Each graph shows a linear function. Find an equation for it’s inverse and graph it’s inverse. The first one is done for you.

4. 5.


6. Examine the graphs you drew in problems 4 and 5. How does the dotted like y=x relate to the graphs of f(x) and f^-1(x)?

Answer:

6j+6

Step-by-step explanation:

I think it would be 6j+6 unless you didn't add the full problem.

The density of benzene in English units is 9.69 lb/ft³.

Mass per unit volume is measured using density. It can be calculated by dividing an object's mass by its volume. A crucial physical characteristic of matter is density, which has an impact on how objects behave in various settings. A valuable tool for determining the concentration of a specific object or material is density. The more mass an object has for a particular volume, the higher its density. The unit of measurement for density is kilograms per cubic meter (kg/m³).

Benzene has a specific gravity of 0.97, making it 0.97 times heavier than water. The weight of water, which is 62.427 lb/ft³, must be multiplied by the specific gravity to determine the specific weight of benzene.

Benzene has a specific gravity of 0.97, making it 0.97 times heavier than water. The weight of water, which is 62.427 lb/ft³, must be multiplied by the specific gravity to determine the specific weight of benzene. As a result, benzene has a specific gravity of 60.7 lb/ft³.

We must divide the specific weight of benzene by the weight of 1 cubic foot of benzene, which is 6.24lb, in order to determine the density of benzene in English units. As a result, benzene has a density of 9.69 lb/ft³ in English units.

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The surface area of the prism is 142 square in

From the question, we have the following parameters that can be used in our computation:

The net of a rectangular prism

The surface area of the prism is the sum of the individual shapes that make up the net

Using the above as a guide, we have the following:

Surface area = 2 * 7 * 3 + 2 * 5 * 3 + 2 * 5 * 7

Evaluate the sum of products

Surface area = 142

Hence, the surface area is 142 square in

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The entries in the matrix correspond to whether or not the two elements in the set are related or not related according to the complement of the original relation.

To find the matrix for the complement of a relation, r, given the matrix representing r on a finite set a, you first need to determine the size of the matrix, which is equal to the number of elements in the set. The matrix for the complement of r is simply the matrix for r with all of its entries negated. In other words, you switch all of the 1's to 0's and all of the 0's to 1's.

For example, if the matrix for r is:

[tex]\left[\begin{array}{ccc}1&0&1\\0&1&0\\1&0&1\end{array}\right][/tex]

The matrix for the complement of r would be:

[tex]\left[\begin{array}{ccc}0&1&0\\1&0&1\\0&1&0\end{array}\right][/tex]

This gives us a matrix that represents the complement of the original relation. The entries in the matrix correspond to whether or not the two elements in the set are related or not related according to the complement of the original relation.

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The expression that represents the amount in grams the caterpillar eats in one day is  C) 14m

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Let, The birth mass of the caterpillar be 'm'.

Given, It eats 1400%, percent of its birth mass in one day.

Therefore, The equation representing the amount, in grams, the caterpillar eats in one day is,

= (1400/100)×m.

= 14×m.

= 14m.

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Answer:12x³ - 36x² + x^5 = (6x²)(2x - 4) + x^5.

Step-by-step explanation:To divide the polynomial 12x³ - 36x² + x^5 by 6x², we can use polynomial long division. Here's the process:

Divide the first term of the dividend (12x³) by the first term of the divisor (6x²). The result is 2x.

Multiply the divisor (6x²) by the quotient (2x) to get 12x³.

Subtract the product from the dividend (12x³ - 36x² + x^5). The result is -24x² + x^5.

Repeat the process for the next term of the dividend, which is -24x². Divide it by the divisor (6x²) and get -4 as the quotient.

Multiply the divisor (6x²) by the quotient (-4) to get -24x².

Subtract the product from the remaining dividend (-24x² + x^5). The result is x^5.

The remainder is x^5, which means that 6x² is a factor of 12x³ - 36x² + x^5, but x^5 is not a factor of 6x².

Therefore, the final answer is:

12x³ - 36x² + x^5 = (6x²)(2x - 4) + x^5.

The domains of the functions are [-8, 6] and [-16, 12]

See attachment for the graph of the function f(2x)

From the graph, we have the following parameters that can be used in our computation:

The x values of f(x) start from -8 and ends at 6

This means that

Domain of f(x): [-8, 6]

For f(2x) after the dilation. the domain is

Domain of f(2x):[-16, 12]

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Answer:

$0.36

Step-by-step explanation:

[tex]\frac{\$2.88}{8}=\$0.36[/tex]

A prime number doesn't have sequence so, it cannot be model with sequence.

Prime numbers are number that can only be divided by itself and 1.

E.g 2,3,5,7,11,13,17,19,23,29 etc.

