solve
f(x)=4x5−8x4+8x2−4x

Answers

Answer 1

Given:

The function is:

[tex]f(x)=4x^5-8x^4+8x^2-4x[/tex]

To find:

The roots of the given equation.

Solution:

We have,

[tex]f(x)=4x^5-8x^4+8x^2-4x[/tex]

For roots, [tex]f(x)=0[/tex].

[tex]4x^5-8x^4+8x^2-4x=0[/tex]

[tex]4x(x^4-2x^3+2x-1)=0[/tex]

[tex]4x((x^4-1)+(-2x^3+2x))=0[/tex]

[tex]4x((x^2+1)(x^2-1)-2x(x^2-1))=0[/tex]

On further simplification, we get

[tex]4x(x^2+1-2x)(x^2-1)=0[/tex]

[tex]4x(x-1)^2(x+1)(x-1)=0[/tex]

[tex]4x(x+1)(x-1)^3=0[/tex]

Using zero product property, we get

[tex]4x=0[/tex]

[tex]x=0[/tex]

Similarly,

[tex]x+1=0[/tex]

[tex]x=-1[/tex]

And,

[tex](x-1)^3=0[/tex]

[tex]x=1[/tex]

Therefore, the zeroes of the given function are [tex]-1,0,1[/tex] and the factor form of the given function is [tex]f(x)=4x(x+1)(x-1)^3[/tex].


Related Questions

7
Setting 3 equal to which ratio would result in a valid proportion?
9
49
18
42
织但

Answers

Answer:

000

Step-by-step explanation:

000

Which of the following is the discriminant of the polynomial below?
X2 +6X+8
A. 8
B. 6
C4
D. 26

Answers

X2 + 6X +8
the answer is C. 4

Explain the relationship between an inda vidual and a society​

Answers

Answer:

The relation between individual and society is very close. Essentially, “society” is the regularities, customs and ground rules of antihuman behavior. ... Man is biologically and psychologically equipped to live in groups, in society. Society has become an essential condition for human life to arise and to continue.

What type of angle is angle R?

A. obtuse
B. right
C. straight
D. acute

Answers

Answer:

A. Obtuse

Step-by-step explanation:

Angle R is greater than 90°.

Answer:

Obtuse

Step-by-step explanation:

We know this because the angle is larger than 90 degrees which is also known as an obtuse :)

pls help

The equation of a line parallel to 6x – 2y + 10 = 0 and passes through the point
(-2,7).

Answers

Answer:

y=3x-1

Step-by-step explanation:

First we need to rewrite 6x-2y+10 =0 into the standard slope form of y=mx+b when done you get y=3x+5Next we need an equation that passes through the point (-2,7). Now remember equations that are parallel have the same slope so the equation should look like y=3xIn standard slope form the b is the y-intercept. We now need to plug in the x ordered pair value into the standard slope equation. y=3(-2)+5 to get y=-1 meaning -1 is the y-intercept Therefore the answer is y=3x-1

Answer:

Y = 3X + 13

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

6x - 2y + 10 = 0 ( subtract 6x + 10 from both sides )

- 2y = - 6x - 10 ( divide terms by - 2 )

y = 3x + 5 ← in slope- intercept form

with slope m = 3

Parallel lines have equal slopes , so

y = 3x + c ← is the partial equation

To find c substitute (- 2, 7 ) into the partial equation

7 = - 6 + c ⇒ c = 7 + 6 = 13

y = 3x + 13 ← equation of line in slope- intercept form

I WILL GIVE BRAINLIEST

Answers

Answer:

A

Step-by-step explanation:

(f(-3+h)-f(-3))/h=(5(-3+h)^2-5(-3)^2)/h=(5*(-3+h-3)(-3+h+3))/h=-30*h/h=-30

HELP PLEASE!!!
Find the length of AB.
А.53.74
B.26.05
C.96.95
D.84.79

Answers

Answer:

Step-by-step explanation:

Sin 61  = 47/X

(X=AB)

X = 53.73764119

The Sine or Sinθ in a right-angle triangle is the ratio of its perpendicular to its Hypotenuse. The correct option is A.

