Which of the following is a polynomial function in standard form with zeros at 0, 2, and 4? f(x) = x(x + 2)(x + 4) f(x) = x(x – 2)(x – 4) f(x) = x3 – 6x2 + 8x f(x) = x3 + 6x2 + 8x

Answers

Answer 1

Answer:

f(x) = x^3 - 6x^2+8x

Step-by-step explanation:

Remember while you are studying polynomial functions that zeros are just the solutions (and are the x-intercepts on the graph).

The question said the zeros were 0, 2 and 4, so if you were solving the equation you would get:

x=0 and x=2 and x=4

Just "undo" that last step of solving and you get:

x = 0 and

x - 4 = 0 and

x - 2 = 0

These are the factors of the function and they do look just like the second option of answers on your question. But that is in factored form and they asked you for standard form.

so f(x)=x(x-2)(x-4) is almost there, but you need to multiply all the factors back together.

(x - 2)(x - 4)

use FOIL or distributive property or area model(box) method to multiply and get

x^2 - 6x + 8

Then multiply in the x using distributive property.

f(x) = x(x^2-6x+8)

f(x) = x^3 - 6x^2 + 8x

That's the final answer (the third choice of answers on your post.) I think of this as a "working backwards" problem because you start with solutions (zeros means solutions!) and work backwards to find factors, then the function.


Related Questions

Pls help I cant figure it out ;-;

Answers

Answer:

coke red

Step-by-step explanation:

correct me if im wrong

Ok so I even looked it up and it looked like it was coke so coke I guess

x^2 + 10x + 21 = 0

Solve for x using "Completing the Square"

Answers

Answer:

[tex]x=-7,-3[/tex]

Step-by-step explanation:

Completing the square means you are changing the polynomial so that it is a perfect square trinomial. Since the middle term is 10, we need the last term to be 25 since 5+5=10, thus, 5*5=25:

[tex]x^2+10x+21=0\\x^2+10x+21+4=0+4\\x^2+10x+25=4\\(x+5)^2=4\\x+5=\pm2\\x=-7,-3[/tex]

As you can see, because we change [tex]x^2+10x+21[/tex] to [tex]x^2+10x+25[/tex] by adding 4 to both sides, we were able to reduce it to [tex](x+5)^2[/tex], a perfect square, and solve the rest of the problem.

x= -3 & -7 to the quadratic equation!

Simplify the expression.
c^-6 d^4/c^-16 d^14

Answers

Answer:

[tex]\red{\frac{ {c}^{10}}{{d}^{10} } }[/tex]

Step-by-step explanation:

[tex] \huge \: \frac{ {c}^{ - 6} {d}^{4}}{ {c}^{ - 16} {d}^{14} } \\ \\ = \huge \: \frac{ {c}^{16 - 6}}{{d}^{14 - 4} } \\ \\ = \huge \: \red{\frac{ {c}^{10}}{{d}^{10} } }[/tex]

Which of the following sets of numbers could be the side lengths of a right triangle?

3, 4, and 7
9, 40, and 42
8, 15, and 16
20, 21, and 29

Answers

Answer:

9, 40, and 42

Step-by-step explanation:

Answer:

9, 40,and 42 is the answer

Step-by-step explanation:

9. Frigid Boards purchases one of its snowboards for $395 less a retail trade discount of 15% and a loyalty discount of 4%. Its markup on selling price percentage on all snowboards is 21%. At the end of the season, any leftover snowboards are marked down by 10%. What is the sale price for the snowboard?

Answers

The sale price for the snowboard after the trade and loyalty discount of 15% and 4% will be 351.01 dollars.

What is the percentage?

The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.

