Are the following two functions inverses of one another? Use function composition to explain your answer.

Answer:

The Answer is

A "a line passing through the points (1, 9) and (3, 19)"

Because

when you make X=1 in the equation "Y=5x+4" then y will be 9

& when you make X=3 then Y will be 19

which gives you the points (1,9) & (3,19)

The inequality expression that represents the given word problems is; 41p + 10 ≤ 265

Algebraic word problems are defined as the questions that require translation of sentences into equations, and then solving those equations using a single variable.

Now, we are told that the School gymnasium can hold 256 people and that there must be 10 staff members in attendance.

Now, we are told that there are 41 award recipients and that each recipient is to invite the same number of people as guests. Now, if the number of guests each award recipients is to invite is denoted as p, the the inequality representing this problem is expressed as;

41p + 10 ≤ 265

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The concept given here is Trigonometric expression, are non-routine appearing problems.  The answer is 0, π/2, 3π/2.

These expressions represent the connections between digression and the sine/ cosine functions. These expressions are complementary trigonometric individualities by description. While we solve trigonometric expressions, it is best to change everything into sine or cosine.

Given:

n= integer

sin²(θ) = 2sin²(θ/2)

[2sin(θ/2)cos(θ/2)]² =  2sin²(θ/2)

4sin²(θ/2)cos²(θ/2) = 2sin²(θ/2)

4sin²(θ/2)cos²(θ/2) -  2sin²(θ/2) = 0

2sin²(θ/2) [2cos²(θ/2) - 1] = 0

sin(θ/2) = 0

θ/2 = nπ

θ = 2nπ

θ = 0, π, 2π

Since,

θ = 0

2cos²(θ/2)-1 = 0

cosθ = 0

x= π/2 + πn

so,

θ = π/2 , 3π/2.

So, we can conclude that the solutions will be 0, π/2, 3π/2.

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The domain of the graph is 2 ≤ x ≤ 5.

Domain refers to the specific space of a website, including a domain name, associated IP address and a set of web pages that are hosted by a web server. Domain names are used to identify websites, and they are often used as a way to easily access a website. Domain names are assigned to each web server, allowing users to access the website by typing in the domain name instead of the IP address.

This means that all x-values must be greater than or equal to 2 and less than or equal to 5 in order for them to be part of the domain. This can also be written in interval notation as [2,5].

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The values of x that make the rational expression undefined are x = -2 and x = 5.The rational expression is undefined when the denominator is equal to zero.

To determine which values of x make the rational expression undefined, we can set the denominator equal to zero and solve for x.

Let's look at our rational expression:

(x + 2)(x - 5) = 0

We can simplify this expression to solve for x:

x + 2 = 0

x - 5 = 0

From these equations, we can solve for x:

x = -2

x = 5

Therefore, all the values of x that make the rational expression undefined are x = -2 and x = 5.

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[tex]x=106^{\circ}[/tex] (linear pair)

[tex]y=106^{\circ}[/tex] (corresponding angles with [tex]x[/tex])

[tex]z=106^{\circ}[/tex] (vertical angles with [tex]y[/tex])

The measure of angles x, y, and z are  106 degree.

The following are  total angle measurements: An angles that add up to 180 degrees.

When two rays are united at a common point, an angle is created. The two rays are referred to as the arms of the angle, while the common point is referred to as the node or vertex. The symbol "" stands for the angle. The Latin word "Angulus" is where the term "angle" originated. Find out more about angles and lines here.

x = 180 - 76 = 106 degree

so,

x = 106 degree is linear pair

y is 106 degree  is corresponding angles with

z is 106 vertical angles with

The measure of angles x, y, and z are  106 degree.

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A seven-sided polygon is called a heptagon. A polygon with seven sides, seven angles, and seven edges is referred to as a heptagon. A heptagon's total number of angles comes to 900°.

It is also occasionally referred to as a septagon, though this usage is not advised because it combines the Latin prefix sept- (derived from septua-, meaning "seven") with the Greek suffix -gon (from gonia, meaning "angle").

A heptagon can be drawn using fourteen diagonals. Heptagon is also referred to as septagon on occasion. The Greek terms "heptá," which means "seven," and "gna," which means "angle," are combined to form the English word "heptagon. There are seven vertices, seven angles, and seven sides to it. A heptagon's internal angles add up to 900°.

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Answer:The total cost of the painted frame is therefore $4 + $1.6 = $<<4+1.6=5.6>>5.6. This is the price that Tori charges for the painted frames.

Step-by-step explanation:Tori buys a wooden picture frame and the necessary paint for $4. To make a profit, she increases the price of the frames by 40%, so she needs to add $4 * 40/100 = $<<4*40/100=1.6>>1.6 to the cost of the frame.

