Find the domain and real zeros of the gillen Function. f(x) = (x-3)^2 x ³_ 3x² + 2X​

Answers

Answer 1
To find the domain of a function, we need to identify any values of x that would result in undefined expressions. In this case, the function f(x) contains only algebraic operations, so the domain of f(x) is all real numbers, or (-∞, ∞).

To find the real zeros of the function, we need to solve for the values of x that make the expression equal to zero. So we start by setting f(x) = 0 and then simplifying the resulting equation:

f(x) = (x-3)^2 x³ - 3x² + 2x = 0

Factor out an x from the right-hand side of the equation:

x (x-3)^2 (x² - 3x + 2) = 0

The real zeros of the function are the values of x that make the left-hand side of the equation equal to zero. So we solve each factor for x:

x = 0, x = 3, and x² - 3x + 2 = 0

The quadratic equation x² - 3x + 2 = 0 can be factored as (x-1)(x-2) = 0, so the solutions are x = 1 and x = 2.

Therefore, the real zeros of the function are x = 0, x = 1, x = 2, and x = 3.

Related Questions

Question Below.
Answers: 250|253|254|255|307|433|434|435|507|.
First to answer this question the quickest is rewarded branliest + 100 points

Answers

Answer:

Minimum--> 250

Q1--> 255

Q2--> (Median): 307

Q3--> 433

Maximum-->507

Step-by-step explanation:

To find the five-number summary of this data set, we need to determine the minimum value, maximum value, and three quartiles (Q1, Q2, Q3) which divide the data into four equal parts.

First, we need to sort the data set in ascending order:

{ 250, 253, 255, 267, 307, 425, 433, 435, 507 }

Minimum: 250

Maximum: 507

To find the quartiles, we need to find the median of the entire data set (Q2) and then the medians of the two halves of the data set, which will give us Q1 and Q3.

Q2 (Median): The median of the entire data set can be found by averaging the two middle numbers.

Q1: The median of the lower half of the data set is 255, which is the middle value of { 250, 253, 255, 267, 307 }. Therefore, Q1 = 255.

Q3: The median of the upper half of the data set is 433, which is the middle value of { 425, 433, 435, 507 }. Therefore, Q3 = 433.

(CO 3) A bottle of water is supposed to have 20 ounces. The bottling company has determined that 96% of bottles have the correct amount. Which of the following describes a binomial experiment that would determine the probability that a case of 36 bottles has all bottles properly filled?
Group of answer choices
a. n=0, p=36, x=98
b. n=20, p=0.98, x=36
c. n=36, p=0.96, x=36
d. n=36, p=0.98, x=1

Answers

The parameter to describes a binomial experiment that would determine the probability that a case of 36 bottles has all bottles properly filled is x = 36, p = 0.96 and n = 36. So, the right choice for answer is option (c).

A binomial experiment is an experiment using a fixed number of independent trials with only two outcomes. These experiments'outcomes are defined as either success or failure. The following requirements for experiment are :

Each fixed trial performed in the experiment had only two possible outcomes. One result will be marked as a success and the other as a failure.The probability of success in each trial must remain the same for each trial conducted. It is represented by p.Each trial in the experiment must be independent of the other trials.

Water Quantity in a bottle = 20 ounces

According to bottling company, the percentage of bottle with correct amount = 96% = 0.96

so, probability of success, p = 0.96

Probability for 36 bottles has all bottles properly filled, that is x = 36. Now, looking the all choice, we conclude option(c) is correct choice.

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Trey purchases 200 shares of Turner stock for per share. Trey pays in cash to complete the purchase. One year​ later, Trey sells the stock for per share. Part 2 Calculate the return that Trey earned on his investment of .

Answers

Answer: Formula

Step-by-step explanation:

Stocks x per share = return

Trey's return on investment, if the stock paid no dividends during the year, is 14.29%.

