes within the system" is untrue. This is so because the context level DFD reflects the total functionality of the system.

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what is the largest integer that is a divisor of (n 1)(n 3)(n 5)(n 7)(n 9) (n 1)(n 3)(n 5)(n 7)(n 9) for all positive even integers nn?

Answers

The largest integer that is a divisor of (n+1)(n+3)(n+5)(n+7)(n+9) is 15

Divisor of a Number :  

A Divisor is any number that divides a given number completely or with a reminder. Where a factor, is a divisor that divides the number entirely and leaves no remainder.

Here we have,

(n + 1)(n + 3)(n + 5)(n + 7)(n + 9)  

And n is a positive even integer  

For n = 2 ⇒  (2 + 1)(2 + 3)(2 + 5)(2 + 7)(2 + 9) = (3× 5 × 7 × 9 × 11 )    

For n = 4 ⇒   (4 + 1)(4 + 3)(4 + 5)(4 + 7)(4 + 9) = (5× 7 × 9 × 11 × 13 )

and so on.

From the above calculations,

we can say that (n + 1); (n + 3); (n + 5); (n + 7); (n + 9) are 5 consecutive odd numbers  

In every 5 consecutive odd positive integers,

One of them is always divisible by 3

And one of them is always divisible by 5.

Therefore,

(n + 1)(n + 3)(n + 5)(n + 7)(n + 9) will be divisible by both 3 and 5

As we know product of 3 and 5 = 15

then (n + 1)(n + 3)(n + 5)(n + 7)(n + 9) will also divisible by 15

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The complete question is

What is the largest integer that is a divisor of (n+1)(n+3)(n+5)(n+7)(n+9) for all positive even integers n?  

(A) 3         (B)  5        (C)  11          (D) 15             (E)  165    

Anwer this and you will get brainest

Anwer this and you will get brainest

Answers

Answer:

The answer is C

Step-by-step explanation:

I had to redo the answer cause someone took it down for know reason but there you go.

2) The ratio of adults to children in the sports club is 5:2.
There are 120 adults in the club. How many children are
there?

Answers

Answer:

48 children

Step-by-step explanation:

For every 5 adults there are 2 children.

so for every 1 adult there is 2/5 of a child.

So number of children = 120 * 2/5

= 240/5

= 48.

"Which expression is NOT equivalent to the sum of 36 + 54?
a) 18( 2+3 )
b) 4( 9+6 )
c) 3( 12+18 )
d) 2(18+27 )
*plzzzz helppp*

Answers

Answer:

B equals 60 and 36+54 = 90

Answer:

b

Step-by-step explanation:

4.9=36

4.6=24

36+24

What is the estimate of 1,578

Answers

1,600

thats the estimate

Due 03/24/21 11:5 Exit 4-6: MathXL for School: Practice & Problem Solving Question Help X 4.6.PS-13 Design An art class is making a mural for their school which has a triangle drawn in the middle. The length of the bottom of the triangle is x. Another side is 10 more than three times the length of the bottom of the triangle. The last side is 1 more than the bottom of the triangle. plz hurry!!!​

Answers

Answer:

\(x < - 9\)

Step-by-step explanation:

We can only find the range of the values of x by using triangle inequality,

\(x + 1 + x > 3x + 10 \\ \\ 1 - 10 > 3x - 2x \\ \\ - 9 > x\)

Multiply through both sides by -1, we get,

\(x < - 9\)

This means x = -10, -11, ... (which is not realistic because a side of a triangle cannot be a negative number)

Due 03/24/21 11:5 Exit 4-6: MathXL for School: Practice &amp; Problem Solving Question Help X 4.6.PS-13

The sum of two-thirds a
number and eighteen is twenty-three. What is the number?

Answers

number = x

2/3x + 18 = 23

2/3x = 5

x = 15/2 = 7.5

forestry ranger is in a stand 200 feet in the air. There is an angle of
depression of 35 degrees to a campfire. How far is it from the base of the
stand to the campfire?
Hunter ic a deer stand 10 feet above the ground. There is an angle c

Answers

The distance from the base of the stand to the campfire is 285.6 feet.

The angle of depression of 35 degrees.

Let's denote the distance from the base of the stand to the campfire as "x."

Since we know that,

The values of all trigonometric functions depending on the ratio of sides in a right-angled triangle are defined as trigonometric ratios. The trigonometric ratios of any acute angle are the ratios of the sides of a right-angled triangle with respect to that acute angle.

Using the tangent function, we have:

tan(35 degrees) = opposite/adjacent

tan(35 degrees) = 200/x

To find the value of x, we can rearrange the equation:

x = 200 / tan(35 degrees)

x ≈ 200 / 0.7002

x ≈ 285.6 feet

Therefore, the distance from the base of the stand to the campfire is 285.6 feet.

