Which graph represents the polynomial function?

f(x)=−x3+x2+9x−9

Answer:

A=113 cm²

Step-by-step explanation:

If the length of the rope is 6 cm

then the radius of the circle we draw is 6 cm.

Area of the circle is A = π·r²

A = π·6² ≈ 3.14· 36 ≈ 113cm²

Answer:

A

Step-by-step explanation:

the answer is A because it is absolute so it would actually be x + 3

For the given data set

Minimum = 48

Lower quartile = 55

Median = 63.5

Upper quartile = 74

Maximum = 80

Interquartile range = 19

From the question, we are to determine the minimum, lower quartile, median, upper quartile, maximum, and interquartile range of the given data set

The given data set is

48, 50, 54, 56, 63, 63, 64, 68, 74, 74, 79, 80

Minimum = 48

Lower quartile = (54+56)/2

Lower quartile = 110/2

Lower quartile = 55

Median = (63+64)/2

Median = 127/2

Median = 63.5

Upper quartile = (74+74)/2

Upper quartile = 148/2

Upper quartile = 74

Maximum = 80

Interquartile range = Upper quartile - Lower quartile

Interquartile range = 74 - 55

Interquartile range = 19

Hence, for the given data set

Minimum = 48

Lower quartile = 55

Median = 63.5

Upper quartile = 74

Maximum = 80

Interquartile range = 19

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La ecuación estándar de la circunferencia es (x - 0.5)² + y² = 2.5².

En este problema debemos derivar la ecuación estándar de la circunferencia, cuyo diámetro está comprendido por el segmento de recta entre los puntos A(x, y) = (3, - 4) y B(x, y) = (- 2, - 4). La ecuación estándar de la circunferencia se presenta a continuación:

(x - h)² + (y - k)² = r²     (1)

Donde:

El centro de la circunferencia es el punto medio del segmento de recta AB:

(h, k) = 0.5 · (3, - 4) + 0.5 · (- 2, 4)

(h, k) = (1.5, - 2) + (- 1, 2)

(h, k) = (0.5, 0)

Y el radio de la circunferencia es la mitad de la longitud del segmento de recta AB:

[tex]r = \frac{1}{2}\cdot \sqrt{(-2 - 3)^{2}+[-4 - (-4)]^{2}}[/tex]

r = 2.5

Por tanto, la ecuación estándar de la circunferencia es (x - 0.5)² + y² = 2.5².

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A major advantage of a direct implementation is that people whose roles span modules do not have to switch back and forth between old and new modules.

With this technique, the machine is implemented and tested to make certain it plays well. Then the antique machine is removed and the brand new one is put in its area without any overlap or restricted rollout.

There are three predominant methods used: phased implementation, direct changeover, and parallel going for walks. Phased implementation: A staged technique whereby one part of the overall system that desires change is changed.

Structures implementation is the process of defining how the data device needs to be built (i.e., physical machine design), ensuring that the records gadget is operational and used, and ensuring that the information device meets greatly preferred i.e. nice warranty.

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Answer:

31. (98,765 x 9) + 3 = 888,888

32. (12,345 x 9) + 6 + 111,111

33. 3367 x 15 + 50,505

34. 15,873 x 28 = 555,555

35. 33,334 x 33,334 = 1,111,155,556

36. 11,111 x 11,111 = 123,454,321

41. 3 + 9 + 27 + 81 + 243 = 3(243 -1) / 2

42.  1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + 1/5x6 = 5/6

hope this helps

Answer:

see the step-by-step explanation

Step-by-step explanation:

31. (98,765 x 9) + 3 = = 888,888

32. (12,345 x 9) + 6 + 111,111

33. 3367 x 15 + 50,505

34. 15,873 x 28 = 555,555

35. 33,334 x 33,334 = 1,111,155,556

36. 11,111 x 11,111 = 123,454,321

41.3+9+27+81 +243 = 3(243-1)/2

42. 1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + 1/5x6 = 5/6

If the function is [tex](x-3)^{-2}[/tex] and  f(4) − f(1) = f '(c)(4 − 1) then there is not any answer.

