what is the rate of change/slope

The various types of inverse function are the inverse of trigonometric functions, rational functions, hyperbolic functions and log functions

If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by f⁻¹or F⁻¹.

A function accepts values, performs particular operations on these values and generates an output. The inverse function agrees with the resultant, operates and reaches back to the original function.

The various types of inverse function are:

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The author gives a detailed description of a healthy ecology D. To contrast how the town changed once the ecology was compromised with the use of harmful pesticides.

What is the ecology about?

Ecology also teaches us about the benefits of ecosystems and how to use the Earth's resources in a way that protects the environment for future generations. We can learn more about our surroundings thanks to the various fields of ecology, which include statistical ecology, marine ecology, and vegetation ecology.

With the help of this information, we can manage our natural resources, protect human health, and improve the environment. In this case, the author give a detailed description of a healthy ecology.

The correct option is D.

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The perimeter of triangle CED is 58 in

What is a Parallelogram ?

A unique variety of quadrilateral called a parallelogram has both pairs of its opposite sides parallel and equal.

Parallelograms' characteristics

(1) The opposing sides of a parallelogram are parallel to one another. In this case, AB || CD and AC || BD

(2) A parallelogram has equal-length opposing sides. In this case, AB = CD and AC = BD

(3) In a parallelogram, the measurements of the opposing angles are equal. In this case, A Equals C and B = D.

(4) The total of all the angles of a parallelogram, like all other quadrilaterals, is 360°.

(5) A parallelogram has neighboring or contiguous angles that sum to 180 degrees. As a result, A + B, B + C, C + D, and D + A all equal 180 degrees.

(6) A parallelogram's diagonals cut each other in half. In this case, OA = OC and OB = OD

(7) The parallelogram in the figure is split into two congruent triangles by the diagonals AC and BD.

The diagonals of a parallelogram bisect each other AC = 2 CE

Substitute AC= 50 into AC = 2CE = 50 = 2CE

Calculate 50 = 2 CE=>  CE = 25

The diagonals of a parallelogram bisect each other BD = 2DE

Substitute BD= 30 into BD = 2DE =>  30 = 2DE

Calculate 30 = 2DE  => DE = 15

Opposite sides of parallelogram are congruent AB = CD

Substitute AB = 18 into AB = CD =>  CD = 18

Perimeter of a triangle PΔCDE = CE + CD + DE

Substitute  CE = 25, DE = 15, CD = 18.

PΔCDE = CE + CD + DE

PΔCDE = 25+ 18 + 15

PΔCDE = 58 in

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Answer:

-2

Step-by-step explanation:

a is -3

d is -1

you subtract the two

-3 - (-1)

when you have two negatives they cancel each other out and become positive

-3 + 1

-3 + 1 = -2

that is your answer

Answer:

We can be able to use compatible numbers to estimate the quotient of 925/29 if the whole number that is part of the decimal is less than the divisor, we need to be able to rename the decimal.

Step-by-step explanation:

Answer:

576 ft squared

Step-by-step explanation:

8 x 72 ft= 576 total area

Hope this helps!

There are four basic properties of numbers: commutative, associative, distributive, and identity.

1.Commutative Property

a. Addition

. When two numbers are added, the sum is the same regardless of the order in which the numbers are added.

3 + 5 = 8       or       5 + 3 = 8

b. Multiplication. When two numbers are multiplied together, the product is the same regardless of the order in which the numbers are multiplied.

3 x 5 = 15       or       5 x 3 = 15

2.Associative Property

a. Addition. When three or more numbers are added, the sum is the same regardless of the way in which the numbers are grouped.

6 + (4 + 3) = 13   or   (6 + 4) + 3 = 13

b. Multiplication. When three or more numbers are multiplied, the product is the same regardless of the way in which the numbers are grouped.

6 x (4 x 3) = 72   or   (6 x 4) x 3 = 72

3.Distributive Property

The sum of two numbers times a third number is equal to the sum of each addend times the third number.

5 x (7 + 2) = 45   or   5 x 7 + 5 x 2 = 45

4.Identity Property

a. Addition. The sum of any number and zero is that number.

12 + 0 = 12

b. Multiplication, The product of any number and one is that number.

18 x 1 = 18

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The equation that best defines the length of the equal piece is 4x+2¹-12

We should know that an equation is a mathematical model that shows the equality of two sides of an expression

Based on the given condition 12-24=4*x

Applying multiplicative distribution -12=4x

Rearrange the equation 4x=-12

Calculate the product of the quotient x=-3

Now 24feet divided by -3 =-4

Since it deals with length =4

In conclusion the equation that determines the length of each equal piece is  4x+2¹-12

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Answer:

The height of the 4th bounce would be 4.7458321; rounded would be 4.8.

Step-by-step explanation:

We can figure this question out by first converting the 83% into a decimal, by bringing back 2 decimal places:

0.83.

And then setting up this equation:

0.83 x 10 = 8.3

Now, this is for 1 bounce. We have to do this 4 more times:

0.83 x 8.3 = 6.889

3rd time:

0.83 x 6.889 = 5.71787

4th time:

0.83 x 5.71787 = 4.7458321.

Now, we can round this answer to:

4.8

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Total 56 pencils are needed for the exam.

Multiplication is one of the arithmetic operation used to find total numbers of items or things.

Given,

Total students in the classroom = 28

Total number of pencils needed by each student for the exam=2 pencils

Total number of pencils needed for the exam are,

= Total student ×  Number of pencils needed by each student

= 28 × 2

= 56 pencils

Hence , The total number of pencils needed by the students for the exam would be 56 .

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Using trigonometric ratio the distance to the control tower is 750.7ft

In trigonometry, there are six trigonometric ratios, namely, sine, cosine, tangent, secant, cosecant, and cotangent. These ratios are written as sin, cos, tan, sec, cosec(or csc), and cot in short.

The values of these trigonometric ratios can be calculated using the measure of an acute angle, θ in the right-angled triangle given below. This implies that the value of the ratio of any two sides of the triangle here depends on angle C.

Using trigonometric ratio, the distance is

tan θ = opposite / adjacent

tan 47 = x / 700

x = 700 tan 47

x = 750.7 ft

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The sphere's radius is 5, and its center is at (0, 3, -4).

A sphere is a geometrical object that resembles a two-dimensional circle in three dimensions.

In three-dimensional space, a sphere is a collection of points that are all located at the same distance from a single point.

The radius of the sphere is denoted by the letter r, and the given point is its center.

List a few typical sphere examples from everyday life.

In everyday objects, sphere shapes can be found in the form of marbles, balls, oranges, yarn, and bubbles.

So, the center and radius of the sphere will be:

We have the sphere's equation, which is given by and has a radius of r.

(x - h)² + (y - k)² + (z - l)² = r² ...(1)

We must convert the following equation in order to determine the center and radius of the provided sphere.

x² + y² + z² - 6y + 8z = 0

By combining the x, y, and z terms and filling in the square, we obtain

x² + (y² - 6y + 9) +(z² + 8z + 16) = 9 + 16

(x - 0)² + (y - 3)² + (z + 4)² = 52

So, the sphere's center is at (0, 3, -4) and its radius is 5.

Therefore, the sphere's radius is 5, and its center is at (0, 3, -4).

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Complete question:

Find the center and radius of the sphere x2 + y2 + z2 - 6y + 8z = 0.

In order to show that △ ABC ≅ △ DEF by SAS congruence, we need the sides of triangles ABC and DEF with the angle between the respective sides.

Triangle congruence: Two triangles are said to be congruent if all three of their corresponding sides and all three of their corresponding angles have the same measurements. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved. "" is the congruence symbol. When two figures are comparable to one another in terms of their size and shape, this is what mathematicians mean by congruence. In essence, there are four congruence principles that demonstrate if two triangles are congruent. However, locating all six dimensions is essential. As a result, the congruence of triangles can be assessed using just three of the six variables.