So, note that this sequence doesn't have a pattern, it is neither Geometry Progression nor Arithmetic Progression.

Now, let take look at the model given

If n is prime, then 2n-1 is prime

Let take 5 for

n=5 is a prime number

2n-1=2(5)-1=10-1=9

9 is not a prime number so the model doesn't work

A prime number doesn't have sequence so, it cannot be model with sequence.

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Therefore , the solution of the given problem of percentage comes out to be $239.6 price he will pay on first store and $419.3 on second store.

In mathematics, a percentage is any value that can be written as a fraction of 100. There are also sporadic uses of the abbreviations "pct.," "pct," or "pc." However, it is commonly indicated by the "%" mark. The proportional amount is flat and lacks any dimensions. Since percentages have a numerator of 100, they can be thought of as fractions. The percent symbol (%) must come after a number to denote that it is a percentage.

Here,
Given :

Price of television is $599

a)

First store is :

=> 50/100 * 599

=> 299.5

and

additional 20% discount :

=> 20/100 * 299.5

=> 59.9

current price =299.5 -59.9 =  $239.6

b)

=> 30/100 * 599

=> 179.7

=> 599 - 179.7

=> $419.3

Therefore , the solution of the given problem of percentage comes out to be $239.6 price he will pay on first store and $419.3 on second store.

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Answer:

In this section we will discuss the method of graphing an equation in two variables. In other words, we will sketch a picture of an equation in two variables.

Step-by-step explanation:

The solution to the inequality 10 x 2^n > 1000 + 500n is given as follows:

n < -1.995 or n > 9.119.

The intervals for which a function is positive are the intervals for which the function graph lies above the x-axis.

The inequality for this problem is given as follows:

10 x 2^n > 1000 + 500n

Moving everything on the expression to the left side, the inequality is given as follows:

10 x 2^n - 1000 - 500n > 0.

Hence the function that we must obtain where it is positive is given as follows:

f(n) = 10 x 2^n - 1000 - 500n.

From the image given at the end of the answer, the interval is given as follows:

n < -1.995 or n > 9.119.

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The process to graph a line is described below, and the graph of the linear equation is on the image at the end.

I will help you to graph the first line step-by-step.

The linear equation we want to graph is:y = (3/2)*x + 3

First, we need to find two points on the line.

We can do that by evaluating the equation in two different values of x.

If x = 0:

y = (3/2)*0 + 3 = 3

We have the point (0, 3)

if x = 2:

We wil get:y = (3/2)*2 + 3 = 6

We have the point (2, 6)

Now you just need to graph these two points on a coordinate axis and then draw a line that connects them.

That line is the graph of the linear equation.

The graph can be seen on the image at the end.

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The probability number of times to roll the number cube to result in a prime number 12 times is 24

How to determine the number of times?

The given parameters are:

Number cube = 6 sides

Number of times= 12

The probability of obtaining a prime number in a six-sided die is:

P(Prime) = 3/6

The number of times (n) is then calculated as:

p * n = 12

Substitute known values

3/6 * n = 12

Evaluate the fraction

1/2 * n = 12

Multiply both sides by 2

n = 24

Hence, the number of times is 24

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Answer:

  MN = 9

Step-by-step explanation:

You want MN if KL : LM : MN = 2 : 3 : 1 and KN = 54.

The fraction of the total length that is segment MN is ...

  MN/KN = 1/(2+3+1) = 1/6

Multiplying by KN, we have ...

  MN = 1/6·KN = 1/6·54 = 9

The length of MN is 9.

The surface area of a cylinder can be calculated as the sum of the area of the two circular bases and the lateral surface area, which is the area of a rectangle with length equal to the circumference of the base and width equal to the height of the cylinder.

The formula for the surface area of a cylinder is:

[tex]$A = 2\pi r^2 + 2\pi rh$[/tex], where $r$ is the radius and $h$ is the height.

In this case, we know that the radius is 3 inches and the surface area is square inches. To find the height of the cylinder, we can rearrange the formula to solve for $h$:

[tex]$A = 2\pi \cdot 3^2 + 2\pi \cdot 3h = 18\pi + 6\pi h$[/tex]

Dividing both sides by [tex]$6\pi$:[/tex]

[tex]$3 + h = \frac{A}{6\pi}$[/tex]

So, the height of the cylinder in inches is[tex]$h = \frac{A}{6\pi} - 3$.[/tex]

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The solution is, the Bank of Peace will pay Marco more in interest over the 3-year period, Marco should choose the Bank of Peace to get the most interest, the total amount of interest that Marco will earn from the Bank of Trust over the 3-year period is, = £870.

Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.

here, we have,

To determine which bank will give Marco the most interest over the 3-year period, we need to calculate the total amount of interest that each bank will pay Marco over the 3 years.

