what is the inverse of f(x)=5/x+3

A pair of corresponding angles, alternate interior angles, and alternate exterior angles include the following:

Corresponding angles: ∠1 ≅ ∠5.

Alternate interior angles: ∠4 ≅ ∠6.

Alternate exterior angles: ∠2 ≅ ∠8

In Mathematics, corresponding angles can be defined as a postulate (theorem) which states that corresponding angles are always congruent when the transversal intersects two (2) parallel lines:

∠1 ≅ ∠5

By applying the alternate interior angles theorem to parallel lines m and n, we have the following congruent angles:

∠4 ≅ ∠6

By applying the alternate exterior angles theorem to parallel lines m and n, we have the following congruent angles:

∠2 ≅ ∠8

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The speed that a tsunami can travel is modeled by the equation s = 356 StartRoot d EndRoot , where S is the speed in kilometers per hour and d is the average depth of the water in kilometers.

This is written mathematically as:

S = 356√d

S = 200km/hr

Hence:

200km/hr = 356√d

Divide both sides by 356

200/356 = 356√d/356

√d = 200/356

Square both sides

(√d)² = (200/356)²

d =(0.5617977528)²

d = 0.3156167151km

Approximately = 0.32km

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The mistake katie has made is included an extra length, the correct option is C.

We are given that;

The table of lengths of caterpillars

Now,

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Katie has made the mistake of including an extra length in her diagram. She has included the length 81 twice in the stem-and-leaf diagram, once in the row for 5 and once in the row for 8. However, there is only one caterpillar with a length of 81 mm in the data. Therefore, she should remove one of the 81s from her diagram.

Therefore, by algebra the answer will be included extra length.

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a) To find the number of students getting more than 45 marks, we count the students whose marks are greater than 45 in the given list.

In the given list, the students with marks greater than 45 are: 50, 49, 47, 48, 49, 48, 47, 49, 48, 50, 47, 49, 48, 46, 47, 48, 47.

Counting these numbers, we find that there are 17 students who obtained more than 45 marks.

b) To find the number of students getting less than 45 marks, we count the students whose marks are less than 45 in the given list.

In the given list, the students with marks less than 45 are: 44, 44, 42, 41, 41, 42, 41, 44, 44, 42, 45, 45, 45, 44, 45.

Counting these numbers, we find that there are 15 students who obtained less than 45 marks.

c) To find the maximum number of students getting the same marks, we look for the mark that appears most frequently in the given list.

In the given list, the marks obtained by the students are: 44, 50, 44, 49, 42, 47, 45, 42, 44, 48, 49, 48, 47, 49, 47, 41, 45, 48, 41, 48, 41, 42, 47, 49, 49, 48, 50, 47, 49, 48, 46, 44, 45, 45, 46, 44, 42, 47, 48, 45.

Counting the frequency of each mark, we find that the marks 47 and 48 appear most frequently, with a count of 6 each. Therefore, the maximum number of students getting the same marks is 6.

d) To find the average marks obtained by the students in the class, we sum up all the marks and divide by the total number of students.

Total marks = 44 + 50 + 44 + 49 + 42 + 47 + 45 + 42 + 44 + 48 + 49 + 48 + 47 + 49 + 47 + 41 + 45 + 48 + 41 + 48 + 41 + 42 + 47 + 49 + 49 + 48 + 50 + 47 + 49 + 48 + 46 + 44 + 45 + 45 + 46 + 44 + 42 + 47 + 48 + 45

           = 1912

Total number of students = 40

Average marks = Total marks / Total number of students

                 = 1912 / 40

                 = 47.8

Therefore, the average marks obtained by the students in the class is 47.8.

e) To find the number of students getting more than the average marks, we count the students whose marks are greater than 47.8.

In the given list, the students with marks greater than 47.8 are: 50, 50, 49, 48, 49, 48, 49, 48, 50, 49, 49, 48, 48, 50, 49, 49, 48, 48, 47, 49, 49, 48, 50, 47,

49, 49, 48, 50, 47, 49, 49, 48, 48, 49, 48, 47, 48, 49, 49, 48, 50, 49.

Counting these numbers, we find that there are 40 students who obtained more than the average marks.

These symbolic representations use the symbols ∧ (and) to indicate that all conditions must be true, ∨ (or) to indicate that at least one condition must be true, and ¬ (not) to negate a statement.

Using the given symbols ∧ (and), ∨ (or), and ¬ (not), we can represent the statements as follows:

Let h = "John is healthy," w = "John is wealthy," and s = "John is wise."

John is healthy and wealthy but not wise.

Symbolic form:

h ∧ w ∧ ¬s

John is not wealthy but he is healthy and wise.

Symbolic form:

¬w ∧ h ∧ s

John is neither healthy, wealthy, nor wise.

Symbolic form:

¬h ∧ ¬w ∧ ¬s

John is neither wealthy nor wise, but he is healthy.

Symbolic form:

¬w ∧ ¬s ∧ h

John is wealthy, but he is not both healthy and wise.

Symbolic form:

w ∧ (¬h ∨ ¬s)

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The optimal solution for the linear programming problem is X1 = 5, X2 = 10, S1 = 0, and S2 = 0.

Based on the given table, the linear programming model can be represented as follows:

Objective function:

Maximize Z = 50X1 + 40X2

Constraints:

Subject to:

X1 + 5X2 + S1 = 20

X1 + 5X2 + S2 = 30

X1, X2, S1, S2 ≥ 0

Solution Group of the Primary Program:

The solution group represents the values of the decision variables (X1, X2) and the slack variables (S1, S2) that satisfy the constraints and optimize the objective function.

From the given table, the solution group is as follows:

X1 = 5

X2 = 10

S1 = 0

S2 = 0

This means that the optimal solution for the linear programming problem is X1 = 5, X2 = 10, S1 = 0, and S2 = 0, which maximizes the objective function Z = 50X1 + 40X2.

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The pattern is formed by adding 4 tiles to the previous cross.

In the first cross, there is 1 tile on each arm. In the second cross, there are 5 tiles on each arm, which is 4 more than the first cross. In the third cross, there are 9 tiles on each arm, which is 4 more than the second cross. And so on.

The following formula can be used to calculate the number of tiles in the nth cross:

tiles = 4 × (n - 1) + 1

where n = number of the cross.

For example, to calculate the number of tiles in the 4th cross, use the following formula:

tiles = 4 × (4 - 1) + 1 = 17

Therefore, there are 17 tiles in the 4th cross.

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Answer: D

Step-by-step explanation:

you can just note the points where the 2 lines meet and note down the x values

The circumference of a circle is calculated using the formula:

[tex]\sf\:C = 2 \pi r \\[/tex]

where C represents the circumference and r represents the radius of the circle.

Given that the radius of the circle is one meter (r = 1), we can substitute this value into the formula to find the circumference:

[tex]\sf\:C = 2 \pi (1) \\[/tex]

[tex]\sf\:C = 2 \pi \\[/tex]

Therefore, the circumference of a circle with a radius of one meter is [tex]\sf\:2 \pi \\[/tex] meters.

The best example of a numerical statistical question among the given options is How many minutes of music do students listen to on average? The correct option is B.

The objective of this topic is to gather numerical data (musical minutes) and find an average value that represents a measure of central tendency. It focuses on the actions of a certain demographic—students—and how they listen to music.

By requesting the average, the questioner shows curiosity in learning about the typical or average behaviour of students with relation to their musical listening preferences.

It is a good illustration of a numerical statistical inquiry since it is written in a way that makes it possible to gather quantitative data.

Thus, the correct option is B.

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The best example of a numerical statistical question is How many minutes of music do students listen to on average, the correct option is B.

We are given that;

Four options

Now,

A numerical statistical question is a question that can be answered with a numerical value that varies from one individual or group to another. A numerical statistical question also implies that there is more than one possible answer and that the answer can be analyzed using statistical methods.

Therefore, by statistics the answer will be How many minutes of music do students listen to on average.

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The scale factor k is 2.

Given that 2 quadrilateral that KLMJ and K'L'M'J'.

To find the scale factor by inspection method.

Consider the given data and  inspection method gives,

In quadrilateral KLMN, KL = 2 units, LM = 6 units, MJ = 5 units,

KJ =  6 units.

In quadrilateral K'L'M'J', K'L' = 4 units, L'M' = 12 units, M'J'= 10 units,

K'J '=  12 units.

That implies,

Quadrilateral K'L'M'J' is twice the quadrilateral KLMN.

Thus, k =  2.

Therefore, the scale factor k is 2.

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Answer:

right π/2

Step-by-step explanation:

The function f(x) = 2sin(x - π/2) is a sine function with a period of 2π, an amplitude of 2, and a phase shift of π/2. The phase shift of π/2 causes the graph of the function to be shifted π/2 units to the right. .

Therefore, the correct answer is right π/2

Answer:

Jane spent on coffee.

She started with $80 on her gift card and ended with $49.76, so she spent:

80 - 49.76 = $30.24

We know that she bought coffee that cost $7.56 per pound, so we can set up an equation to find how many pounds of coffee she bought:

7.56x = 30.24

where x is the number of pounds of coffee she bought.

Solving for x, we get:

x = 30.24 / 7.56 = 4

So Jane bought 4 pounds of coffee with her gift card.

[tex] \sqrt[5]{ {2}^{13} \times {3}^{5} } [/tex]

[tex] \sqrt[5]{ {2}^{13} } [/tex]

We can say that 120 is 80% of 150.The percentage that 120 is of 150 will be the length of this line divided by the length of the entire double number line (which is 100%).

To use the double number line diagram to find what percent 120 is of 150, we first need to plot the two numbers on the double number line. We can do this by drawing a horizontal line and labeling it with the two numbers, 120 and 150, and then dividing the line into equal segments.

Next, we can find the difference between the two numbers (150-120=30) and use this to label the corresponding points on the double number line. The point representing 120 should be 3/4 of the way between the two numbers (since 120 is 3/4 of 150).

Finally, we can use the double number line to find the percentage that 120 is of 150. To do this, we can draw a vertical line from the point representing 120 up to the top of the double number line.

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Answer:

TWO CRACKERS

Step-by-step explanation:

I'm assuming they want to find x. Here we see that these two are similar triangles, so the sides are reflective. 5x/5 should be equal to 4/x, so 5x/5 = 4/x. If we use cross multiplying we get 5x^2 = 20. divide both sides by 5 and we get x^2 = 4 or x = 2.

Hope this helped

The maximum area Wayne can enclose for Vayla's bunnies is 126.5625 square feet.

The perimeter of a rectangle is given by the formula: P = 2L + 2W.

In this case, the perimeter is given as 45 feet: 2L + 2W = 45.

Rearranging the equation for the perimeter, we have: 2L = 45 - 2W.

Solving for L, we get: L = (45 - 2W)/2 = 22.5 - W.

Now, we can express the area A in terms of W:

A = L x W = (22.5 - W) x W.

To find the maximum area, we take the derivative of the area with respect to W and set it equal to zero:

dA/dW = 22.5 - 2W = 0.

22.5 - 2W = 0

2W = 22.5

W = 22.5/2

W = 11.25.

and, L = 22.5 - W

L = 22.5 - 11.25

L = 11.25.

Therefore, the dimensions of the rectangle that will maximize the area with 45 feet of fencing are L = 11.25 feet and W = 11.25 feet.

Finally, we can calculate the maximum area:

A = L x W

A = 11.25 x 11.25

A = 126.5625 square feet.

Thus, the maximum area Wayne can enclose for Vayla's bunnies is 126.5625 square feet.

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Answer:

let the percentage be x.

32 = x% of 80

32 = x/100 *80

32 = 80x/100

32*100 = 80x

0.32 = 80x

0.32/80 = x

x = 0.004

x = 40/100

x = 40%

1. Find the graph of the parabola attached below

2. Vertex (-4, 2)   Focus (-7/2, 2)  Directrix (x = -9/2)  Endpoints (-7/2, 1) (-7/2, 3)

For the parabola,  x = 1/2(y-2)² - 4 we will use the equation x = 4p(y-k)² + h,

Vertex → (h, k)

In our given equation, (y - 2) → (y - k), so k = 2. The term on the rightmost side of our equation (-4) → h in the form, so we know h = -4. ∴  vertex (-4, 2).

focus → (h, k) = (-4, 2); P = 1/2

Parabola is symmetric around the x axis and so the focus lies a distance P, from the center, along the x axis.

∴  Focus is (-4 + p, 2)

(-4 + 1/2, 2) ⇒ (-7/2, 2)

directrix → x = d

Parabola is symmetric around the x axis and therefore the directrix is a line paralled to the y axis a distance away from the ceter (-4, 2) x coordinate.

∴ x = -4 - p   ⇒ x = -4 - 1/2

x = 9/2

focal chord endpoints →

The focus of the parabola is (-7/2, 2).

The y-coordinate of the focus is 2, so the y-coordinates of the endpoints of the focal chord are 2 + 1 and 2 - 1, → 3 and 1.