What is Sine (Sinθ)?

The Sine or Sinθ in a right-angle triangle is the ratio of its perpendicular to its Hypotenuse. It is given as,

Sin(θ) = Perpendicular/Hypotenuse

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

The hypotenuse is the longest side of the triangle.

In the given triangle, for ∠B we can write the perpendicular is 47, and the hypotenuse is AB.

Using the Sine ratio for the angle B, we can writte,

Sin(∠B) = AC/AB

Sin(61°) = 47/AB

AB = 53.74 units

Hence, the correct option is A.

Learn more about Sine:

https://brainly.com/question/21286835

#SPJ2

What is the value of l n e Superscript 4

Answers

Answer:

4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

the scale of a map is 1cm to 12km what is the distance on land if the length from town A to town B on the map is 15cm​

Answers

Answer:

180 km

Step-by-step explanation:

1 cm=12 km

15 cm=12×15=180 km

The formula for the lateral surface area of a cone—that’s the surface that isn’t the base—is π × r × sqrt(h² + r²); h is the height of the cone and r is the radius of its base. A circular #2 pencil is 6 mm in diameter, and a pencil sharpener creates a cone-shaped end that is 20 mm in height. Find the surface area of the sharpened part of the pencil.

Answers

Cool cool cool cool cool cool get yo

100 divided by 3.2 Thank u

Answers

Answer:

31.25

Step-by-step explanation:

125/4

= 31.25

For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).

-7x + 8, -12x + 12, -17x + 16, . . .

Possible anwers:
-5x + 4
5x + 4
-5x - 4
5x-4

Answers

Answer:

The first one is the answer.

Step-by-step explanation:

It's an arithmetic sequence. It has a common difference.

d = an - a_n-1

an = -12x + 12

a_n-1 = - 7x + 8

d = -12x + 12 - (-7x + 8)

d = -12x + 12 + 7x - 8

d = -5x + 4

Try  it. Let's try for the third term

-12x + 12 - 5x + 4

- 17x + 15 which is exactly what the third term is.

Between which two intergers does -3 7/8 lie?​

Answers

Answer:

Step-by-step explanation:

-4 and -3

Answer:

-4 and 3 because I tookt the test and the other guy was right too

Uma maneira de realizar a operação 9972 - 9 de forma rápida e correta é calculando 1 000 * 994, que é igual a 994 000. A igualdade que justifica esse fato está expressa em:

a) (a + b)² = a² + b² + 2ab
//
b) a² - b² = (a + b)(a - b)
//
c) a² - b² = (a - b)²
//
d) (a - b)² = a² - 2ab + b²
//
e) a² - b² = 1 000(a + b)

Answers

Answer:

a)

Step-by-step explanation:

Step by step solution please

Answers

Answer: A, C, D

Step-by-step explanation:

To find which logarith simplifies to 2, we first need to know how they work.

We now know that [tex]log_a(a^x)=x[/tex].

This tells us that only A, C, D would work.

[tex]8^2=64\\ \\6^2=36\\\\10^2=100[/tex]

Note: whenever you have a log that doesn;t specify the base, it is always 10, as shown in D.

Find the missing angles indicated by small letters in each of the diagram. ​

Answers

Answer:

a) X=75°

y= 105°

b) b= 120°

a=45°

d) r=75°

q=37°

p= 37°

e) y=100°

X= 143°

Step-by-step explanation:

soln no. a

here,

X+50+55=180(sum of all angle of triangle)

or, X= 180-105

or, X= 75°

again,

X+y = 180 (straight angle)

or, y= 180-75

or, y= 105°

soln no b

here,

b+60=180(straight angle)

or, b = 180 - 60

or, b = 120°

again,

a+60+75=180(sum of all angle of triangle)

or, a = 180- 135

or, a = 45°

soln no. d

here,

r=70°( alternate angle)

again,

73°+q+r=180( sum of all angle of triangle)

or,q=180-143

or,q=37°

again,

p=q=37(alternate angle)

soln no. e

y+80=180(straight angle)

or,y= 180-80

or, y = 100°

again,

63+80+<RMB=180(sum of all angles of triangle)

or, 143+<RMB=180

or, <RMB=180-143

or,<RMB= 37°

again,

X+ <RMB= 180(straight angle)

or,X= 180°-37°

or, X = 143°

Matching Functions
Directions: On the next page are (5) graphs, (5) equations, (5) tables, and (5) unique properties. They are out of
order. Your performance task is to match the equation, table, and property to the correct graph.

