How to divide function?​

The appropriate fraction produced by the expression is -32/9.

Any function that can be expressed as a rational fraction, which is an algebraic fraction in which both the numerator and the denominator are polynomials, is referred to as a rational function.

Given the function below:

6x-5/3 = 5x + 9

Cross multiply

6x - 5 = 3(5x + 9)

Expand to have:

6x - 5 = 3(5x) + 3(9)

6x - 5 = 15x + 27

6x - 15x = 27 + 5

-9x = 32

Divide both sides by -9

-9x/-9 = 32/-9
x = -32/9

Hence the result of the expression as an improper fraction is -32/9.

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Answer:

F

Step-by-step explanation:

Answer:

C) 12.75

Step-by-step explanation:

4x=51

x=51/4

x=12.75

To solve this differential equation by making the change of variable u = x + y, we first need to find an expression for y' in terms of u.

Using the chain rule, we have:

du/dx = d/dx (x + y) = 1 + dy/dx

Solving for dy/dx, we get:

dy/dx = du/dx - 1

Substituting into the given differential equation, we have:

5(du/dx - 1) = x + y

Multiplying both sides by dx and rearranging, we get:

5 du/(x + y - 5) = dx

Now we can integrate both sides with respect to their respective variables.

On the left-hand side, we use the substitution u = x + y, which gives:

5 du/u-5 = dx

Integrating both sides yields:

5 ln|u-5| = x+C1

where C1 is a constant of integration.

Substituting back for u = x + y, we have:

5 ln|x+y-5| = x+C1

which can be written as:

ln|x+y-5|^5 = x+C2

where C2 = 5C1.

Exponentiating both sides gives:

|x+y-5|^5 = e^(x+C2) = Ce^x

where C = e^C2.

Taking the fifth root of both sides and using the absolute value notation, we finally arrive at the general solution:

|x+y-5| = (Ce^x)^(1/5)

or

x + y - 5 = ±(Ce^x)^(1/5)

where the sign of the right-hand side depends on the sign of x + y - 5.

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The maximum amount you can earn is $540

a. y = 13.50x , 10 <= x <= 40
b. x = 10, y = 135; x = 20, y= 270; x = 30, y = 405; x = 40, y = 540
c. Domain: 10 <= x <= 40; Range: 0 <= y <= 540
d. The minimum amount you can earn in a week with this job is $135. The maximum amount you can earn is $540.

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The perimeter of the figure or the amount of black cord required is given by P = 110.18 feet

The amount of fabric required for each figure is given by A = 222.985 feet²

The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.

Perimeter P of rectangle = 2 ( Length + Width )

Given data ,

Let the perimeter of the figure be represented as P

Let the amount of fabric required be A = area of the figure

Now , the length and width of the perimeter of rectangle are 16 feet and 10 feet respectively

The height and base of the triangle is 1.73 feet and 2 feet respectively

The side length of the square is 7 feet

The circle at the center has a diameter of 3 feet so the radius is 1.5 feet

Now , the perimeter of rectangle P = 2 ( L + B ) = 2 ( 16 + 10 )

The perimeter of rectangle = 2 x 26 = 52 feet

The area of rectangle = 16 x 10 = 160 feet²

The perimeter of 4 triangles = 4 x ( 3 x 1.73 ) = 20.76 feet

The area of 4 triangles = 4 ( ( 1/2 ) x 1.73 x 2 ) = 6.92 feet²

The circumference of the circle = 2πr = 2 x 3.14 x 1.5 = 9.42 feet

The area of circle = πr² = 3.14 x 1.5 x 1.5 = 7.065 feet²

The perimeter of square = 4a = 4 x 7 = 28 feet

The area of square = a² = 49 feet²

Now , the amount of black cord required = perimeter of rectangle + perimeter of 4 triangles + circumference of the circle + perimeter of square

The amount of black cord required P = 110.18 feet

And , the amount of fabric required A = area of rectangle + area of 4 triangles + area of circle + area of square

The amount of fabric required A = 222.985 feet²

Hence , the amount of black cord required is 110.18 feet and the amount of fabric required is 222.985 feet²

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Answer:

2,3,5

Step-by-step explanation:

Answer:

B. C. E

Step-by-step explanation:

Answer:

There were 76 childrens and 14 adults.

Step-by-step explanation:

Since the group has a total of 90 children and adults, then the sum of the number of adults with the number of children must be equal to 90 as shown below:

children + adults = 90

Since the total cost for their tickets was 548 then the number of children multiplied by the price of their ticket summed by the number of adults multiplied by the price of their ticket must be equal to that. We have:

5*children + 12*adults = 548

With these two equations we have a system of equations shown below:

children + adults = 90

5*children + 12*adults = 548

In order to solve this we will multiply the first equation by -5, and sum both equations we have:

-5*children - 5*adults = -450

5*children + 12*adults = 548

7*adults = 98

adults = 98/7 = 14

children + 14 = 90

children = 90 - 14 = 76

There were 76 childrens and 14 adults.

We can solve the triangle using the law of sines and law of cosines. To use the law of sines, we know that sin β/ b = sin γ/ c and

sin α/ a = sin γ/ c where α, β, and γ are the angles in the triangle.

We have two equations, so we can solve for b and γ: sin β/ b = sin γ/ c

=> sin 21°/ b = sin γ/10

=> sin γ = 10sin 21° / b.

sin α/ a = sin γ/ c

=> sin α/7 = sin γ/10

=> sin γ = 10sin α/7.

Therefore, 10sin 21° / b = 10sin α/7, and we can solve for α:

sin α = 7sin 21°/b

=> α = sin-1(7sin 21°/b).

We can then use the fact that the sum of angles in a triangle is 180° to solve for γ: γ = 180° - α - β.

To use the law of cosines, we know that a² = b² + c² - 2bc cos α.

We have a, c, and α, so we can solve for b: b² = a² + c² - 2ac cos β.

We have a, b, and c, so we can solve for the perimeter, P = a + b + c, and the semiperimeter, s = P/2.

Once we have the perimeter, we can use Heron's formula to find the area: A = sqrt(s(s - a)(s - b)(s - c)).

The approximate values of a, b, and γ, rounded to one decimal place, are:a ≈ 7.6b ≈ 4.2γ ≈ 138.0°

The area is approximately A ≈ 24.2.

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Initial value is your y intercept, and to find that you just need to substitute 0 for x. Anything to the power of 0 is just 1. So you get 34.2(1), which means that your initial value is 34.2.

Answer:

=-52

Step-by-step explanation:

The graph for the linear equation y=24x, will be a straight line having coordinate (1,24) i.e. B.

What is a linear equation, exactly?

A linear equation is a first-degree algebraic equation in which each term is either a constant or the product of a constant and a single variable (degree 1). A linear equation is stated as y = mx + b, where y is the dependent variable, x is the independent variable, m is the line's slope, and b= y-intercept .

A linear equation's graph is a straight line. The line's slope decides how steep it is, and the y-intercept indicates where the line crosses the y-axis. Linear equations are used to model relationships between variables that are directly proportional to each other, such as distance and time, or cost and quantity.

Now,

Given equation is y=24x

then for  x,    y is

              1,    24

              2,   48

              3,    72

              4,     96

Hence, the graph will be as represented in option 2.

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Answer: 30m

Step-by-step explanation:

Given :

Rachel is sitting in a tree 15 feet above the ground.

A minute ago, she spotted a skunk 40 feet from the base of the tree walking closer to her. Now, the skunk is 20 feet from the base of the tree.

The diagonal line from Rachel to the skunk is the distance between them.

To Find :

How much closer is the skunk to Rachel now than it was a minute ago.

Solution :

Initial distance,

\(d_i=\sqrt{15^2+40^2}\\\\d_i=42.72\ feet\)

Final distance,

\(d_f=\sqrt{15^2+20^2}\\\\d_f=25\ feet\)

Therefore, skunk is ( 42.72 - 25 ) = 17.72  feet closer to Rachel now than it was a minute ago.

