solve by using substitution 2x-3y=-12 and x+y=9

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\int\limits \frac{x^3+1}{x^3-x} dx }} \end{gathered}$}[/tex]

We rewrite the integrand.

     [tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\frac{x^3+1}{x^3+x}=1+\frac{1}{x-1}-\frac{1}{x} }} \end{gathered}$}[/tex]

We integrate terms by terms:

The integral of the constants have this constant multiplied by the variable of integration.

        [tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\int\limits 1 \ dx=x } } \end{gathered}$}[/tex]

That u = x -1. Then that du = dx and we put du.

         [tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\int\limits\frac{1}{u} \ du }} \end{gathered}$}[/tex]

Integral 1/u is log(u). If you now substitute u further into:

              [tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{log(x-1) }} \end{gathered}$}[/tex]

The integral of the product of a function by a constant is the constant times the integral of this function:

           [tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\int\limits\left(-\frac{1}{x}\right)dx=-\int\limits\frac{1}{x}dx }} \end{gathered}$}[/tex]

Integral 1/u is log(x). Therefore, the result is: -log(x).

The result is: x - log(x) + log(x - 1)

Profit function = P(x) = 11x - 264 and 24 Units must be produced for the business to break even.

What is a Profit function?

A mathematical link between a company's overall profit and output is called a profit function. It is greatest when the firm's marginal revenue and cost are equal. It is equal to total revenue minus total costs.

How to calculate the profit function?

Profit function = Revenue function - Cost function

P(x) = R(x) - C(x)

Here, we have

R(x) = 12x

C(x) = x + 264

by applying the Profit function formula, we get

P(x) = 12x - x - 264

P(x) = 11x - 264

At this point, there is no profit or loss.

so, at break-even P(x) = 0

11x - 264 = 0

x = 24

Hence, Profit function = P(x) = 11x - 264, and 24 Units must be produced for the business to break even.

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Answer:

1) The top angle = 128°

Right angle = 52°

Bottom angle = 128°

Left angle = 52°

2) The top angle = 159°

Right angle = 21°

Left angle = 21°

Step-by-step explanation:

The left problem would involve verticle angles being congruent to each other.

[tex]5x + 2 = x + 42\\\\6y + 8 = 7y - 12[/tex]

Solve each equation:

[tex]5x + 2 = x + 42\\4x = 40\\x = 10[/tex]

[tex]6y + 8 = 7y - 12\\20 = y[/tex]

Substitute:

The top angle = 128°

Right angle = 52°

Bottom angle = 128°

Left angle = 52°

The right problem would involve supplementary angles.

[tex]\frac{1}{4}y - 1 + 27x + 24 = 180\\\\27x + 24 + 4x + 1 = 180[/tex]

Solve for second equation (for simplicity) :

[tex]27x + 24 + 4x + 1 = 180\\31x + 25 = 180\\31 = 155\\x = 5[/tex]

Substitute x = 5 into other equation :

[tex]\frac{1}{4}y - 1 + 27x + 24 = 180\\\frac{1}{4}y - 1 + 27(5) + 24 = 180\\\frac{1}{4}y = 22\\y = 88[/tex]

Substitute :

The top angle = 159°

Right angle = 21°

Left angle = 21°

Answer: 6 and 2

Step-by-step explanation:

to find your factors, you want to set the equation equal to 0 and find what adds up to your middle term and multiplies to your last term

[tex]x^{2} -8x+8=-4\\x^{2} -8x+12=0\\(x-6) (x-2) = 0\\x-6= 0\\x-2=0\\x=6\\x=2[/tex]

The curved surface area of a cylinder is 24cm²

Given the following data;

Base circumference = 4 cm

Height = 6 cm

Suppose that:

Radius of the considered cylinder = 'r' units

Height of the considered cylinder = 'h' units

Then, the curved surface area of that cylinder is 2πr h

To find the curved surface area (CSA) of the cylinder we have;

CSA of a cylinder = 2πrh

But 2πr = 4 cm

Now Substituting the values into the equation, we have,

CSA of a cylinder = 6 x 4

CSA of a cylinder = 24 cm²

Hence, The curved surface area of a cylinder is 24cm²

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Answer:

Step-by-step explanation:

the anser is 3 + 5 =8

Answer:

The circumcenter of a triangle is the point where the three perpendicular bisectors of the sides of the triangle intersect.

