Use the fundamental theorem of algebra to determine the number of roots for each polynomial function
shown.
f(x) = (x2+6)2

Answers

Answer 1

Answer:

4 roots.

Step-by-step explanation:

The number of roots is equal to the degree of the function

For example

f(x) = x^2  has 2 roots because the highest exponent is 2.

f(x) = x^3 + 2x - 1  has 3 roots , because the function is of degree 3.

(x^2+ 6)^2  = x^4 + 12x^2 + 36   so because of the x^4 it is of degree 4 and has 4 roots.


Related Questions

Avni designs a game in which a player either wins or loses 4 points during each turn. Which equation

represents all numbers of points, p, a player may have after his or her first turn of the game?

O p = 4

O p = -4

O pl = 4

Op = -4

Answers

Answer:

Equation to represent all number of points = |4|

Step-by-step explanation:

We are told that a player either wins or loses 4 points during each turn. This means a player could either gain 4 points or loose 4 points. When writing this in Mathematical terms its means either -4 or +4.

Now, since possible number of turns is -4 or 4, then we can represent this with the absolute value symbol.

Thus, it's |4|

How is completing the square beneficial ? Edge 2020 key words

Answers

Allows you to factor a function that was previously not able to be factored
Allows you to factor

Unit rate for 150 students in 3 classes.

Answers

Answer:

Step-by-step explanation:

150 students/3 classes= 50 students per class

50 students per class 150/3 = 50

David noticed that locker 49 was changed exactly 3 times it was opened by Student one closed by student seven and open my Student 49 what other lockers were changed exactly 3 times what is the relationship between these numbers

Answers

Answer:

The other lockers that were changed exactly 3 times are:

Locker 1 and Locker 7

Step-by-step explanation:

Question: What other lockers were changed exactly 3 times?

Answer: Lockers 1 and 7

How?

Locker 1 was opened by a student other than student 1; it was closed by a student other than student one; and it was opened by student 1.

Same happened with Locker 7.

The relationship between these numbers is an associative relationship.

Give the Domain and Range of H={(-2,-3),(5,9),(5,-2)}
Write your answer using set notations

Answers

Domain = {-2, 5}Range = {-3, -2, 9}

The domain is the set of possible x values or inputs. We list each unique x value once (ignoring any repeats)

The range is the set of possible y outputs. Convention is to sort the values from smallest to largest.

This relation is not a function because the x value x = 5 corresponds to multiple y values.

Three and a half more than a number

Answers

Answer:

x + 3.5

Step-by-step explanation:

You are adding

hopefully this helps you:)

John invests $200 at 4.5% compounded annually. About how long will it take for John’s investment to double in value?

Answers

Answer:

The number of years needed is 15.75 years.

Step-by-step explanation:

The investment amount (present value) = $200

Interest rate =4.5%

Double of investment = $400

Now we have to find the time or number of years in which the investment amount will be doubled. So, just use the below formula to find the number of years.

Future value = present value ×(1+interest rate)^n

400 = 200×(1+4.5%)^n

N = 15.75 years

The number of years required to double the amount is 15.75 years.

To which graph does the point (8;-2) belong?

Answers

quadrant 4

.................

Answer:

Quadrant 4

Step-by-step explanation:

In Quadrant 4 the x-axis is positive (+) and the y-axis is negative (-). Here is the point plotted on a coordinate grid to help you understand better.

Hope this helps :)

Write the quadratic equation whose roots are -4 and 4 and whose leading coeffiecient is 3. Use the letter X to represent the variavble.

Answers

Answer:

3x^2 - 48 = 0

Step-by-step explanation:

The roots of a quadratic equation whose roots are -4 and 4, means that valid solutions for the quadratic equation are -4 and 4.

The two forms we know for the quadratic equation are the factored binomials:

(ax + cy)(bx + dz) = 0

and the full equation

ax^2 + bx + c = 0

We will start with the factored form:

(x + 4) ( x - 4) = 0

Note that if we solve this, we get the roots:  x + 4 = 0  ==> -4 && x - 4 = 0 ==> 4

Now we apply foil to get the unfactored form:

(x + 4) (x - 4) = 0

x * x + x * -4 + 4 * x + 4 * -4 = 0

x^2 + -4x + 4x + -16 = 0

x^2 - 16 = 0

And now we want the leading coefficient to be 3.