Therefore, the endpoints of the focal chord are:

(-7/2, 3) and (-7/2, 1).

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The height of the pyramid is of about 88.5 in.

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side,  is equals to the sum of the squares of the lengths of the other two sides.

Hence the equation for the theorem is given as follows:

c² = a² + b².

In which:

The parameters for this problem are given as follows:

Hence the height h is obtained as follows:

h² + 19.6² = 90.6²

[tex]h = \sqrt{90.6^2 - 19.6^2}[/tex]

h = 88.5 in.

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The interest for Part 1 is approximately $385.10.

The interest for Part 2 is approximately $709.31.

The formula is as follows:

Interest is calculated as follows: Principal * Rate * Time

Where

Part 1:

$132,000 is the principal.

(Decimal) Rate = 12% = 0.12

Time = 8 days/365 days.

How much interest is there in Part 1?

Interest is calculated as follows : $132,000 * 0.12 * (8/365) = $385.10

Therefore, the interest for Part 1 is approximately $385.10.

Part 2:

$106,750 as the principal

(Decimal) Rate = 12% = 0.12

Time = 20 days / 365 days.

How much interest will there be in Part 2

Interest is calculated as follows : $106,750 * 0.12 * (20/365) = $709.31

Therefore, the interest for Part 2 is approximately $709.31.

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Rounding to the nearest tenth of a centimeter, the slant height is approximately 43.1 centimeters.

The lateral area of a cone is given by the formula L = πrs, where L is the lateral area, r is the radius, and s is the slant height.

We are given that the lateral area L is equal to 612π m², and the radius r is 14.2 cm (0.142 m).

We can rearrange the formula to solve for the slant height s:

L = πrs

612π = π × 14.2 × s

Dividing both sides by π and 14.2:

612 = s × 14.2

Now, solve for s:

s = 612 / 14.2

s ≈ 43.0986

L = rs, where L is the lateral area, r is the radius, and s is the slant height, gives the lateral area of a cone.

We are informed that the radius r is 14.2 cm (0.142 m), and the lateral area L is equivalent to 612 m2.

To solve for the slant height s, we may rewrite the formula as follows:

L = πrs 612π = π × 14.2 × s

612 = s 14.2 after dividing both sides by and 14.2

Next, find the value of s: s = 612 / 14.2 s 43.0986

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Hello!

(3x⁶y⁴)(-4x²y³)

= -12x⁶y⁴x²y³

= -12x⁸y⁷

The discontinuity in the function is represented by the graph at x = 3

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

The graph

By definition, the discontinuity in a function is a point in the function of a graph where the points are not connected with each other

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

The function has a gap at x = 3

This means that the discontinuity in the function is at x = 3

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It is not a statistical question to ask "How much did Adventure Rapids water park make on opening day this year?"

The process of obtaining information and using it to infer or derive conclusions about a population or phenomenon is known as statistical question-solving. It usually concentrates on trends, patterns, or connections between various variables.

Instead of attempting to analyse or comprehend facts, the inquiry in question asks for a single numerical value (the amount of money made on opening day).

Making statistical inferences or generalising from a sample to the population are not involved. As a result, it does not satisfy the requirements for a statistical question.

Thus, the answer is no.

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It is noticed that the factors then the x-intercepts are the same value as that of factors.

Given that, the quadratic equation represented on the graph in factored form is y=(x-3)(x+2).

From the graph, x-intercepts are x=-2 and x=3.

The vertex of the given quadratic graph is (0.5, -6)

Therefore, it is noticed that the factors then the x-intercepts are the same value as that of factors.

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The y-intercept of the line of best fit, which is the point (0, 3) in this case, indicates the initial value of the dependent variable (y) when there are no guests or pizzas (x = 0).

In the context of the scatter plot and the equation for the line of best fit, the y-intercept represents the value of the dependent variable (y) when the independent variable (x) is zero. The y-axis in the scatter plot represents the dependent variable, which could be the number of guests or pizzas. The x-axis represents the independent variable, which could be the number of orders or time.

The y-intercept of the line of best fit, which is the point (0, 3) in this case, indicates the initial value of the dependent variable (y) when there are no guests or pizzas (x = 0). In terms of the number of guests and pizzas, the y-intercept of 3 suggests that even without any guests or orders, there is a base value of 3 for the dependent variable. This could represent a fixed cost or a minimum number of pizzas that need to be prepared or served regardless of the number of guests.

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Answer: WHat are you asking?

Step-by-step explanation: