(08.07 MC)
A polynomial function is shown below:

f(x) = x3 − 3x2 − 4x + 12

Which graph best represents the function? (5 points)

(08.07 MC)A Polynomial Function Is Shown Below:f(x) = X3 3x2 4x + 12Which Graph Best Represents The Function?

Answers

Answer 1

Answer:

Graph A (first graph from top to bottom)

Step-by-step explanation:

Given [tex]f(x)=x^3-3x^2-4x+12[/tex], since the degree of the polynomial is 3, the function must be odd and will resemble the shown shape in the graphs. The degree of 3 indicates that there are 3 zeroes, whether distinct or non-distinct. Therefore, the graph must intersect the x-axis at these three points.

Factoring the polynomial:

[tex]f(x)=x^3-3x^2-4x+12,\\f(x)=(x+2)(x-2)(x-3),\\\begin{cases}x+2=0, x=-2\\x-2=0, x=2\\x-3=, x=3\end{cases}[/tex]

Thus, the three zeroes of this function are [tex]x=-2, x=2, x=3[/tex] and the graph must intersection the x-axis at these points. The y-intercept of any graph occurs when [tex]x=0[/tex]. Thus, the y-coordinate of the y-intercept is equal to [tex]y=0^3-3(0^2)-4(0)+12,\\y=12[/tex] and the y-intercept is (0, 12).

The graph that corresponds with this is graph A.


Related Questions

số 37 không có ước nào là số nguyên tố
nhận xét trên đúng hay sai ?

Answers

Chào Đứa bé!!

Được thôi, nếu vậy câu trả lời cho của bạn câu hỏi là có/thật

I hope it helps u!!

Just comment if u have any questions :-)

please help me and explain

Answers

Answer:

y = 2x + 1

Step-by-step explanation:

the line passes (0, 1) and (2, 5)

the slope = (5-1)/(2-0) = 4/2 = 2

the equation :

y - 1 = 2( x -0)

y-1 = 2x

=> y = 2x + 1

Describe, in your own words, what "convenience sampling" is. 1 point

Answers

Answer:

It is a type of non-probability sampling that involves the sample being drawn from that part of the population that is close at hand

Butch will miss an important TV program while taking his statistics exam, so he sets
both his VCRs to record it. The first one records 70% of the time, and the second one
records 60% of the time. What is the probability that he gets home after the exam and
finds? (We assume that events A and B are independent, so with P(A)=0.7 and
P(B) = 0.6 respectively.)
(a) No copies of his program?
(b) One copy of his program?

Answers

Answer:

b

Step-by-step explanation:

this because both VCSs were recording on the same time hence Butch will have two copies of record and the A vcr having an Extra of what B vcr will

please help me i will give brainlist to the correct answer​

Answers

Answer:

<ABC = 27

< BAC = 126

Step-by-step explanation:

<C = <B since it is an isosceles triangle.  We know this since AC - AB

<C = 27 so <ABC = 27

The sum of the angles of a triangle = 180

A + B+ C = 180

A + 27+27 = 180

A + 54 =180

A = 180-54

A =126

< BAC = 126

Pls solve this question:
it is about Square and square roots
if u answer, then I will mark you as brilliant
[tex]\sqrt{2.3} multiplied \sqrt{2.3[/tex]

Answers

Answer:

2.3

Step-by-step explanation:

if you mean √2.3×√2.3 then the answer is 2.3 because √2.3×√2.3= (√2.3)² and that square cuts the square root and what remains is 2.3 which is the answer.

a/c + b/c = a+b/c The answer is 2.3

Find the area of this regular polygon. Round to the nearest tenth. 8.8 ft

Answers

Answer:

I don't really know but I'm pretty sure u can fix it and answer this question

A sales analyst listed the probabilities of profits and losses in dollars for a certain company. Find the mean, µ for the probability distribution.

x P(x)
-500 0.076
-250 0.191
0 0.265
250 0.316
500 0.152

Answers

Answer:

The mean is [tex]\mu = 69.25[/tex]

Step-by-step explanation:

We are given the following distribution:

P(x = -500) = 0.076

P(x = -250) = 0.191

P(x = 0) = 0.265

P(x = 250) = 0.316

P(x = 500) = 0.152

Find the mean, µ for the probability distribution.