3x^2 - 16  = 0

This looks like what we want; however, now with the leading 3, our solutions are no long +4 and -4.  So, we need to re-evaluate.

Going back to the binomials with the idea of a leading 3, let's rewrite them to still give us the solutions 4 and -4, but with the 3 included:

(3x + 12) (x - 4) = 0

Note, we simply multipled one binomial by 3 to maintain the roots of the original, but also incorporate the leading 3.

3x + 12 = 0              x - 4 = 0

3x = -12                        x = 4

x = -4

So now, we simply apply foil to this new equation of binomials to get our final quadratic equation:

(3x + 12) (x - 4) = 0

3x * x + 3x * -4 + 12 * x + 12 * -4 = 0

3x^2 + -12x + 12x + -48 = 0

3x^2 - 48 = 0

This is our quadratic equation we wish to use.

Note, we could have gotten this same equation by simply multiplying the original (x^2 - 16) = 0 by 3.

Cheers.

Which is the graph of y<2x-1

Answers

Answer:

the last one is the only one with a y intercept of -1

Step-by-step explanation:

a turtle crawled at a speed of 1.2 meters per minute for nine minutes how far did the turtle crawl

Answers

Answer:

10.8 meters

Step-by-step explanation:

1.2 times 9 minutes= 10.8

Answer:

10.8 meters

Step-by-step explanation:

9 * 1.2 = 10.8

A pink crayon is made with 12 ml

Answers

Answer:

ok

Step-by-step explanation:

Paul says that in the number 6,367, one 6 is 10 times as great as the other 6. Is he correct?

Answers

Answer:

Yes

Step-by-step explanation:

6,000 is 10 times greater than 60

Yes because the 6 that’s in the thousands place way larger then the other 6

Simplify: 2 + 7(1 - 3x)


2 + 14x
16x
9-27x
9 - 21x

Answers

Answer:

9 - 21x  

Step-by-step explanation:

Simplify the following:

7 (1 - 3 x) + 2

Hint: | Distribute 7 over 1 - 3 x.

7 (1 - 3 x) = 7 - 21 x:

7 - 21 x + 2

Hint: | Add the numbers in -21 x + 2 + 7 together.

Add like terms. 2 + 7 = 9:

9 - 21 x

Hint: | Factor out the greatest common divisor of the coefficients of 9 - 21 x.

Factor 3 out of 9 - 21 x:

Answer: 3 (3 - 7 x)

(of the given solutions it's the only correct one, but can be further simplifued to 3 (3 - 7 x)

What is the value of the 5 in the number 975,178

Answers

It’s in the thousands place

Answer:

thousands place

Step-by-step explanation:

Factor completely 4x^4− 20x^3 + 12x^2

Answers

Answer:

Step-by-step explanation:

4x^2(x^2 - 5x + 6)

4x^2(x - 3)(x - 2)

FIRST TO ANSWER GETS BRAINLYEST!!!!!!

Answers

Answer:

m ≈ 3

Step-by-step explanation:

3.53631284916 x 10^3 ≈ 3 x 10^3

x2+9-8x in standard form

Answers

Answer:

x^2 - 8x + 9

Step-by-step explanation:

Please write x2+9-8x as x^2 + 9 - 8x.  The " ^ " indicates exponentiation.

Next, please write x^2 + 9 - 8x in descending powers of x:

x^2 - 8x + 9

Thirty randomly selected students took the calculus final. If the sample mean was 95 and the standard deviation was 6.6, construct a 99% confidence interval for the mean score of all students.a) 91.69 < μ < 98.31b) 92.95 < μ < 97.05c) 91.68 < μ < 98.32d) 92.03 < μ < 97.97

Answers

Answer: c) 91.68 < μ < 98.32

Step-by-step explanation:

Let μ  be the mean score of all students.

Let [tex]\overline{x}[/tex] represents the sample mean score.