Step-by-step explanation:

The process of calculation of circumcenter has been given below.

What is circumcenter of a triangle?

Circumcenter of a triangle is the point of intersection of the perpendicular bisectors of every sides of the triangle.

Let the coordinate of A, B, C [tex]\Delta[/tex] ABC be ([tex]x_1, y_1[/tex]), [tex](x_2, y_2)[/tex] and [tex](x_3, y_3)[/tex] respectively and let the coordinate of circumcenter of [tex]\Delta ABC[/tex] is (x, y)

We need to find the length of AB, BC and AC

The length will be obtained in terms of x and y

On solving the equations, we will obtain the value of x and y

The value of x and y is the required coordinate of the circumcenter.

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(4.25,6.5) is the solution of the equation.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The estimate is pretty close for both equations. For the first equation, the estimate results in a value that is only 0.2125 units away from the constant.

For the second equation, the estimate results in a value that is only 0.25 units away from the constant.

The solution lies at approximately (4.25,6.5).

Hence (4.25,6.5) is the solution of the equation.

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The trigonometric equation 2sin3x - √3 = 0 is  expressed as x = π/9 + 2πn/3,  2π/9 + 2πn/3

A trigonometric equation is defined as an equation involving one or more trigonometric ratios of unknown angles

Given: 2sin3x - √3 = 0

2sin3x - √3 = 0

2sin3x = √3

sin3x = √3/2

3x = sin⁻¹√3/2           (Note: sin⁻¹√3/2 = 60° = π/3 in radian)

3x = π/3, π -3            (Note: sine  is positive in 1st and 2nd quadrant)

3x = π/3, 2π/3

x = π/9, 2π/9

x = π/9 + 2πn/3,  2π/9 + 2πn/3

Therefore, 2sin3x - √3 = 0 can be expressed as x = π/9 + 2πn/3,  2π/9 + 2πn/3

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Answer:

b) associative

Step-by-step explanation:

The associative property of multiplication was used to change the position of the parentheses

Answer:

Graph 1:     y = (-3x/5) + 1

Graph 2:    y = 4

Step-by-step explanation:

Both functions are linear, so we can use a linear equation to model these functions. Using slope-intercept form, "y=mx+b" will be easiest, since the graph is shown.

Graph 1:

(1 - (-2))/(0 - 5) = (1 + 2)/-5 = -3/5 = slope

y-intercept (0, 1)

y = (-3x/5) + 1

Graph 2:

(4 - 4)/(1 - 0) = 0 = slope

y-intercept (0, 4)

y = 0x + 4

y = 4

Answer:

First equation : [tex]y=-\frac{3}{5}x +1[/tex]

Second equation : y = 4

Step-by-step explanation:

We want to write equations for the two given lines in slope intercept form

y = mx + b

Where m = slope and b = y intercept

Identifying the y intercept

First lets find the y intercept.

The y intercepts is where the line passes the y axis.

By looking at the first line it appears that the line passes the y axis at (0,1) meaning the y intercept is 1 so b = 1

Identifying the slope

We can find the slope using the slope formula

slope = (y1-y2)/(x1-x2)
Where the values of x and y derive from any two points on the line. (x1,y1) and (x2,y2)

The points used may vary as there are many options however I have chosen (0,1) and (-5,4)

So (x1,y1) = (0,1) and (x2,y2) = (-5,4)

Meaning x1 = 0 , y1 = 1 , x2 = -5 and y2 = 4

( we now plug these into the slope formula )

Again recall slope = (y1-y2)/(x1-x2)  

==> plug in x1 = 0 , y1 = 1 , x2 = -5 and y2 = 4

slope = (1-4)/(0-(-5))

==> reduce subtraction

slope = -3/5

so our slope(m) is -3/5

Plugging in slope and y intercept into slope intercept form

Finally we plug in the values of m and b into slope intercept form to get the equation

Again we have y = mx + b

m = -3/5 and b = 1

So our equation is y = -3/5x + 1

Identifying equation for second line

When we have a horizontal line our equation is going to be put in y = b form where b = the y value that the line crosses. (or y intercept)

Here the line goes through the y value of 4 so b = 4

Hence, the equation of the second line would be y = 4

The population of California by the year 2020 is  41 million.

