What is the function of this

What Is The Function Of This

Answers

Answer 1

Answer:

f(x) = x⁴ + 2x³ - 3x² - 4x + 4

Step-by-step explanation:

we have 3 turnarounds and no negative y values (so, it should be a function based on x⁴), 2 of these turnarounds are also directly on the x-axis (y=0).

f(0) = 4

f(1) = 0

f(-2) = 0

an equation based on x⁴ would have 4 interceptions with the x-axis. since we have only 2 here, then there must be 2 pairs of equal interceptions.

based on the known x-interceptions (x=1, x=-2) we can start with the approach

(x-1)(x+2)

this world give us a quadratic equation (based on x²).

the trick is now to get this to x⁴ without adding additional x-interceptions. that is done by simply "reusing" the ones we already used.

(x-1)(x+2)(x-1)(x+2) = (x-1)²(x+2)²

(x-1)²(x+2)² = (x² - 2x + 1)(x² + 4x + 4) =

x⁴ - 2x³ + x² + 4x³ - 8x² + 4x + 4x² - 8x + 4 =

x⁴ + 2x³ - 3x² - 4x + 4


Related Questions

Choose the model that represents the same function as the values in the table.

x r(x)
-4 -4
2 8
5 14
7 18

Answers

X -> times 2 -> plus 4 -> r(x)

Step-by-step explanation:

-4=x -4=r(x) -4 x 2=-8 -8+4=-4

Answer:

If on imagine math then its on the picture, have a nice day!

Step-by-step explanation:

please help me (geometry)

Answers

Answer:

x = 7

Step-by-step explanation:

When two parallel lines are cut by a transversal, the corresponding angles are equal.

8x +2 = 7x + 9

Subtract 2 from both sides

8x = 7x + 9 - 2

8x = 7x + 7

Subtract 7x from both sides

8x - 7x = 7

x = 7

Answer:

x=7

Step-by-step explanation:

The 2 given angles are vertical to each other, so that means they are equal to each other.

To solve, set up an equation:

[tex]7x+9=8x+2[/tex]

Solve by isolating the variable. [Subtract and divide]

[tex]7x=8x-7[/tex]

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

Multiply both sides by -1 to get rid of the negative sign.

[tex]x=7[/tex]

I hope this helps!

Plz help!! I need it ASAP

Answers

Answer:

you save $500 for 7 years at 6% compounding continuously

what is the final value...

A = $500 [tex]e^{.06(7)}[/tex]

Step-by-step explanation:

Suggest a fundamentally and conceptually different way that is always under the control of the researcher of making the margin of error smaller.

Answers

Step-by-step explanation:

First, we may wonder, what does the term margin of error mean? Put simply, the margin of error is a measure of the degree to which research results do not reflect the views of the total studied population. In other words, it tells readers how much confidence they should have in the results presented.

It has often been suggested that a fundamentally and conceptually effective way that is always under the control of the researcher of making the margin of error smaller is to increase the sample size of the research. This basically involves collecting more sample data which thus leads to a closer estimate of the view of the entire population.

Johnny can build 3 1/2 lego planes in 60 minutes. How many can he build in 40 minutes? Simplify answer completely

Answers

Answer:

2 [tex]\frac{1}{3}[/tex] planes

Step-by-step explanation:

Set up a ratio.

planes over time.

Because the time is given in minutes. No conversion necessary.

[tex]\frac{planes}{time}[/tex] = [tex]\frac{3.5}{60}[/tex] = [tex]\frac{x}{40}[/tex]

Cross Multiply

60 (x) = 3.5 (40)

60x = 140      Divide by 60, both sides.

x = 2.333 repeating also know as 2 [tex]\frac{1}{3}[/tex].

Please help pleaseeee

Answers

Answer:

32/33

Step-by-step explanation:

We first need to find out how many square yards are vacuumed every one minute.

Let's set up a chart:

yards        minutes

8/11      -->    3/4

y          -->     1

Here, y is the number of yards it takes to vacuum in one minute. Next, we can use cross-multiplication to find out y.