As per given , we have

Sample size : n= 30

Sample mean : [tex]\overline{x}=95[/tex]

Sample standard deviation: [tex]s=6.6[/tex]

Significance level [tex]\alpha=0.01[/tex]

Now, Confidence interval of mean when population standard deviation is unknown is given by :-

[tex]\overline{x}\pm t_{\alpha/2, df}\dfrac{s}{\sqrt{n}}[/tex]

Degree of freedom = n-1 = 29

Critical two-tailed t-value : [tex]t_{0.01/2,29}=t_{0.005,29}=2.756[/tex] [By students' t distribution table]

Confidence interval of mean will be:

[tex]95\pm (2.756)\dfrac{6.6}{\sqrt{30}}\\\\=95\pm (2.756)\dfrac{6.6}{5.47722557}\\\\=95\pm (2.756)(1.205)\\\\=95\pm 3.32\\\\= (95-3.32, 95+3.32)\\\\=(91.68,\ 98.32)[/tex]

i.e. a 99% confidence interval for the mean score of all students : 91.68 < μ < 98.32

So correct option is c) .

Which number is equivalent to
A 2
B 9
с
81
729

Answers

The answer to the question is A i believe

The answer would be

B. 9

Add 6 and 8 the add p

Answers

Answer:

Step-by-step explanation:

6 + 8 + p = 14 + p

Answer: 14+p

Step-by-step explanation:  We have to add these numbers-

6 + 8 + p

14+p

(Since we don't know the value of p this is how far we can simplify )

*BRAINLIEST* The lines below are parallel. If the slope of the green line is 8/5, what is the slope of the red line?​

Answers

If the two lines are parallel, then they have the same slope of 8/5
Answer:  8/5

Any two parallel lines always have the same slope (but different y intercepts)

The equation of the green line is y = (8/5)x+6

The equation of the red line is y = (8/5)x-3

Slope intercept form is y = mx+b with m as the slope and b as the y intercept.

The slopes must be the same so that each time the line goes up some amount, we move to the right the same amount. Think of a set of stairs to possibly visualize what I mean. If the slopes are different (even slightly), then the lines will intersect at some point and we wouldn't have parallel lines.

I am a real number I am a rational number I am not a natural number I am less than -13 what number am I

Answers

Answer:

Any number less than -13.

Step-by-step explanation:

If the number is real and rational and non-natural, this means that it can be any number in the negative number space.

Additionally, since the number has to be less than -13, then the number could be any number less than -13.

With all these things considered, the number is any number less than -13 that is real and rational.

Cheers.

it’s -13 because it either can be less or more

Which of the following fractions is greater than 2/5 and less than 3/5 ?

Answers

Answer:the answer would be 2.5/5

Evaluate a + b for a = -46 and b = 34.

Answers

Answer:

-12

Step-by-step explanation:

a + b

a = -46

b = 34

-46 + 34 = -12

Dhshshsjehsjsjjsjssjsjsjsjsjsjshshdhdhdhdjdjdjdjhdbd djdhdhdjjdjdjdjdjdjd

Answers

Answer:

Dhshshshhshsjehsjsjjsjssjsjsjsjsjsjjshhdhddhhdjdjddjdjjhdhdkdhjsdfggdhjjjjd

Step-by-step explanation:

If 1,000 gallons of oil cost $4,861, what is the cost of 35 gallons

Answers

Answer:

$170.14

Step-by-step explanation:

4,861 / 1,000 = $4.861 per gallon

35 x $4.681 = $170.135, so you need to round up to the nearest penny

Step-by-step explanation:

For 1000 gallons=$4861

For 1 gallon =$4861/1000

For 35 gallons=$4861/1000 x 35=170.135

Someone help me please i attached a picture...

Answers

Answer:

the perimeter is 13yd + 13yd + 5yd +5yd = 36yd

the area is 5yd + 5yd = 10yd, 10yd × 12yd ÷ 2 = 60yd

What is (-9)+9 simplified

Answers

Answer:

the answer is zero

Step-by-step explanation:

-9+9=0

According to the U.S. Census Bureau, as of April 1, 2000, the total population of the United States was about 3 x 10^8 . The population of Vermont was 6 × 10^5 . The population of the U.S. was how many times the population of Vermont in April of 2000?

2 times
500 times
1,000 times
50,000 times

Answers

Divide US population by Vermont :

3x 10^8 / 6x10^5

3/6 = 1/2 = 0.5

10^8 / 10^5 = 10^3

0.5 x 10^3 = 500

The answer is 500 times

All we need to do is divide.

3*10^8/6*10^5

0.5^8-5

0.5^3

500

Therefore, the answer is 500 times.

