How many distinct and real roots can an nth-degree polynomial have?

Answers

Answer 1

The fundamental theorem of algegra is often cited to say that an n-th degree polynomial has n roots. They may not always be distinct, and they may not always be real.

An n-th degree polynomial may have up to n distinct real roots.

Related Questions

One of the factors of 6x3 − 864x is

A. 4
B. X^2
C. X + 12
D. X - 8

Answers

The answer is C. X+12

Consider the expression [tex]6x^3-864x.[/tex] This expression consists of two terms: [tex]6x^3[/tex] and [tex]-864x.[/tex]

These two terms have common factors 6 and x, because:

[tex]6x^3=6x\cdot x^2;[/tex][tex]-864x=6x\cdot (-144).[/tex]

Then

[tex]6x^3-864x=6x(x^2-144).[/tex]

You know that [tex]144=12^2.[/tex] Use the formula for the difference of squares:

[tex]x^2-144=x^2-12^2=(x-12)(x+12).[/tex]

Therefore,

[tex]6x^3-864=6x(x-12)(x+12).[/tex]

Answer: correct choice is C.

algebra 2 unit 2 question. connexus.

Answers

From the graph we can infer that our function crosses the x-axis at -2.5, 0.5, and 1.5, so those are the zeroes of the function.
Next, lets convert those decimals into fractions by adding a denominator 1 to each decimal and multiply both its numerator and denominator by a power 10 that lets us get rid of the decimal point:
[tex]( \frac{-2.5}{1} )( \frac{10}{10} )= \frac{-25}{10} =- \frac{5}{2} [/tex]
[tex]( \frac{0.5}{1} )( \frac{10}{10} )= \frac{5}{10} = \frac{1}{2} [/tex]
[tex]( \frac{1.5}{1} )( \frac{10}{10} )= \frac{15}{10} = \frac{3}{2} [/tex]

Since we know that each one of those points is a zero of the function ([tex]x=0[/tex]), we can replace each value into our [tex]x=0[/tex], and work backwards to get our binomials:
[tex]x=- \frac{5}{2} [/tex]
[tex]2x=-5[/tex]
[tex]2x+5=0[/tex]
So, our first binomial is [tex](2x+5)[/tex]

[tex]x= \frac{1}{2} [/tex]
[tex]2x=1[/tex]
[tex]2x-1=0[/tex]
So, our second binomial is [tex](2x-1)[/tex]

[tex]x= \frac{3}{2} [/tex]
[tex]2x=3[/tex]
[tex]2x-3=0[/tex]
So, our next binomial is [tex](2x-3)[/tex]

Now lets put all together to find the equation of our function:
[tex]y=(2x+5)(2x-1)(2x-3)[/tex]
And of course, we can rewrite it in a different order:
[tex]y=(2x-1)(2x-3)(2x+5)[/tex]

We can conclude that the equation that most likely represents the graph of the function is [tex]y=(2x-1)(2x-3)(2x+5)[/tex]

Final answer:

The subject of this question is Mathematics, specifically Algebra 2.

Explanation:

The subject of this question is Mathematics, specifically Algebra 2.

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A rectangle is 1/2 feet long and 3/4 feet wide. What is the area of the rectangle?

Answers

3/8 because to find the area you multiply both numbers so 1*3 is 3 and 2*4 is 8 so your answer should be 3/8

The area of the rectangle having a length of 1.2 feet and a width of 3/4 feet is 3/8 sq feet.

What are the area and perimeter of a rectangle?

We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.

We know the area of a rectangle is (length×width).

Given, A rectangle is 1/2 feet long and 3/4 feet wide.

Therefore, The area of this rectangle is,

= (1/2×3/4) sq feet.

= 3/8 sq feet.

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Choose the correct box of the best buy available.
a .a box of cookies for $1.89
b. two boxes of cookies for $3.69

Answers

1.89 times 2 is $3.78 which is more than 3.69, so the answer is b.

The correct answer is B because if you do the multiplication between 1.89 times 2 and it will give you $3.78 which is more than 3.69

Tiny's Tattoo Parlor sold 389 tattoos this month. 43 of those tattoos were arm tattoos. Based on this data, what is a reasonable estimate of the probability that the next customer does not get an arm tattoo?

Answers

Answer:

346/389

Step-by-step explanation:

correct on khan academy!

The reasonable estimate of the probability that the next customer does not get an arm tattoo is 346/389.

What is Probability?

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1.

Here, Based on the given conditions, formulate

Probability = Favorable outcome / Total outcome

Calculate the sum or difference: (389-43)/389

get the result: 346/389

Thus.the reasonable estimate of the probability that the next customer does not get an arm tattoo is 346/389.

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△ABC∼△LMN , AB is 8 inches, BC is 14 inches, and LM is 12 inches.

What is MN ?

Answers

Similar triangles have side lengths that are proportional.
We setup a proportion using the given information.

AB/LM = BC/MN

8/12 = 14/MN

8(MN) = 12 * 14

8(MN) = 168

MN = 168/8

MN = 21

16 might be your answer if not I am truly dearly sorry

helppppppppppppppppppppppp

Answers

Answer:
log base 2 of 100 is about 1/4 the value of log base 6 of 20

Explanation:
We will get the value of each of them separately and then compare these values.
log base 2 of 100 = 6.6438
log base 6 of 20 = 1.6719

Comparing these values, we will find that:
log base 2 of 100 is about 1/4 the value of log base 6 of 20

Hope this helps :)

Suppose that F(x) = x^3 and G(x) = (4x)^3 − 5. Which statement best compares the graphs of F(x) and G(x)?

A.The graph of G(x) is the graph of F(x) stretched vertically and shifted 5 units down.
B.The graph of G(x) is the graph of F(x) stretched horizontally and shifted 5 units down.
C.The graph of G(x) is the graph of F(x) compressed vertically and shifted 5 units down.
D.The graph of G(x) is the graph of F(x) compressed horizontally and shifted 5 units down.

Answers

Final answer:

The graph of G(x) is the graph of F(x) stretched horizontally by a factor of 4 and shifted 5 units down.

Explanation:

Comparing the functions [tex]F(x) = x^3[/tex] and [tex]G(x) = (4x)^3 - 5[/tex]reveals the relationship between their graphs. G(x) is a horizontal stretch of F(x) by a factor of 4 due to the presence of "4x." Additionally, the constant term "-5" shifts the graph downward by 5 units. Consequently, G(x) can be accurately characterized as a horizontal stretching of F(x) and a vertical shift downward by 5 units, altering the shape and position of the original cubic function F(x).

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BRAINLIESTTT ASAP!!!!!!!!!

Answers

find where the blue and red lines touch
the answer would be -3.5 and -0.5

the first choice is the correct one

What are the solutions to the equation?

n^2−8n+16=25

Enter your answers in the boxes.

n1=

n2=

Answers

To factor the equation, first make sure the right hand side is equal to 0. Do this by subtracting 25 from both sides of the equation.
The equation becomes,
n^2-8n-9 = 0

Factoring the equation now gives you (n-9)(n+1) = 0.
In order to find the solutions to this equation, find values of 'n' that make the equation equal to 0.

In this case, if n is 9 or -1, we get the answer 0.

Proof: (9-9)(n+1) => (0)(n+1) = 0
or (n-9)(-1+1) => (n-9)(0) = 0.

Hope this made sense! If it didn't, please ask questions!

Answer:

help

Step-by-step explanation:

how many fluorine atoms are found in 1.92 grams of AsF3?

Answers

First you need to find out how many moles of AsF3 are in 1.92 grams.
The molar mass of AsF3 is 131.918 g/mole so
1.92 g * (1 mole)/(131.918g) = .0146 moles AsF3

Each mole of AsF3 has 6.02 x10^23 molecules of AsF3 and each molecule of AsF3 has 3 flourines, so you need to convert from moles to molecules AsF3 to atoms of F
0.146 moles AsF3 * (6.02 x 10^23 molecules AsF3)/(1 mole AsF3) * (3 atoms F)/(1 molecule AsF3) = 2.64 x 10^22 atoms F

Math question help :)

Answers

You have two similar triangles.
Use corresponding parts of the two triangles.
If two triangles are similar, then the lengths of corresponding parts are proportional.
The small triangle has a vertical side that measures 6 ft. That side corresponds to the height of the tree, h, in the large triangle.
The small triangle has a horizontal side that measures 10 ft. That side corresponds to the side of the large triangle that measures 40 ft.