Frigid Boards purchases one of its snowboards for $395 less a retail trade discount of 15% and a loyalty discount of 4%. Then the price of the snowboards will be

⇒ $ 395 × 0.85 × 0.96

⇒ $ 322.32

Its markup on selling price percentage on all snowboards is 21%, then we have

⇒ $ 322.32 × 1.21

⇒ $ 390.01

At the end of the season, any leftover snowboards are marked down by 10%, then we have

⇒ $ 390.01 × 0.90

⇒ $ 351.01

More about the percentage link is given below.

https://brainly.com/question/8011401

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Brennan has been playing a game where he can create towns and help his empire expand. Each town he has allows him to create 1.15 times as many villagers as he had in the one before. The game gave Brennan 5 villagers to start with. Explain to Brennan how to create an equation to predict the number of villagers in any specific town. Then show how to use your equation to solve for the number of villagers he can create to live in the 15th town.

Answers

Answer:

Use the geometric sequence formula since you are multiplying each town's villagers by the amount your teacher gave you.

Step-by-step explanation:

Plug in the parts of the formula from the numbers given in the question, then you can calculate the number of villagers needed for the 15th town.

Answer:

35.375 Villagers Live in the 15th village

Step-by-step explanation:

Brennan can use the Geometric Sequence formula to predict the number of villagers in the 15th town.

(work attached)

please help me Find m< G

Answers

Answer:

70°

Step-by-step explanation:

All angles in a kite equal 360°.∠F≅∠H. 360-(90+90+110) will get you the answer.

A restaurant has a soup-and-salad lunch with the choices listed in the table below. A soup and a salad are selected at random.

What is the probability that tomato soup and a garden salad are selected?


A 1/6


B 1/5


C 1/3


D 5/6

Answers

Answer:

I think it is B) 1/5, but I am not sure.

use the equation f(x)=0.003x²-0.083x+2.514. Predict the value for x+20 years.
When x=20 years,f(x)=?

Answers

Answer:

2.054

Step-by-step explanation:

put the value of x in f(x)

The set of ordered pairs below is a relation. {(1, 5), (0, 2), (-1, -1), (-2, -4)} What is the range of the relation?

Answers

Answer:

{ - 4, - 1, 2, 5 }

Step-by-step explanation:

the range is the values of y from the ordered pairs in the relation

range = { - 4, - 1, 2, 5 }

In this picture, m∠XOZ = 77° and m∠YOZ = 40°. If m∠XOY = (5x + 16)°, what is the value of x?

A. 20.2
B. 37
C. 4.2
D. 2.1

PLSSSS HELP!!

Answers

Step-by-step explanation:

ang xoz = ang yoz + 5x+16

77 = 44 + 5x+16

77 = 5x+60

5x= 17

x= 3.4

which description represents the expression 5x - 9 ?

Answers

hello!

5x-9 means

9 less than the product of a number and 5

5 times x minus 9

the product of 5 and a number minus 9

note:-

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)

Given h of x equals 3 times the square root of x plus 2 end root, which of the following statements describes h(x)?

The function h(x) is increasing on the interval (–∞, –2).
The function h(x) is decreasing on the interval (2, ∞).
The function h(x) is decreasing on the interval (–∞, 2).
The function h(x) is increasing on the interval (–2, ∞).

Answers

Answer:

The function h(x) is increasing on the interval (-2, ∞)

Step-by-step explanation:

Given function:  [tex]h(x)=3 \sqrt{x+2}[/tex]

We cannot square root a negative number, therefore the domain (x-values) is restricted:

[tex]x+2\geq 0 \implies x\geq -2[/tex]

Therefore, [tex]h(x)\geq 0[/tex]

⇒ The function h(x) is increasing on the interval (-2, ∞)

Answer:

FLVS ANSWER D-  The function h(x) is increasing on the interval (–2, ∞).

Step-by-step explanation:

you dont need one

HELP!! What is the surface area of this figure?

Answers

Answer:

448 is the answer

Step-by-step explanation:

If u need complete solution do let me know

Answer:

448 yd^2.