Hence, this is the required solution.

Answer:

x = 60

Step-by-step explanation:

Given

\(\sqrt{x+4}\) - 7 = 1 ( add 7 to both sides )

\(\sqrt{x+4}\) = 8 ( square both sides )

(\(\sqrt{x+4}\) )² = 8² , that is

x + 4 = 64 ( subtract 4 from both sides )

x = 60

Answer:

9 inches

Step-by-step explanation:

To find the height of the model of the Great Pyramid of Giza, we can use the formula for the volume of a pyramid:

Volume = (1/3) * base_area * height

Given that the base of the model is a square with sides measuring 15 inches, the base area is calculated by multiplying the length of one side by itself:

Base_area = 15 inches * 15 inches = 225 square inches

We are also given that the volume of the model is 675 cubic inches. Plugging in the values into the volume formula:

675 cubic inches = (1/3) * 225 square inches * height

To find the height, we can isolate it in the equation:

height = (675 cubic inches) / [(1/3) * 225 square inches]

height = (675 cubic inches) / (75 square inches)

height = 9 inches

Therefore, the height of the model of the Great Pyramid of Giza is 9 inches.

The dividend in 2018 was $2.95, and it is expected to grow at a rate of 7.4% for the next five years and 2.6% thereafter. With an equity cost of capital of 8.6%, the value per share at the end of 2018 can be calculated.

To calculate the value per share at the end of 2018, we need to discount the expected future dividends using the dividend-discount model. The model assumes that the value of a stock is equal to the present value of all its expected future dividends.

First, we need to calculate the dividends for each year from 2019 to 2023. We start with the dividend in 2018, which was $2.95. We then increase it by 7.4% each year for the next five years:

Dividend in 2019 = $2.95 * (1 + 7.4%) = $3.17

Dividend in 2020 = $3.17 * (1 + 7.4%) = $3.40

Dividend in 2021 = $3.40 * (1 + 7.4%) = $3.65

Dividend in 2022 = $3.65 * (1 + 7.4%) = $3.92

Dividend in 2023 = $3.92 * (1 + 7.4%) = $4.22

After 2023, the dividend is expected to grow at a rate of 2.6% per year. To find the value per share at the end of 2018, we discount the future dividends to their present value using the equity cost of capital of 8.6%.

The present value of the dividends can be calculated as follows:

PV = (D1 / (1 + r)) + (D2 / (1 + r)^2) + ... + (Dn / (1 + r)^n)

where PV is the present value, D1 to Dn are the dividends for each year, r is the equity cost of capital, and n is the number of years.

In this case, n = 5 because we are discounting the dividends for the next five years. Let's calculate the present value:

PV = ($3.17 / (1 + 8.6%)) + ($3.40 / (1 + 8.6%)^2) + ($3.65 / (1 + 8.6%)^3) + ($3.92 / (1 + 8.6%)^4) + ($4.22 / (1 + 8.6%)^5)

PV = $3.17 / 1.086 + $3.40 / 1.086^2 + $3.65 / 1.086^3 + $3.92 / 1.086^4 + $4.22 / 1.086^5

PV ≈ $2.91 + $3.07 + $3.24 + $3.41 + $3.59

PV ≈ $16.22

Therefore, the estimated value per share of Procter and Gamble at the end of 2018 using the dividend-discount model is approximately $16.22.

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The dividend in 2018 was $2.95, and it is expected to grow at a rate of 7.4% for the next five years and 2.6% thereafter. With an equity cost of capital of 8.6%, the value per share at the end of 2018 can be calculated.