To find the mean, we multiply each outcome by its probability. So

[tex]\mu = -500*0.076 - 250*0.191 + 0*0.265 + 250*0.316 + 500*0.152 = 69.25[/tex]

The mean is [tex]\mu = 69.25[/tex]

Ricky is playing a racing game on PS5.
• He earns 20 points every 1 level he passes.
• He earns 24 points for every 15 laps.
• He drove 45 laps and passed 6 levels.
How many points did Ricky earn?

Answers

Answer:

192 points

Step-by-step explanation:

he earned 120 points for passing 6 levels and getting 20 points per level

he earned 72 points for racing 45 laps and getting 24 points per every 15 laps

There are 13 apples in a basket. 4 of these apples are green. The rest are red. what is the ratio?​

Answers

Answer:

9:4 4:13

Step-by-step explanation:

Answer:

a) 9:4  b) 13 : 9

Step-by-step explanation:

13 = total

4 = green

13-4   ( which Is 9) = red

Ratio of red apples to green apples?

9:4

RATIO of all apples to red

13: 9

Instructions: Find the area of the sector. Round your answer to the nearest tenth.
I’ll mark brainliest please help

Answers

Answer:

75.7m^2

Step-by-step explanation:

[tex] \frac{30}{360} \times \pi {r}^{2} \\ \frac{30}{360} \times \frac{22}{7} \times {17}^{2} \\ \frac{1}{12} \times \frac{22}{7} \times 289 \\ 75.6904761905 = 75.7[/tex]

-1/13-10/39 in lowest terms

Answers

Step-by-step explanation:

the answer is already as simplified as it could be

Over what interval is the function decreasing? f(x)=(3−x)^2 + 5

Answers

Answer: It decreases on the interval   (-infinity, 3)

This is the same as saying -infinity < x < 3, or simply x < 3

=============================================================

Work Shown:

f(x) = (3−x)^2 + 5

f(x) = (-x+3)^2 + 5

f(x) = (-1(x-3))^2 + 5

f(x) = (-1)^2*(x-3)^2 + 5

f(x) = 1(x-3)^2 + 5

The last equation is in the form y = a(x-h)^2 + k

We have a = 1, h = 3 and k = 5

The vertex is (h,k) = (3,5)

Since 'a' is positive, this means the function decreases on the left and increases on the right (forming a parabola that opens upward). See below.

So the function is decreasing when x < 3, which represents everything to the left of the vertex.

We can expand that out to -infinity < x < 3 which converts to the interval notation (-infinity, 3)

3x + 1 over 4y2

What is the value of the expression above when x = 3 and y = 4? You must show all work and calculations to receive full credit.

Answers

Answer:

5/32

Step-by-step explanation:

(3x+1)/4y^2

(3(3)+1)/[4(4)^2]

(3*3+1)/[4(4)(4)]

(9+1)/[4*16]

10/64

simplify

5/32

The value of the expression at x = 3 and y = 4 is  [tex]\frac{5}{32}[/tex]   .

Concept:Firstly we will convert the expression into numerical form.Then, we will substitute the value of x & y respectively in the expression and simplify it.

How to solve the given question?Converting the expression into numerical form.
∴ Let [tex]F(x,y) = \frac{3x+1}{4y^2}[/tex]
Substituting x = 3 and y = 4 in the given expression.
∴[tex]F(x = 3,y =4) = \frac{3(3)+1}{4(4)^2} = \frac{10}{64}[/tex]
∴ [tex]F(3,4) = \frac{5}{32}[/tex]

Thus, the value of the expression at x = 3 and y = 4 is  [tex]\frac{5}{32}[/tex]   .

Learn more about expressions here:

https://brainly.com/question/723406

#SPJ2

Match each inequality to the number line that represents its solution

Answers

Answer:

x - 51 [tex]\leq[/tex] 43

x - 99 [tex]\leq[/tex] -104

75 < 69 - x

150 + x ≤ 144

Step-by-step explanation:

HELP ME PLSSSS!!!
f(x) = x2 What is g(x)?

A. g(x) = 2x²
B. g(x)=1/2x2
C. g(x)=(1/2x)2
D. g(x)=1/4x2

Answers

Answer:

B. g(x)=1/2x2

Step-by-step explanation:

Function f(x):

[tex]f(x) = x^2[/tex]

At [tex]x = 2, y = f(2) = 2^2 = 4[/tex]

Function g:

Function g is a division of function f by a value. When [tex]x = 2, y = 2[/tex], that is, the value of f is divided by two, and thus, the correct answer is given by option b.

What base makes the equation below true?

Note: A number should be entered, not a word.

Answers

Answer:

4

Step-by-step explanation:

in base 4

21 = (2 * 4) + (1 * 1) = 9

help please step by step

Answers

Answer:

1. 33km

2. 1.2ft

3. 16in

4. 20.1ft

5. 7.2yd

6. 38mi

Step-by-step explanation:

1. 10+11+12=33km

2. 1/2(1.8+0.6)1=1.2ft

3. 5+5+3+3=16in

4. 4.1+2.7+5.4+7.9=20.1ft

5. 1.8+1.8+1.8+1.8=7.2yd

6. 12+7+12+7=38mi

what is the midpoint of the segment shown below? (3,5) (2,2)

Answers

(X, Y) = (5/2, 7/2)

Answer:

(5/2, 7/2)

Step-by-step explanation:

Use the midpoint formula to solve for the midpoint:

[tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\\\\(\frac{3+2}{2},\frac{5+2}{2})\\\\(\frac{5}{2},\frac{7}{2})[/tex]

ASAP PLEASE!!The table and the relative frequency histogram show the distribution of the number of tails and three coins are tossed. Find the probability P(T=3). write your answer as a fraction.

Answers

Given:

The table and the relative frequency histogram show the distribution of the number of tails and three coins are tossed.

To find:

The probability [tex]P(T=3)[/tex].

Solution:

In the given table T represents the number of tails.

From the given table it is clear that the value of probability is [tex]\dfrac{1}{8}[/tex] and [tex]T=3[/tex]. So,

[tex]P(T=3)=\dfrac{1}{8}[/tex]

Therefore, the probability [tex]P(T=3)[/tex] is equal to [tex]\dfrac{1}{8}[/tex].

5. In ALMN if mL = 48° and mZN = 24", then
O ALMN is an obtuse isosceles triangle
O ALMN is an acute scalene triangle
O ALMN is an obtuse scalene triangle
O ALMN is an acute right triangle
None of the above

Answers

9514 1404 393

Answer:

  (c)  ΔLMN is an obtuse scalene triangle

Step-by-step explanation:

The two given angles are different measures and total less than 90°. That means the third angle will be more than 90°, an obtuse angle. Since all of the angles are different, the triangle is scalene.

  ΔLMN is an obtuse scalene triangle

HW HELP ASAP PLZZZZZ

Answers

Answer:

3

Step-by-step explanation:

I think its 3 because when we add 2 to x the graphic must be continue two step to right

petrol and engine oil has to mix in the ratio 5 : 2 for a certain motorcycle how much engine oil is needed to mix with 10 litres of petrol ​

Answers

Answer:

Step-by-step explanation:

Set this up as a ratio of proportions of petrol : oil

[tex]\frac{p}{o}[/tex] and if the ratio of the mix has to be 5p to 2 oil then:

[tex]\frac{p}{o}:\frac{5}{2}[/tex]  We need to find how much oil, x, is needed to mix with 10 liters of petrol. Completing the proportion with that ratio gives us the problem in its entirety:

[tex]\frac{p}{o}:\frac{5}{2}=\frac{10}{x}[/tex] and cross multiply

5x = 20 so

x = 4 liters of oil are needed to mix with 10 liters of petrol.

|x+2|+4=11
A) x=5,-9

Answers

Answer:

the mod always gives positive answers

so the answer will be

Step-by-step explanation:

x+2+4=11

x+6=11

x=11-6

x=5

answer is x is 5

Answer:

x=5,9

Step-by-step explanation:

|x+2|+4=11

|x+2| = 7

next you get two answers by adding two or subtracting two. SO the right answer should be 5 and 9. A is wrong . I DONT SEE THE OTHER ANSWER CHOICES BUT THIS IS WHAT I GOT.