The term population has to do with the number of people that live in a place or a town. We have the following information from the question;

Initial population (Po) = 37 million

Population growth rate (r) = 1.0%

Time interval (t) = 10 years

P = The population of the city of California at the time t

Now using the formula;

P = Poe^rt

P = 37 * 10^6 e^0.01 * 10

P = 4.089 * 10^7 or 41 million

They would have a population of 41 million in ten years.

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Answer:

$231

Step-by-step explanation:

3 hours for 70 dollars an hour we multiply 70 by 3

70x3

210

And then to get the 10 percent tip we multiply 210 by .10

210x.10

21

And now we add 210 and 21 to get 231

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The independent variable while calculating the volume of a rectangular prisms with equal base area and different height is the height

The input values for a specific function are represented by the independent variable (x).

During an experiment, the independent variables are kept under control. The outputs of the function are represented by the dependent variable (y). The quantities being measured are the dependent variables in an experiment.

As regard the problem, the base area is a constant, the volume calculated is the dependent variable while the height iis the independent variable.

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The cost of producing 24 computer desks is $4440   .

In the question ,

it is given that ,

the equation representing the cost of producing "x" computer desks is

y = 60x + 3000 ,

we need to find the cost of producing 24 computer desks ,

substituting x = 24 in the cost equation for producing computer desks ,

we get ,

y = 60(24) + 3000

On further simplification ,

we get ,

= 1440 + 3000

Adding the numbers ,

we get ,

= 4440

the cost is $4440 .

Therefore , The cost of producing 24 computer desks is $4440   .

The given question is incomplete , the complete question is

The cost in dollars y of producing x computer desks is given by y = 60x + 3000 , Find the cost of producing 24 computer desks .

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The inequality that can be used to represent the total number of days Rashaad can rent the car while staying within his budget is d ≤ 4 .

The  rental car company charges $53 per day to rent a car and $0.08 for every mile driven.

Rashaad wants to rent a car, knowing that: He plans to drive 475 miles. He has at most $250 to spend.

Therefore, the inequality to represent the total number of days Rashaad can rent  the car can be represented as follows:

Therefore,

53d + 0.08(475) ≤ 250

53d + 38 ≤ 250

53d ≤ 250 - 38

53d ≤ 212

divide both sides of the inequality by 53

53d / 53 ≤ 212 / 53

d ≤ 4

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A cube is a three-dimensional solid object which has six square faces, facets or sides, and each meeting at a vertex.

How to find the Volume of a cube?

Volume is defined as the measurement of space occupied by the three-dimensional object.

Volume (V) = s³  where

V=volume

S=sides

V= (1/3b³)³

applying the power law of indices

V = (1/3b)∧9 cubic units

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The values for the stated domain of the function are-

F(-4) = 10; F(2) = 4; F(0) = 0.

As per the stated function.

F(x) = 6-x

The domain for the function are-

-4,2,6

The value of the function are, put each value in the place of x in the function.

F(-4) = 6 - (-4)

F(-4) = 6 + 4

F(-4) = 10

F(2) = 6 - 2

F(2) = 4

F(6) = 6 - 6

F(0) = 0

Thus, the values for the stated domain of the function are- 10, 4 and 0 respectively.

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Answer: 224 student ride the bus to school each day.

Step-by-step explanation:

In megan random sample of 60 students number of students preferred riding bus is found out to be 42 student.

Student riding the bus if the total number of students in the bus is 320

ratio of the student surveyed  to the student ride bus =

                                                                      =

Assuming the total number of   student riding bus = x

now,

                                           x =  224

hence, 224 student ride the bus to school each day.