The total cost of the painted frame is therefore $4 + $1.6 = $<<4+1.6=5.6>>5.6. This is the price that Tori charges for the painted frames.

Answer:

Step-by-step explanation:

To determine whether two triangles are comparable, compare the ratios of their corresponding sides. The triangles are identical if the ratios of the respective sides are the same. The "side-side-side" (SSS) similarity criteria is used for this.

To demonstrate that the three triangles are similar, examine the ratios of the corresponding angles. The triangles are identical if the ratios of the respective angles are equal. The "angle-angle-angle" (AAA) similarity criteria is used for this.

To determine whether three triangles are comparable, measure and compare the ratios of at least three matching angles.

Answer:

need more in fo

Step-by-step explanation:

312 different 5-digit even numbers can be found using the given digits which are 0, 1 , 2, 3, 4 , 5.

Even numbers can be made by placing either 0 or 2 or 4 at the rightmost digit, meaning that even numbers end at either 0 or 2 or 4.

Now consider these three cases individually:

Case 1 where the rightmost digit is 0:

Available digits = 0, 1 , 2, 3, 4 , 5.

Now you can write either 1 or 2 or 3 or 4 or 5 in the leftmost digit's place.

So, the number of ways of filling the leftmost digit = 5

When the leftmost digit has been written, then you are left with 4 digits to be placed between the leftmost digit and the rightmost digit via 4 different ways.

Proceeding this way, the next 3 and then 2 digits can be filled in 3 and 2 different ways respectively.

Thus, the number of possible numbers = 5 . 4. 3. 2 = 120

Case 2 where the rightmost digit is 2:

Available digits = 0, 1, 3 , 4 ,5

Now you can write either 1 or 3 or 4 or 5 in the leftmost digit's place. But not 0, because it makes the resulting number a four-digit number.

So, the number of ways of filling the leftmost digit = 4

When the leftmost digit has been written, then you are left with 4 digits to be placed between the leftmost digit and the rightmost digit via 4 different ways.

Proceeding this way, the next 3 and then 2 digits can be filled in 3 and 2 different ways respectively.

Thus, the number of possible numbers = 4 . 4. 3. 2 =  96

Case 3 where the rightmost digit is 4:

Available digits = 0 , 1, 2, 3, 5

Now you can write either 1,  2 or 3 or 5 in the leftmost digit's place. But not 0, because it makes the resulting number a four-digit number.

So, the number of ways of filling the leftmost digit = 4

When the leftmost digit has been written, then you are left with 4 digits to be placed between the leftmost digit and the rightmost digit via 4 different ways.

Proceeding this way, the next 3 and then 2 digits can be filled in 3 and 2 different ways respectively.

Thus, the number of possible numbers = 4 . 4. 3. 2 = 96

So, the total number of arrangements can be calculated as follows:

= 120 + 96 + 96

= 312

312 different 5-digit even numbers can be made using the given digits which are 0, 1 , 2, 3, 4 , 5.

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The minimum number of bundles of shingles needed to cover the roof of the Square pyramid is 5.

A three-dimensional geometric shape having a square base and four triangular faces/sides that meet at a single point (called a vertex) is called a square pyramid. It is called a pentahedron, due to its five faces.

Given, the roof of a shed is a square base pyramid. if one bundle of shingles covers 40 ft². Also given, the height of the slant is 8.2ft. and the base is 9 ft.

From the general formula of the surface area of a square pyramid (A)

= [tex]a^{2} + 2a\sqrt{a^{2} /4 + h^{2} }[/tex]

Since we do not need to calculate the area of the base thus we will remove a² which is the area from the equation.

the surface area of a square pyramid (A) = [tex]2*9\sqrt{9^{2} /4 + 8.2^{2} }[/tex]

the surface area of a square pyramid (A) = 168.3 ft²

Since one bundle of shingles covers 40ft^2 Thus for covering 168.3 ft square we are gonna need 5 bundles of shingles.

Therefore, The Square pyramid's roof can be finished with as few as 5 bundles of shingles.

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The parent function is 2 units to the left in the graph, which is shifted vertically.

What exactly is a math graph?

In mathematics, "graph" can refer to (at least) two different things. In elementary mathematics, the term "graph" designates a plot or a function graph. A graph is, in the language of mathematicians, a set of points and the connections between some subset of those points (which may be empty).

A vertical shift in a graph is a transformation that moves the graph up or down along the y-axis, without changing the shape of the graph. The amount of the shift is determined by the value of a constant in the function's equation. For example, in the equation y = f(x) + k, where k is a constant, a positive value of k will result in a shift upward and a negative value of k will result in a shift downward.