6 ft corresponds to h
10 ft corresponds to 40 ft

[tex] \dfrac{6}{h} = \dfrac{10}{40} [/tex]

Answer:

Step-by-step explanation:

I think its D.

What is the interior angle if the outside equals 110?

Answers

Interior and exterior angles are supplementary. The corresponding interior angle is 180° -110° = 70°.

You have a cd-rw drive that advertises speeds of 32x/12x/48x. what is the read speed of the drive?

Answers

When you have CD-RW drive that advertises speeds of 32x/12x/48x, the first speed that you encounter from left to right is the writing speed, the next one is the rewrite speed, and the last one is the reading speed.
Knowing this we can tell that our CD-RW drive has:
32x of writing speed
12x of rewriting speed
48x of reading speed

We can conclude that the reading speed of our CD-RW drive is 48x

help me please asap and plz be correct :)

Answers

The radii are all equal, so
.. AI = BI
.. 3x +7 = 5x -11
.. 18 = 2x
.. 9 = x

Then
.. AI = 3x +7
.. = 3*9 +7
.. = 34

AI = 34

Sue's Sushi placed two orders with its fish supplier. One order was for 15 pounds of salmon and 8 pounds of tuna; the order totaled $259. The other order was for 12 pounds of salmon and 6 pounds of tuna; this order totaled $204. What is the cost for one pound of salmon and one pound of tuna?

Answers

x= salmon cost per pound
y= tuna cost per pound

$15x + $8y= $259
$12x + $6y= $204

Solve for one variable in one equation and substitute it in the other equation.

15x + 8y= 259
subtract both sides by 8y
15x= 259 - 8y
divide both sides by 15
x=(259-8y)/15

Substitute in second equation

12x + 6y= 204
12((259-8y)/15) + 6y= 204
multiply everything by 15 to eliminate fraction

(15)(12(259-8y)/15) + (15)(6y)= (204)(15)
(12*259) + (12*-8y) + 90y= 3060
multiply inside parentheses

3108 - 96y + 90y= 3060
combine like terms & subtract 3108 from both sides

-6y= -48
divide both sides by -6

y= $8 cost of tuna per pound

Substitute y=8 in either equation
15x + 8y= 259
15x + 8(8)= 259
15x + 64= 259
15x= 195
x= $13 cost of salmon per pound

CHECK:
12x + 6y= 204
12(13) + 6(8)= 204
156 + 48= 204
204= 204

ANSWER: One pound of salmon costs $13 and one pound of tuna costs $8.

Hope this helps! :)

PLEASE HELP ME QUICKLY!!!

BRAINLIEST AVAILABLE TO CORRECT ANSWER

Answers

I would like to know the possible answers since I can’t infer whether the total price is changed, but i would assume that m would need to increase if that’s the case when b is halved, and that when m is tripled b and mx would increase since prices would be going up

Reggie currently has a square rug in his living room. He is moving soon and has determined that for his new living room, he will need a rug that has a width that is two feet shorter than his current rug and a length that is five feet longer than his current rug. Let x represents the side measure of Reggie's current rug, in feet. Determine the equation that represents the area, y, in square feet, of the rug needed for his new living room.

y = x2 + 3x - 10

y = x2 - 7x + 10

y = x2 - 3x - 10

y = x2 + 7x + 10

Answers

Answer:
y = x² + 3x - 10

Explanation:
Reggie's current rug has a square shape.
This means that:
length of rug = x ft
width of rug = x ft

For the new rug:
1- the length is 5 ft longer than the current rug. This means that:
new length = x + 5 ft
2- the width is 2 ft shorter than the current rug. This means that:
new width = x - 2 ft

The area of the new rug can be calculated as follows:
area of new rug = new length * new width
area of new rug = (x + 5)(x - 2)
area of new rug = x(x) - 2(x) + 5(x) - 5(2)
area of new rug = x² - 2x + 5x - 10
area of new rug = x² + 3x - 10 ft²

Hope this helps :)

Answer:

C. y = x² + 3x - 10

Step-by-step explanation:

Reggie's current rug has a square shape.

This means that:

length of rug = x ft

width of rug = x ft

For the new rug:

1- the length is 5 ft longer than the current rug. This means that:

new length = x + 5 ft

2- the width is 2 ft shorter than the current rug. This means that:

new width = x - 2 ft

The area of the new rug can be calculated as follows:

area of new rug = new length * new width

area of new rug = (x + 5)(x - 2)

area of new rug = x(x) - 2(x) + 5(x) - 5(2)

area of new rug = x² - 2x + 5x - 10

area of new rug = x² + 3x - 10 ft²

Just took the test <3.

A $4,000.00 principal earns 5% interest, compounded annually. After 4 years, what is the balance in the account?
$500,000.00
$4,862.03
$4,600.00
$20,250.00
24.
A $6,000.00 principal earns 8% interest, compounded semiannually. After 35 years, what is the balance in the account?
$22,800.00
$39,600.00
$88,712.07
$93,429.71
25.
A tractor costs $15,450.00 and depreciates in value by 14% per year. How much will the tractor be worth after 3 years? $22,889.85
$15,408.00
$8,451.28
$9,827.07

Answers

4000(1.05)⁴=$4862.03

6000(1+ .08/2)^35(2)=$93429.71

15450(.86)³=$9827.07

the first one is a
the second one is b
the third is a

a cylinder has a circumgerence of 12pi cm and a height that is half the radius. what is the total surface

Answers

[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r\quad \begin{cases} r=radius\\ -----\\ C=12\pi \end{cases}\implies 12\pi =2\pi r\implies \cfrac{12\pi }{2\pi }=r\implies 6=r\\\\ -------------------------------\\\\ \textit{total surface of a cylinder}\\\\ S=2\pi r(h+r)\quad \begin{cases} r=6\\ h=\stackrel{half~of~r}{3} \end{cases}\implies S= 2\pi (6)(3+6)[/tex]

and surely you know how much that is.

Which pair of measurements is equivalent?
8,600 mg, 86 g
2,500 g, 250 kg
3.4 kg, 3,400 g
480 g, 4.8 mg

Answers

Let's look at each pair and change it so the first one in the pair will be what the second one will be converted to.
8,600 mg = 86,000 mg; So now, the first one is not equivalent.
2,500 g = 250,000 g; Not that one either.
3.4 kg = 3.4 kg; This one is correct. We can check by checking the last pair.
480 g = .0048 g; Nope.
So 3.4 kg, 3400 g would be the correct answer.

Answer:

3.4 kg, 3,400 g

a basketball player made 27 free throws in her last 45 tries. what is the experimental probability that she will make her next free throw?

Answers

Hey mark me brainlest but ur answer is 27/45

Bess ur day.

Today a car is valued at $42000. The value is expected to decrease at a rate of 8% each year. Choose the equation that can be used to solve the problem.
A.) y=42000(1+.08)^6
B.) y=42000(1+6)^8
C.) y=42000(1−.08)^6
D.) y=42000(1−.8)^6
And then: What is the value of the car expected to be 6 years from now?
This is the only question I don't understand, someone help please!

Answers

i think the correct answer is

C.) y=42000(1−.08)^6

as for what it will cost in six years:

25466.91

not sure if you have to include the decimal or round it.

Answer:

Option (c) is correct.

[tex]y=42000(1-0.08)^6[/tex] equation that can be used to solve the given problem and the value of the car expected to be 6 years from now is $25466.91

Step-by-step explanation:

Given : Today a car is valued at $42000. The value is expected to decrease at a rate of 8% each year.

We have to choose the equation that can be used to solve the given problem.

We know

Depreciation formula given as,

[tex]A=P(1-\frac{r}{100} )^n[/tex]

Where A is the amount value after depreciation.

P is present value

r is depreciate rate.

n is time period.

Given : P = 42000 and r= 8% also given time period is 6.

Substitute , we have,

[tex]y=42000(1-\frac{8}{100} )^6[/tex]

Simplify , we have,

[tex]y=42000(1-0.08)^6[/tex]

Simplify we get,

[tex]y=25466.91[/tex]

Thus, [tex]y=42000(1-0.08)^6[/tex] equation that can be used to solve the given problem and the value of the car expected to be 6 years from now is $25466.91

Using the graph below, what is the 10th term of the arithmetic sequence?

A.a10 = 26

B.a10 = 31

C.a10 = 30

D.a10 = 436

Answers

Final answer:

The 10th term of an arithmetic sequence can be found using the formula an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, n is the term number, and d is the common difference. Without the graph or additional information, we cannot compute the 10th term for the given sequence.

Explanation:

The question asks us to determine the 10th term of an arithmetic sequence using a provided graph. Unfortunately, the actual graph is not provided in the question. An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant, known as the common difference. To find the 10th term of an arithmetic sequence, we would use the formula:

an = a1 + (n - 1)d

where an is the nth term of the sequence, a1 is the first term, n is the term number, and d is the common difference. However, without the graph or additional information such as the first term or the common difference, we cannot accurately determine the 10th term, and any answer from the provided options would be purely a guess.

Final answer:

To find the 10th term of an arithmetic sequence, we need to use the formula an = a1 + (n-1)d, where an is the nth term, a1 is the first term, n is the position of the term, and d is the common difference. In this case, the common difference is -3. Substituting the values into the formula, the 10th term is -24.

Explanation:

To find the 10th term of an arithmetic sequence, we need to identify the common difference and use the formula:

an = a1 + (n-1)d

where an is the nth term, a1 is the first term, n is the position of the term, and d is the common difference.

In this case, the given sequence is 3; 14; 11; 5; 16; 17; 28; 41; 31; 18. By comparing the terms, we can see that the common difference is -3.

Substituting the values into the formula:

a10 = 3 + (10-1)(-3) = 3 - 27 = -24

The 10th term of the arithmetic sequence is -24.

Analyze the key features of the graph of the quadratic function f(x) = -x2 + 2x + 10. A. Does the parabola open up or down?
B. Is the vertex a minimum or a maximum?
C. Identify the axis of symmetry, vertex and the y-intercept of the parabola.

Answers

see the attached graphic

the parabola open down
the vertex is a maximum
the axis of symmetry is the y axis
the y-intercept of the parabola.is the point (0,10)

SOS

Answer

A: Down

B: Max

AOS: x = 1Vertex: (1, 11)Y-Int: (0, 10)

Step-by-step explanation:

A: If the leading coefficient (a) is positive, the graph opens UP. If it is negative, the graph opens DOWN.

B: Anytime the graph goes UP, there's a minimum. Anytime the graph goes DOWN, there's a maximum

AOS: [tex]x = \frac{-b}{2a}, a=-1, b=2, c=10[/tex]

Vertex: [tex](\frac{-b}{2a}, y)[/tex]

Y-INT: let x=0 and solve for y. The coordinate of the y-intercept is (0, y).

Hope this helps!!

How could you find an equation of a quadratic function with the zeroes of -3 and 1?

Answers

Hello,

The simpliest quadratic function is y=(x+3)(x-1)
or y=x²+2x-3

△JKL∼△QRS , JK is 8 centimeters, QR is 12 centimeters, and RS is 9 centimeters.

What is KL ?

Enter your answer in the box.

Answers

Answer:

The measure of KL is 6 centimeters.

Step-by-step explanation:

It is given that △JKL∼△QRS.

The corresponding sides of two similar triangles are proportional.

[tex]\frac{JK}{QR}=\frac{KL}{RS}[/tex]

[tex]\frac{8}{12}=\frac{KL}{9}[/tex]

[tex]8\times 9=KL\times 12[/tex]

Divide both sides by 12.

[tex]KL=\frac{72}{12}[/tex]

[tex]KL=6[/tex]

Therefore we can say that if △JKL∼△QRS, then the measure of KL is 6 centimeters.

Answer:

Step-by-step explanation:

He did too much math lol, a simple way of this is by dividing both sides initially.

12/9 = 1.5
9/1.5 = 6

The domain of f(x) is the set of all real values except 7, and the domain of g(x) is the set of all real values except –3. What describes the domain of (gºf)(x)?

Answers

The function g°f(x) can be written as g(f(x)), which means that you take a random x, put it into f(x) which gives you a value (let's call it y). You then put y into g(y) and you find the result.

Therefore the Domain you are looking for in words is every x that can be put into f(x) and that gives you a value y that can be put in g(y).

Mathematically:
Dom (g°f) = {x ∈ Dom(f) | f(x) ∈ Dom(g)}

In your case:
Dom (g°f) = { x ∈ R - {7} | f(x) ∈ R - {-3} }

I need to spend exactly £200, how?

Answers

You can just rent dancers for 4 hours 4 * 50 = 200

Jenna throws a stone off a pier and into the ocean. The graph models how the height of the stone, above sea level, changes over time.

Select from the drop-down menu to interpret the decreasing interval of the graph.

The stone was falling toward the water from

https://static.k12.com/nextgen_media/assets/8090396-NG_AL1_O_07_012_Quiz_05.png

Answers

0.5 after it was thrown until 1.5 after it was thrown

This should get you a hundred on the 4.11 quiz. :)

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Cad cream inc., an ice cream company, has collaborated with bite snack inc., a food manufacturing company, to come up with a third company, cream bite inc. this new company manufactures energy bars with a variety of flavors. in this context, cream bite inc. is a _____. 2 In some countries it is quite --------- to use the correct title when talking to business colleagues.A. offensive B. likely C. formal D. tricky Name 3 things you can do to manage your weight. PLEASE HELP!!!! THANK YOU!!!The graph of the function y = x2 is shown. How will the graph change if the equation is changed to y = 2x2?A)The parabola will become wider.B)The parabola will become narrower.C)The parabola will move up 2 units.D)The parabola will move down 2 units. simplify the expression (3x^4y^-5)3 What is Mary's motivation for exploring the many rooms of Misselthwaite manorA. SHE WANTS TO GET AWAY FROM MARTHA B. SHE IS CURIOUS ABOUT HER NEW SURROUNDINGS C. SHE WANTS TO CAUSE TROUBLE D. SHE IS BORED BECAUSE ITS RAINING OUTSIDE THIS IS THE SECRET GARDEN THIS IS IN ELA. NEED IT ASAP RIGHT NOW PLEASE THANKS Why doesn't the Moon move away from Earth? Its orbit is too small. Its inertia is too strong. Earth's gravity is strong. Earth's gravity is weak. How do jellyfish reproduce? Explain, in complete sentences, the process and use the words polyp and medusa. Christian got a haircut yesterday afternoon if the hair stylist charged $18 and christian gave 20% tip how much dod he pay for the haircut The students were going to school.Los estudiantes va a la escuela.Los estudiantes van a la escuela.Los estudiantes iba a la escuela.Los estudiantes iban a la escuela. Which foundation drawing matches this orthographic drawing? ( just tell me what picture) How do the levels of reproductive hormones regulate or influence the human menstrual cycle? Examine the terms below. Then write a short paragraph about new immigrants in the United States using all three terms. a. Assimilate b. ethnic groups c. nativist According to the Transitive Property of Congruence: If CDEF and EFGH, then _____A. CDEFB. EFEFC. CDGHD. EFGHIf you're reading this the answer is C The ultimate source of energy to support most life on earth is _____. see concept 10.1 (page 189) Under _____ uncertainty avoidance employees are willing to change jobs more frequently Chris is making a poster for Bike Safety Week. The diameter of circle A is 14 in.If the area of circle B is the area of circle A, what is the area of circle B? (Use 3.14 for .) A car travels 3 times around a traffic circle whose radius is 80 feet. What is the distance the car will travel? Use 3.14 for . Enter your answer in the box. ft Question 2 of 10 Multiple Choice: Please select the best answer and click "submit." Read this passage: A local nursing home is seeking a dependable, honest, and considerate individual to work as a caregiver for several elderly patients. Qualified candidates should have CPR and first aid training, at least a year of caregiving experience, and a passion for serving the elderly with kindness. Based on the information in the classified ad, which information should you highlight in your cover letter? A.Your experience caring for your elderly grandmother B.Your previous experience as a restaurant server C.Your intention of becoming a registered nurse D.Your ideas for helping the elderly When scientists determined that the earth was round rather than flat, this was a ___________?