Step-by-step explanation:

Answer:

x=21/5, x=4.2, or x=4 1/5

Step-by-step explanation:

Answer:

an= -50n +200

Step-by-step explanation:

an = a1+(n-1)d=150-50n+50=-50n+200

Answer: 21

Step-by-step explanation

if the premier is 97 the square value of x is 21

Answer:

(-6,5)(-3,-3)y

here is an equation I hope this helps :) <3

The inequality expression has a solution of (-oo, -5]

From the question, the inequality is given as

7 x plus 5 less than or equals minus 30

The above inequality can be re-written as follows

7x + 5 ≤ -30

There are constants to add or subtract in the expression

So, we start by subtracting both sides of the expression by the constant -5

This gives

7x ≤ -35

Divide both sides by 7

So, we have the following representation

x ≤ -5

Express as interval notation

(-oo, -5]

Hence, the solution to the expression is (-oo, -5]

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Answer: $306

Step-by-step explanation:

You can find the answer by multiplying 9 by each of the values.

14 * 9 = 126

20 * 9 = 180

Add these values together and you get 306 !

ANSWER 2m(m-8)(m-5)

EXPLANATION

Factor the expression: 2m(m²-13m+40)

Rewrite the term: 2m(m²-8m-5m+40)

Regroup terms into two proportional parts : 2m((m²-8m)+(-5m+40))

Factor the expression: 2m(m(m-8)-5(m-8))

Factor the expression: 2m(m-8)(m-5)

Answer: 2m(m-8)(m-5)

Answer:

f) Line l.

g) ∠1 and ∠3,  ∠2 and ∠4,  ∠5 and ∠7,  ∠6 and ∠8.

h) ∠3 and ∠6,  ∠2 and ∠7.

i) ∠4 and ∠5,  ∠1 and ∠8.

j) ∠2 and ∠3,  ∠6 and ∠7.

Step-by-step explanation:

The transversal is a line that crosses two other lines in the same plane at two distinct points.

Therefore, the transversal line of the given diagram is line l as it crosses lines j and k.

Corresponding angles are pairs of angles that are in the same position relative to both lines crossed by the transversal.

Alternate interior angles are pairs of angles on the inner side of the two lines that the transversal crosses, but on opposite sides of the transversal.

Alternate exterior angles are pairs of angles on the outer side of the two lines that the transversal crosses, but on opposite sides of the transversal.

Consecutive interior angles are pairs of angles on the inner side of the two lines that the transversal crosses, and are on the same side of the transversal.

The value of tα/2 of the t-test is 2.898

A t-test is a statistical test that is used to compare the means of two groups. tα/2 refers to the t critical value from the t-distribution table that corresponds to α/2

Given:  n = 18 and a 99% confidence interval

We have to find the critical t value for 99% confidence level and sample size of 18

Degrees of freedom = n - 1 = 17

α = 1 - 0.99 = 0.01

α/2 = 0.01/2 = 0.005

In the t table (check the attached image), we have to check the value against the column 0.005 and for 17 degrees of freedom.

The value obtained from the table is 2.898

Therefore, tα/2 = 2.898

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Answer:

A: 25,500

B: 14,600

C: 10,900

Step-by-step explanation:

This is what we know:

a = b + c

a + b + c = 51,000       Substitute in a for b + c

a + a = 51000  Combine like terms.

2a = 51000  Divide both sides by 2

a = 25,500

28a + 16b + 12c = 1078400   Substitute in 25.600 for a

28(25500) + 16b + 12c = 1078400

714000 + 16b + 12c = 1078400  Subtract 714000 from both sides

16b + 12 c = 364400

25500 +b + c = 51000  Subtract 25500 from both sides

b + c + = 25500    Multiply this equation all the way through by -12 and add it to the bold equation above it.

-12b -12c = -306000

16b + 12c = 364400

4b = 58400   divide both sides by 4

b = 14600

a + b + c = 51000  Plug in what we know

25500 + 14600 + c = 51000

40100 + c = 51000  Subtract 40100 from both sides

c = 10900

Answer: I think A? not fully sure

Step-by-step explanation: