Simplify the expression ( 6x3-5x) + (2x3 + x 2+ 10x).​

The given expression log(cx) + 3 log(cy) - 5 log(cx) + log(cx) + 3 log(cy) - 5 log(x) can be expressed as a single logarithm, which is log(\((cy)^6 / (cx)^4 / x^5\)) after simplification.

To express the given expression as a single logarithm and simplify, we can use the properties of logarithms.

The given expression is:

log(cx) + 3 log(cy) - 5 log(cx) + log(cx) + 3 log(cy) - 5 log(x)

We can combine the logarithms using the properties of addition and subtraction:

log(cx) - 5 log(cx) + log(cx) + 3 log(cy) + 3 log(cy) - 5 log(x)

Now, we can simplify the expression:

-4 log(cx) + 6 log(cy) - 5 log(x)

We can further simplify the expression by combining the coefficients:

log((cy)^6 / (cx)^4) - log(x^5)

Now, we can simplify the expression by subtracting the logarithms:

log((cy)^6 / (cx)^4 / x^5)

Therefore, the simplified expression is log((cy)^6 / (cx)^4 / x^5), where '^' denotes exponentiation.

In summary, the given expression can be expressed as a single logarithm, which is log(\((cy)^6 / (cx)^4 / x^5\)) after simplification.

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Answer: (1)-8

Step-by-step explanation: −6r+18=k(x−15)

Step 1: Flip the equation.

kx−15k=−6r+18

Step 2: Factor out variable k.

k(x−15)=−6r+18

Step 3: Divide both sides by x-15.

k(x−15)/x-15 =

−6r+18/x-15

k= −6r+18/x-15= -8

The range of the graph shown is

range { y | y < 0 }

When a figure is transported from one place to another without changing its size, shape, or orientation, a translation takes place.

All of a function's x-values, or inputs, make up the domain, and all of a function's y-values, or outputs, make up the range.

The graph's entire range, from lower to upper numbers vertically, represents the range.

The translation downwards, means that the graph moved down and considering the image of the attached graph, the effect of the translation means that the range to be numbers less than zero

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Answer:

4

Step-by-step explanation:

The point at which the direction of fastest change of the function f(x, y) = x² + y² - 2x - 6y is in the direction of vector i + j is (3/2, 7/2).

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

To find the points at which the direction of fastest change of the function f(x, y) = x² + y² - 2x - 6y is in the direction of vector i + j, we need to find the gradient vector of the function and equate it to the given direction vector.

The gradient vector of the function f(x, y) is given by:

∇f(x, y) = [∂f/∂x, ∂f/∂y]

Taking partial derivatives of f(x, y) with respect to x and y:

∂f/∂x = 2x - 2

∂f/∂y = 2y - 6

Setting the gradient vector equal to the given direction vector i + j:

[2x - 2, 2y - 6] = [1, 1]

Equating the corresponding components, we have:

2x - 2 = 1

2y - 6 = 1

Solving these equations, we get:

2x = 3  =>  x = 3/2

2y = 7  =>  y = 7/2

Therefore, the point at which the direction of fastest change of the function f(x, y) = x² + y² - 2x - 6y is in the direction of vector i + j is (3/2, 7/2).

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Challenge To travel on vacation, a family wants to rent a car. Company A bills $70.50 plus 17 cents each mile. Charges from Company B are $30.50 plus 8 per mile. For every x miles that Company A charges, Company B is (39.24x)

Before figuring out their difference for x miles, we must first determine their difference for one mile.

Difference per mile = ($70.50 + $0.14) - ($30.50 + $0.90)

= $70.64 - $31.40

= $39.24

Difference for x miles = $39.24 × x miles

= $(39.24x)

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Step-by-step explanation:

Use midpoint formula: Xa+Xb/2 ; Ya +Yb/2

Therefore midpoint is -½ ; -3

The height of the cylindrical package is 7 in.

volume of the cylindrical package (v) = 87.92 in³,

radius of the cylinder = 2 inches and π = 3.14

volume of a cylinder = πr²h

where r is the radius, and h is the height of the cylinder

substituting the given values in the formula, we have:

87.92 = 3.14 × 2² × h

87.92 = 12.56h

h = 87.92/12.56

h = 7 in

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Answer:

Its 25.2

Step-by-step explanation:

14.4 + 10.8

If friend house is 10.8 miles north and 14.4 miles east of the bank then distance of person's house from bank is 18 miles.

Pythagoras theorem says that in a right angled triangle the square of hypotenuse is equal to the sum of squares of base and perpendicular of that triangle.

\(H^{2} =B^{2} +P^{2}\) in which P is perpendicular, B is base, H is hypotenuse of triangle.

When we express person's house,his friend's house and bank on the surface then it will look like a right angled triangle.

H=\(\sqrt{B^{2} +P^{2}}\)

=\(\sqrt{10.8^{2} +14.4^{2} }\)

=\(\sqrt{324}\)

=18 miles

Hence the distance of person's house from bank is 18 miles.

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Question is wrong as the right question is that calculate the distance between person's house and bank.

The inverse of the given function f(x) = 3x + 7 can be shown as f⁻¹(x) = (x - 7)/3, making option A the right choice.

In the question, we are given a function f(x) = 3x + 7, and are asked to identify its inverse.

To find the inverse, we first equate the function f(x) to a variable y, to get:

f(x) = y,

or, 3x + 7 = y.

Now, in the above equation, we try to isolate the variable x.

3x + 7 = y,

or, 3x + 7 - 7 = y - 7 {Subtracting 7 from both sides},

or, 3x = y - 7 {Simplifying},

or, 3x/3 = (y - 7)/3 {Dividing both sides by 3},

or, x = (y - 7)/3 {Simplifying}.

Thus, we get an equation x = (y - 7)/3.

Now, we change the equations to get: y = (x - 7)/3, which is the required inverse function f⁻¹(x).

Thus, the inverse of the given function f(x) = 3x + 7 can be shown as f⁻¹(x) = (x - 7)/3, making option A the right choice.

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Solving the equations for the total number of adults and children and respective ticket costs, we find out that the number of adults and children that attended the movie theater are 13 adults and 6 children.

It is given to us that -

A total of 19 people attended the movie theater which was a mix of adults and children

Each adult ticket was $9

Each child’s ticket was $5.50.

Total cost for the party was $150

We have to find out the number of adults and children that attended the movie theater.

Let us assume that the number of adults and children that attended the movie theater be \(x\) and \(y\) respectively.

Since, a total of 19 people attended the movie theater including both adults and children, we can say that -

\(x+y=19\) ------ (1)

It is also given that each adult ticket was $9 and each child’s ticket was $5.50. So,

For \(x\) adults, the ticket price = \(9x\), and

For \(y\) children, the ticket price = \(5.5y\)

It is given that the total cost for the party was $150

\(= > 9x+5.5y=150\) ------- (2)

From equation (1), we have

\(x+y=19\\= > y =19-x\) ------ (3)

Substituting this value of \(y\) in equation (2),

\(= > 9x+5.5y=150\\= > 9x+5.5(19-x)=150\\= > 9x +104.5-5.5x=150\\= > 3.5x=45.5\\= > x=13\)------ (4)

Substituting this value of \(x\) from equation (4) in equation (3), we get

\(y=19-x\\= > y=19-13\\= > y=6\)

Thus, solving the equations, we find out that the number of adults and children that attended the movie theater are 13 adults and 6 children.

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The solution for given algebraic-equation 2x - 6 = 12, using transposition method or algebra tiles method is 9. And the first step will be transferring (-6) to right hand side by converting it into (+6)

What is an algebraic-equation?

If two things are equal, an equation declares it. For the purpose of solving the equation, variables are added, subtracted, multiplied, and divided. As long as both sides receive the same treatment, the equation will remain balanced. Algebra If you want to represent integers (or constants) and variables, you can use a set of square and rectangular figure tiles called tiles. The shape of each tile is tied to the unit square in this visual, area-based paradigm.

As per the given equation, algebra tiles are arranged. the variable represented by circle. Taking two tiles of the variable 'x' as it is tice of the variable 'x'. And the numbers represented by square tiles.

The steps to find solution is as follows:

2x - 6 = 12

2x = 12 + 6

2x = 18

x = 18 ÷ 2

x = 9

9 is the solution of the given equation.

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Refer to the attachment for the tiles.

Answer:

540,000,000,000

Step-by-step explanation:

An easy way to remember how to solve these problems when you have this many zeroes is to multiply the numbers other that zero together and add however many zeroes are in the problem or equation. Hope this helped!!

Answer: UWU look at the screenshot please hope I helped good luck U3U U3U

Step-by-step explanation:

Answer:3320

Step-by-step explanation:

Answer: 16 containers?

Step-by-step explanation:

Number of oatmeal cookies with Kiara = 30

Number of chocolate chips cookies with Kiara = 48

To find the greatest number of container neded so that there are equal amount of each cookies in each , we have to find the HCF of 30 and 48 .

Factors of 32 = 1 , 2 , 4 , 6 , 8 , 16 and 32

Factors of 48 = 1 , 2 , 3 , 4 , 6 , 8 , 12 , 16 , 24 and 48

Common and highest among these factors = 16

Which means 16 is the HCF of 32 and 48 .

∴ Kiara will need 16 plastic containers .