We have,

Purchase price per share: $50

Number of shares purchased: 200

Total purchase cost (excluding loan interest):

Purchase price per share * Number of shares purchased

= $50 * 200

= $10,000

Loan amount: $5,000

Loan interest rate: 10%

Interest paid on the loan:

Loan amount * Interest rate

= $5,000 * 10%

= $500

Total purchase cost (including loan interest):

Total purchase cost + Loan interest

= $10,000 + $500

= $10,500

Selling price per share: $60

Total revenue from selling the stock:

Selling price per share * Number of shares sold

= $60 * 200

= $12,000

Return on investment (ROI):

(Total revenue - Total purchase cost) / Total purchase cost

ROI = ($12,000 - $10,500) / $10,500

Simplifying the expression:

ROI = $1,500 / $10,500

ROI = 0.1429 (approximately)

To express the ROI as a percentage:

ROI as a percentage = 0.1429 * 100 = 14.29%

Therefore,

Trey's return on investment, if the stock paid no dividends during the year, is 14.29%.

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The complete question:

Trey purchases 200 shares of Turner stock for $50 per share.

Trey pays $5,000 in cash and borrows $5,000 from his broker at 10 percent interest to complete the purchase.

One year later, Trey sells the stock for $60 per share.

Trey's return, if the stock paid no dividends during the year, is?

If 7 men can finish a work in 84 days , then 12 men can finish the same work in 96 days. True / False?​

Answers

Answer:

false

Step-by-step explanation:

if there r more men working then it will take less time to finish the same work not more

please help me i need it

Answers

Answer:

75 degrees

Step-by-step explanation:

Since angle ABD = angle ABC + angle CBD, and we know each of those, we can add them to get the answer.

30+45=75 degrees.

a machine in a factory makes 2 1/4 pounds of nails in 1 1/2 hours. At what rate in pounds
per hour does the machine makes nails?

Answers

Answer:

a machine in a factory makes 2 1/4 pounds of nails in 1 1/2 hours. At what rate in pounds

per hour does the machine makes nails?

True or False. A hypothesis is a speculation.

Justify your answer.

Answers

Yes a hypothesis is a speculation because you assuming what’s going to happen based on prior knowledge and what happened before

Solve for x. Round to the nearest tenth, if necessary

Answers

Answer: 1.0

Step-by-step explanation:

sohcahtoa means you use sine.

sin(37) = 0.6/x

xsin(37) = 0.6

x = 0.6/sin(37)

x = 0.996

x = 1.0

At the 2022 Winter Olympics, one country won a total of 150 medals. A circle graph of the medals is shown.

a circle graph titled 2022 Winter Olympic Medals, with three sections labeled gold 20 percent, silver 30 percent, and bronze 50 percent

How many gold and bronze medals were won?

50
70
105
120

Answers

Answer:

70 gold and bronze

Step-by-step explanation:

Add gold at 20 percent and bronze at 50 percent to get 70 percent gold and bronze.

What is the least common denominator of the fractions in the sum 1/8 + 1/9?

Answers

This means that the lowest goal (LCD) is 72 and that the total of 1/8 and 1/9 stated with one common denominator = 72 is 17/72.

What or who is a denominator?

The denominator of a fraction, which represents many spaced evenly out parts are utilized to split an object, is the smallest amount inside the fraction. The fraction is divided by it. The denominator in this situation is 4, suggesting there are four parts altogether.

The fractions mentioned have 8 and 9 as their denominators. Multiples of 8 include 8, 16, 24, 32, 40, 48, 56, 64, 72, and 80, while multiples of 9 include 9, 18, 27, 36, 45, 54, 63, 72, and 81.

It is evident that 72 will be the first common number of 8 and 9. Hence, for 1/8 and 1/9, its least common factor (LCD) is 72.

We must express every fraction with denominator 72 in order to sum the fraction with a common denominator:

1/8 Equals 9/72 (with multiplying both the numerator and the denominator by 9)

1/9 Equals 8/72 (with multiplying both the denominator and the numerator by 8)

We can now combine the fractions:

1/8 plus 1/9 = 9/72 plus 8/72

= 17/72

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It was incorrect. A=80-B, C=70-B.
(80-b) +b+(70-b)=100. Therefore:
80-70-b=100
B= - 90. Negative number,
So, A=170
C=160. Correct answer

Answers

The values of A, B, and C are 30, 50, and 20, respectively.

What is the sum?

The sum is the result of adding two or more numbers together. The sum is found by performing the operation of addition, which involves combining the values of two or more quantities to find the total or the sum.

If A = 80 - B and C = 70 - B, and the sum of A, B, and C is 100, then we can write:

A + B + C = 100

Substituting A and C with their given values, we get:

(80 - B) + B + (70 - B) = 100

Simplifying and combining like terms, we get:

150 - B = 100

Subtracting 150 from both sides, we get:

-B = -50

Dividing both sides by -1, we get:

B = 50

Now that we know B = 50, we can substitute this value back into the equations for A and C:

A = 80 - B = 80 - 50 = 30

C = 70 - B = 70 - 50 = 20

Therefore, the values of A, B, and C are 30, 50, and 20, respectively.

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A survey of eighty students at a certain college reveals that
36 takes english
32 take history
32 take political science
16 takes political science and history
16 takes history and English
14 takes political science and English
6 takes all three

How many students offer only English ​

Answers

By set theοry the number οf students whο οffer οnly English is 12.

What is Set theοry?

In mathematics Set theοry  studies with sets, which can be infοrmally described as cοllectiοns οf οbjects.  Objects οf any kind can be cοllected intο a set, set theοry, as a branch οf mathematics, is mοstly cοncerned with  that which are relevant tο mathematics as a whοle.

Given that,

A survey οf eighty students at a certain cοllege reveals that

36 takes English

32 take histοry

32 take pοlitical science

16 takes pοlitical science and histοry

16 takes histοry and English

14 takes pοlitical science and English

6 takes all three

Sο n(s)=80 [ Since the number οf students is 80]

The number οf students whο takes English is denοted by n(E)=36

The number οf students whο takes Histοry is denοted by n(H)=32

The number οf students whο takes Pοlitical Science is denοted by n(P)=32

By set theοry

The number οf students whο takes Pοlitical Science and Histοry is denοted by n(P∩H)=16

The number οf students whο takes English and Histοry is denοted by n(E∩H)=16

The number οf students whο takes Pοlitical Science and English is denοted by n(P∩E)=14

The number οf students whο takes Pοlitical Science, English and Histοry is denοted by n(P∩E∩H)=6

Frοm set theοry ,

n(P∪E∪H) = n(E)+n(H)+n(P)- n(P∩H)-n(H∩E)-n(P∩E)+n(P∩E∩H)

                 = 36+32+32-16-16-14+6

                 = 60

Sο the number οf students whο take nοne οf the subjects is (80-60)=20

Hence the number οf students whο οffer οnly English is 12.

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The quadratic regression corresponding to the number of birds f(x) in a park relative to the number of people x in the same park is given by f(x) = -0.1536x² + 3.3915x +88.738. Use the quadratic regression to estimate the number of people in the park when there are 80 birds. Round your answer to the nearest whole number. en is Provide your answer below: people An

Answers

The quadratic regression function f(x) = -0.1536x² + 3.3915x + 88.738, then estimate value for the number of people in the park when there are 80 birds is equals to the 24.

A quadratic regression is the process of finding the equation of the parabola that best fits a set of data. An equation of the form, y = ax² + bx + c where a≠0. We have a quadratic regression function is defined by f(x) = -0.1536x² + 3.3915x +88.738 --(1), where, f(x) = the number of birds in a park relative to the number of people x in the same park. We have to determine quadratic regression to estimate the number of people in the park when there are 80 birds. Now, f(x) = 80, substitute the known value in equation (1),

=> 80 = -0.1536x² + 3.3915x +88.738

=>0.1536x²- 3.3915x -88.738 + 80 = 0

=> 0.1536x²- 3.3915x - 8.738 = 0

=> x² - 22.08x - 56.88 = 0 --(2)

Using the quadratic formula for solution of (2), x = (-b ±√b² - 4ac)/2a, for ax² + bx + c = 0. So, [tex]x =\frac{ -(-22.08) ± \sqrt{(22.08)² + 4× 56.88}}{2}[/tex]

=> x = 24.41 or - 2.3331

but number of people can't be negative hence, the required value is 24.41 ~ 24.