Congruency Requirements:

SSS (Side-Side-Side)

SAS (Side-Angle-Side)

ASA (Angle-Side-Angle)

AAS (Angle-Angle-Side)

RHS (Right angle-Hypotenuse-Side) 

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The area of triangle ABC is 18cm².

A triangle is a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees.

This property is called angle sum property of a triangle. A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry.

= 72*sin(75)*cos(75)

= 36*(2sin(75)cos(75))

= 36*sin(150)

=  18

In conclusion, the area of the triangle is 18cm².

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Using the formula of simple interest and concept of percentage, the amount earned per year is $9542 and the amount spent on freight is $6396

Simple interest is calculated with the following formula: S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100.

1) To solve the amount earned every year, we have to use the formula of simple interest here;

S.I = 73400(1 + 0.13*1)

S.I = 82,942.00

The interest earned per year will be

82942 - 73400 = 9,542.00

2) Using percentage concept here

x = 0.06 * 106600

x = 6396

The amount spent on freight is $6396

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If triangle has 2 congruent sides and 2 congruent angles ,such a triangle is known as Isosceles triangle.

What is congruent triangle?

Congruence of triangles: 2 triangles square {measure} aforesaid to be congruent if all 3 corresponding sides square measure equal and every one the 3 corresponding angles square measure equal in measure. These triangles may be slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with one another. The image of congruity is’ ≅’.

Main Body:

A triangle with two congruent sides and congruent base angles is termed as an isosceles triangle.

If two sides of a triangle are congruent, then by isosceles triangle property, the angles opposite to these sides are congruent.

That is, base angles of the triangle are congruent.

Then, such a triangle is known as Isosceles triangle.

Therefore, option B is correct.

The actual question with option is in figure.

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The inequality is equivalent to 5+y+b0.

A positive number divided by both sides of an inequality results in an equal inequality. And if the inequality symbol is reversed, division on both sides of an inequality with a negative value results in an analogous inequality.

Inequalities that convey the same information are referred to as equivalent inequalities.

In mathematics, larger than symbol (>), less than symbol (), less than or equal to symbol (), and not equal to symbol () are the five inequality symbols.

Algebraic equations with equivalent solutions or roots are called equivalent equations. An analogous equation is one that is created by adding or removing the identical quantity or expression from both sides of a given equation.

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The relation:

(9, -1) (4,2) (5,3) (8, -1) (3, 0)

Is a function, because each element of the domain appears only once.

A relation maps elements from a set, called the domain, into elements from another set, called the range.

Such that the element x being mapped into the element y is written as:

(x, y).

A relation is a function only if each element in the domain is mapped into only one element of the range.

Here we have the relation:

{  (9, -1) (4,2) (5,3) (8, -1) (3, 0)}

We can see that no element of the domain appears twice, so yes, this is a function.

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The function f(x) is represented by the graph attached below. The domain of the graph is given by [-5,5] or {x | -5 ≤ x ≤ 5 ,x ∈ R} .

A function's domain in mathematics is the set of potential inputs that it can take. It can also be written as b, where f is the function.

Formally speaking, X is the domain of f given a function. It is important to note that, in terms of contemporary mathematics, a function's domain is a part of its definition rather than a property.

The function f can be graphed in the Cartesian coordinate system in the uncommon case where X and Y are both subsets of. In this instance, the function's graph, which is projected onto the graph's x-axis, serves as a representation of the domain.

A real function, f, may not be defined for all possible values of the variable if it is specified in a formula. The natural domain, also known as the domain de definition of f, is the set of real numbers to which the formula in this case can be evaluated to either a real number. It is common to refer to a partial function as just a function and its natural domain as just a domain.

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The used postulate is explained below.

What is congruent triangles?

Two triangles are stated to be congruent if the 3 facets and the 3 angles of each the angles are same in any orientation.