Best of Luck!

Other Questions
Future tense 1. The train_______ at 11:45(to leave) 2. We______ dinner at a nice restaurant on Saturday, but we haven't booked a table yet.(to have) 3. My ski instructor believes it_______ in the mountains tomorrow evening.(to snow) 4. On Sunday at 8 o'clock I______ my friend.( to meet) 5. They________to London on Friday evening at 8:15.(to fly) 6. Wait I______ you to the station.(to drive) 7. The English lesson________at 8:45.(to start) 8. I_______my sister in April.(to see) 9. Look at the clouds-it______in few minutes.(to rain) 10. Listen! There's someone at the door. I________the door for you. (to open) Empire Company is a manufacturer of smartphones. Its controller resigned in October 2017.An inexperienced assistant accountant has prepared the following income statement for the month of October 2017.EMPIRE COMPANYIncome StatementFor the Month Ended October 31, 2017Sales Revenue $780,000Less: Operating Expenses Raw materials purchases $264,000 Direct labor costs 190,000 Advertising expense 90,000 Selling and administrative salaries 75,000 Rent on factory facilities 60,000 Depreciation on sales equipment 45,000 Depreciation on factory equipment 31,000 Indirect labor cost 28,000 Utilities expense 12,000 Insurance expense 8,000 803,000Net loss ($23,000)Prior to October 2017, the company had been profitable every month. The company's president is concerned about the accuracy of the income statement. As her friend, you have been asked to review the income statement and make necessary corrections. After examining other manufacturing cost data, you have acquired additional information as follows.1. Inventory balances at the beginning and end of October were: October 1 October 31Raw materials $18,000 $29,000Work in process 20,000 14,000Finished goods 30,000 50,0002. Only 75% of the utility expense and 60% of the insurance expense apply to factory operations. The remaining amounts should be charged to selling and administrative activities.Instructions:a. Prepare a schedule of cost of goods manufactured for October 2017.b. Prepare a correct income statement for October 2017. Find the diameter of a cone that has a volume of 83.74 cubic inches and a height of 5 inches An image point of a transformation has coordinates Y'(2, -4). If the pre-image point had coordinates Y(6, -12), what was the transformation and scale factor? reflection with scale factor 3 reflection with scale factor dilation with scale factor 3 dilation with scale factor Read this passage below and answer the question."If I only had a silk!" sighed Meg. "Mother says I may when I'm eighteen perhaps, but two years is an everlasting time to wait.""I'm sure our pops look like silk, and they are nice enough for us. Yours is as good as new, but I forgot the burn and the tear in mine. Whatever shall I do? The burn shows badly, and I can't take any out."What can you infer about Meg based on this passage?She doesnt care much about fashion.She thinks she should wait until she is older to attend the dance.She is embarrassed by Jos sense of style.She would like to buy a new dress. Solve the equation -4 = 5 -x. The Flash can travel 400 m in just 5.2 minutes. What is his average velocity in m/s? Boston and New York were both founded as? The proton has a mass of? How do you think the mass of an object affects how much friction get exerted on the object by a rough surface? Solve the inequality. A. >> O B. x >7 C. x>-5 ) D. x if a cubic container has a side length of 50.0cm, what is the volume in liter? Complete the paragraph to explain how Angelina can notify readers that her report is just a draft. Angelina has decided to add the word DRAFT to the of the pages of her report as a watermark. To do this, she needs to navigate to the tab and then to the command group to click the Watermark icon and then the DRAFT option. If she wanted to include additional text, such as her initials, she could create a watermark. Which property is used in the problem below?2 (x + 4) = 2 x + 8the associative property the commutative propertythe distributive propertythe additive identity property which of the questions can be answered through science? what is the best water sport? why should we value honesty? why does water change into steam? what is the most important thing in life? Which explorer sailed the furthest NORTH?(2.1)O VespucciO PizarroO CabotO Columbus what is the domain and range of f(x)=2x+3 2. What is the name of the large island just south of Florida? A person is seeking a job in the lumber industry. Which Texas region would likely offer them the best opportunity for finding a job? Can yall help me? Answer the following Questions about Thank You Ma'am1. How does the author show us the type of person Mrs. Luella Bates Washington Jones is?2. How does the author show us the type of person the boy is?3. How does social pressure influence both of these characters?