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The prime factors of 625 and 1000 are listed below

1000: 2 * 2 * 2 * 5 * 5 * 5

625: 5 * 5 * 5 * 5

reducing 625/1000 gives 5/8

The prime numbers that divide a positive integer exactly are said to be its prime factors. Integer factorization, often known as prime factorization, is the process of locating these integers.

The prime factorization of 625 and 1000 are

1000: 2 * 2 * 2 * 5 * 5 * 5

625: 5 * 5 * 5 * 5

Reducing 625 / 1000

= (5 * 5 * 5 * 5) / ( 2 * 2 * 2 * 5 * 5 * 5 )

= 5 / (2 * 2 * 2)

= 5 / 8

the term 625 / 1000 is reduced to 5/8

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The product of given matrices is not possible.

A set of numbers arranged in rows and columns so as to form a rectangular array. The numbers are called the elements, or entries, of the matrix.

Given that;

The matrix is,

⇒ [tex]\left[\begin{array}{ccc}3&2&5\\2&3&1\\\end{array}\right] * \left[\begin{array}{ccc}4&5&-5\\5&-1&6\\\end{array}\right][/tex]

Now,

Since, The matrix is,

⇒ [tex]\left[\begin{array}{ccc}3&2&5\\2&3&1\\\end{array}\right] * \left[\begin{array}{ccc}4&5&-5\\5&-1&6\\\end{array}\right][/tex]

Here, The product of matrix is not possible because number of column (3) in first matrix is not equal to the number of row (2) in second matrix.

So, The product of given matrices is not possible.

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[tex]x=106^{\circ}[/tex] (linear pair)

[tex]y=106^{\circ}[/tex] (corresponding angles with [tex]x[/tex])

[tex]z=106^{\circ}[/tex] (vertical angles with [tex]y[/tex])

5 type A bags and 6 type B bags will be purchased by the farmer.

Type A includes 3 pounds of corn and 9 pounds of oats each bag.

2 pounds of oats and 10 pounds of corn are included in each bag of type B.

The mixture must include at least 57 pounds of oats and 75 pounds of maize, according to the farmer.

Allow the farmer to mix the types. Feed equals x pounds.

x pounds, and type B feed.

Oats when combined weigh 9x + 2y pounds.

3x plus 10 pounds of corn when combined

9x + 2y = 57 ———— is the equation for oats. (1)

3x + 10y = 75 is the equation for corn. ————- (2)

Add the result of multiplying equation (2) by 3 to equation (1)

3(3x + 10y) - (9x + 2y) = 75×3 - 57

9x + 30y - 9x - 2y = 225 - 57

28y = 168

[tex]$y=\frac{168}{28}$[/tex]

y = 6 bags

the equation (1)

9x + 2×6 = 57

9x + 12 = 57

9x = 57 - 12

9x = 45

x = 5 bags

Since there are 15 bags of each variety available at the store, each bag is priced at $4.

As a result, the price of 5 bags of type A and 6 bags of type B will be equal to (54) + (64).

= 20 + 24

= $44

The farmer will purchase 6 type B bags and 5 type A bags.

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5 type A bags and 6 type B bags will be purchased by the farmer.

Type A includes 3 pounds of corn and 9 pounds of oats each bag.

2 pounds of oats and 10 pounds of corn are included in each bag of type B.

The mixture must include at least 57 pounds of oats and 75 pounds of maize, according to the farmer.

Allow the farmer to mix the types. Feed equals x pounds.

x pounds, and type B feed.

Oats when combined weigh 9x + 2y pounds.

3x plus 10 pounds of corn when combined

9x + 2y = 57 ———— is the equation for oats. (1)

3x + 10y = 75 is the equation for corn. ————- (2)

Add the result of multiplying equation (2) by 3 to equation (1)

3(3x + 10y) - (9x + 2y) = 75×3 - 57

9x + 30y - 9x - 2y = 225 - 57

28y = 168

y = 168/28

y = 6

y = 6 bags

the equation (1)

9x + 2×6 = 57

9x + 12 = 57

9x = 57 - 12

9x = 45

x = 5 bags

Since there are 15 bags of each variety available at the store, each bag is priced at $4.

As a result, the price of 5 bags of type A and 6 bags of type B will be equal to (54) + (64).

= 20 + 24

= $44

The farmer will purchase 6 type B bags and 5 type A bags.

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To graph a natural log function, plot points on the coordinate plane and connect them with a smooth curve. The graph will be shaped like an "S" and will have asymptotes at x = 0 and y = 0.