First, let's consider the Bank of Peace.

Since the interest rate is 2.5% per year and is compounded annually, Marco will earn 2.5/100 * £15000 = £375 in interest in the first year. In the second year, the interest will be calculated on the original £15000 plus the £375 of interest earned in the first year, for a total of £15000 + £375 = £15375.

So Marco will earn 2.5/100 * £15375 = £383.44 in interest in the second year. In the third year, the interest will be calculated on the original £15000 plus the £375 of interest earned in the first year and the £383.44 of interest earned in the second year, for a total of

£15000 + £375 + £383.44 = £15728.44.

So Marco will earn 2.5/100 * £15728.44 = £391.71 in interest in the third year.

Therefore, the total amount of interest that Marco will earn from the Bank of Peace over the 3-year period is £375 + £383.44 + £391.71 = £1150.15.

Now let's consider the Bank of Trust. In the first year, Marco will earn 3.8/100 * £15000 = £570 in interest.

In the second year, the interest rate is 1%, so Marco will earn 1/100 * £15000 = £150 in interest. In the third year, Marco will also earn £150 in interest.

Therefore, the total amount of interest that Marco will earn from the Bank of Trust over the 3-year period is £570 + £150 + £150 = £870.

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The domain and the range of the function and its inverse is increasing.

In order to use the given linear function to complete the table, we would have to substitute each of the values of x (x-values) into the linear function and then evaluate as follows;

When the value of x = -1, the linear function is given by;

f(x) = 3x + 2

f(-1) = 3(-1) + 2

f(-1) = -1.

When the value of x = -2/3, the linear function is given by;

f(x) = 3x + 2

f(-2/3) = 3(-2/3) + 2

f(-2/3) = 0.

When the value of x = -1/3, the linear function is given by;

f(x) = 3x + 2

f(-1/3) = 3(-1/3) + 2

f(-1/3) = 1.

When the value of x = 1/3, the linear function is given by;

f(x) = 3x + 2

f(1/3) = 3(1/3) + 2

f(1/3) = 3.

When the value of x = -1, the inverse function is given by;

f⁻¹(x) = 1/3(x) - 2/3

f⁻¹(-1) = 1/3(-1) - 2/3

f⁻¹(-1) = -0.9999

When the value of x = 0, the inverse function is given by;

f⁻¹(x) = 1/3(x) - 2/3

f⁻¹(0) = 1/3(0) - 2/3

f⁻¹(0) = -2/3.

When the value of x = 1, the inverse function is given by;

f⁻¹(x) = 1/3(x) - 2/3

f⁻¹(1) = 1/3(1) - 2/3

f⁻¹(1) = -1.

When the value of x = 3, the inverse function is given by;

f⁻¹(x) = 1/3(x) - 2/3

f⁻¹(3) = 1/3(3) - 2/3

f⁻¹(3) = 1/3.

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Answer:

7:40 PM

Step-by-step explanation:

A correlation coefficient of -0.9 means that there is a strong negative linear relationship between two variables, while a correlation coefficient of 0 means that there is no linear relationship between the two variables.

When two variables have a strong negative linear connection, the values of one variable grow while the values of the other variable fall, and vice versa. When there is no linear relationship, the values of the two variables are more densely packed around the line of best fit, resulting in a smaller standard deviation.

When there is no linear relationship between two variables, the values of the variables are randomly distributed, and there is no consistent link between them. The standard deviation is bigger in this case because the values of the two variables are more spaced apart.

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The minimal value of n for which there is at least a 0.90 probability of the system functioning is 4, which is the smallest conceivable value.

The likelihood of a 3 out of 5 system working was calculated to be 0.9914.

Think about the 3 out of 4 system.

A minimum probability of 0.90 must exist for 3 out of 4 systems to function.

Calculate the likelihood that a 3 out of 4 system will function as follows:

[tex]P (X ≥ 3) = 1 - P (X < 3) = 1 - P (X = 0) - P (X = 1) - P (X = 2)[/tex]

A three out of four system having a good chance of working is 0.9477.

Take a look at a 3 out of 3 system.

See if the likelihood of a 3 out of 3 system operating is at least 0.90.

Calculate the likelihood that a 3 out of 3 system will function as follows:

[tex]P (X ≥ 3) = 1 - P (X < 3) = 1 - P (X = 0) - P (X = 1) - P (X = 2)[/tex]

A three-out-of-three system's likelihood of success is 0.7290.

Since the likelihood of the system functioning is at least 0.90 for a number of n as little as 4, that value is the smallest feasible.

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When 3 is the input, the output is 10. When 10 is the input, the output is 15.

It should be noted that the input for the function is time, measured in hours. The output of the function is energy usage, measured in kilo watts.