A square has an area of 81 cm2.
Find the perimeter of the square

Answers

Area = side²

=> 81cm² = side ²

=> √81cm² = side

=> 9cm = side

Perimeter = 4 × side

=> Perimeter = 4 × 9cm

=> Perimeter = 36cm

Step-by-step explanation:

[tex]here \: is \: your \: solution : - \\ \\ Given :- \\ \\ = > area \: of \: square \: = 81cm {}^{2} \\ \\ = > we \: need \: to \: find \: perimeter \\ \\ for \: this \: we \: have \: to \: find \: its \: side. \\ \\ = > area \: of \: square \: = side { }^{2} \\ \\ = > side {}^{2} = 81cm {}^{2} \\ \\ = > \: side \: = \sqrt{} 81cm \\ \\ = > side = \sqrt{9 \times 9} \\ \\ = > side \: = 9 \: cm \\ \\ now \: we \: can \: find \: (perimeter) \\ \\ = > perimeter \: of \: square \: = 4 \times side \\ \\ = > perimeter = (4 \times 9 )cm \\ \\ = > perimeter \: of \: square = 36cm \\ \\ HOPE \: IT \: HELPS \: (. ❛ ᴗ ❛.)[/tex]

increase 6800 by 12%

Answers

Answer:

Step-by-step explanation:

6,800, percentage increased by 12% (percent) of its value = 7,616  

20, percentage increased by 1,000% (percent) of its value = 220  

1,000,000, percentage increased by 0.49% (percent) of its value = 1,004,900

Answer:

7616

hope it helps

mark brainliest please

A delivery truck manager takes a sample of 25 delivery trucks and calculates the sample mean and sample standard deviation for the cost of operation. A 95% confidence interval for the population mean cost is constructed and found to be $253 to $320. He reasons that this interval contains the mean operating cost for the entire fleet of delivery trucks since the sample mean is contained in this interval.

Required:
a. Do you agree with his reasoning?
b. How would you interpret this confidence interval?
c. Is this an appropriate use of a confidence interval?
d. Concerning your answers to parts a through c, what assumptions did you make (if any)? Does the Central Limit Theorem apply? Why or why not?
e. How does this apply or could apply to your profession?

Answers

Answer:

a) No.

b) Lies between 253 and 320.

c) No.

d) Central limit theorem is not applicable here.

e) The process of estimation can always help us make the right prediction about future sales, demands, costs, profits, and so on based on the past data or any such data available and hence take the correct decision

Step-by-step explanation:

1) No I do not agree, it's just because the mean should be always within the confidence interval. in this case, the above statement doesn't satisfy the condition.  

2)The true mean values at 95% confidence interval lies between 253 and 320.  

3) No, because this is only used for the difference in mean. If there is a difference then the mean is different.  

4) Central limit theorem is not applicable here. Since the sample size is very small, it better to use t distribution rather which indicated normal data.  

in case the sample size is greater than 30, we can then apply the central limit theorem.

5) The process of estimation can always help us make the right prediction about future sales, demands, costs, profits, and so on based on the past data or any such data available and hence take the correct decision.

what is the product of -3y²(-4y³+y-9)​

Answers

Answer:

-3y²(-4y³+y-9)​

-9y(-63y-9)

567y-81y

4 8 6 y

Which term describes the ability to repay debt?
A
capacity
B.
creditworthiness
c. capability

Answers

Answer:

B. Creditworthiness

Step-by-step explanation:

❣️(◍•Jess bregoli•◍)❣️

#keep learning!!

Answer:

B

Step-by-step explanation:

In isosceles △HAM, m∡A =32°, . What is m∠H?

Answers

Answer:

This all I can do

Step-by-step explanation:

m∠F. 20 In the diagram below, LATE is an isosceles ... 32 In the diagram of JEA below, m∠JEA = 90 and m∠EAJ = 48. ... cylinder that has a height of 15 cm and a diameter of 12 cm? ... If m∠HAM = 12, what is m∠AMT ? 1) 12. 2) 78. 3) 84.