1. Multiply 1 by 8/11 to get... 8/11

2. Multiply 3/4 by y to get... 3/4y

3. Equate them: 8/11 = 3/4y

4. Divide both sides of the equation by 3/4 OR multiply both sides of the equation by 4/3 to isolate y, the variable

5. This gives us 32/33 = y

If A=(0,0) and B=(8,2), what is the length of AB

Answers

Answer:

[tex]\boxed{\sf Distance_{AB}= 8.24 \ units }[/tex]

Step-by-step explanation:

Here two points are given to us and we need to find the distance between the two points . The given points are , A(0,0) and B(8,2) . The distance between the two points can be found out using the Distance Formula , which is ,

Distance Formula:-

[tex]\sf\implies \green{ Distance =\sqrt{ (x_2-x_1)^2+(y_2-y_1)^2}}[/tex]

Therefore on substituting the respective values ,we can find the Distance as ,

[tex]\sf\longrightarrow Distance = \sqrt{ ( 0 - 8)^2 + (0-2)^2} [/tex]

Simplify the brackets ,

[tex]\sf\longrightarrow Distance =\sqrt{ (-8)^2+(-2)^2}[/tex]

Square the numbers inside the squareroot ,

[tex]\sf\longrightarrow Distance =\sqrt{ 64 + 4} [/tex]

Add the numbers inside the squareroot ,

[tex]\sf\longrightarrow Distance = \sqrt{68} [/tex]

Find the value of squareroot,

[tex]\sf\longrightarrow \boxed{\blue{\sf Distance = 8.24 \ units }}[/tex]

Hence the distance between the two points is 8.24 units .

The graph of a logarithmic function IS shown below.

What is the domain of the function?
A.x<0
B.x>0
C.x<1
D. All real numbers

Answers

Answer:

Step-by-step explanation:

The domain includes all the "allowed" x values. Looking at the graph, it appears to start a tiny tiny bit to the right of 0, so it doesn't include 0. It also does not go to the left of 0. Therefore, the domain of the graph is x > 0

Solve for x.
10x – 79 = 2x + 49
x = [?]

Answers

Answer:

[tex]x = 16[/tex]

Step-by-step explanation:

Step 1:  Add 79 to both sides

[tex]10x - 79 + 79 = 2x + 49 + 79[/tex]

[tex]10x = 2x + 128[/tex]

Step 2:  Subtract 2x from both sides

[tex]10x - 2x = 2x - 2x + 128[/tex]

[tex]8x = 128[/tex]

Step 3:  Divide 8 from both sides

[tex]\frac{8x}{8} = \frac{128}{8}[/tex]

[tex]x = 16[/tex]

Answer:  [tex]x = 16[/tex]

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Step-by-step explanation:

x=16

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Answers

Answer:

3/16

Step-by-step explanation:

-3*-1=3, 4*4=16

Answer:

3/16

Step-by-step explanation:

Multiply both the numerators (top number) and denominators (bottom numbers) together

-3 x -1 = 3....bc negative times negative always equals positive

4 x 4 = 16

Please help out will give brainliest to the first person

Answers

Answer:

b = 74

Step-by-step explanation:

The exterior angle is equal to the sum of the opposite interior angles in a triangle

b-44 + b+18 = b+48

2b-26 = b+48

Subtract b from each side

2b-b-26 =b+48-b

b-26 = 48

Add 26 to each side

b-26+26 = 48+26

b =74

help help help it is simple one​

Answers

Answer:

[tex] 3^{ -x+3}[/tex]

Step-by-step explanation:

We need to simplify out the given exponential expression . The given expression to us is ,

[tex]\rm\implies \dfrac{\dfrac{1}{3}}{3^{x-4}} [/tex]

We can use the Law of Exponents to simplify the given expression . Recall that ,

[tex]\rm\implies \red{\dfrac{a^m}{a^n}= a^{m-n}}[/tex]

Note that , we can write ,

[tex]\rm\implies \dfrac{1}{3}= 3^{-1}[/tex]

Therefore our expression becomes ,

[tex]\rm\implies \dfrac{ 3^{-1}}{3^{x-4}}[/tex]

Simpify using the Law of Exponents ,

[tex]\rm\implies 3^{ -1 - ( x - 4 )}[/tex]

Open the brackets in exponent ,

[tex]\rm\implies 3^{ -1 - x +4 }[/tex]

Simplify to get final expression ,

[tex]\rm\implies \boxed{\quad \blue{ 3^{-x+3} \quad}}[/tex]

The melting point of mercury is about 1/4 of the melting point of krypton. The melting point of mercury is -39c. Write and solve an equation to find the melting point of krypton.