From the information, the energy usage of a light bulb is a function. The input for the function is time measured in hours. The output of the function is energy usage, measured in Kilo watts. E (energy) is a function of t (time).

The graph of the function will show energy usage on the y axis and time on the x axis.

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The ratio of flutes to tubas in a middle school band is 5 to 2, which represents the number of flutes for every 2 tubas in the band. This ratio can be written in three different ways to express the same relationship between the number of flutes and tubas:

5:2 - This is the fraction form of the ratio, where the number of flutes is written before the colon and the number of tubas is written after the colon.

5/2 - This is the fraction form of the ratio, where the numerator represents the number of flutes and the denominator represents the number of tubas.

2.5 flutes per tuba - This is the rate form of the ratio, where the number of flutes is written as the number of flutes per tuba. This way of expressing the ratio is commonly used to show the average number of flutes for every 1 tuba in the band.

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The value of a is 0 and b is 1.55

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

We have to find the values of "a" and "b",

we can use the exchange rate £1 = €1.55.

When the number of pounds is 0,

The equivalent number of euros is 0 × €1.55 = €0,

so (0, a) = (0, 0).

a=0

The number of pounds is 1

The equivalent number of euros is 1 × €1.55 = €1.55,

so (1, b) = (1, 1.55).

b=1.55

Hence, the values of a is 0 and b is 1.55

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All the possible values of the polynomial are given below, with the complete explanation.

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

Given:

We have a function polynomial,

f(x) = -x⁴ + x³ - 7x² + 9x + 18.

A). The degree of the polynomial is 4.

That means, it has 4 zeros.

B).  Using p/q:

The factor of constant term 18 are ±2, ±3, ±6, ±9, ±18.

The factor of leading coefficient -1 are ±1.

Now, by p/q,

all possible rational zeros = ±2, ±3, ±6, ±9, ±18.

C). Using Descartes' Rule of Signs,

There are 3 times the sign changes for the positive and negative both times.

So, the possible positive number of roots are 3 or 3-2 = 1.

The possible negative number of roots are 3 or 3-2 = 1.

And the complex roots comes in the pair.

So, there are 2 possible complex roots if there is only a negative and a positive roots.

D). From the attached graph,

the end behavior of the polynomial is negative infinity.

Therefore, all the required values are given above.

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Since <1 and <2 are vertical angles, they are equal, so m<2 = 8x - 15 = 8(6) - 15 = 39°  , Since <2 is supplementary to <3,  m<3 = 180° - 39° m<3 = 141°

Vertical angles are angles that are opposite each other when two lines cross. They always have the same measure and are supplementary angles (add up to 180°). Vertical angles are also known as opposite angles or vertically opposite angles. When two lines intersect, four angles are formed. The two pairs of angles opposite each other are known as vertical angles. This is because the lines that they share are vertical to each other, which is why they are also known as vertically opposite angles. Vertical angles can be found in a variety of shapes and figures, including parallelograms, triangles, and quadrilaterals. They can be used to solve many mathematical problems and are an important concept to learn in geometry.

4x + 9 = 8x - 15

4x - 8x = -15 - 9

-4x = -24

x = 6

Therefore, m<2 = 8x - 15 = 8(6) - 15 = 39°

Since <2 is supplementary to <3,

m<3 = 180° - 39°

m<3 = 141°

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No, the method of equivalent pipes cannot be used to find a single hypothetical pipe that is equivalent to the pipe system of problem 3.12.6.

This is because the method of equivalent pipes is used to combine two or more pipes into one pipe to simplify a system. In problem 3.12.6, the given system already consists of only one pipe. Therefore, it is not possible to use the method of equivalent pipes to determine an equivalent pipe.The method of equivalent pipes is used to calculate the head losses for a system of pipes with multiple branches and junctions, using the Loss Coefficient Method and Hazen-Williams Equation. The method of equivalent pipes allows us to convert a complex pipe network into an equivalent pipe with a single diameter and length. However, this method cannot be used for a pipe system with no branches and junctions, such as the one in problem 3.12.6.

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No, it is average  that Neymar and Luis would have the same tastes and rank a given set of bundles equally. Everyone has unique preferences and tastes that are shaped by their individual experiences.

It is unlikely that Neymar and Luis would have the same tastes and rank a given set of bundles equally. This is because everyone's preferences and tastes are shaped by their individual experiences. Even though Neymar and Luis may have similar backgrounds, they may have had different experiences that have shaped their tastes. For example, Neymar may have had a different upbringing than Luis, which may have resulted in different tastes and preferences. Additionally, Neymar and Luis may have had different life experiences that have shaped their individual tastes. Therefore, it is unlikely that Neymar and Luis would have the same tastes and rank a given set of bundles equally.

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