Answers

Answer:

Graph A → Equation A → Table B → Property D

Graph D → Equation B → Table A → Property B

Graph B → Equation C → Table C → Property E

Graph C → Equation D → Table E → Property A

Graph E → Equation E → Table D → Property C

Step-by-step explanation:

Graph A corresponds to equation A, x·y = 2, and Table B → Property D

xy = 2 has a vertical asymptote at x = 0, and a horizontal asymptote at y = 0

y = 2/x, when x = 0, y = ∞

Graph D corresponds to equation B, [tex]-\left | x\right |[/tex] + 1 which corresponds to table A → Property B

The domain extends from (-∞, ∞), and [1, -∞)

Graph B corresponds to equation C, -(x + 2)² which gives the values in Table C and Property E wich is a horizontal shift of 2 units left and a reflection across the x-axis

Graph C corresponds to equation D, (1/3)·x - 2, which gives the values on Table E and Property A

The y-intercept of (1/3)·x - 2 = (0, -2), and the x-intercept = (6, 0)

Graph E corresponds to equation E, x³ = y, which gives the values on Table D  Property C, y is x cubed

Suppose that 65% of the people who inquire about investments at a certain brokerage firm end up investing in stocks, 38% end up investing in bonds, and 36% end up investing in both stocks and bonds. What is the probability that a person who inquires about investments at this firm will invest in stocks or bonds (or both)?

Answers

Answer:

0.67 = 67% probability that a person who inquires about investments at this firm will invest in stocks or bonds (or both).

Step-by-step explanation:

This question is solved treating these probabilities as Venn events.

I am going to say that:

Event A: Person invests in stocks.

Event B: Person invests in bonds.

65% of the people who inquire about investments at a certain brokerage firm end up investing in stocks

This means that [tex]P(A) = 0.65[/tex]

38% end up investing in bonds

This means that [tex]P(B) = 0.38[/tex]

36% end up investing in both stocks and bonds.

This means that [tex]P(A \cap B) = 0.36[/tex]

What is the probability that a person who inquires about investments at this firm will invest in stocks or bonds (or both)?

This is [tex]P(A \cup B)[/tex], given by the following equation:

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]

Considering the values we have for this problem:

[tex]P(A \cup B) = 0.65 + 0.38 - 0.36 = 0.67[/tex]

0.67 = 67% probability that a person who inquires about investments at this firm will invest in stocks or bonds (or both).

Cos (x-[tex]\frac{5}{6}[/tex])=[tex]\frac{\sqrt{2} }{2}[/tex]

Answers

Answer:

Solution given;

Cos (x-[tex]\frac{5}{6}[/tex])=[tex]\frac{\sqrt{2} }{2}[/tex]

Cos (x-[tex]\frac{5}{6}[/tex])=Cos45°

equating corresponding value

(x-[tex]\frac{5}{6}[/tex])=45°

x=45°+5/6

x=45.83°

Instructions: Find the measure of the indicated angle to the nearest degree.
4
?
16

Answers

Answer:

Sinx=4/16=1/4

x=Sin^-1(1/4)

? =14.47°

OAmalOHopeO

The measure of the unknown angle is approximately 14°.

What are trigonometric ratios in terms of a right-angle triangle?

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjacent/hypotenuse and

tan = opposite/adjacent.

From, The given diagram, With respect to the reference unknown angle,

the opposite side is 4 units and the hypotenuse is 16 units.

We know, sin = opposite/hypotenuse.

Therefore, sinФ = 4/16.

sinФ = 1/4.

Ф = sin⁻¹(1/4).