Other Questions
Please help i need a complete answer In your opinion can science and religion coexist? Religion is based on faith, science on reason/proof? Are they in conflict? Cite to be a religious story/idea that seems to be against science. 1017 A sequence starts at 300 and 40 is subtracted each timee.30026022001800...The sequence continues in the same way,What is the first number in the sequence which is less than zerol?[11] Need help ASAP What is the total distance the monkey has traveled when she completes her 10th swing? Question 1 of 20 What did Cassie do during her date with Mitchell on Day Three? Industrialized CitiesWhat is the purpose of this source?O to describe the challenges faced by those livingoutside of the citiesO to show similarities in the living conditions of thoseinside and outside of the citiesThe industrial cities were different from those founded inearlier times. The modern downtown was created, and itwas connected to outlying areas by streetcars andcommuter rails. Middle-class professionals found it easyto get from their homes outside the city to their jobs, andback home at the end of the day.Not everyone was fortunate enough to live outside thecity. Working-class immigrant families lived in thepoorest parts of the city in tenement buildings that lackedlight and fresh air. As urban areas became more crowded,they grew more unsafe and unsanitary. Epidemics ofdiseases such as cholera and yellow fever spread quickly.Fires, crime, and poverty were common.to contrast the different living conditions for themiddle and working classesto show the positive effects of urbanization for thosewho lived in industrialized citiesIntro It twice the difference of a number and gig add to 4 the result is 22 more than four time the number. Find the number.PLEASE HELP!!!!!!!!!!!!!!!!!will mark brainlist Find the area of the circle.452.16 ft237.68 ft21808.64 ft2113.04 ft2 What process allows a single cell to grow into a multi-cellular organism? A manufacturer of cell phone screens is concerned because 12 percent of the screens manufactured using a previous process were rejected at the final inspection and could not be sold. A new process is introduced that is intended to reduce the proportion of rejected screens. After the process has been in place for several months a random sample of 100 screens is selected and inspected. Of the 100 screens 6 are rejected. What are the appropriate hypotheses to investigate whether the new process reduces the population proportion of screens that will be rejected?A. H0:p=0.12Ha:p0.12 BC. H0:p=0.06Ha:p0.06 DE. H0:p=0.12Ha:p help,its very important :) help help help help help help where does reabsorbtion of glucose take place?glomerulusbowman's capsule2nd coiled tubule1st coiled tubule Why did World War I deeply affect American modernist writers? Select all that apply.Many of the writers were unsure who won the war.They witnessed a war that killed and injured millions.Writers weren't allowed to write anything during the war.The established sense of order and traditional powers collapsed Match the below mention gas law.____________ states that the volume of a gas is directly proportional to the temperature of the gas, while pressure and number Of moles are kept constant (V/T = constant). All temperatures must be in kelvins when used in gas law calculations. __________ states that the volume of the gas varies inversely to the pressure on the gas, while temperature and number of moles are kept constant (PV = constant). ____________ states that the volume of a gas is directly proportional to the number of moles of the gas, while pressure and temperature are kept constant (V/n constant). 1. Boyle's law 2. Charles's law 3. Avogadro's law There are on average 43 g of sugar and 355 mL can of soda please calculate the molarity of sugar in the can of soda the molar mass of sugar is 342.2 g/mol A box with mass 25.14 kg is sliding at rest from the top of the slope with height 13.30 mand slope angle 30 degree, suppose the coefficient of friction of the slope surface is0.25, find (neglect air resistance,take g=10 m/s^2)The friction force experienced by the box.00) The acceleration of the box along the slope.(1) The time T required for the object to reach the bottom of the slope from the slope top. Explain why, when a force is applied to a piece of steel, it does not break but justchanges its shape. 234910-1NS-6-7-8-9Which three statements correctly describe key features of the function graphed here? Bridgeport Company buys and sells securities expecting to make money on short-term price movements. Bridgeport purchased 150,000 shares of Intel common stock at $20 per share on December 1. On December 31, Intel common stock's market price was $23 per share. Select the appropriate adjusting journal entry on December 31, if any.a. Dr. Investment in Intel $450,000 Cr. Cash $450,000b. Dr. Investment in Intel $450,000 Cr. OCI $450,000c. No entry is needed.d. Dr. Investment in Intel $450,000 Cr. Net unrealized holding gains/losses - (P&L) $450,000 How do different species evolve overtime Which fraction equals the ratio of rise to run between the points (0, 0) and (6, 7)? A. B. C. D.