Step-by-step explanation:

The surface area consists of 3 rectangles and 2 congruent triangles

= 12*11 + 2 * 10*11 + 2 * 1/2 * 12*8

= 132 + 220 + 96

= 448 yd^2.

Felix's kitchen table is round and has a radius of 3 feet. What is the tabletop's area?
use 3.14

Answers

Answer:

28.26 ft squared

Step-by-step explanation:

Area is pi*r^2

3.14*(3)^2

3.14*9

28.26

if sin = 3/5, than cos =

Answers

Answer:

cos θ = 4/5

Explanation given below in the image,

I hope my answer helps you.

If the annual interest rate 4%, how long does it tke for you investment of $10,000 to grow to $15,000

Answers

If the interest per quarter is 4% (but interest is only compounded annually), then it will take (72 / 4) = 18 quarters or 4.5 years to double the principal. If the population of a nation increases at the rate of 1% per month, it will double in 72 months, or six years. Hope this helps ! Have a good day! :)

Please help for brainliest :(

Given the figure below, find the values of x and z.

Answers

Answer:

Below in bold.

Step-by-step explanation:

z = 87 degrees ( vertical angles)

9x - 87 = 180 - z   ( adjacent angles are supplementary)

9x - 87 = 180 - 87  

9x = 180

x = 20 degrees.

To save money for his daughter's college tuition, Pablo invests $279 every quarter in an annuity that pays 6% interest, compounded quarterly. Payments will be made at the end of each quarter. Find the total value of the annuity in 22 years. Do not round any intermediate computations, and round your final answer to the nearest cent

Answers

[tex]~~~~~~~~~~~~\stackrel{\textit{payments at the end of the period}}{\textit{Future Value of an ordinary annuity}} \\\\ A=pymnt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right] \\\\\\ ~~~~~~ \begin{cases} A=\textit{accumulated amount}\\ pymnt=\textit{periodic payments}\dotfill &279\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &22 \end{cases}[/tex]

[tex]A=279 \left[ \cfrac{\left( 1+\frac{0.06}{4} \right)^{4 \cdot 22}-1}{\frac{0.06}{4}} \right]\implies A=279\left[\cfrac{1.015^{88}~~ - ~~1}{0.015} \right] \\\\[-0.35em] ~\dotfill\\\\ ~\hfill A\approx 50348.47~\hfill[/tex]

Find the value of y for the given value of x.

y=2−9x;x=2/3

Answers

Answer:

-4

Step-by-step explanation:

y=2-9×(2/3)=2-6= -4

Julia has 2 chemistry books and 3 math books. In her rush to get to class, she grabs two books without stopping to look. What is the probability that she pulls out a math book and a chemistry book?

Answers

Answer:

P(M &C) = 0.24

Step-by-step explanation:

Chemistry book will be denoted by C

Mathematics book will be denoted by M

5C2 = 10

There are 10 possible ways in which she can choose two books from the 5 books.

The probability of choosing a chemistry book:

P(C) = 2/5

The probability of choosing a mathematics book:

P(M) = 3/5

Probability of choosing a chemistry book and a mathematics book:

P(M &C) = (2/5) × (3/5)

P(M &C) = 0.24 or 24%

The probability that she pulls out a math book and a chemistry book will be 0.24.

What is mean by Probability?

The term probability refers to the likelihood of an event occurring

Given that;

Julia has 2 chemistry books and 3 math books.

Now,

Since, Julia has 2 chemistry books and 3 math books.

