50 points hlep Explain how to graph a polynomial function in factored form. What do the factors mean in terms of the polynomial? Graph f(x)=(x−2)^2 (x+1) (x−4)

Answers

Answer 1

Answer:

Given function: [tex]f(x)=(x-2)^2 (x+1) (x-4)[/tex]

The factors give us the zeros (x-intercepts) of the graph.

To find the zeros, set the function to zero and solve for x:

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

Therefore,

[tex](x-2)^2=0\implies x-2=0 \implies x=2[/tex]

[tex](x+1)=0\implies x=-1[/tex]

[tex](x-4)=0 \implies x=4[/tex]

So the zeros are at (2, 0)  (-1, 0) and (4, 0)

The multiplicity of a zero is the number of times the factor appears in the fully factored form of the polynomial, i.e. the exponent on the corresponding factor.

[tex]x = 2[/tex] has a multiplicity of 2[tex]x=-1[/tex] has a multiplicity of 1[tex]x=4[/tex] has a multiplicity of 1

If the zero has an even multiplicity, the graph touches and bounces off the x-axis at that point.

If the zero has an odd multiplicity, the graph crosses the x-axis at that point.

To find the y-intercept, expand the function:

[tex]f(x)=x^4-7x^3+12x^2+4x-16[/tex]

Set [tex]x = 0[/tex] and solve:

[tex]f(0)=(0)^4-7(0)^3+12(0)^2+4(0)-16=-16[/tex]

Therefore, the y-intercept is at (0, -16)

The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.

As the leading degree is 4 (even) and the leading coefficient is positive, the end behavior of the function is:

[tex]f(x) \rightarrow + \infty \textsf{ as } x \rightarrow - \infty[/tex]

[tex]f(x) \rightarrow + \infty \textsf{ as } x \rightarrow + \infty[/tex]

50 Points Hlep Explain How To Graph A Polynomial Function In Factored Form. What Do The Factors Mean

Related Questions

the selling price of a product is $20 and the markup is $4 What percentage of the selling price does the markup represent

Answers

Answer:

20%

Step-by-step explanation:

The ratio of 20 to 4 can be simplified to 5:1, by switching it around, we get 1/5. 1/5 as a percentage can be expressed as 20%

Answer:

20%

Step-by-step explanation:

Given the following question:

20% of 20

To find the answer we will use the formula to calculate percentages.

[tex]\frac{p\times n}{100}[/tex]
[tex]\frac{20\times20}{100}[/tex]
[tex]20\times20=400[/tex]
[tex]400\div100=4[/tex]
[tex]=4[/tex]

20% of 20 is 4, which means your answer is "20%."

Hope this helps.

Let f(x) = logx

What is the average rate of change of f(x) from 4 to 6?

Round to the nearest hundredth.

(a.) 0.09
(b.) 0.18
(c.) 0.20
(d.) 0.41

Answers

(a.) 0.09

equation:

f(x) = log(x)

rate of change:

[tex]\sf \rightarrow \sf \dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\sf \rightarrow \sf \dfrac{log(4) -log(6)}{4-6}[/tex]

[tex]\sf \rightarrow 0.088[/tex]

[tex]\sf \rightarrow 0.09[/tex]

Answer:

[tex]A.\: 0.09[/tex]

Step-by-step explanation:

Rate of Change is: [tex]\frac{y{_1-y{_2} } }{x_2-x_1}[/tex]

[tex]\frac{log(4)-log (6)}{4-6}[/tex]

[tex]0.088[/tex]

[tex]0.09[/tex]

The mass of a carbon-12 atom is 1.99\times 10^{-23}1.99×10

−23

grams. The mass of a neutron is 1.68\times 10^{-24}1.68×10

−24

grams. How many times greater is the mass of a carbon-12 atom than the mass of a neutron? Write your answer in standard notation, rounding to the nearest tenth.

Answers

Answer:

If the mass of one electron is 9.11 x 10-28 g, and you are looking for the mass of a mole of electrons, you need to understand Avogadro's number.  One mole is 6.02 x 1023 particles.  So you will have to multiply (6.02 x 1023) x (9.11 x 10-28 g) to get your answer of  5.48 x 10-4 grams (answer rounded to significant figures)

Step-by-step explanation:

1.2 x 10¹ times  greater is the mass of a carbon-12 atom than the mass of a neutron

What is Division?

A division is a process of splitting a specific amount into equal parts.

To find the ratio of the mass of a carbon-12 atom to the mass of a neutron, we can divide the mass of carbon-12 by the mass of a neutron:

(1.99×10⁻²³ grams) / (1.68×10⁻²⁴ grams)

= 11.8 grams

This means the mass of a carbon-12 atom is 11.8 times greater than the mass of a neutron. Written in standard notation and rounded to the nearest tenth, the answer is 1.2 x 10¹

Hence, 1.2 x 10¹ times  greater is the mass of a carbon-12 atom than the mass of a neutron

To learn more on Division click:

https://brainly.com/question/21416852

#SPJ2

A hall is thrown straight up, from 3 m above the ground, with a velocity of 14m/s. When does it hit the ground? Use the vertical motion formula.

Answers

In this question, to find the total height first, we must also take into consideration the acceleration due to gravity as well. To find the distance by which acceleration due to gravity pulls the ball down must know the Initial velocity.

In the answer key, it says that gravity changes the ball's height by a distance of -5t^2

Is initial velocity in this question 0 or 14m/s? Because if it is 14, then gravity should change the balls position by -(14+5t^2), not -5t^2, because if I remember correctly, the formula for finding distance is vt(initial velocity)+(1/2)at^2 ,and not just (1/2)at^2

A triangular prism with 5 faces.

A triangular prism has faces.

Answers

Answer:

Pentahedron

Step-by-step explanation:

A triangular prism with 5 faces is called Pentahedron.

It has 5 faces,  6 vertices and 9 edges.

5 faces -  Two are triangular faces and three are rectangular faces.

Answer:

its has 5 faces

Step-by-step explanation:

Find the value of xxx, yyy, and zzz in the parallelogram below.

Answers

Answer:

Step-by-step explanation:

Opposite angles of a parallelogram are congruent, so:

[tex]112=y-9 \longrightarrow y=121[/tex]

and adjacent angles are supplementary, so:

[tex]112+x+1=112+z+3=180 \longrightarrow x=67, z=65[/tex]

Which of the following would be appropriate to measure in centimeters

Answers

Answer:

c

Step-by-step explanation:

Factor 48e+180 using greatest common factor

Answers

12

48 = 24 × 31

180 = 22 × 32 × 51

please help me with this

Answers

Answer:

y-5=3/4(x-6)

Step-by-step explanation:

The picture you posted is a bit unclear and difficult to look at, but that's alright.

This is a simple question if you understand that the point slope for equation is: y-y1 = m(x-x1).

m is the slope and (x1,y1) is a point on the graph.

So, if you input the point (6,5) on the graph, it works.

You can double check with the other equations to see that they are all wrong!

Please help asap! I will gave brainlest!

Answers

Answer:

√2 + √6 / 4

Step-by-step explanation:

We know cos(-θ) = cosθ.

Therefore, cos(-15°) = cos15°.

cos15° = cos(45 - 30)

cos15° = cos45cos30 + sin45sin30cos15° = (1/√2)(1/2) + (1/√2)(√3/2)cos15° = 1/2√2 + √3/2√2cos15° = √3 + 1 / 2√2cos15° = (√3 + 1)(√2) / 4cos15° = √2 + √6 / 4Option 1

Do you know the tricks to multiplying variables?

Answers

Answer:

yes I know how to to multiple variables.

Two similar solid cones have their radii 15cm and 25cm respectively, if the volume of the bigger cone is 325cm³. Calculate (a) the linear scale factor (b) the volume scale factor (c) volume of the smaller cone​

Answers

Answer:

The length scale factor = \(\frac{24}{6} = 4\)

The area scale factor = \(4^2 = 16\)

\[\text{Larger area} = 16 \times \text{smaller area}\]

\[50.3 \times 16 = 804.8\]

The area of the large clock face is approximately 804.8 cm2.

Step-by-step explanation:

The length scale factor = \(\frac{24}{6} = 4\)

The area scale factor = \(4^2 = 16\)

\[\text{Larger area} = 16 \times \text{smaller area}\]

\[50.3 \times 16 = 804.8\]

The area of the large clock face is approximately 804.8 cm2.

Answer:

a) the linear scale factor = 5/3

b) the volume scale factor = 125/27

c) 70.2 cm³

Step-by-step explanation:

r₁ = 15 cm, r₂ = 25 cm

r₂/r₁ = 25/15 = 5/3

They are similar, so h₂/h₁ = 5/3

a) the linear scale factor = 5/3

b) the volume scale factor = (5/3)³ = 125/27

c) V₂/V₁ = 125/27

Given V₂ = 325 cm³, V₁ = 325*27/125 = 70.2 cm³

Need help not sure if I got this right???????????

Answers

Yes it is right. Thats how you do that probably band skip school and ya get your class code for your the wym was your class code class starts tomorrow morning so I gotta get to


2. Get the difference between 7 and the sum of 1.0006 and 4.06.
3

Answers

Given:

The difference between 7 and the sum of 1.0006 and 4.06.

To find:

The mathematical expression for given statement and it value.