Given function is [tex](x-3)^{-2}[/tex] and  f(4) − f(1) = f '(c)(4 − 1).

In this question we have to apply the mean value theorem, which says that given a secant line between points A and B, there is at least a point C that belongs to the curve and the derivative of that curve exists.

We begin by calculating f(2) and f(5):

f(2)=[tex](2-3)^{-2}[/tex]

f(2)=1

f(5)=[tex](5-3)^{-2}[/tex]

f(5)=1

And the slope of the function:

[tex]f^{1}[/tex](x)=[tex]f(5)-f(2)/(5-2)[/tex]

[tex]f^{1}[/tex](c)=0

Now,

[tex]f^{1} (x)=-2*(x-3)^{-3}[/tex]

=-2[tex](x-3)^{-3}[/tex]

=0

-2 is not equal to 0. So there is not any answer.

Hence if the function is [tex](x-3)^{-2}[/tex] and  f(4) − f(1) = f '(c)(4 − 1) then there is not any answer.

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If machine a can make 350 widgets in 1 hour and machine b can make 250 widgets in 1 hour then by forming equation we will get that both machines have to work for one hour and 40 minutes to make 1000 widgets.

Given that machine a can make 350 widgets in 1 hour, and machine b can make 250 widgets in 1 hour.

How much time will both machines take to make 1000 widgets?

Suppose the time taken by both machines be x hours. Time is equal because both the machines need to work together.

According to the question the equation will be as under:

350x+250x=1000

600x=1000

x=1000/600

x=10/6

x=5/3

x=1.67

Converting 0.67 to minutes 0.67*60=40.2

Adding will result 1 hour and 40 minutes.

Hence if machine a can make 350 widgets in 1 hour and machine b can make 250 widgets in 1 hour then by forming equation we will get that both machines have to work for one hour and 40 minutes to make 1000 widgets.

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The angle between the two extreme vectors of Sofia bats is 74.60 degrees.

In this question,

The angle between two vectors will be deferred by a single point, which is called as the shortest angle at which we have to turn around one of the vectors to the position of co-directional with another vector.

The extreme vectors of Sofia bats are  [tex]\vec u = < -8, 12 >[/tex] and [tex]\vec v = < -8, 12 >[/tex]

The angle between the vectors is

[tex]\theta = cos^{-1} \frac{\vec u.\vec v}{||\vec u|| ||\vec v||}[/tex]

The dot product is calculated as

[tex]\vec u. \vec v = (-8)(13)+(12)(15)[/tex]

⇒ [tex]-104+180[/tex]

⇒ 76

The magnitude can be calculated as

[tex]||\vec u|| = \sqrt{(-8 )^{2} +(12)^{2} }[/tex]

⇒ [tex]\sqrt{64+144}[/tex]

⇒ [tex]\sqrt{208}[/tex]

[tex]||\vec v|| = \sqrt{(13 )^{2} +(15)^{2} }[/tex]

⇒ [tex]\sqrt{169+225}[/tex]

⇒ [tex]\sqrt{394}[/tex]

Thus the angle between the vectors is

[tex]\theta = cos^{-1} \frac{76}{(\sqrt{208} )(\sqrt{394} )}[/tex]

⇒ [tex]\theta = cos^{-1} \frac{76}{\sqrt{81952} }[/tex]

⇒ [tex]\theta = cos^{-1} \frac{76}{286.27 }[/tex]

⇒ [tex]\theta = cos^{-1} (0.2654)[/tex]

⇒ [tex]\theta=74.60[/tex]

Hence we can conclude that the angle between the two extreme vectors of Sofia bats is 74.60 degrees.

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Answer:

C

Step-by-step explanation:

For any function x, inverse will = 1/x. so the answer is C

Answer:

C. [tex]f^{-1}(x) = \frac{1}{5} x[/tex]

Step-by-step explanation:

The question is asking to find [tex]f^{-1}(x)[/tex] of f(x)=5x, which is the same as finding the inverse of the function.

To find the inverse of a function, we first need to replace f(x) with y.

The function will therefore be:

y = 5x

Now, we solve the equation for x.

So divide both sides by 5.

y = 5x

÷5  ÷5

_________

[tex]\frac{y}{5} = x[/tex]

Now, we replace x with y and y with x.

[tex]\frac{x}{5} = y[/tex]

Finally, we replace y with [tex]f^{-1}(x)[/tex].

[tex]\frac{x}{5} = f^{-1}(x)[/tex]

We can re-write this though, to make it easier to read.

We can write [tex]f^{-1}(x)[/tex] first, and rewrite [tex]\frac{x}{5}[/tex] as [tex]\frac{1}{5}x[/tex].

[tex]f^{-1}(x) = \frac{1}{5} x[/tex]

Therefore, the answer is C.

Debido a restricciones de extensión y la características del ejercicio, recomendamos leer la explicación de esta pregunta para mayores detalles sobre la adición de números enteros.

En este ejercicio tenemos un grupo de sumas con números enteros positivos y negativos, en las cuales se prueba la capacidad del estudiante para realizar varias operaciones en serie (adición, sustracción) y comprender las diferencias entre números positivos, negativos y neutros. Ahora procedemos a determinar el resultado de cada una de las expresiones:

20 + 50 + 30 + 7 = 107

30 + 5 + 2 = 37

- 200 - 50 - 70 - 8 = - 328

- 500 + 100 - 20 + 50 = - 370

10 - 5 = 5

20 + 50 - 25 - 10 = 35

- 100 + 20 = - 80

- 30 + 5 + 4 - 20 + 8 = - 33

- 258 + 8 = - 250

- 10 + 20 + 520 - 100 + 8 = 438

- 20 - 5 - 42 + 3 = - 64

1000 - 200 + 50 + 30 - 45 + 75 - 87 + 90 + 50 - 100 + 50 - 10 = 903

- 400 + 500 - 200 - 50 + 48 + 8 - 47 - 50 = - 191

300 + 20 - 50 + 30 - 84 + 35 - 7 + 20 - 40 + 10 - 45 + 65 + 8 - 55 = 207

800 + 50 - 69 + 8 - 35 + 85 - 54 + 40 + 85 + 74 - 32 - 8 + 65 - 27 = 982

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Step-by-step explanation:

This is trigonometry. Focusing on Y initially, we can see that Y is the opposite, and 32 is the hypotenuse. Therefore, we must use sin:

[tex] \sin(60) = \frac{y}{32} [/tex]

[tex]y = \sin(60) \times 32[/tex]

[tex]y \approx28[/tex]

Next X. We can see that X is the adjacent, and 32 is the hypotenuse, so we must use cos:

[tex] \cos(60) = \frac{x}{32} [/tex]

[tex]x = \cos(60) \times 32[/tex]

[tex]x = 16[/tex]

Now let's look at A. We can see that a is the adjacent, and 12 is the opposite, so we must use tan:

[tex] \tan(60) = \frac{12}{a} [/tex]

[tex]a = \frac{12}{ \tan(60) } [/tex]

[tex]a \approx7[/tex]

Now, B. We can see that B is the hypotenuse, and 12 is the opposite, so we must use sin:

[tex] \sin(60) = \frac{12}{b} [/tex]

[tex]b = \frac{12}{ \sin(60) } [/tex]

[tex]b \approx14[/tex]

Answer:

Below in bold.

Step-by-step explanation:

The first triangle is a 30-60-90 triangle,

so the sides are in the ratio 2 : 1 : √3,  where 2 is the hypotenuse, the 1 is adjacent to 60 degree angle and the √3 is opposite the 60 degree angle.

So x = 1/2 * 32 = 16

and y = 16√3  or 27.71 to nearest hundredth.

The second one is the same special triangle, so

√3/2 = 12/b

b = 24/√3

 = 8√3  or 13.86  to nearest hundredth.

a = 1/2 b = 4√3 or 6.93 to nearest hundredth.