Hence, Total number of books = 2 + 3 = 5

So, The probability to choosing a chemistry book = 2/5

And, The probability to choosing a math book = 3/5

Thus, The probability that she pulls out a math book and a chemistry book is,

⇒ 2/5 × 3/5

⇒ 6/25

⇒ 0.24

Learn more about the probability visit:

https://brainly.com/question/13604758

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I NEED HELP ASAP!!!!!!!!
QUESTION BELOW

Answers

Answer:

Step-by-step explanation:

9. To stitch a shirt, 2 m 15 cm cloth is needed. Out of 40 m cloth, how many shirts can be stitched and how much cloth will remain? (Hint : convert data in cm.)​

Answers

Answer:

1 Shirt and 185cm remaining cloth

Step-by-step explanation:

2m and 15cm = 215cm

40m = 400cm

400/215=1.860465116

A shirt cant be in decimal so we remove the decimals, and take the as the answer. For the decimals, they are the remaining cloth.. to calculate the amount of remaining cloth we do:

1.860465116-1

=860465116

215*860465116=185cm

For the given equation, find the value of M when x=3. 2x+m=7

Answers

[tex]m = 1[/tex]

Step-by-step explanation:

[tex]2x + m = 7[/tex]

insert x=3 into the equation

[tex]2(3) + m = 7[/tex]

multiply

[tex]6 + m = 7[/tex]

subtract 6 on both sides

[tex]6 - 6 + m = 7 - 6[/tex]

[tex]m = 7 - 6[/tex]

simplify

[tex]m = 1[/tex]

Kurtis is watching a movie. The movie lasts 280 min. Kurtis has watched 30% of the movie so far. How many minutes of the movie has Kurtis watched? Show your Work.

Answers

Answer:

ok so this is just multiplycation

30% is also 0.3 so

280*0.3=84

84 minutes or

1 hour 24 minutes

Hope This Helps!!!

Answer: 23810645.03820431-24

Step-by-step explanation:

Used my brain :)

evelyn invests $3200.00 in an account for 9 months at a 5% annual interest rate, what is evelyns total amount in her account at the end of the term?

Answers

Answer:

3320

Step-by-step explanation:

So, 9 months is 9/12 of a year which is 3/4.

Each month they get 5/12% of their total money, so 9x5/12=3.75%.

3320

v(x)=x^2-25
————-
2x^2+13x+15

Describe the domain in complete sentences.

Write the domain in inequality notation.

Answers

Answer:

  -∞ < x < -5 ∪ -5 < x < -3/2 ∪ -3/2 < x < ∞

Step-by-step explanation:

The domain of any polynomial is "all real numbers." The domain of any rational function excludes any values of the variable that result in the denominator being 0. The function is "undefined" there.

__

  [tex]v(x)=\dfrac{x^2-25}{2x^2+13x+15}=\dfrac{(x+5)(x-5)}{(x+5)(2x+3)}\qquad x\notin \{-5,-\dfrac{3}{2}\}[/tex]

The values x=-5 and x=-3/2 make the denominator of v(x) become 0, so those values are excluded from the domain of v(x). The function is "undefined" when its denominator is zero.

  -∞ < x < -5 ∪ -5 < x < -3/2 ∪ -3/2 < x < ∞

_____

Additional comment

The numerator and denominator factors (x+5) cancel each other, so there is no vertical asymptote at x=-5. Rather, the function has a "hole" there, where it is undefined. The limit as the function approaches x=-5 from either direction is v(x) = 10/7.

what is the diameter of a circle with a circumference of 84.78 inches?use 3.14 for pi,show your work please

Answers

Answer:

27 inches

Step-by-step explanation:

the formula for the circumference is 2 × pi × r

so: 2 × pi × r = 84.78

so 84.78/2pi = r

r = 13.5

we want the diameter which is 2 x r

so the diameter is 27

What is the surface area of this figure?

Enter your answer in the box.

ft²

Answers

786 ft^2. Is the surface area

Two gears are connected and rotating at the same time. The smaller gear completes 2 1/2 rotations every time the larger gear completes 1/4 of a rotation.


How many rotations does the smaller gear complete when the larger gear completes 1 rotation?


A.1/10

B. 5/8

C. 5

D. 10

Answers

The small does 2 1/2 for 1/4 of the large. Multiply by 4 to get a full rotation of the large one:


2 1/2 x 4 = 10


answer: D. 10

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