If f(x)=x^3-12x^2+35x-24f(x)=x 3 −12x 2 +35x−24 and f(8)=0f(8)=0, then find all of the zeros of f(x)f(x) algebraically.

Answers

Answer 1

Answer:

The zeros of f(x) are: (x - 1), (x - 3) and (x - 8)

Step-by-step explanation:

Given

[tex]f(x)=x^3-12x^2+35x-24[/tex]

[tex]f(8) = 0[/tex]

Required

Find all zeros of the f(x)

If [tex]f(8) = 0[/tex] then:

[tex]x = 8[/tex]

And [tex]x - 8[/tex] is a factor

Divide f(x) by x - 8

[tex]\frac{f(x)}{x - 8} = \frac{x^3-12x^2+35x-24}{x - 8}[/tex]

Expand the numerator

[tex]\frac{f(x)}{x - 8} = \frac{x^3 - 4x^2 -8x^2 + 3x + 32x - 24}{x - 8}[/tex]

Rewrite as:

[tex]\frac{f(x)}{x - 8} = \frac{x^3 - 4x^2 + 3x - 8x^2 +32x - 24}{x - 8}[/tex]

Factorize

[tex]\frac{f(x)}{x - 8} = \frac{(x^2 - 4x + 3)(x - 8)}{x - 8}[/tex]

Expand

[tex]\frac{f(x)}{x - 8} = \frac{(x^2 -x - 3x + 3)(x - 8)}{x - 8}[/tex]

Factorize

[tex]\frac{f(x)}{x - 8} = \frac{(x - 1)(x - 3)(x - 8)}{x - 8}[/tex]

[tex]\frac{f(x)}{x - 8} = (x - 1)(x - 3)[/tex]

Multiply both sides by x - 8

[tex]f(x) = (x - 1)(x - 3)(x - 8)[/tex]

Hence, the zeros of f(x) are: (x - 1), (x - 3) and (x - 8)


Related Questions

Dare to do this if you are geiness
Express 750×900as a product of it prime factors using exponents
Who did this get a follow and marked as brainliest​

Answers

Answer:

2^3 x 3^3 x 5^4

Step-by-step explanation:

750 x 900 = 675000

675000 = 2 x 2 x 2 x 3 x 3 x 3 x 5 x 5 x 5 x 5

Which in product of prime factors is = 2 to the power of 3 x 3 to the power of 3 x 5 to the power of 4

Find the unit rate for each Lean Cuisine Entree. Show your
work
Please show work worth 40 points

Answers

Answer: 60

Step-by-step explanation:10 x 6 = 60 ( Also, 6x6x6x6x6x6x6x6x6x6 = 60

convert the following decimals into rational numbers:
1.4325​

Answers

Answer

[tex]\frac{573}{400}[/tex]

step-by-step explanation:

[tex]\frac{1.4325}{1}[/tex] ×  [tex]\frac{10000}{10000}[/tex]  =  [tex]\frac{14325}{10000}[/tex]

Simplify

[tex]\frac{14325}{10000}[/tex] ÷[tex]\frac{25}{25}[/tex] = [tex]\frac{573}{400}[/tex]

If a triangle has side lengths of 28,45, and 50, is the triangle acute,obtuse,or right?

Answers

Answer:

Acute i think

Step-by-step explanation:

Answer:

acute

Step-by-step explanation:

plz help asap I'll mark brainliest!!!​

Answers

1280 bc if you multiply 320 by 4 that will be 1280
ANSWER

1280

EXPLINSTION

because

help plss thank you -
Which statement correctly describes the number 0.81382?
A.
The number is rational because it is a terminating decimal.
B.
The number is rational because it is a repeating, non-terminating decimal.
C.
The number is irrational because it is a non-repeating, non-terminating decimal.
D.
The number is irrational because it is a repeating decimal.

Answers

A is correct! Have a good day!

0.81382 is a rational number because it is a terminating decimal.

What is rational number?

A rational number is a number that is expressed as the ratio of two integers, where the denominator should not be equal to zero, and also whose behavior is known.

What is irrational number?

An irrational number is a type of real number which cannot be represented as a simple fraction and also whose behavior is not known.

According to the given question.

We have a number 0.81382

The above number is not repeating but terminating.

Therefore, we can say that the above number is rational because it is a terminating decimal.

Hence, 0.81382 is a rational number because it is a terminating decimal.

Find out more information about rational and irrational number here:

https://brainly.com/question/17450097

#SPJ2

Parallel Lines cut by a transversal

Answers

Answer:

110

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Set the two given equations equal to each other (alternate angles i think)

12x + 2 = 11x + 11

**simplify and pull x to one side**

x = 9

**now insert x=9 into one equation (I choose 12x+2**

12(9) + 2 = 108 + 2 =110

A

Please help me will give Brain

Answers

Answer: i BELIEVE YOUR ANSWER IS

.....  