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A surveyor wants to know the length of a tunnel built through a mountain. According to his equipment, he is located 120 meters from one entrance of the tunnel, at an angle of 42° to the perpendicular. Also according to his equipment, he is 101 meters from the other entrance of the tunnel, at an angle of 28⁰ to the perpendicular. Based on these measurements, find the length of the entire tunnel. Do not round any intermediate computations. Round your answer to the nearest tenth. Note that the figure below is not drawn to scale. 120 meters 42° 28° 101 meters​

Answers

The length of the entire tunnel is 127.88 meters by using cosine law or formulae.

Here we can use the formulae of cosine when two sides a and b and angle between then is given we can apply it.

\(c^{2} =a^{2} +b^{2} -2ab cos (\alpha )\)

Let us take surveyor as point A

one end of the tunnel denoted by point B

other end of the tunnel denoted by point C.

The length of AB is 101 meters

length of AC is 120 meters.

Measure of angle at point A = 42° + 28° =70°

Now lets find the length of tunnel

=\(\sqrt{(120^{2})+(101^{2})-2.(120)(101) cos (70) }\)

=\(\sqrt{14400+10201-24240(0.34)}\)

=\(\sqrt{24601-8246}\)

\(\sqrt{16355}\)

=127.88 meters.

Hence the length of the entire tunnel is 127.88 meters.

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A surveyor wants to know the length of a tunnel built through a mountain. According to his equipment,

Triangle ABC is similar to triangle EFD. What scale factor is required

to dilate triangle ABC so that its image, A'B'C' , is congruent to

triangle EFD ?

Answers

The scale factor required to dilate triangle ABC so that its image A'B'C' is congruent to triangle EFD is equal to the ratio of any corresponding pair of sides of the two triangles.

If two triangles are similar, it means that their corresponding angles are congruent and their corresponding sides are in proportion. In other words, if we denote the scale factor between two similar triangles as k, then we have:

AB / EF = BC / FD = AC / ED = k

To dilate triangle ABC to a congruent triangle A'B'C', we need to scale all its sides by the same factor. Let's denote this factor as x. Then the new side lengths are:

A'B' = Ax

B'C' = Bx

A'C' = Cx

To make the resulting triangle congruent to EFD, we need these new side lengths to be equal to the corresponding side lengths of EFD. That is:

A'B' = EF

B'C' = FD

A'C' = ED

Substituting the expressions for A'B', B'C', and A'C', we get:

Ax = EF

Bx = FD

Cx = ED

Dividing each of these equations by the corresponding side length in ABC, we get:

A = EF / AB

B = FD / BC

C = ED / AC

Since ABC is similar to EFD, we know that A = B = C = k. Therefore, we have:

k = EF / AB = FD / BC = ED / AC

This means that the scale factor required to dilate triangle ABC so that its image A'B'C' is congruent to triangle EFD is equal to the ratio of any corresponding pair of sides of the two triangles.

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Order the expressions by choosing >,

Order the expressions by choosing &gt;,

Answers

Answer:

1. 3^4 x 3^3 < 3^12

2. 3^3 x 4^3 < 12^4

3. 3^4 x 4^3 > 12^3

Calcula el volumen de un cono cuyo radio de la base mide 8 cm y cuya altura mide 1 m.

Answers

Por lo tanto, el volume del cono es de 2134.68 cm³

Para calcular el volumen de un cono necesitamos conocer dos medidas importantes: el radio de la base y la altura del cono. En este caso, sabemos que el radio de la base es de 8 cm y la altura es de 1 m.
Lo primero que debemos hacer es convertir la altura a la misma unidad que el radio de la base, en este caso, a centímetros. Sabemos que 1 metro es igual a 100 centímetros, por lo tanto:

Altura en cm = 1 m * 100 cm/m = 100 cm
Con esta información, podemos utilizar la fórmula del volumen de un cono:
Volumen = (1/3) * π * radio² * altura
Reemplazando los valores que conocemos, obtenemos:
Volumen = (1/3) * π * (8 cm)² * (100 cm)
Volumen = (1/3) * π * 64 cm² * 100 cm
Volumen = (1/3) * π * 6400 cm³
Volumen = 2134.68 cm³

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Dell Eatery employs one worker whose job it is to load apple pies on outgoing company cars. Cars arrive at the loading gate at an average of 48 per day, or 6 per hour, according to a Poisson distribution. The worker loads them at a rate of 8 per hour, following approximately the exponential distribution in service times. a. Determine the operating characteristics of this loading gate problem. [6 Marks] b. What is the probability that there will be more than six cars either being loaded or waiting? [2 Marks] Formulae L= μ−λ
λ

W= μ−λ
1

L q

W q

rho
P 0


= μ(μ−λ)
λ 2

= μ(μ−λ)
λ

= μ
λ

=1− μ
λ


P n>k

=( μ
λ

) k+1

Answers

The required probability is 0.4408.

The operating characteristics of the loading gate problem are:

L = λ/ (μ - λ)

W = 1/ (μ - λ)

Lq = λ^2 / μ (μ - λ)

Wq = λ / μ (μ - λ)

ρ = λ / μ

P0 = 1 - λ / μ

Where, L represents the average number of cars either being loaded or waiting.

W represents the average time a car spends either being loaded or waiting.

Lq represents the average number of cars waiting.

Wq represents the average waiting time of a car.

ρ represents the utilization factor.

ρ = λ / μ represents the ratio of time the worker spends loading cars to the total time the system is busy.

P0 represents the probability that the system is empty.

The probability that there will be more than six cars either being loaded or waiting is to be determined. That is,

P (n > 6) = 1 - P (n ≤ 6)

Now, the probability of having less than or equal to six cars in the system at a given time,

P (n ≤ 6) = Σn = 0^6 [λ^n / n! * (μ - λ)^n]

Putting the values of λ and μ, we get,

P (n ≤ 6) = Σn = 0^6 [(6/ 48)^n / n! * (8/ 48)^n]

P (n ≤ 6) = [(6/ 48)^0 / 0! * (8/ 48)^0] + [(6/ 48)^1 / 1! * (8/ 48)^1] + [(6/ 48)^2 / 2! * (8/ 48)^2] + [(6/ 48)^3 / 3! * (8/ 48)^3] + [(6/ 48)^4 / 4! * (8/ 48)^4] + [(6/ 48)^5 / 5! * (8/ 48)^5] + [(6/ 48)^6 / 6! * (8/ 48)^6]P (n ≤ 6) = 0.5592

Now, P (n > 6) = 1 - P (n ≤ 6) = 1 - 0.5592 = 0.4408

Therefore, the required probability is 0.4408.

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HELP PLZZ
A bowl mixed vegetables contains carrots, broccoli, and cauliflower. If the bowl contains 80 vegetables pieces, and 25% of the pieces are carrots, how many carrots are in the bowl?
The bowl contains ____ Carrots.​

Answers

Answer:

20.

Step-by-step explanation:

25% of 80 is 20, so the answer may be 20 pieces of carrot.

Hope this is correct. Have a great day

Answer:20

Step-by-step explanation:


another retake !! help it’s due today

another retake !! help its due today

Answers

Answer:

Maurico started with more :)

Step-by-step explanation:

Mariah started with 150 while Maurico started with around 190 so he has more to start with :)

Have a great day!

Please rate and mark brainliest!

Answer:

Mauricio

Step-by-step explanation:

To find who started with more money in their savings account, we want to observe the savings in $ when time=0 years

So by looking at the table of Mariah's savings, we see that when t=0 she had S=150$

By looking at the graph which describes Muaricio's savings as a function of time, we can see that when time=0 or x=0, y=S=190$

In other words, the y-intercept is the initial amount of savings.

190>150

:P

Hope this helps, it would be appreciated if you made me brainliest.

in a study of breast cancer, a mother was considered exposed if she first gave birth at 30 years of age or older. among 1,628 mothers who were exposed, 31 subsequently developed breast cancer. among the 4,450 mothers who first gave birth before the age of 30, 65 subsequently developed breast cancer. what type of study design was used for this investigation of the association age at first birth and breast cancer?

Answers

The compared to mothers who gave birth for the first time at the age of under 30 to determine the incidence of breast cancer.

The study design used for this investigation of the association between age at first birth and breast cancer is Cohort Study.What is a cohort study?A cohort study is an analytical research approach in which a group of people with a shared trait or experience are followed over time. Cohort studies are used to determine the incidence of a disease, changes in morbidity and mortality rates, and to recognize risk factors for a disease. In this study of breast cancer, the mothers who gave birth for the first time at the age of 30 or older were considered exposed, and they were compared to mothers who gave birth for the first time at the age of under 30 to determine the incidence of breast cancer.

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It costs $2 to download a song and $12 to download an entire album. Jorge has $50 to spend on downloading music. Create an inequality that represents the number of songs (s ) and albums (a ) that Jorge could download.

I need a inequality

Answers

The inequality to represent the given situation is 2s+12a≤50.

Given that, it costs $2 to download a song and $12 to download an entire album.

What are inequalities?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Jorge has $50 to spend on downloading music.

Let the number of songs be s and the number of albums be a.

So, inequality to represent the given situation is

2s+12a≤50

Therefore, the inequality to represent the given situation is 2s+12a≤50.