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What is the difference between the points (8, 10) and (8, 4) on coordinate plane

Answers

Answer:

6 units

Step-by-step explanation:

(8, 10 ) → (8, 4 )

since the x- coordinates of each point are the same, both 8

then this is a vertical straight line

the difference is then the absolute value of the difference in the y- coordinates, that is

| 10 - 4 | = | 6 | = 6

or

| 4 - 10 | = | - 6 | = | 6 | = 6

Graham wants to take snowboarding lessons at a nearby ski resort that charges $40 per week. The resort also charges a one-time equipment-rental fee of $99 for uninterrupted enrollment in classes. The resort requires that learners pay for three weeks of classes at a time​

Answers

Answer:

$40+99=136  For 1 week

For 3 weeks it would be $120

A kettle is sold at a profit equal to one-fourth of its cost price. Find the profit percentage.​

Answers

Answer:

25%

Step-by-step explanation:

If the cost price could be 100

Then there's A/Q

One-fourth is always 100/4 = 25%

25% is the profit percentage because if the kettle is sold at a profit of 1/4th of the price, what’s 1/4th in percentage? 25%

PLEASE GUYS HELP!!

Solve 2(x + 3) = 18

Answers

Answer:

[tex]\mathrm{x=6}[/tex]

Step-by-step explanation:

[tex]\mathrm{2\left(x+3\right)=18}[/tex]

Divide both sides by 2:-

[tex]\mathrm{\cfrac{2\left(x+3\right)}{2}=\cfrac{18}{2}}[/tex]

Simplify:-

[tex]\mathrm{x+3=\cfrac{18}{2} }[/tex]

[tex]\mathrm{x+3=9}[/tex]

Subtract 3 from both sides:-

[tex]\mathrm{x+3-3=9-3}[/tex]

[tex]\mathrm{x=6}[/tex]

_____________________

Hope this helps!

Can someone help me with this please,thanksss

Answers

Answer:

gradient= rise \ run

and cuz line is coming downward

it will be negative

so your answer is

- 5\6

Calculate
√4.7² +2.55
Give your answer to 1 significant figure

Answers

Answer: 3.53

Step-by-step


Find the surface area of the rectangular prism below:
3m
2m
2.4 m
- 2.4 m
3 m

Answers

The surface area of the rectangular prism is 72 square meters.

Describe Rectangular Prism?

A rectangular prism, also known as a rectangular parallelepiped, is a three-dimensional figure that consists of six rectangular faces. It is a polyhedron with two identical and parallel bases, which are rectangles, and four rectangular lateral faces. The height of the prism is the perpendicular distance between the two bases. The volume of a rectangular prism is given by the formula V = l × w × h, where l, w, and h are the length, width, and height of the prism, respectively. The surface area of a rectangular prism is given by the formula SA = 2lw + 2lh + 2wh, where l, w, and h have the same meanings as in the volume formula. Rectangular prisms are commonly encountered in everyday life, such as in the shape of boxes, rooms, and buildings.

The surface area of a rectangular prism can be found by adding up the area of all its faces.

Area of blue rectangles:

= 2 x (length x width)

= 2 x (2.4m x 2m)

= 9.6m²

Area of green rectangles:

= 2 x (length x width)

= 2 x (2.4m x 3m)

= 14.4m²

Area of yellow rectangles:

= 2 x (length x width)

= 2 x (2m x 3m)

= 12m²

Total surface area = sum of all face areas

= (2 x blue rectangles) + (2 x green rectangles) + (2 x yellow rectangles)

= 2(9.6m²) + 2(14.4m²) + 2(12m²)

= 19.2m² + 28.8m² + 24m²

= 72m²

Therefore, the surface area of the rectangular prism is 72 square meters.