Solution:

Sum of 1.0006 and 4.06 = [tex](1.0006+4.06)[/tex]

The expression for the difference between 7 and the sum of 1.0006 and 4.06 is

[tex]7-(1.0006+4.06)[/tex]

On simplification, we get

[tex]7-(1.0006+4.06)=7-5.0606[/tex]

[tex]7-(1.0006+4.06)=1.9394[/tex]

Therefore, the difference between 7 and the sum of 1.0006 and 4.06 is 1.9394.

You buy cheese in 1lb bags. Your receipt for burritos requires 0.7 ounces of cheese per serving. How many servings can you make

Answers

Answer:

Step-by-step explanation:

(5,-5) (6,-6) (7,-7) (8,-8) what is the slope

Answers

The correct answer it’s 1

Answer:

i think its straight line

A flower bed is in the shape of a triangle with one side twice the length of the shortest side and the third side is 29 feet more
than the length of the shortest side. Find the dimensions if the perimeter is 141 feet.
What is the length of the shortest side?
The length of the shortest side is
(1)
What is the length of the second side?
The length of the second side is
(2)
What is the length of the third side?
The length of the third side is
(3)

Answers

Answer:

Step-by-step explanation:

8y8yy89y99u98u89y7t8y7i6u7i9jo

Use the volume formula to find the volume of the prism.




A. 21 cubic units B. 42 cubic units C. 27 cubic units D. 9 cubic units

Answers

Answer:

D Because

Step-by-step explanation:

1/2 +1/2 is 1 so 1+1+3+4 is 9

HOPE THIS HELP! :)

maths I need help asap it's about sequence and functions good rewards!​

Answers

Answer:

a₄ = 50

Step-by-step explanation:

work back from the seventh term a₇ using the reverse of the term to term rule , that is

divide by 2 then subtract 3

a₇ = 442

a₆ = 442 ÷ 2 - 3 = 221 - 3 = 218

a₅ = 218 ÷ 2 - 3 = 109 - 3 = 106

a₄ = 106 ÷ 2 - 3 = 53 - 3 = 50

Answer:

[tex]a_{4}=50[/tex]

Step-by-step explanation:

[tex]a_{4} = 50[/tex]

a₇ = 442

a₆ = 442 ÷ 2 - 3 = 221 - 3 = 218

a₅ = 218 ÷ 2 - 3 = 109 - 3 = 106

a₄ = 106 ÷ 2 - 3 = 53 - 3 = 50

Each batch of cookies is 8.9 oz. What is the weight of 2.5 batches of cookies

Answers

Answer:22.25 oz

Step-by-step explanation:

1 batch of cookies = 8.9 oz

2.5 batches of cookies = x oz

cross multiply

1x=8.9(2.5)

x=22.25 oz

For a project in his Geometry class, Elijah uses a mirror on the ground to measure the height of his school building. He walks a distance of 8.25 meters from the school, then places a mirror on flat on the ground, marked with an X at the center. He then steps 0.8 meters to the other side of the mirror, until he can see the top of the school clearly marked in the X. His partner measures the distance from his eyes to the ground to be 1.45 meters. How tall is the school? Round your answer to the nearest hundredth of a meter.

Answers

The school is about 14.95 meters tall, and the mirror is 8.25 meters from the school.

What is trigonometric ratio?

Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.

Let Ф represent the angle Elijah makes with the ground, hence:

tanФ = 1.45/0.8

Ф = 61.11°

The angle of elevation to the building is 61.11°. Let h represent the height of the building.

tan(61.11°) = h/8.25

h = 14.95

The school is about 14.95 meters tall, and the mirror is 8.25 meters from the school.

Find out more on trigonometric ratio at: https://brainly.com/question/24349828

What is the value of the expression?

(7 2/3−4 8/9)+(5 2/3−2 1/2)

Enter your answer as a mixed number in simplest form by filling in the boxes.

Answers

Answer:

  5 17/18

Step-by-step explanation:

Your calculator can help with this.

__

The integer parts of the mixed numbers can be dealt with separately. The fractional parts are added and subtracted using a common denominator. Here, that denominator is the least common multiple (LCM) of 2, 3, and 9, so is 18.

  ((7 2/3) -(4 8/9)) +((5 2/3)) -(2 1/2))

  = (7 2/3) +(5 2/3) -((4 8/9) +(2 1/2))

  = 12 4/3 -(6 +8/9 +1/2)

  = 13 6/18 -(6 +16/18 +9/18)

  = 13 6/18 -(6 +25/18) = 13 6/18 -(7 7/18)

  = (13 -7) +(6/18 -7/18)

  = 6 -1/18

  = 5 17/18

__

Additional comment

Doing the math in the manner shown above means you can mostly do it without a calculator. If you like, you can convert all of the numbers to improper fractions, then add those. This often requires a calculator.

  = (138/18 -88/18) +(102/18 -45/18)

  = 50/18 +57/18

  = 107/18 = 5 17/18

Question: In the expression: 4x-5+6x-8

a: Identify the third term (options listed)
- (-6x)
- (-5)
- (6x)
- (-8)

b: is it a constant or a variable term?

c: what is the coefficient? (options listed)
- (6)
- (-6)
- (8)

d: simplified (options listed)
- (10x-3)
- (-1x-2)
- (10x-13)​

Answers

Answer:

a -(-6x)

b variay term

c-(-6)

d no answer

The speed of a tidal wave, s, in hundreds of miles per hour can be modeled by the equation, [tex]s=\sqrt{t} -2t+6[/tex] , where t represents the time from its origin in hours. The graph of the tidal wave is shown.

Answers

Using it's concept, it is found that the domain of the function regarding the speed of the tidal wave is explained by:

[0, 4]: relating to the time of the tidal wave from it's origin in hours, restricted by the inability for the speed to be lees than zero.

What is the domain of a function?

It is the set that contains all possible input values for the function. In a graph, it is given by the x-values, that is, the horizontal axis values.

In this graph, the horizontal axis assumes values between 0 and 4, which is the time after the wave, and considering that the wave cannot be less than zero. Hence, the correct option is:

[0, 4]: relating to the time of the tidal wave from it's origin in hours, restricted by the inability for the speed to be lees than zero.

More can be learned about the domain of a function at https://brainly.com/question/25897115

In which number is the digit 5 one hundred times larger than it is in the number 253

Answers

Answer:

The 5 would be in the Thousands place

Step-by-step explanation:

Hope this helps any

QUESTION 1
The general term of the sequence is given by Tn= an + bn + c T2-T1 = 4; T3; -T2 = 6; T4-T3 = 8 and T2 = 6

1.1 Calculate a, b and c ​

Answers

Answer:

The general term of the sequence is given by

T

n

=

a

n

2

+

b

n

+

c

The general term of the sequence is given by

T

n

=

a

n

2

+

b

n

+

c

Calculate a,b and c

Determine the 12th term of the sequence.

grade12 general-term sequence series

Share your questions and answers with your friends.

answer comment

1 Answer

0

0

T3 - 6=6

T3=12

then T2-T1=4

6-T1=4

T1=2

T4-T3=8

T4-12=8

T4=20

Therefore terms= 2,6,12,20

1st difference= 4,6,8

2nd difference= 2,2,....

2a=2

a=1

3a+b=4

3(1) + b=4

b= 1

a+b+c= 2

c= 2-1- 1= 0

giving Tn= n^2 + n

T12 = 12^2 + 12 = 156

A triangular pane of glass has a height of 44 inches and an area of 440 square inches. What is the length of the base of the pane?

Answers

Answer:

  20 inches

Step-by-step explanation:

The base, height, and area of a triangle are related by the formula ...

  A = 1/2bh

If you know two of these, you can use this formula to find the third.

  440 in² = 1/2b(44 in)

  (440 in²)/(22 in) = b = 20 in . . . . . . divide by the coefficient of b

The length of the base is 20 inches.

The following histogram shows the relative frequencies of the hieight recorded to the nearest inch of population of women the mean of the population is 64.97 inches and the standard deviation is 2.66 inches

Answers

The following histogram shows the relative frequencies of the height recorded to the nearest inch of population of women the mean of the population is 64.97 inches and the standard deviation is 2.66 inches

(a) Based on the histogram, what is the probability that the selected woman will have a height of at least 67 inches? Show your work

Answer:

0.22268

Step-by-step explanation:

z-score is z = (x-μ)/σ,

where x is the raw score

μ is the population mean

σ is the population standard deviation.

(a) Based on the histogram, what is the probability that the selected woman will have a height of at least 67 inches? Show your work

At least means equal to or greater than 67 inches

z = 67 - 64.97/2.66

z = 0.76316

P-value from Z-Table:

P(x<67) = 0.77732

P(x>67) = 1 - P(x<67) = 0.22268

The probability that the selected woman will have a height of at least 67 inches is 0.22268

Determine whether the pair of triangles is congruent.

Choose the correct answer below.

Congruent
Not congruent

Answers

Answer:

not congruent

Step-by-step explanation:

congruent is just a fancy way of saying the same in geometry. so to check if its congruent, see if all side lengths correspond to another side length on the other triangle. they do not, so they can't be congruent

hope this helped :)

Which of the following is true?

A |−5| < 4
B |−4| < |−5|
C |−5| < |4|
D |−4| < −5

Answers

B is true

Step-by-step explanation:

because no number with them to lines can be a negative

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