A natural logarithm (ln) function is a function of the form y = ln(x). To graph this type of function, you will need to plot points on the coordinate plane and connect them with a smooth curve. The graph of a natural logarithm will be shaped like an "S". The graph will have two asymptotes: one at x = 0 and one at y = 0. This means that the function will approach but never reach either of these values. To plot points on the graph, you can use a chart of values or you can use a graphing calculator. To find the exact coordinates of points, you can use the natural logarithm function on your calculator. Once you have plotted several points, you can connect them with a smooth curve to get the graph of the natural logarithm.

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The requied inequality is 0 ≤ p 2720 shows the possible power, p, that the waste-to-energy facilities in the United States are capable of producing.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

We can write the inequality as follows:

0 ≤ p 2720

This inequality states that the power p that the waste-to-energy facilities in the United States are capable of producing is greater than or equal to 0 megawatts, and less than or equal to 2720 megawatts.

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The amount that Erika pays for living x months in that apartment is given by the linear equation below.

C(x) = $200 + $800*x

We know that there is an initial charge of $200, plus $800 for each month.

So, the cost after the first month is:

C = $200 + $800 = $1000

After the second month the cost is:

C' = $1000 + $800 = $1800

And so on, each month we add $800 to the total cost, then the total cost after x months is modeled by the linear equation below:

C(x) = $200 + $800*x

That is the expression that gives the total amount that Erika has paid after living x months in that apartment.

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The linear function passing through points (0,3) and (4,6) is defined as follows:

f(x) = 0.75x + 3.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which the parameters are given as follows:

The function passes through point (0,3), meaning that when x = 0, y = 3, hence the intercept b is given as follows:

b = 3.

Given two points, the slope is calculated as the change in y divided by the change in x, hence:

m = (6 - 3)/(4 - 0) = 3/4 = 0.75.

Thus the linear function f(x) is defined as follows:

f(x) = 0.75x + 3.

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The value of x will be; x = 4

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

We are given that the equation 6x-9 = 15

Here, we need to solve for x;

Add 9 to both sides

6x-9+9 = 15+9

6x = 24

x = 24/6

x = 4

Therefore, the solution will be as;

x = 4

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Answer:

108 blueberries

Step-by-step explanation:

18 * 6 = 108

Answer:

Lisa used 108 blueberries in her blueberry muffins.

Step-by-step explanation:

18 x 6 = 108

1/5/2023

7:04PM

Vertical lines that are dotted at: as a result, and the numerator is zero. The graphed function is as follows: 1 / (x+3)(x-7)

The study of mathematics comprises the study of quantities and their variations, equations and associated structures, shapes and their positions, and locations where they can be found. A combination of inputs and corresponding outputs are referred to as a "function," which describes the relationship between them. The term "function" refers to an association between inputs and outputs where each input produces a single, unique result. There are two domains, or scopes, assigned to each function. Usually, the symbol f is used to signify functions (x). X is the input. There are four basic categories of functions that are available: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

given

X values for which the function is not defined, or points beyond a function's domain, are referred to as vertical asymptotes;

These vertical asymptotes are shown in a graph by vertical lines that are dashed.

A value of x when the function's denominator equals zero serves as an illustration.

In this diagram:

Vertical lines that are dotted at: as a result, and the numerator is zero.

The graphed function is as follows: 1 / (x+3)(x-7)

And option C provides the right response.

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Answer:

15

Step-by-step explanation:

We use the format (x, y) to write the coordinates in format XY. Coordinates XY is a coordinate that use in Cartesian coordinate.

What is Cartesian coordinate?

Cartesian coordinate is system to draw a specific location of an unique point in the numerical condition that oriented in the two constant line where the vertical line called ordinate or Y and the horizontal line called abscess or X. The Cartesian coordinate commonly use in architecture or  a design of a certain object that has a certain dilate with its original plan. This design later is use to control the construction process of the original object.

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To round a number to the nearest 100, one look at the tens digit. If the tens digit is 5 or more, round up. If the tens digit is 4 or less, round down.

To round a number to the nearest hundred, you can divide the number by 100, round the result to the nearest integer, and then multiply the result by 100. For example, to round 345 to the nearest hundred, you can divide 345 by 100 to get 3.45, round 3.45 to 3, and then multiply 3 by 100 to get 300. Therefore, 345 rounded to the nearest hundred is 300.

Here are some more examples:

478 rounded to the nearest hundred is 500

391 rounded to the nearest hundred is 400

622 rounded to the nearest hundred is 600

719 rounded to the nearest hundred is 700

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Complete question

How can you round off numbers rounded to the nearest hundred?

Answer: x=13 units

Step-by-step explanation:

Answer:

32−4x=12,

25 over x end fraction plus 4 equals 9 ((25)/(x)+ 4 equals 9), and

x over 5 end fraction plus 5 equals 6 ((x)/(5) plus 5 equals 6)