Ф = 14°.

learn more about trig ratios here :

https://brainly.com/question/14977354

#SPJ7

can y’all help me out

Answers

Answer:

B: y = {-13, -5, 3, 15}

Step-by-step explanation:

Let's plug each x-value into this equation: f(x) = 4x + 3

Domain: {-4, -2, 0, 3}

First, let's start with -4:

f(x) = 4x + 3

y = 4x + 3

y = 4(-4) + 3

y = -16 + 3

y = -13

Next, let's do -2:

f(x) = 4x + 3

y = 4x + 3

y = 4(-2) + 3

y = -8 + 3

y = -5

After that, let's do 0:

f(x) = 4x + 3

y = 4x + 3

y = 4(0) + 3

y = 0 + 3

y = 3

Finally, let's do 3:

f(x) = 4x + 3

y = 4x + 3

y = 4(3) + 3

y = 12 + 3

y = 15

Now that we have all our y-values, let's set up the range:

Range (y-values): {-13, -5, 3, 15}

As you can see, the only answer choice that includes this range is B;

{-13, -5, 3, 15}.

Help: A marching band is rehearsing. 4/5 of the marching band members play percussion instruments. 4/6 of the percussionists play the snare drum. What fraction of all the band members play the snare drum.

Answers

Answer: 1.2/5 Marching band members play the snare drum.

Step-by-step explanation:

4/5 Band Members Play Percussion Instruments. (80%)

4/6 Play The Snare Drum. (66% of the 80%)

1/5 Band Members Do NOT play percussion. (20%)

80 - 66 = 14%

14 + 20 = 24%

1/5 = 20%

1.5/5 = 30%

1.2/5 = 24%

1.2/5 Marching band members play the snare drum.

Copy and complete the table.

Answers

Answer:

See pic below.

Step-by-step explanation:

Wich graph is the result of the reflection f(x) =1/4(8)^x across the y axis and then across the x- axis

Answers

Answer:

I assume that the function is:

[tex]f(x) = \frac{1}{4}*8^x[/tex]

Now let's describe the general transformations that we need to use in this problem.

Reflection across the x-axis:

For a general function f(x), a reflection across the x-axis is written as:

g(x) = -f(x)

Reflection across the y-axis:

For a general function f(x), a reflection across the y-axis is written as:

g(x) = f(-x)

Then a reflection across the y-axis, and then a reflection across the x-axis is just:

g(x) = -(f(-x)) = -f(-x)

In this case, we have:

[tex]f(x) = \frac{1}{4}*8^x[/tex]

then:

[tex]g(x) = -f(-x) = -\frac{1}{4}*8^{-x}[/tex]

Now we can graph this, to get the graph you can see below:

When (8x − 4) = 2x is solved, the result is:

Answers

Answer:

x = 1

General Formulas and Concepts:

Pre-Algebra

Distributive Property

Equality Properties

Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of Equality

Algebra I

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

Identify

1/2(8x - 4) = 2x

Step 2: Solve for x

[Distributive Property] Distribute 1/2:                                                              4x - 2 = 2x[Subtraction Property of Equality] Subtract 2x on both sides:                      2x - 2 = 0[Addition Property of Equality] Add 2 on both sides:                                    2x = 2[Division Property of Equality] Divide 2 on both sides:                                  x = 1

Answer:

x = 2/3

Step-by-step explanation:

(8x − 4) = 2x

8x - 4 = 2x

6x = 4

x = 2/3

I NEEDDD HELPPPP ASAPPPP ITS URGENTTT!!!!

Answers

Answer:

(x-6)^2+(y-14)^2=4

Step-by-step explanation:

Aman age is 2 times of his son's age after 5 years sum of their age will be 70 find their present age ​

Answers

Answer:

aman's son's age = 20

aman's age = 40

Step-by-step explanation:

let aman's son's age be x

aman's age = 2x

2x+5+x+5 = 70

3x+10=70

3x = 60

x = 20

2x = 40

If patient's current ledger balance is $238.00, the patient's fees for today are $117 and the patient paid $100.00 today, what is the patient's new balance:

Answers

Answer:

$138

but if the 117 was paid it would be $21

Step-by-step explanation:

The patient's new balance is $255

What is Algebra?