When angles and facet blanketed in among those angles of 1 triangle are identical as any other one, each those triangle are Congruent.

This standards of congruency is is aware of as ASA criterion as a facet blanketed among angles are all identical.

Two triangles are congruent, if angles and the facet blanketed among them in a single triangle is same to the 2 angles and the facet blanketed among them of the alternative triangle.

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The slope of the perpendicular line to the equation 5x - 4y = -24, is: 4/5.

The slope values of two lines which lie perpendicular to each other on a coordinate plane are always negative reciprocals to each other.

Rewrite the equation, 5x - 4y = -24 in slope-intercept form:

5x - 4y = -24

-4y = 5x - 24

Divide both sides by -4

-4y/-4 = 5x/-4 - 24/-4

y = -5/4x + 6

The slope of y = -5/4x + 6 is -5/4. The negative reciprocal of -5/4 is 4/5. Thus, the slope of the line that is perpendicular to the equation of the given line is: 4/5.

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Answer:

To find a polynomial, you must identify the terms, coefficients, and degrees. The degree of a polynomial is the highest exponent of the variable in the equation. The coefficients of a polynomial are the values that are multiplied by the variables. The terms of a polynomial are the pieces of the equation, including the coefficients and the variables. After identifying the terms, coefficients, and degree of the polynomial, you can write it in standard form.

Step-by-step explanation:

The area of the rectangular paper left after two semi circles are cut out of it is 186.96 cm².

A rectangle is a closed 2-D shape, having 4 sides, 4 corners, and 4 right angles (90°).The opposite sides of a rectangle are equal and parallel.

To caluculate the area of the paper that remains, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the area of the paper left is 186.96 cm².

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Answer:

c = 5m + 30

Step-by-step explanation:

It is given that:

c = total amount of chickens.

m = total amount of months.

x = amount of chickens per month.

30 is the base amount that Junior will have no matter how much months have passed.

Plug in 4 for m (months), and 50 for c (total amount of chicken) in the given equation:

c = xm + 30

50 = x(4) + 30

50 = 4x + 30

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. PEMDAS is the order of operations, and stands for:

Parenthesis

Exponent (& root)

Multiplication

Division

Addition

Subtraction

~

First, subtract 30 from both sides of the equation:

50 = 4x + 30

50 (-30) = 4x + 30 (-30)

50 - 30 = 4x

20 = 4x

Next, divide 4 from both sides of the equation:

(20)/4 = (4x)/4

x = 20/4

x = 5

The amount of chicken per month is 5.

Set the equation. Plug in 5 for x in the given equation:

c = xm + 30

c = 5m + 30

c = 5m + 30 is your answer.

Check. Plug in time per month and find the number of chickens:

Time in months = 0 ; Number of Chickens = 30

(30) = 5(0) + 30

30 = 0 + 30

30 = 30

Time in months = 4 ; Number of chickens = 50

(50) = 5(4) + 30

50 = 20 + 30

50 = 50

Time in months = 720 ; Number of chickens 3630

(3630) = 5(720) + 30

3630 = 3600 + 30

3630 = 3630

~

The range of a graph can be found using the values depicted on the y-axis.

According to the question,

We have the following information:

We have a graph and we need to know how do we find the range of that graph.

We know that the domain of a graph is the collection or in other words set of input values depicted on x -axis and the range of a graph is the set of possible output values portrayed on y-axis of the graph.

In noting down the range of a graph, we first list down the down value and then the up value or in other words we move from down to up in order to find the range of a graph.

Hence, the range of a graph can be found using the values depicted on the y-axis.

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Answer: -23

Step-by-step explanation:

[tex]jk^2 -m=(-5)(2^2)-3=-5(4)-3=-20-3=-23[/tex]

Answer:

At least 8 rows

Step-by-step explanation:

45 divided by 9 is 5. That is 5 rows

9x3= 27 and there are 23 adults. So that is 3 rows

5+3=8

8 rows in total.

Answer:

A)  61.93 minutes

B)  40.93 minutes

Step-by-step explanation:

Newton's law of cooling

[tex]T(t)=T_S+(T_0-T_S)e^{-kt}[/tex]

where:

Given values:

Substitute the given values into the formula and solve for k:

[tex]\implies 60=20+(90-20)e^{-25k}[/tex]

[tex]\implies 40=70e^{-25k}[/tex]

[tex]\implies e^{-25k}=\dfrac{4}{7}[/tex]

[tex]\implies \ln e^{-25k}=\ln \dfrac{4}{7}[/tex]

[tex]\implies -25k \ln e=\ln \dfrac{4}{7}[/tex]

[tex]\implies -25k=\ln \dfrac{4}{7}[/tex]

[tex]\implies k=-\dfrac{1}{25}\ln \dfrac{4}{7}[/tex]

Given values:

Substitute the given values into the formula and solve for t:

[tex]\implies 30=20+(60-20)e^{\frac{1}{25}t\ln \frac{4}{7}}[/tex]

[tex]\implies 10=40e^{\frac{1}{25}t\ln \frac{4}{7}}[/tex]

[tex]\implies e^{\frac{1}{25}t\ln \frac{4}{7}}=\dfrac{1}{4}[/tex]

[tex]\implies \ln e^{{\frac{1}{25}t\ln \frac{4}{7}}}=\ln \dfrac{1}{4}[/tex]

[tex]\implies {\dfrac{1}{25}t\ln \dfrac{4}{7}}\ln e=\ln \dfrac{1}{4}[/tex]

[tex]\implies {\dfrac{1}{25}t\ln \dfrac{4}{7}}=\ln \dfrac{1}{4}[/tex]

[tex]\implies t=\dfrac{\ln \dfrac{1}{4}}{{\frac{1}{25}\ln \frac{4}{7}}}[/tex]

[tex]\implies t=61.93063129...[/tex]

[tex]\implies t=61.93\;\; \sf minutes[/tex]

Given values:

Substitute the given values into the formula and solve for t:

[tex]\implies 30=-10+(90-(-10))e^{\frac{1}{25}t\ln \frac{4}{7}}[/tex]

[tex]\implies 40=100e^{\frac{1}{25}t\ln \frac{4}{7}}[/tex]

[tex]\implies e^{\frac{1}{25}t\ln \frac{4}{7}}=0.4[/tex]

[tex]\implies \ln e^{\frac{1}{25}t\ln \frac{4}{7}}=\ln 0.4[/tex]

[tex]\implies{\dfrac{1}{25}t\ln \dfrac{4}{7}}\ln e=\ln 0.4[/tex]

[tex]\implies {\dfrac{1}{25}t\ln \dfrac{4}{7}}=\ln 0.4[/tex]

[tex]\implies t=\dfrac{\ln 0.4}{{\frac{1}{25}\ln \frac{4}{7}}}[/tex]

[tex]\implies t=40.93392072...[/tex]

[tex]\implies t=40.93\;\; \sf minutes[/tex]

The area of the larger floor is 64 square units when w = 8 and l = 8. which is the correct answer would be an option (B).

To compare the values, we must first calculate each given situation. The area of any given rectangle is length times width.

If w = 7 and l = 9

A = l × w = 8 × 6 = 48

If w = 8 and l = 8

A = l × w = 8 × 8 = 64

So, the second case would obtain a larger area.

Therefore, the area of the larger floor is 64 square units when w = 8 and l = 8.

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The amount of time it will take both of them is 5.5 days, if Ann and Ben work together

The given parameters are

Ann = 10 days

Ben = 12 days

Represent the number of days it takes both of them with T

So, we have the following equation

1/T = 1/Ann + 1/Ben

Substitute the known values in the above equation, so, we have the following representation

1/T = 1/10 + 1/12

So, we have

1/T = (12 + 10)/120

1/T = 22/120

Take the reciprocal of both sides

T = 120/22

Evaluate

T = 5.5

Hence, it will take them 5.5 days

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