Which of the following represents the factorization of the trinomial below?
- 4x3 - 4x2 +24 x
O A. -4(x2-2)(x+3)
B. -4(x2 + 2)(x+3)
O C. -4x(x + 2)(x+3)
D. -4x(x - 2)(x+3)

Answers

Answer 1

Answer:

D. -4x(x - 2)(x+3)

Step-by-step explanation:

We are given the following trinomial:

[tex]-4x^3 - 4x^2 + 24x[/tex]

-4x is the common term, so:

[tex]-4x(\frac{-4x^3}{-4x} - \frac{4x^2}{-4x^3} + \frac{24x}{-4x}) = -4x(x^2+x-6)[/tex]

The second degree polynomial can also be factored, finding it's roots.

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]

[tex]\Delta = b^{2} - 4ac[/tex]

x² + x - 6

Quadratic equation with [tex]a = 1, b = 1, c = -6[/tex]

So

[tex]\Delta = 1^{2} - 4(1)(-6) = 25[/tex]

[tex]x_{1} = \frac{-1 + \sqrt{25}}{2} = 2[/tex]

[tex]x_{2} = \frac{-1 - \sqrt{25}}{2} = -3[/tex]

So

[tex]x^2 + x - 6 = (x - 2)(x - (-3)) = (x - 2)(x + 3)[/tex]

The complete factorization is:

[tex]-4x(x^2+x-6) = -4x(x - 2)(x + 3)[/tex]

Thus the correct answer is given by option d.


Related Questions

Please help it’s due today

Answers

Answer:

67 degrees

Step-by-step explanation:

23 + 90 = 113

180 - 113 = 67

What will be the value of median of a moderately asymmetrical distribution? If the mean and mode are 30 and 24 respectively.

Answers

The mean, the median and the mode are measures of central tendency, and they are related in some many ways, depending on the type of distribution.

The median of the moderately asymmetrical distribution is 26

The given parameters are:

[tex]Mean = 30[/tex]

[tex]Mode = 24[/tex]

For a moderately asymmetrical distribution, the mean, median and mode are related by the following equation:

[tex]Mode = 3 * Median - 2 * Mean[/tex]

Substitute known values

[tex]30= 3 * Median - 2 * 24[/tex]

[tex]30= 3 * Median - 48[/tex]

Collect like terms

[tex]3 * Median =30+ 48[/tex]

[tex]3 * Median =78[/tex]

Divide both sides by 3

[tex]Median =26[/tex]

Read more at:

https://brainly.com/question/15669207

find coordinate of a point on x axis which is at a distance of 5 units from (5,4)​

Answers

Step-by-step explanation:

Hi there!

Please see attached picture for your answer.

Hope it helps!

Need answers in 2 minutes ASAP

Answers

Undo multiplying by 3/5 by multiplying by the reciprocal or dividing by 3/5.
That would be my answer, although it kind of depends on what you are learning at the moment… hope this helps!

The table shows a set of conditional relative frequencies of drivers in a survey planning to buy a used vehicle next, based on how they obtained their current vehicle.

Which interpretation of the relative frequencies given is the most appropriate?

A. The greatest number of drivers who plan to buy used are those who leased their current vehicle.
B. The majority of drivers who will buy used next time bought their current vehicle used.
C. Of drivers who bought their current vehicle used, about 4 percent will buy new next time, almost 95 percent will buy used next time, and about 1 percent will lease next time.
D. Of drivers who bought new, 3.9 percent will buy used next time; of drivers who bought used, 94.8 percent will buy used again; of drivers who leased, 1.3 percent will buy used.

Answers

The majority of drivers who will buy used next time bought their current vehicle used. The correct option is B.

What are statistics?

Any affiliations, financing, or financial holdings that could be seen as influencing the review's objectivity to give rise to potential bias.

Such elements might consist of, but are not limited to, the following: Employment, professional associations, paid consulting, and participation in groups that support relevant causes.

The given table is:-

Current vehicle      Buy used

Bought new             0.039

Bought Used           0.948

Leased                     0.013

Total                         1.000

In the given table it is observed that the majority of drivers who will buy used next time bought their current vehicle used. The correct option is B.

To know more about statistics follow

https://brainly.com/question/28344445

#SPJ2

Find each question solutions.Please

Answers

Answer:

Dependent variable = Total daily cost

Independent variable = number of items manufactured

2500 ;

9750

Step-by-step explanation:

Given the cost function in. A manufacturing company :

C(x) = 7.25x + 2500 ; Where

C(x) = total daily cost

x = number of items manufactured

The Independent variable is the variable whose value causes a change in the measured variable, this is the number of items manufactured, and the variable which charges as the predictor variable charges is the dependent variable (Total daily cost).