B

Step-by-step explanation:

Arthur is organising his collection of dvds he has 135 altogether. The ratio of comedy films to action horror is 6 : 8 : 1

Answers

Answer: See explanation

Step-by-step explanation:

The number of comedy films will be:

= 6/(6+8+1) × 135

= 6/15 × 135

= 54 comedy films

The number of action films will be:

= 8/(6+8+1) × 135

= 8/15 × 135

= 72 action films

The number of horror films will be:

= 1/(6+8+1) × 135

= 1/15 × 135

= 9 horror films

Express 0.361 as a fraction
where the 6 and 1 is recurring

Answers

Answer:

179/495

Step-by-step explanation:

x = 0.3616161..........  ---------------(I)

Multiply by 1000

1000x = 361.616161......

Multiply (I) by 10

10x = 3.616161........

1000x = 361.6161......

    10x =      3.6161........   {Now subtract}

  990x=  358

         x = 358/990

 x = 179/495

Ian rode in a taxi to get to an airport. The total cost of his taxi ride was more than $12. Write and solve an inequality to find the possible distances, in miles, Ian could have traveled in the taxi. Show or explain how you got your answer.

Answers

Missing Part:

The initial fee for a taxi ride is $2.60.  Each mile traveled in a taxi costs an additional $2.50.

Answer:

[tex]2.60 + 2.50x > 12[/tex]

[tex]x >3.76[/tex]

Step-by-step explanation:

Given

[tex]Initial = 2.60[/tex]

[tex]Rate = 2.50[/tex] per mile

Required

Miles traveled for more than $12

First, we represent the given parameters as an equation.

Represent miles with x and cost with y

So:

[tex]y = Initial + Rate * x[/tex]

[tex]y = 2.60 + 2.50 * x[/tex]

[tex]y = 2.60 + 2.50 x[/tex]

In Ian case, the distance traveled is more than $12.

This is represented as:

[tex]2.60 + 2.50x > y[/tex]

Substitute 12 for y

[tex]2.60 + 2.50x > 12[/tex]

Make 2.50x the subject

[tex]2.50x > 12 - 2.60[/tex]

[tex]2.50x > 9.40[/tex]

Make x the subject

[tex]x >9.40/2.50[/tex]

[tex]x >3.76[/tex]

Solve for x. (Round to the nearest tenth)

Answers

Answer:

13.7

Step-by-step explanation:

fill the numbers in using pythagorean theory

[tex]a^{2} + b^{2} = c^{2}[/tex]

(the hypotenuse has to be [tex]c^{2}[/tex])

[tex]9.2^{2} + b^{2} = 16.5^{2}[/tex]

[tex]84.64 + b^{2} = 272.25[/tex]

[tex]b^{2} = 187.61[/tex]

(to get [tex]b[/tex] alone you have to find the square root of both sides)

[tex]b = 13.69707[/tex]

round that and you get

[tex]b = 13.7[/tex]!

Solve for X
[tex] \frac{3x - 2}{3x + 1} = 3[/tex]
help pls​

Answers

The answer is x = -5/6

And in decimal form it would be, -0.8333333

find the value (s) of the variables (s) in each parallelogram. ​

Answers

Step-by-step explanation:

As we can see it is a parallelogram so here the diagonals bisect so

6y + 1 = 4y + 9

6y - 4y = 9 - 1

2y = 8

y = 8 / 2

y = 4

2x - 5 =x + 7

2x + x = 7 + 5

3x = 12

x = 12 / 3

x = 4

Hope it will help :)

Can someone help me with this?
The possible answers are:

9.04
95.55
90.15
108.51
54.26

Thank you!!!

Answers

Answer:

108.51

Step-by-step explanation:

Please give me the correct answer.Only answer if you're very good at math.

What is the relationship between toppings and price?

A:Fornos charges one euro for every topping.

B:Fornos charges one euro for a plain slice, and one-half euro for each extra topping.

C:Fornos charges one and a half euros for each topping.

D:Fornos charges one-half for each topping. ​

Answers

Answer:

D

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

I need help ......................

Answers

Answer:

this is to hard

Step-by-step explanation:

7, 8 ,9 ,0 10

What is the volume of the prism?



Enter your answer, as a mixed number in simplest form, in the box.


cm³

The figure contains a right rectangular prism. The length of the prism is labeled 6 and one half centimeters, the width is labeled 2 and one half centimeters, and the height is labeled 2 and one half centimeters.

Answers

Answer:

40 [tex]\frac{5}{8}[/tex] [tex]cm^{3}[/tex]

Step-by-step explanation:

The figure is a rectangular prism, so the formula would be Volume = length x width x height.

length =  6 [tex]\frac{1}{2}[/tex] cm

width  =  2 [tex]\frac{1}{2}[/tex] cm

height  =  2 [tex]\frac{1}{2}[/tex] cm

If you plug everything you have in the problem into the volume equation, you would get : Volume = 6 [tex]\frac{1}{2}[/tex] cm x 2 [tex]\frac{1}{2}[/tex] cm x 2 [tex]\frac{1}{2}[/tex] cm.

Without a calculator, I would first turn the mixed numbers into improper fractions.