Answers

Answer:

-156c

Step-by-step explanation:

[tex]\frac{1}{4}[/tex] of krypton melting point is mercury melting point

[tex]\frac{1}{4}[/tex](k) = -39

k = -39(4)

k = -156c

2) How much tax should be paid by a person having annual income RS 240.000?​

Answers

Answer:

What is the Existing / Old tax regime?

Income Range Tax rate Tax to be paid

Up to Rs.2,50,000 0 No tax

Between Rs 2.5 lakhs and Rs 5 lakhs 5% 5% of your taxable income

Between Rs 5 lakhs and Rs 10 lakhs 20% Rs 12,500+ 20% of income above Rs 5 lakhs

Above 10 lakhs 30% Rs 1,12,500+ 30% of income above Rs 10 lakhs

4u + 10 =17
u = ?
help ​

Answers

Answer:

The answer is "1.75".

Step-by-step explanation:

Given:

[tex]\to 4u + 10 =17[/tex]

Find:

[tex]\to u = ?[/tex]

Solution:

[tex]\to 4u + 10 =17\\\\\to 4u = 17-10\\\\\to 4u = 7\\\\\to u = \frac{7}{4}\\\\\to u=1.75[/tex]

DIVISON METHOD OF 527,646,1105​

Answers

Answer:

17 is the answer

Step-by-step explanation:

Factor x4 – 81. Question 20 options: A) (x2 + 3)(x2 – 3) B) (x2 – 9)(x + 3)(x – 3) C) (x2 + 9)(x + 3)(x – 3) D) (x + 3)2(x – 3)2

Answers

Answer:

C is correct

Step-by-step explanation:

A square minus a square can always be factored into the square root of the 1st term plus and minus the square root of the 2nd term. So

x**4 - 81 = (x**2 + 9)(x**2 -9) = (x**2 + 9) (x + 3)(x - 3)

Need help on this!!! 6 points!!!

Answers

Answer:

it appears to be  FALSE....

f(g(x) = 3(13-2x) -7 = 39 - 6x - 7 = 32 - 6x

h(32-5x) = 6(32-6x)

= 192 - 36x

Step-by-step explanation:

pls help ASAP
find the value of z when x = 216

Answers

Answer:

z =   3 [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

z = [tex]\frac{k}{x^{1/3} }[/tex]

5 = [tex]\frac{k}{4}[/tex]

k= 20

~~~~~~~~~~~~~~~

z = [tex]\frac{20}{6}[/tex]

z =  [tex]\frac{10}{3}[/tex] = 3 [tex]\frac{1}{3}[/tex]

Which system is equivalent to y=-2x^2 y=x-2

a) y=-2y^2 x=y-2
b) y=-2y^2+2 x=y+2
c) y=-2y^2-8y-8 x=y+2
d) y=-2y^2+8y-8 x=y-2

Answers

Answer:

answer C

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y&=&-2x^2\\y&=&x-2\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}x&=&y-2\\y&=&-2(y-2)^2\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}x&=&y-2\\y&=&-2y^2-8y-8\\\end{array}\right.\\\\[/tex]


Find the slope of the line

Answers

Answer:

-1

Step-by-step explanation:

y = -1

-1 because that's where the point is on the y-axis.

If ABC ~ AMN and am=6, mb=4 an= 8 then what is the value of nc

Answers

It gonna be 10 boss

HELP! (25 points) i think i might know the answer

Answers

Answer:

[tex]\sqrt{7}[/tex]

Step-by-step explanation:

Grant is a member of a book club. He pays a $10 yearly membership fee and can purchase books through the club for $2.75 each. His total annual cost is a function of the number of books that he purchases in a year. Let b represent the number of books he purchases in a year. Which function, C(b), represents his yearly cost

Answers

C(b) = 2.75b + 10

This is based of the f(x) = mx + b formula, where m is the slope, x is the variable (or input) and b is the y intercept. In this circumstance the slope is 2.75, so we change m for 2.75. The variable is the amount of books so we change it for b (like it says in the word problem), and and 10 is the starting cost, so it’s the y intercept, so we change b for 10.


Hope this helps! Please make me the brainliest, it’s not necessary but appreciated, I put a lot of effort and research into my answers. Have a good day, stay safe and stay healthy.




Segment AB is completely rotated about the y-axis to form a 3-D figure. Find the volume of the figure. The
length of AB is 6.

Answers

Answer:

The volume of the figure is 905 cubic units.

Step-by-step explanation:

Rotation is a method of solid transformation which involve turning a given line, or object about a reference point. In the given question, rotating segment AB completely about the y-axis would form a 3 dimensional figure of a sphere.

volume of a sphere = [tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex]

where r is the radius of the sphere.

Given that AB = 6, then the radius of the sphere = 6

volume of sphere = [tex]\frac{4}{3}[/tex] x [tex]\frac{22}{7}[/tex] x [tex](6)^{3}[/tex]

                              = [tex]\frac{88}{21}[/tex] x 216

                              = 905.14

volume of sphere = 905 cubic units

The volume of the figure is 905 cubic units.

A cone has a volume of 150 cm cubed and a base with an area of 12 cm square. What is the height of the cone?

(I'm asking this again :') No one answered it.)
P.S Its 30 Points now
SO PLEASE HELPPP tyyyy :)

Answers

Answer:

37.5cm

Step-by-step explanation:

V=1/3Bh

150=1/3 12h

150=4h

37.5=h

The height of the cone is 37.7.
Calculation method: area of circle = pi x r^2
Square root(12/3.14) =r
r = 1.95
h = 3 x 150/pi * r^2
h= 450/pi * 1.95^2
h = 143.31/3.8
h = 37.7

20-(+20)-(-65)-(-12)​

Answers

Answer:

77

Step-by-step explanation:

20-(+20)-(-65)-(-12)​

-(-65)-(-12)​

+65-(-12)​

+65+12

77​

Q) 20-(+20)-(-65)-(-12) = ?

→ 20-(+20)-(-65)-(-12)

→ 20 - 20 + 65 + 12

→ {20 - 20} + {65 + 12}

→ 0 + 77

→ 77 is required solution.

determine whether the following polygons are similar. if yes, type 'yes' in the similar box and type in the similarity statement and scale factor. if no, type 'none'​

Answers

Similar: yes

Similarity Statement: AB ~ TQ , BC ~ QR

Scale Factor: 4/3

9 Alicia has a bag that contains 12 apples.
Estimate the mass of the bag of apples.
Give your answer in kilograms.

Answers

Answer:

The key here is estimate, you don't need exact values or more information for this problem. First estimate the mass of an average apple. A quick online search reveals that the mass of an average apple is approximately 100 grams. Multiply by 12 for the bag and convert to whatever units you're asked to express your answer in.

Step-by-step explanation:

At a homecoming pep rally, one student will win free tickets to the homecoming dance. There are 2,400 students attending the pep rally. The student council wants to pull the winning student’s name from a container with the school’s mascot on it. Unfortunately, the container only holds 600 names.

Which method can the student council use to ensure each student has a fair chance of winning?

A.
Randomly assign the 2,400 students to four equal groups. Select a group at random and put all the names from that group in the container. Randomly select the winner from the container.
B.
Put the names of the first 600 students who arrive at the pep rally in the bag. Randomly select the winner from the container.
C.
Select a section of the bleachers and only put the names of students sitting in that section in the container. Randomly select the winner from the container.
D.
Select a grade and only put the names of students from that grade in the container. Randomly select the winner from the container.

Answers

Answer:

A

Step-by-step explanation:

Answer A. Logically speaking there is no fair chance unless they use all the names but we can rule out C by the higher chance of students crowding, B is less likely as selecting winners from students who arrive first would be nearly the same as who bought their tickets first. D, selecting a grade excludes (estimating) around 1500 students or more from being included. A is the only logical answer left and by dividing them randomly you give everyone a full chance.

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