Answer: B, C, E

Step-by-step explanation: a is wrong 32 tens is 320.  B is right. 321 tenths is 32.1 and 48 thousandths is 0.048 so C is correct. 32,148 hundredths is too much but 32,148 thousandths is 32.148

Answer:

D. 2

Step-by-step explanation:

soh cah toa rule

sine equals opposite over hypotenuse,

cosine equals adjacent over hypotenuse, and

tangent equals opposite over adjacent

csc is 1/sin which is hypotenuse over opposite

if csc is -√5/2 then

hypotenuse is -√5

opposite is 2

3rd quadrant on a graph is bottom left

both x and y values are negative

hypotenuse means its a triangle

pythagorean theorem

a^2 + b^2 = c^2

a^2 + 2^2 = (-√5)^2

a^2 + 4 = 5

a = 1 = adjacent

tangent equals opposite over adjacent

tan is 2 / 1 which is 2

third quadrant means it's still positive

because tan is positive in quadrant 3

intmathcom

revisionmathscom

mathworldwolframcom

Answer:

2

Step-by-step explanation:

just because all three numbers are even

Hope this helps

The greatest common factor of 30, 22, and 8 will be 2.

The Highest Common Factor (HCF) of two numbers is the highest possible number that is divisible by both numbers.

In other words, the highest common factor is the common factor between the two numbers but it should be the highest among all common factors.

For example in 6 and 12 6 is the highest common factor.

The factor of 30 ⇒ 2,3,5

The factor of 22 ⇒ 2,11

The factor of 8 ⇒ 2,4

The only common factor among 30,22 and 8 is 2 so it will be the greatest common factor.

Hence "The greatest common factor of 30, 22, and 8 will be 2".

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Answer:

10 degrees

Step-by-step explanation:

8x = 2x + 60

6x = 60

x = 10

Answer:

8x³ - 2x² - 51x - 45

Step-by-step explanation:

(x - 3)(2x + 3)(4x + 5) ← expand the 2nd/3rd factors using FOIL

= (x - 3)(8x² + 10x + 12x + 15)

= (x - 3)(8x² + 22x + 15)

multiply each term in the second factor by each term in the first factor.

x(8x² + 22x + 15) - 3(8x² + 22x + 15) ← distribute parenthesis

= 8x³ + 22x² + 15x - 24x² - 66x - 45 ← collect like terms

= 8x³ - 2x²- 51x - 45

Expand first 2 bracket first to get:

2x^2 + 3x - 6x - 9 & simplify, then expand with last bracket.

2x^2 - 3x - 9 (4x + 5)

2x^2 x 4x = 8x^4

2x^2 x 5 = 10x^2

Repeat for the next two numbers next to the bracket.

You get => 8x^3 + 10x^2 - 12x^2 - 15x - 36x - 45

Final simplified answer of:

8x^3 - 2x^2 - 51x - 45

Hope this helps!

The speed of the wind is 50 miles per hour.

The term speed is defined as the ratio of the distance to the time taken. Now we can see that the movement of the plane and the wind were once in the same direction and then in opposite direction. This could be used to obtain a pair of simultaneous equations that could be used to solve the problem.

Hence;

300 = (250+s)* t = 250t + st ----- (1)

200 = (250-s)* t = 250t   - st  ------- (2)

Adding equations (1) and (2)

500 = 500t

t = 1 hour

To obtain the speed of the wind;

300 =250t + st

300 = 250(1) + (s * 1)

300 = 250 + s

300 - 250 = s

s = 50 miles per hour

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Missing parts;

A plane has a cruising speed of 250 miles per hour when there is no wind. At this speed, the plane flew 300 miles with the wind in the same amount of time it flew 200 miles against the wind. Find the speed of the wind.

The values of a + b, 6a + 9b, |a|, and |a − b| are −3i + 16j, 0i + 108j, 15 and 17 respectively. This can be obtained by using vector addition, vector subtraction and formula to find magnitude of a vector.

Given that,

a = <−9, 12> , b = <6, 4>

These vectors can be rewritten as,

a = <−9, 12> = −9i + 12j

b = <6, 4> = 6i + 4j

a + b = −9i + 12j + 6i + 4j

a + b = −9i + 6i + 12j + 4j

a + b = (−9 + 6)i + (12 + 4)j

a + b = −3i + 16j

6a = 6 (−9i + 12j )

6a = −54i + 72j

9b = 9(6i + 4j)

9b = 54i + 36j

Now add 6a and 9b together,

6a + 9b = −54i + 72j  + 54i + 36j

6a + 9b = −54i + 54i + 72j + 36j

6a + 9b = 0i + 108j

If a = a₁i + a₂j, |a| = √a₁² + a₂²

Here, a = −9i + 12j

|a| = √(−9)² + (12)²

|a| = √81 + 144 = √225

|a| = 15

a - b = −9i + 12j - (6i + 4j)

a - b = −9i - 6i + 12j - 4j

a - b = −15i + 8j

Now use the formula to find the magnitude of a vector,

|a − b| = √(-15)² + (8)²

|a − b| = √225 + 64 = √289

|a − b| = 17

Hence the values of a + b, 6a + 9b, |a|, and |a − b| are −3i + 16j, 0i + 108j, 15 and 17 respectively.

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4710

4709.94107458

The nearest whole number for 4709.94107458 is 4710 since the number 9 after the decimal is greater than 5. Therefore, if you add 1 to 9 before the decimal, you get 10.

Hope this helps :)

Answer:subtraction

Step-by-step explanation: to find out how many fewer tickets were sold on Sunday you would need to subtract 34012 by 29879. The solution would be how many fewer tickets were sold on Sunday compared to Saturday.

Answer:

c

Step-by-step explanation:

if you take the triangle off of the left side and attach it to the left side then you would have a 6 by 4 rectangle that has an area of 24 units squared.

Step-by-step explanation:

In a Mathematics lab. There are some cubes and cuboids of following measurements

(i) One cube of side 4 cm

(ii) One cube of side 6 cm

(iii) 3 cuboids each of dimensions 4cm ×4 cm ×6cm

(iv) 3 cuboids each of dimensions 4cm ×6 cm ×6cm

A student wants to arrange these cubes and cuboids in the form of big cube. Is it

possible to arrange them in the form of big cube? If yes, then find the length of side of

Answer:

B.) x + 4y = 7

Step-by-step explanation:

(Step 1) ----------------------------------------------------------------------------------------------

To find the equation, we first need to find the slope using the point-slope form:

y₁ - y₂ = m(x₁ - x₂)

In this form, "m" represents the slope, "x₁" and "y₁" represent the values from the first point, and "x₂" and "y₂" represent the values from the second point.

Point 1: (-1, 2)                     Point 2: (3, 1)

x₁ = -1                                   x₂ = 3

y₁ = 2                                   y₂ = 1

y₁ - y₂ = m(x₁ - x₂)                                  <----- Point-slope form

2 - 1 = m(-1 - 3)                                      <----- Insert values

1 = m(-4)                                                <----- Subtract

-1/4 = m                                               <----- Divide both sides by -4

(Step 2) ---------------------------------------------------------------------------------------------

The given equations are in the slope-intercept form. The general structure looks like this:

y = mx + b

In this form, "m" represents the slope and "b" represents the y-intercept. To find the y-intercept, you can plug the newfound slope and values from one point into the equation.

x = -1

y = 2

m = -1/4

y = mx + b                                              <----- Slope-intercept form

2 = (-1/4)(-1) + b                                       <----- Insert values

2 = 1/4 + b                                              <----- Multiply -1/4 and -1

8/4 = 1/4 + b                                           <----- Make common denominators

7/4 = b                                                    <----- Subtract both sides by 1/4

(Step 3) ---------------------------------------------------------------------------------------------

The equation in slope-intercept form is thus: y = -1/4x + 7/4.

While this equation is accurate, it seems that it must be slightly manipulated. Therefore, we need to alter this equation to look like one of the answer choices. For instance, we can multiply the entire equation by 4 to remove the denominator.

y = -1/4x + 7/4                                         <----- Equation

4y = -x + 7                                               <----- Multiply all terms by 4    

x + 4y = 7                                               <----- Add "x" to both sides

[tex]\cos(x)[/tex] is an even function, while [tex]\sin(x)[/tex] is odd. This means

[tex]\cos(-x) = \cos(x) \text{ and } \sin(-x) = -\sin(x)[/tex]

[tex]\cot(x)[/tex] is defined by

[tex]\cot(x) = \dfrac{\cos(x)}{\sin(x)}[/tex]

so it is an odd function, since

[tex]\cot(-x) = \dfrac{\cos(-x)}{\sin(-x)} = \dfrac{\cos(x)}{-\sin(x)} = -\cot(x)[/tex]

Putting everything together, it follows that

[tex]\cot(-x) \cos(-x) \sin(-x) = (-\cot(x)) \cos(x) (-\sin(x)) \\\\~~~~~~~~= \cot(x) \cos(x) \sin(x) \\\\ ~~~~~~~~= \cos^2(x)[/tex]

The number of additional days she wants to rent the car for the two specials are equivalent is 5 days.

Compact car:

y = 50 + 6x

Another special:

y = 40 + 8x

let

x = number of additional days

50 + 6x = 40 + 8x

50 - 40 = 8x - 6x

10 = 2x

x = 10/2

x = 5 days

Therefore, the number of additional days she wants to rent the car for, the two specials are equivalent is 5 days.

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The minimum value of data is 24,lower quartile is 29,median is 41, upper quartile is 50 and maximum value is 56 and the interquartile range is 21.

Given a data about ages of 13 history teacher as under:

24, 27, 29, 29, 35, 39, 43, 45, 46, 49, 51, 51, 56.

We are required to find the minimum value, lower quartile,median,upper quartile,maximum value, interquartile range.

The minmum value is 24.

Lower quartile=(n+1)/4 th term

=(13+1)/4

=7/2

=3.5

Lower quartile=(29+29)/2

=29

Median=(n/2)th term

=13/2 th term

=6.5 th term

Median=(39+43)/2

=82/2

=41

Upper quartile=3(n+1)/4   th term

=3(13+1)/4

=3*14/4

=10.5 th term

Upper quartile=(49+51)/2=100/2=50

Inter quartile range=Upper quartile- lower quartile

=50-29

=21

Hence the minimum value of data is 24,lower quartile is 29,median is 41, upper quartile is 50 and maximum value is 56 and the interquartile range is 21.

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Answer: the first one and the third one

Step-by-step explanation:

The prime polynomials from the polynomials are:

1. [tex]x^4[/tex] + 3y²x - 1 and 3. x² - 9x + 3.

Options 1 and 3 are the correct answer.

We have,

A prime polynomial is a polynomial that cannot be factored into a product of two polynomials with integer coefficients.

Let's check each expression to see if it is a prime polynomial:

[tex]x^4[/tex] + 3y²x - 1:

This expression cannot be factored further, so it is a prime polynomial.

9y + 4y² + 12y³:

This expression can be factored as y(9 + 4y + 12y²), so it is not a prime polynomial.

x² - 9x + 3:

This expression cannot be factored further, so it is a prime polynomial.

x² - 3x - 10:

This expression can be factored as (x - 5)(x + 2), so it is not a prime polynomial.

x³ - 512y³:

This expression can be factored as (x - 8y)(x² + 8xy + 64y²), so it is not a prime polynomial.

Thus,

The prime polynomials are:

1. [tex]x^4[/tex] + 3y²x - 1 and 3. x² - 9x + 3.

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1/2 value can be used as the common ratio in an explicit formula that represents the sequence.

Definition of sequence -

A sequence that progresses geometrically has the first term as 12.

Each number is the previous number divided by 2.

so the sequence will be 12, 6, 3, 1.5...........

Explicit formula of a geometric sequence is given by

[tex]T_{n} = ar^{n-1}[/tex]

Where [tex]T_{n}[/tex]  = nth term of the sequence

a = first term

r = common ratio

and n = number of term

In this sequence common ratio = [tex]\frac{Successive term }{previous term}[/tex]

            = 6/12

            =  1/2

Therefore, common ratio will be 1/2.

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