Answer:

y  =  0 ,  5 ,  − 8

(*￣3￣)╭

\(3y^4+9y^3-120y^2=0\\y=0,5,8\)

By using a maclaurin series to obtain the maclaurin series for the given function is  F(x) = x cos(5x) = \(1 - 25x^2/2! + 625x^4/4! - 15625x^6/6! + ...\)

To obtain the Maclaurin series for the function f(x) = x cos(5x), we need to write the Maclaurin series for cos(5x). The Maclaurin series for cos(x) is: \(cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + ...\)

Using this formula, we can substitute 5x for x and obtain the Maclaurin series for cos(5x): cos(5x) =\(1 - (5x)^2/2! + (5x)^4/4! - (5x)^6/6! + ...\)

\(= 1 - 25x^2/2! + 625x^4/4! - 15625x^6/6! + ...\)

We can substitute this series into the original function f(x) = x cos(5x) and obtain its Maclaurin series: f(x) = x cos(5x)

\(= x[1 - 25x^2/2! + 625x^4/4! - 15625x^6/6! + ...]\)

\(= x - 25x^3/2! + 625x^5/4! - 15625x^7/6! + ...\)

This is the Maclaurin series for the function f(x) = x cos(5x). It is obtained by substituting the Maclaurin series for cos(5x) into the original function and simplifying the resulting series. Maclaurin series are useful for approximating functions using polynomials. By truncating the series after a certain number of terms, we can obtain a polynomial that approximates the original function to a certain degree of accuracy. The accuracy of the approximation depends on the number of terms in the series that are used. The more terms we include, the more accurate the approximation will be.

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9514 1404 393

Answer:

  h = S/(2πr)

Step-by-step explanation:

To solve for h, divide both sides of the equation by the coefficient of h.

  S = 2πrh

  S/(2πr) = (2πrh)/(2πr)

  h = S/(2πr)

Answer:

Step-by-step explanation:

since you moved -1 in the x-axis

+1 to reverse it

(-1,5)

and since you moved +6 in the y-axis

-6 to do the reverse

(-1,-1)

Answer:

-3,-1 maybe

Step-by-step explanation:

If the price of 1 dozen of flowers is 4 1/3 dollars, the cost of 3 dozen is three times the cost of 1 dozen, meaning,

Answer: 13 dollars.

Answer:

300

Step-by-step explanation:

volume of rectangle formula:

HEIGHT*WIDTH*LENGHT*

12*10(1/2)*20(1/4= 300

Answer:

2551.5in³

Step-by-step explanation:

this is easy if you know the formula.

volume = l*w*h

= 20.25*10.5*12= 2551.5in³

Mrs. Wright give here explanation against her husband's death that somebody strangled him

The term trifles is a one-act play written by Susan Glaspell

And in that play they represents the two women discuss the life of a woman accused of murdering her husband, here we have also know that while the sheriff and county attorney investigate the scene.

Here we have to know that In Trifles the character names as Mrs. Wright explains her husband's death by saying he died "of a rope around his neck."

And here she also claims that someone strangled him and she also explains her situation in order to explain his demise.

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I don't know I really needed help on this one

Answer:

Step-by-step explanation:

correct one is b

The partial derivative diffusivity equation for spherical flow is ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t, and for hemispherical flow, it is the same equation.

1. The partial derivative diffusivity equation for spherical flow is derived from the spherical coordinate system and applies to radial flow in a spherical geometry. It can be expressed as ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t.

2. The partial derivative diffusivity equation for hemispherical flow is derived from the hemispherical coordinate system and applies to radial flow in a hemispherical geometry. It can be expressed as ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t.

1. For the derivation of the partial derivative diffusivity equation for spherical flow, we consider a spherical coordinate system with the radial direction (r), the azimuthal angle (θ), and the polar angle (φ). By assuming steady-state flow and neglecting the other coordinate directions, we focus on radial flow. Applying the Laplace operator (∇²) in spherical coordinates, we obtain ∇²p = (1/r²) (∂/∂r) (r² ∂p/∂r). Simplifying this expression, we arrive at ∂²p/∂r² + (1/r) ∂p/∂r.

2. Similarly, for the derivation of the partial derivative diffusivity equation for hemispherical flow, we consider a hemispherical coordinate system with the radial direction (r), the azimuthal angle (θ), and the elevation angle (ε). Again, assuming steady-state flow and neglecting the other coordinate directions, we focus on radial flow. Applying the Laplace operator (∇²) in hemispherical coordinates, we obtain ∇²p = (1/r²) (∂/∂r) (r² ∂p/∂r). Simplifying this expression, we arrive at ∂²p/∂r² + (1/r) ∂p/∂r.

In both cases, the term ϕμC/k ∂p/∂t represents the source or sink term, where ϕ is the porosity, μ is the fluid viscosity, C is the compressibility, k is the permeability, and ∂p/∂t is the change in pressure over time.

These equations are commonly used in fluid mechanics and petroleum engineering to describe radial flow behavior in spherical and hemispherical geometries, respectively.

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