2.)

C(0) ;

C(x) = 7.25x + 2500

Put x = 0

C(0) = 7.25(0) + 2500

Cost = 2500

This is the total daily cost even if no items are produced, this is probably the fixed cost of daily production.

3.)

C(1000)

C(x) = 7.25x + 2500

Put x = 1000

C(0) = 7.25(1000) + 2500

Cost = 7250 + 2500

Cost = 9750

This is the total cost including variable cost of producing 1000 items.

Compare 8/3 and 19/8.

Answers

Answer:

8/3 > 19/8

Step-by-step explanation:

Get a common denominator

8/3 *8/8 = 64/24

19/8 *3/3 =57/24

Comparing the numerators

64>57

8/3 > 19/8

A line passes through the point (12,-4) and is perpendicular to the line with the equation y=6x +3

Answers

Answer:

y= -(1/6)x -2

Step-by-step explanation:

We know:

y= mx +b is the general equation of the line

Was given:

y= 6x +3, has the slope m=6

Find the equation of the line

y= -(1/6)x + b, perpendicular lines have their slope negative reciprocal m=-1/6

Find the y-intercept that is b

for point (x=12, y= -4) the equation of our line becomes

-4 = -(1/6)(12) + b, multiply a fraction and a number  (a/b)*c = ab/c

-4 = -12/6 +b, simplify the fraction

-4 = -2 + b , add 2 to both sides

-4+2 = -2+2 +b , solve for b

-2 = b

The equation of the line that passes through the point (12,-4) and is perpendicular to the line with the equation y=6x +3 is :

y= -(1/6)x -2

What is the missing digit?
820,107
– 65□,084

167,023

Answers

3.

We can get this answer by subtracting the answer 167,023 from 820,107, we get 653,084.

Express 456782 to 2 significant figures

Answers

Answer:

the answer for this is 45*10^4

Brenna went to the mall with her mom. They started shopping at 4:47 P.M. First, they spent 26 minutes in the shoe store. Then they spent 1 hour and 13 minutes shopping for a dress for Brenna. Finally, they spent 1 hour and 2 minutes eating dinner at the food court. What time was it when Brenna and her mom finished eating dinner?

Answers

Brenna and her mom finished eating dinner at 7:28 PM

They started shopping at 4:47 PM, and spent 26 minutes in the shoe store.

4:47 + 26 = 5:13 PM

They spent another 1 hour and 13 minutes shopping for a dress.

5:13 + 1 hr 13 min = 6:26 PM

Finally, they spent 1 hour and 2 minutes eating dinner at the food court.

6:26 + 1 hr 2 min = 7:28 PM

Hope this helps :)

Find the area of each shaded region.

Answers

The answer in photo don't forget put heart ♥️

Mia wants to buy 3 notebooks for $1.29 each. What is the expression for the total cost?

Answers

Step-by-step explanation:

Mia want to buy 3 notebook for $1.29 each ,

then total cost =3×1.29

hence, 3×29

1\6+1/12+2/6=2+1+4/12

=7/12

solve 8x=5x+3 pls pls pls​

Answers

Answer:

x = 1

Step-by-step explanation:

8x = 5x + 3

Subtract 5x from both sides

8x - 5x = 5x - 5x + 3

Simplify

3x = 3

Divide both sides by 3

3x/3 = 3/3

Simplify

x = 1

Kane's Furniture Store advertised a table at ​9% discount. The original selling price was ​$109​, and the sale price was ​$100. Was the sale price consistent with the​ ad? Explain.

Answers

Answer:

No, the sale price wasn't consistent with the ad

Step-by-step explanation:

The original selling price is 109. 9% of 109 is 9.81. So the sale price should be 99.19.

The average of a group of data points is called the

Answers

Answer:

mean

Step-by-step explanation:

The mean of a data set is the sum of the values divided by the number of values. The median of a data set is the middle value when the values are written in numerical order. If a data set has an even number of values, the median is the mean of the two middle values.

Average mean..... I

domain of function y=|x|​

Answers

Answer:

All real number

Step-by-step explanation:

The graph of y = x is shown to the right. We can see that it is defined for all x-values because the line will continue to infinity. Thus, the domain of y = x is all real numbers.

Hope this help <3

solve: x^2-x-12÷x+5 ≥ 0

Answers

Answer:

Step-by-step explanation:

x3−x2+5x−12

x

≥0

Let's find the critical points of the inequality.

x3−x2+5x−12

x

=0

x3−x2+5x−12=0(Multiply both sides by x)

(Use cubic formula)

x=1.836169

Check possible critical points.

x=1.836169(Works in original equation)

Critical points:

x=1.836169(Makes both sides equal)

x=0(Makes left denominator equal to 0)

Check intervals in between critical points. (Test values in the intervals to see if they work.)

x<0(Works in original inequality)

0<x≤1.836169(Doesn't work in original inequality)

x≥1.836169(Works in original inequality)

Answer:

x<0 or x≥1.836169

PLease Help! I will give you the brainiest and a lot of points

A survey of 104 college students was taken to determine the musical styles they liked. Of​ those, 22 students listened to​ rock, 23 to​ classical, and 24 to jazz.​ Also, 10 students listened to rock and​ jazz, 8 to rock and​ classical, and 8 to classical and jazz.​ Finally, 6 students listened to all three musical styles. Construct a Venn diagram and determine the cardinality for each region. Use the completed Venn Diagram to answer the following questions.

a. How many listened to only rock​ music?
n​(only ​rock)

b. How many listened to classical and​ jazz, but not​ rock?
n​(classical and​ jazz, not ​rock)

c. How many listened to classical or​ jazz, but not​ rock?
n​(classical or​ jazz, not ​rock)

d. How many listened to music in exactly one of the musical​ styles?
n​(exactly one ​style)

e. How many listened to music in exactly two of the musical​ styles?
n​(exactly two ​styles)

f. How many did not listen to any of the musical​ styles?
n​(none)

Answers

Answer:

A. 22

B. 8

C. 23 + 24

D. 22 + 23 + 24

E. 8 + 8 + 10

F. 104 - (sum of all the given numbers) = 3

87.26+(-25.6)+(-5.4)

Answers

Answer:

= 87.26 + (-25.6) + (-5.4)

=87.26- 25.6 - 5.4

= 87.26 - 31

= 56.26

✌✌✌✌✌

An asset's book value is $43,200 on January 1, Year 6. The asset is being depreciated $600 per month using the straight-line
method. Assuming the asset is sold on July 1, Year 7 for $29,400, the company should record:

Answers

Assuming the asset is sold on July 1, Year 7 for $29,400, the company should record the asset's value as equal to $32,400.

The book value of the asset on January 1, Year 6 was $43,200.The asset is being depreciated at $600 per month using the straight-line method.The asset was sold on July 1, Year 7 for $29,400.The amount of time elapsed until the asset is sold is 18 months.The time elapsed can be considered as the "x-coordinate".The asset's value can be considered as the "y-coordinate".The rate of depreciation can be considered as the slope of the line.The equation formed from the given data is given below :(y-y1) = m(x-x1)y-43,200 = (-600)(18)y = 43,200-10,800y = 32,400

To learn more about equations, visit :

brainly.com/question/10413253

#SPJ1

solve for x please help (show work!)

Answers

Answer:

x = 1/2 or 0.5

Step-by-step explanation:

8(-2x + 1) = 0

Distribute the 8 by multiplying 8 by what's inside of the parenthesis (-2x and 1)

8 * -2x = -16x

8 * 1 = 8

We now have

-16x + 8 = 0

Subtract 8 from both sides

-16x + 8 - 8 = 0 - 8

-16x = -8

Divide both sides by -16

-16x/-16 = -8/-16

x = 1/2

G I V E N :

8( -2x + 1 ) = 0

S O L U T I O N :

8( -2x + 1 ) = 0

Simplify the left hand side

-16x + 8 = 0

Transposing -16x to the other side

8 = 16x

Cross multiplying we get

x = 8/16

x = ½

x = 0.5

Hence the value of x is 0.5 or ½

Please Help Polygons

Answers

Step-by-step explanation:

5.25....................

I need help with 4 x (7 - 3) please show your work

Answers

Answer: 16

Step-by-step explanation:

Take ( 7 - 3 ) and subtract 3 from 7, which gives you 4, then take 4 and multiply it by 4, ( 4x4 ) which gives you 16.

Answer:

16

Step-by-step explanation:

4 * (7 - 3)

Parentheses first

4*(4)

Then multiply

16

Find the missing side of the triangle

Answers

Answer:

approximately 12.7

Step-by-step explanation:

using phythagoras rule,

hyp²=opp²+ adj²

15²=x² + 8²

225=x² + 64

x²=225 - 64

x²= 161

x=12.7

OR

sin ø= 8/15

sin ø=0.53333333

ø=sin(inverse) of 0.53333333

ø=0.563⁰

therefore angle opposite 8 is 0.563

tan 0.563= 8/x

x tan 0.563=8

x= 8/tan 0.563

x= 12.7

Se o preço de 8 potes de nutella é 288 reais, qual e o preço se 5 potes de Nutella

Answers

Carrefour – R$ 18,99.
Dia – R$ 21,19.
Futurama – R$ 19,99.
Hirota – R$ 19,78.
Mambo – R$ 19,90.
Pão de Açúcar – R$ 20,90.
Pastorinho – R$ 19,90.
Sonda – R$ 19,99.

What is the
range of the function in the graph?

Answers

Answer:

Step-by-step explanation:

A resposta é a letra a

Which statements are true of functions? Check all that apply.

Answers

Where the rest of the question?

Answer:

All functions have a dependent variable.

All functions have an independent variable.

A horizontal line is an example of a functional relationship.

the sum of 2 numbers is 18 and there difference is 6

Answers

Answer:

The two numbers are 6 and 12.

Step-by-step explanation:

So, let's start off, with x+y = 18 and x-y = 6.

Algebraically, we can add the above two equation sets, and we find out that 2x = 24, so x = 12. And then, it says the other number must be 6.

You start with a number that when added to the second number you will get 18 and when you subtract the second number from the first you will get 6. The difference between the above two results is 12.

So that difference of 12 is twice the second number; that means the second number is 6. And then using either of the given pieces of information, you can find that the first number is 12.

------------------------------------------------------

In conclusion:

6 + 12 = 18

12 - 18 = 6

find laplace transform of t+t^2 +t^3

Answers

Recall that

[tex]L_s\left\{t^n\right\} = \dfrac{n!}{s^{n+1}}[/tex]

where [tex]L_s\left\{y(t)\}[/tex] is the Laplace transform of y(t) into the s-domain.

Then you have

[tex]L_s\left\{t+t^2+t^3\right\} = \dfrac{1!}{s^{1+1}} + \dfrac{2!}{s^{2+1}} + \dfrac{3!}{s^{3+1}} = \boxed{\dfrac1{s^2} + \dfrac2{s^3} + \dfrac6{s^4}}[/tex]

Other Questions
The mass of an empty crucible was 17.556g. The mass of the crucible and a hydrate was 21.018 g. The mass of the crucible and anhydrous salt (after heating) was 19.641g. A. Calculate the mass of water lost due to heating. B. Calculate the mass percentage of water. the ages of two students are in the ratio of 3:5,if the older is 40yrs. How old is the younger student Hola alguien me puede decir un nuevo final para la pelicula *el gato con botas*Porfavor. Great Green HeistHow does the author reveal the details of the Mid-day PDA Find the length of BC define briefly about kilogram You view tea and scones as perfect complements, and you prefer to consumer one cup of tea with one scone. Also, your indifference curves are plotted with tea on the vertical axis. If you presently have two cups of tea and one scone, what this the marginal rate of substitution (MRS) at this point Let V be the volume of the solid obtained by rotating about the y-axis the region bounded y = sqrt(25x) and y = x^2/25. Find V by slicing & find V by cylindrical shells. Which inequality is represented by the graph?Will give branilest What is the appropriate method? 40 POINTS Ill give brainlist On a coordinate plane, a curved line with a minimum value of (negative 2.5, negative 12) and a maximum value of (0, negative 3) crosses the x-axis at (negative 4, 0) and crosses the y-axis at (0, negative 3).Which statement is true about the graphed function?F(x) < 0 over the interval (, 4)F(x) < 0 over the interval (, 3)F(x) > 0 over the interval (, 3)F(x) > 0 over the interval (, 4) Find the area of sector TOP in (O using the given information. Leave youranswer in terms of .13. r = 5 m, m = 90 degrees Describe the effort of translating tringle abc to tringle a'b'c hi need help with correcting :)Write complete Spanish sentences expressing the affirmative or negative command, depending on if no is present. If no is present in the example, make the command negative. If there is not a no in the example, please form the command in the affirmative.11. no dormir ("o" to "ue" stem change) tarde (late): No te duermas. teachers message: this is not a reflexive verb. add tarde after the verb.13. ponerse la ropa: Ponte la ropa. teachers message: put the accent mark on verb that must be added when adding a reflexive pronoun to the command. answer for brainlyyyyyy PLSSS Total rs 5000 amount shared between sunil and raj in ratio 3:2 1. What do you think will happen if humans pay no heed towards conservation of soil?2. What contribution you will make to fulfill the vision of UAE leaders to achieve the goal of sustainability?Please answer, Urgently needed! Using the applet, explore the results for simulating a group of 30 people and noting whether there is a duplicated birthday (whether at least two people have a matching birthday). Run at least 40 trials. What is the relative frequency of trials that had at least two people with the same birthday The following are the ages (years) of 5 people in a room: 16, 25, 23, 12, 17 A person enters the room. The mean age of the 6 people is now 20. What is the age of the person who entered the room?