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Ruby wants to find the height of the tallest building in her city. She stands 190 feet away from the building. There is a tree 31 feet in front of her, which she knows is 20 feet tall. How tall is the building? (Round to the nearest foot.)

Answers

To solve this problem, we can use similar triangles. Let's call the height of the building "h". Then, we have two similar triangles: one formed by Ruby, the tree, and the top of the tree; and the other formed by Ruby, the building, and the top of the building.

We know that the height of the tree is 20 feet, and the distance from the tree to Ruby is 31 feet. We also know that the distance from Ruby to the building is 190 feet.

Using these values, we can set up a proportion:

h / (190 + 31) = 20 / 31

Simplifying the proportion, we get:

h / 221 = 20 / 31

Multiplying both sides by 221, we get:

h = (20 / 31) * 221

h ≈ 143.23

Therefore, the height of the building is approximately 143 feet. Rounded to the nearest foot, the height of the building is 143 feet.

a movie streaming service offers 12 children movies this is 15% of the total number of movies offerd

Answers

Answer: the movie streaming service offers 80 children's movies

Step-by-step explanation:

Can someone pls help me its delta really annoying

Answers

The cost per boxed lunch is $9.46.

A grain silo has a cylindrical shape. Its radius is 8ft, and its height is 38ft. What is the volume of the silo?
Use the value 3.14 for π, and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.

Answers

Answer:

13487 ft³

Step-by-step explanation:

Volume of a Cylinder: 2πr²*h

π = 3.14

r = 9 ft

h = 53 ft

Volume = 2(3.14)(9)²*53 = 13486.86 ft³

Rounded to nearest whole number

Volume of the Cylindrical Water tank is 13487 ft³

For each of the indefinite integrals below, choose which of the following substitutions would be most helpful in evaluating the integral. Enter the appropriate letter (A,B, or C) in each blank. DO NOT EVALUATE THE INTEGRALS.

Answers

The substitutions that would be most helpful in evaluating the integral are:

1. C (x = 8 secθ)

2. B (x = 8 sinθ)

3. A (x = 8 tanθ)

4. B (x = 8 sinθ)

5. A (x = 8 tanθ)

What are the substitutions that are most helpful?

For problem 1, the substitution x = 8 secθ will be useful because it will transform the integral into a form that can be solved using the substitution u = tanθ.

For problem 2, the substitution x = 8 sinθ will be useful because it will transform the expression inside the integral into a trigonometric function that can be integrated using standard techniques.

For problem 3, the substitution x = 8 tanθ will be useful because it will transform the expression inside the integral into a form that can be solved using integration by parts.

For problem 4, the substitution x = 8 sinθ will be useful because it will transform the expression inside the integral into a form that can be solved using the substitution u = cosθ.

For problem 5, the substitution x = 8 tanθ will be useful because it will transform the expression inside the integral into a form that can be solved using the substitution u = secθ.

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Evaluate the function when x = 3, x = 0, and x = -2.

10. g(x) = 3x
12. h(x) = 1.2x
13. f(x)=1.5x-2
14. h(x)=-4x+1/2
15. f(x)=1/3x + 2/3

Answers

Answer: The answer is -10 :)

Step-by-step explanation:

12)f(x)=2x-6

=》f(3)=2(3)-6

=》6-6=0

f(×)=2x-6

f(0)=-6

=》f(-2)=2(-2)-6

=》-4-6

=-10

13)h(3)=6(3)+2

=》18+2

=20

h(0)=0+2

h=2

(-2)=6(-2)+2

=》-12+2

=-10

what equation can be used to represent the relation shown in the table ?

Answers

check how you get from x to y for each column and find that you times by 7 so:

y = 7x

Decompose the composite figure to find its total area.

Answers

Answer: 36 m^2

Step-by-step explanation: I got it correct trust btw can i get brsainliest

4 feet 4 inch into inch.​

Answers

Answer:

52 inches

Step-by-step explanation:

1 foot=12 inches

4(12)=48 inches

Then you add the other 4 inches.

48+4=52

52 inches

1. bmi calculator: design a program in raptor that prompts user to enter a person's weight in number of pounds and height in number of inches, then calculate that person's body mass index (bmi) using the formula below, and finally display the person's weight, height, and bmi. bmi

Answers

The program uses the conversion factors of 2.205 pounds per kilogram and 39.37 inches per meter to convert the input values to the correct units for the formula.

To design a program in Raptor that prompts the user to enter a person's weight in pounds and height in inches, and then calculates and displays their body mass index (BMI), we can follow these steps:

Start by opening Raptor and creating a new program.

Add three input symbols to prompt the user for their weight, height, and a constant value for BMI. Label each input symbol accordingly.

Add three assignment statements to assign the input values to variables. We can use the labels we assigned to the input symbols as variable names to make the code more readable.

Add two calculation statements to calculate the person's BMI using the formula [tex]BMI = (weight in pounds * 703) / (height in inches)^2.[/tex]Assign the result to the BMI variable.

Add three output symbols to display the person's weight, height, and BMI. We can concatenate strings with the variable values to make the output more informative.

Finally, save the program and run it to test it with different input values.

Here's what the program would look like:

Start

// Prompt the user for weight, height, and BMI

Input "Enter weight in pounds:", weight

Input "Enter height in inches:", height

Input "BMI:", bmi_constant

// Calculate BMI

Set weight_in_kg = weight / 2.205 // Convert weight to kilograms

Set height_in_m = height / 39.37 // Convert height to meters

[tex]Set bmi = weight_in_kg / (height_in_m ^ 2)[/tex] // Calculate BMI

// Display results

Output "Weight: " + weight + " lbs"

Output "Height: " + height + " in"

Output "BMI: " + bmi

Stop

When the program is run, it will prompt the user to enter their weight, height, and a constant value for BMI. It will then calculate the person's BMI using the formula, convert the weight to kilograms and the height to meters, and display the results along with the original weight and height values. The program uses the conversion factors of 2.205 pounds per kilogram and 39.37 inches per meter to convert the input values to the correct units for the formula.

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Check all tha applya. for employees, human relationship skills are particularly important, since they must work with senior managers to make decisions.b. departments in this organization do not have formal leaders.c. this structure violates unity of command, because employees report to more than one manager.d. In this structure, a vertical hierarchical structure provides accountability, while horizontal reporting relationships improve communication.3) The CEO of C & J Construction is considering moving to a virtual network structure. What would be the best to make such a move?a. to create economies of scaleb. to create deeper reserves of skills within the organizationc. to focus on the core competencies of the organization and outsource less mission-critical tasks4) What problem might the CEO expect if the company switches to a virtual network structure?a. decisions will be made at the top of the organization, creating delaysb. employees may feel less loyalty to the reorganized companyc. resources might be duplicated across divisions of the company Anna borrowed N$20 000 at 5% for three and half years. She wants to pay N$8000 on maturity. To achievethis, she is planning to pay 2000 in 10 months, 5000 in 16 months from now. How much should she pay in twoand half years from now to meet her obligation? Every day Jin reads for 0.75 hours in the morning and 1.25 hours in the evening. He uses the expression 0.75d+1.25d to keep track of the number of hours he has read for any number of days, d. If Jin reads for 20 days, how many hours has he read? What is the factored form of x2 - 9x + 20?A. x(x - 9) + 20B. (x-4)(x + 5)C. (x - 4)(x - 5)D. (x2 - 4)(x2 - 5) How would you feel if you were forced to permanently leave your home? What would you take with you if you could only take items you could carry yourself? the decomposition of diethyl ether at 500oc follows first order kinetics with a half-life of 1570 sec. what fraction of the initial amount is left after 4710 sec?