6 [tex]\frac{1}{2}[/tex]  = [tex]\frac{13}{2}[/tex]2 [tex]\frac{1}{2}[/tex] = [tex]\frac{5}{2}[/tex]

Volume = [tex]\frac{13}{2}[/tex] x  [tex]\frac{5}{2}[/tex] x  [tex]\frac{5}{2}[/tex]

When you multiply everything together you should get [tex]\frac{325}{8}[/tex].

As a mixed number, that would be 40 [tex]\frac{5}{8}[/tex] [tex]cm^{3}[/tex].

A father is 20 years older than his son. Five years ago,he was three times as old as his son was.Find their present ages​

Answers

Answer:

Dad=35, Son=15

Step-by-step explanation:

Well since the dad is 20 year older then the son we can call the son x and the dad x+20. Now five years ago the father was 3 times older then the so we construct the following equation:

x+20−5=3(x−5)

x+15=3x-15

x=15

So now we know that the sons age is 15 meanimg that since the dads 20 years older then him, his age is 20+15 which is 35!

The number of hot drinks sold in a café decreases as the weather becomes warmer. What type of correlation does this statement show?

Answers

It’s a bc its the only one that actually makes sense :0:00:

pleaseeee Answer! Will Mark as Brainliest for the Best Answer

Answers

p^4 s^5 y^-7 z^-1
................................

Answer:

[tex]p^{4} s^{5} y^{-7} z^{-1}[/tex]

Step-by-step explanation:

[tex]\frac{1}{y^{7} } = y^{-7}[/tex]

[tex]\frac{1}{z} = z^{-1}[/tex]

what should be added to
11/21 to make it
19/21

Answers

To find what needs to be added subtract the two numbers:

19/21 - 11/21 = 8/21

You need to add 8/21 to 11/21 to get 19/21

oof oof oof I need help again lol

Answers

Answer:

The first one is 0.6

The second one is -2.8

The third one is -3

Step-by-step explanation:

Have a nice day! :)

Answer all the four q

Answers

Answer:

MATHMATICS - MTHMTCS

SEPTEMBER - SPTMBR

ANCILLARY - NCLLR

PTERODACTYL-PTRDCTL

Hopefully this helps <3

The temperature at 5:00 am functions

Answers

Answer:

t2 =  37 °F

Step-by-step explanation:

t

1

=52

F

g=3

F/hr

triangle similarity i think ... picture included * SIN COS TAN

Answers

Answer:

d = 105tan(37°)

Step-by-step explanation:

opposite (o) = d

adjacent (a) = 105

Angle A = 90 - 53 = 37°

Therefore,

the correct equation would be

tan(A°) = opposite/adjacent

tan(37°) = d/105

d = 105tan(37°) ✅

d = 105 × 0.7535540501

d ≈ 79.12 units

______________

#IndonesianPride

- kexcvi

46−[38−{27−(15−13−2¯¯¯¯¯¯¯¯¯¯¯¯¯)}]
=

Answers

Answer:

46-38-27-15+13+2

=-17

6. Ria purchased a car for
$14,775. Sales tax in her
county is 6.8%.
a. What is the total price of
the car including tax?

b. If she puts $2,100 down,
how much will she be
financing?

c. What will her monthly
payment be if the term of
the loan is 72 months with
an APR of 3.5%?

Answers

9514 1404 393

Answer:

  a) $15,779.70

  b) $13,679.70

  c) $210.92

Step-by-step explanation:

a) When tax is added, the total cost is ...

  total = price × (1 +tax rate)

  total = $14,775 × 1.068 = $15,779.70

__

b) The amount financed is the difference between the total cost and the down payment.

  financed = total - down35

  financed = $15,779.70 -2100 = $13,679.70

__

c) The monthly payment is found using the amortization formula. It can also be found using any of a number of financial calculators, spreadsheets, or apps.

  A = P(r/12)/(1 -(1 +r/12)^-n) . . . . annual rate r, n monthly payments, principal P

  A = $13,679.70(0.035/12)/(1 -(1 +0.035/12)^-72) ≈ $210.92

6.5 ft 6 ft- 11 ft N 5 ft What is the surface area? A 258 square feet B 195 square feet C 228 square feet D 330 square feet​

Answers

Answer:

Step-by-step explanation:

area of base = 5×11 = 55 ft²

area of triangle = ½×5×6 = 15 ft²

area of rectangular face = 6.5×11 = 71.5 ft²

surface area = 55 + 2×15 + 2×71.5 = 228 ft²

Write a real life scenarlo that can be represented by the integer -55

Answers

Answer:

I deposit $500 in my bank from my check this week. I have to withdraw $550 from my bank to pay my medical bills. I am short -55/55 dollars so I wait to pay my medical bills.

I owe $60 to my school for damage on a school laptop. I only have $5 so I am 55 dollars short.

I withdraw $2,000 from my bank to deposit $1950 a week later. I want to deposit the same amount of money I put last week. I am short 55 dollars.

Step-by-step explanation:

I put different scenarios because I didn't know if any of them were good enough.

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