To calculate the value per share at the end of 2018, we need to discount the expected future dividends using the dividend-discount model.
The model assumes that the value of a stock is equal to the present value of all its expected future dividends. First, we need to calculate the dividends for each year from 2019 to 2023. We start with the dividend in 2018, which was $2.95. We then increase it by 7.4% each year for the next five years:

Dividend in 2019 = $2.95 * (1 + 7.4%) = $3.17
Dividend in 2020 = $3.17 * (1 + 7.4%) = $3.40
Dividend in 2021 = $3.40 * (1 + 7.4%) = $3.65
Dividend in 2022 = $3.65 * (1 + 7.4%) = $3.92
Dividend in 2023 = $3.92 * (1 + 7.4%) = $4.22

After 2023, the dividend is expected to grow at a rate of 2.6% per year. To find the value per share at the end of 2018, we discount the future dividends to their present value using the equity cost of capital of 8.6%.
The present value of the dividends can be calculated as follows:
PV = (D1 / (1 + r)) + (D2 / (1 + r)^2) + ... + (Dn / (1 + r)^n) where PV is the present value, D1 to Dn are the dividends for each year, r is the equity cost of capital, and n is the number of years.

In this case, n = 5 because we are discounting the dividends for the next five years. Let's calculate the present value: PV = ($3.17 / (1 + 8.6%)) + ($3.40 / (1 + 8.6%)^2) + ($3.65 / (1 + 8.6%)^3) + ($3.92 / (1 + 8.6%)^4) + ($4.22 / (1 + 8.6%)^5)
PV = $3.17 / 1.086 + $3.40 / 1.086^2 + $3.65 / 1.086^3 + $3.92 / 1.086^4 + $4.22 / 1.086^5
PV ≈ $2.91 + $3.07 + $3.24 + $3.41 + $3.59
PV ≈ $16.22
Therefore, the estimated value per share of Procter and Gamble at the end of 2018 using the dividend-discount model is approximately $16.22.

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Answer:

it's not a square number cause it says 5⁹ and ⁹ is not squared ³ is

Answer:

He can cut 15 1/2 meter strips.

Step-by-step explanation:

10 1/2 meter strips are 5 meters in length.

5 1/2 meter strips are 2.5 meters in length.

5 + 2.5 = 7.5 meters in length

Answer:

Range = 5

Mode = 7

Step-by-step explanation:

To find range we first need to find the highest number and the lowest number

3 , 4 , 4 , 7 , 7 ,7 ,7 7, 8

least number = 3

highest number = 8

now substract the lowest number from the highest to get the range

= 8-3

= 5

range = 5

Mode : the most common number in the list will be our mode

7 is our mode as it came 5 time in the list

The probability that exactly two couples state incompatibility as the reason is equal to the probability of two couples citing incompatibility and two couples not citing it.

HTML formatted answer: Given: 65% of all divorce cases cite incompatibility as the underlying reason. To find: Probability that exactly two will state incompatibility as the reason. Solution: As per the given data, The probability of citing incompatibility as the underlying reason for divorce is 65%.

Then, the probability of citing any other reason is (100% - 65%) = 35%.Let the probability of citing incompatibility by any couple as A, and the probability of not citing incompatibility by any couple as B. Here, the total couples filing for divorce = 4. Probability of two couples citing incompatibility and two couples not citing it.P(2C, incompatibility and 2C, not incompatibility)= \[\left( \begin{matrix}
  4  \\
  2  \\
\end{matrix} \right)\] × 0.65² × 0.35²The probability of choosing any 2 out of 4 couples = \[\left( \begin{matrix}
  4  \\
  2  \\
\end{matrix} \right)\] = 6The probability of 2 couples citing incompatibility = 0.65²The probability of 2 couples not citing incompatibility = 0.35²Hence,The probability that exactly two couples state incompatibility as the reason isP(2C, incompatibility) = \[\left( \begin{matrix}
  4  \\
  2  \\
\end{matrix} \right)\] × 0.65² × 0.35² = 6 × 0.4225 × 0.1225 = 0.3218Therefore, the required probability is 0.3218.

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The correct interpretation is For every hour the electrician works, her pay will increase by $32. The correct option is A.

What is the equation of a line?

A line is a flat, one-dimensional structure that can go on forever in both directions and is straight. A line's equation is given by, y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is the y-intercept.

Given that an electrician bills a one-time flat service cost for accepting a task and an additional hourly rate for finishing it. The function E(x) = 135 + 32x, where x is the number of hours she works on the task and 135 is her flat service fee, can be used to express the amount an electrician bills per job.

The slope interpretation for the presented problem is that the electrician's income will rise by $32 for every hour that she works.

Therefore, the accurate interpretation is that the electrician's pay will rise by $32 for every hour that she works.

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Answer: 4.25

 x

10

−

4

Step-by-step explanation:

Answer:

4.25x10^-9

Step-by-step explanation:

The nearest whole number, the estimated time required by the 50th unit is 47 minutes.Therefore, the correct option is b. 48 minutes.

Given the 13th unit requires 87 minutes and 26th unit requires 64 minutes.To find the estimated time required by the 50th unit, we need to use the equation of the linear equation of the line.Let's find the value of m (slope).`m = (64 - 87)/(26 - 13)m = -23/13`Let's find the value of b (y-intercept).`b = 87 - (-23/13) × 13b = 87 + 23b = 110`

Therefore, the equation of the line can be written as:y = -23/13 x + 110Let's substitute the value of x as 50 and find the value of y (time required by the 50th unit).`y = -23/13 × 50 + 110y = 47.31`Rounded to the nearest whole number, the estimated time required by the 50th unit is 47 minutes.Therefore, the correct option is b. 48 minutes.

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The single equation of second order is x′′ - 9x + 2y = 0, the roots of the auxiliary equation are r1 = 3 and r2 = -3. The homogeneous solution is x(t) = c1e^(3t) + c2e^(-3t).The particular solution is x(t) = 2e^(3t) + e^(-3t) and y(t) = -e^(3t) + 4e^(-3t).The unique solution that satisfies the system is x(t) = 4e^(3t) + e^(-3t) and y(t) = 3e^(3t) + 3e^(-3t).

Given that a system of first-order differential equations is represented as follows:x′ = x + 2y y′ = 4x − y.

The system of equations can be transformed into a single equation of second order by differentiating the first equation and substituting the second equation as follows:x′′ = (x′)′ = (x + 2y)′ = x′ + 2y′ = x′ + 2(4x − y) = 9x − 2y.

The single equation of second order is x′′ - 9x + 2y = 0Now we have the auxiliary equation: r² - 9 = 0.

.

The roots of the auxiliary equation are r1 = 3 and r2 = -3. The homogeneous solution is thus:x(t) = c1e^(3t) + c2e^(-3t).

Next, let's find the particular solution by putting it in the original equation and solving for the constants.

We have:x(t) = 2e^(3t) + 1e^(-3t)y(t) = -1e^(3t) + 4e^(-3t)The particular solution is:x(t) = 2e^(3t) + e^(-3t)y(t) = -e^(3t) + 4e^(-3t).

Therefore, the general solution is x(t) = c1e^(3t) + c2e^(-3t) + 2e^(3t) + e^(-3t)and y(t) = -e^(3t) + 4e^(-3t) - e^(3t) + 4e^(-3t).

Simplifying, we get:x(t) = c1e^(3t) + c2e^(-3t) + 3e^(3t) + e^(-3t)y(t) = 3e^(3t) + 3e^(-3t)For x(0) = 2, we get:c1 + c2 + 4 = 2For y(0) = -1, we get:3 + 3 = -1Therefore, c1 + c2 = -2 and c1 = -3, c2 = 1.

The unique solution that satisfies the system is thus:x(t) = -3e^(3t) + e^(-3t) + 3e^(3t) + e^(-3t) = 4e^(3t) + e^(-3t)y(t) = 3e^(3t) + 3e^(-3t).

The single equation of second order is x′′ - 9x + 2y = 0, the roots of the auxiliary equation are r1 = 3 and r2 = -3.

The homogeneous solution is x(t) = c1e^(3t) + c2e^(-3t).The particular solution is x(t) = 2e^(3t) + e^(-3t) and y(t) = -e^(3t) + 4e^(-3t).

The unique solution that satisfies the system is x(t) = 4e^(3t) + e^(-3t) and y(t) = 3e^(3t) + 3e^(-3t).

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