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Mr. Estrada's car can travel no more than 510 miles on one full tank of gasoline. After filling up the tank with gasoline, he traveled 194 miles in the car. Write an inequality that represents the values of m, the number of miles Mr. Estrada can travel in the car with the remaining gasoline in the tank and solve.
please help me!! this is due very soon

Answers

Answer:

Step-by-step explanation:

The required inequality x + m ≤ 510, and the distance is 316 miles.

What is inequality?

Inequity occurs when two phrases are joined by a sign such as "not equal to," "more than," or "less than." The inequality illustrates the larger than and less than the relationship between variables and numbers.

Given that Mr. Estrada's car can only drive 510 miles on a full tank of petrol. He drove the car 194 miles after filling up the tank with gasoline.

Let,

x miles = distance already traveled

m miles = distance miles can travel with remaining gas

510 = max. miles can travel on a full tank

As per the given question,

The inequality will be written as,

x + m ≤ 510

194 + m ≤ 510

m ≤ 510 - 194

Apply the subtraction operation, and we get

m ≤ 316

Therefore, the required inequality x + m ≤ 510, and the distance is 316 miles.

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Pls help me please

Pls help me please

Answers

i think its the whole number

plz help, will give brainiest
(08.01, 08.02, 08.03 HC)
Create a factorable polynomial with a GCF of 3x. Rewrite that polynomial in two other equivalent forms. Explain how each form was created. (10 points)

Answers

Answer:

4x^2 + 8x + 4

4(x^2 + 2x + 1) - remove GCF of 4

4(x + 1)(x + 1) - factor

4(x + 1)^2 - collect like terms

Step-by-step explanation:

Then also expand it out by distributing:

21x^3 + 35x²

Form 1:

21x^3 + 35x² - unfactored

Form 2:

7x²(3x + 5) - factored with GCF of 7x² brought to the front

Update:

You could also multiply two binomials and make a quadratic.

Example:

(7x + 2)(3x + 5)

7x(3x + 5) + 2(3x + 5)

= 21x² + 35x + 6x + 10

= 21x² + 41x + 10

The favorable polynomial with a GCF of 3x will be 21x² + 41x + 10.

What is a polynomial?


A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.

The polynomial will be solved as below:-

21x³ + 35x²

Form 1:

21x³ + 35x² - unfactored

Form 2:

7x²(3x + 5) - factored with GCF of 7x² brought to the front

You could also multiply two binomials and make a quadratic.

E = (7x + 2)(3x + 5)

E = 7x(3x + 5) + 2(3x + 5)

E = 21x² + 35x + 6x + 10

E = 21x² + 41x + 10

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prove that √-2 is irrational using strong induction

Answers

Using strong induction, we can prove that the square root of -2 is irrational by showing that it cannot be expressed as a fraction of coprime odd integers.

To prove that √-2 is irrational using strong induction, we need to show that for any natural number n, if the square root of -2 can be expressed as a fraction a/b, where a and b are coprime integers, then a and b must be odd.

We can start by using the base case, n = 1. Assume that √-2 can be expressed as a fraction a/b where a and b are coprime integers. Then, we have

√-2 = a/b

Squaring both sides gives

-2 = a^2/b^2

Multiplying both sides by b^2 gives

-2b^2 = a^2

This implies that a^2 is even, and therefore a is also even. We can express a as 2k for some integer k, which means

-2b^2 = (2k)^2

Simplifying, we get

-2b^2 = 4k^2

Dividing both sides by -2 gives

b^2 = -2k^2

This implies that b^2 is even, which means that b is also even. However, this contradicts our assumption that a and b are coprime integers. Therefore, √-2 cannot be expressed as a fraction a/b where a and b are coprime integers.

Now, let's assume that for all n ≤ k, the square root of -2 cannot be expressed as a fraction a/b where a and b are coprime integers with a and b odd. We want to prove that this also holds for n = k+1.

Assume that √-2 can be expressed as a fraction a/b where a and b are coprime integers with a and b odd. Then, we have

√-2 = a/b

Squaring both sides gives

-2 = a^2/b^2

Multiplying both sides by b^2 gives

-2b^2 = a^2

This implies that a^2 is even, and therefore a is also even. We can express a as 2k for some integer k, which means

-2b^2 = (2k)^2

Simplifying, we get

-2b^2 = 4k^2

Dividing both sides by -2 gives

b^2 = -2k^2

This implies that b^2 is even, which means that b is also even. However, this contradicts our assumption that a and b are coprime integers with a and b odd. Therefore, √-2 cannot be expressed as a fraction a/b where a and b are coprime integers with a and b odd.

By strong induction, we have proven that for any natural number n, the square root of -2 cannot be expressed as a fraction a/b where a and b are coprime integers with a and b odd. Therefore, √-2 is irrational.

To know more about induction:

https://brainly.com/question/31099433

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