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given;

Patient's current ledger balance = $238.00

The patient's fees for today = $117

The patient paid $100.00 today

Now, balance including todays pay= $238.00+$117

=$355

Patient payed 100 so,

=355-100

=255

Therefore, the answer of this algebraic problem will be $255

More about the Algebra link is given below.

brainly.com/question/953809

#SPJ2

SEE QUESTION IN IMAGE

Answers

Answer:

48

Probability of dying on the birthday is:

1/365

Probability of not dying on the birthday is:

1 - 1/365 = 364/36549

Probability of blue-eyed boy is:

1/2*1/4 = 1/850

Total frequencies = 10

Frequency of 7 and greater is 4: 7, 8, 9, 10

Required probability:

4/10 = 2/5

Please help me with this

Answers

2x^2 -7x + 14 =0 is the standard form
Other Questions
Select the correct answer. If x- 12sqrt x +36 = 0 , what is the value of x? According to the interest parity condition, if the domestic interest rate is 12 percent and the foreign interest rate is 10 percent, then the expected _________ of the foreign currency must be _________ percent. Group of answer choices I miss the equation, point D. Devin volunteers at Big Pup Rescue. He is mixing up shampoo solution for the dog washing station. He needs 2 cups of shampoo concentrate for every 9 cups of water. Devin will use 36 cups of water.How much shampoo concentrate should Devin add to the water to make the shampoo solution? A participant missed several study visits and the research site staff becomes aware of a participant's death searching through public records. What is the most appropriate next course of action?A. Report this as a serious adverse event (SAE).B. Report this as an adverse event (AE).C. No action is required.D. Contact the Study Physician for instructions on next steps proving lines parallel!!! please help Days before a presidential election, a nationwide random sample of registered voters was taken. Based on this random sample, it was reported that "52% of registered voters plan on voting for Robert Smith with a margin of error of 3%." The margin of error was based on a 95% confidence level. Fill in the blanks to obtain a correct interpretation of this confidence interval. We are ___________ confident that the ___________ of registered voters ___________ planning on voting for Robert Smith is between ___________ and ___________. 5a + 18 < 27 pre algibra A minor bought an Ernie Banks baseball card from a baseball card store. The card was marked $12, and the inexperienced clerk who sold it did not know the store owner, who was gone at the time of the sale, meant it to be sold for $1,200. Can the owner get the card back because of the minors lack of capacity? Why? How did the church change from 1200 to 1450? What was its response to the growing power of monarchs? How great an influence did the Church have on secular events? Marwick Corporation issues 8%, 5-year bonds with a par value of $1,100,000 and semiannual interest payments. On the issue date, the annual market rate for these bonds is 6%.What is the bond's issue (selling) price, assuming the following Present Value factors:1n = i = Present value of an annuity Present value of 1 (Series of payments) (Single sum)5 8% 3.9927 0.680610 4% 8.1109 0.67565 6% 4.2124 0.747310 3% 8.5302 0.7441 Cars arrive at an automatic car wash system every 10 minutes on average. The cars inter-arrival times are exponentially distributed. Washing time for each is 6 minutes per car and is purely deterministic (i.e., the waiting line system is M/D/c). Assuming that the car wash has a single bay to serve the cars, what is the average number of cars waiting in line (L.)? -8z^{-2} Write the expression using only positive exponents. Assume no denominator equals zero. use the ratio of a 45-45-99 triangle to solve for the variables. Vail skied 2 km north, 2 km west, 1 km north, and 2 km west. How far was she from her starting point? pls help geometry! Surface area According to Newton's third law of physics, who would have strong muscles: a long-distance runner or a runner who jumps hurdles? 1. I . like tea.2. He . play football in the afternoon.3. You . go to bed at midnight.4. They.do the homework on weekends.5. The bus .arrive at 8.30 a.m.6. My brother .finish work at 8 p.m.7. Our friends . live in a big house.8. The cat . like me. Compare the ways in which cliques and gangs are alike. Find the number in which 4 has highest value.6050.48376834.25906986.04326748.9251