Need help please……..

The input and the output of a function are key components in understanding how a function operates. The input refers to the value or values that are given to the function as an argument, while the output refers to the result or results that the function returns after processing the input.

In other words, the input is what you provide to the function, and the output is what you get in return. The input can be a single value or a set of values, depending on the requirements of the function. The output can also be a single value or a collection of values, again depending on the function's purpose.

It's important to note that the input and output of a function are not always the same. The function may perform calculations or transformations on the input, and the output may be different from the input. This transformation is what gives functions their ability to perform specific tasks and solve problems.

In summary, the input is what you give to a function, and the output is what you get in return after the function processes the input.

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Answer:

\( 5\sqrt{3} \)

Step-by-step explanation:

here

tan(60)= p/b

\( \sqrt{3 } = \frac{y}{5} \)

\(y = 5\sqrt{3} \)

Answer:

C=9

Step-by-step explanation:

If A, B, and C are all single digits the mimimum sum for AB would be 10 as it is a two-digit number (or 11 if you do not consider 0 a digit)

AB-(A+B)=C

10-(1+0)=9 or 11-(1+1)=9

therefore C=9

Answer:

either c or d

Step-by-step explanation:

The absolute value expression must be isolated on one side of the inequality before solving. either and or...OR  

Answer:

11

Step-by-step explanation:

there are 11 spaces between the points

just count the number of spaces, no calculations needed.

Answer:

False

Step-by-step explanation:

This is false because a population represents all and not some. A population is the collection of all outcomes, responses, measurements, or counts that are of interest. It is not a collection of 'some' outcomes. It is a collection of 'all' outcomes.

A population data set is a set which contains all the items or elements of a specified group or data set. It is a complete list of all the possible data values.

The sample of a population are drawn out of a population. They are A subset of a population.

The value is 7/4 = 1.75

From the question, we have

\(2\frac{1}{2} -\frac{3}{4} \\=\frac{5}{2} -\frac{3}{4} \\=\frac{10-3}{4}\\=\frac{7}{4}=1.75\)

Subtraction:

The act of deleting items from a collection is represented by subtraction. Subtraction is denoted by the minus sign. For instance, supposing there are nine oranges stacked together (as indicated in the above image), four oranges are taken out and put in a basket, leaving nine – four oranges, or five oranges, in the stack. Therefore, 9 minus 4 equals 5, or the difference between 9 and 4. Different kinds of numbers can also use subtraction, which is not just applicable to natural numbers. This means that we can use several sets of objects, such as negative numbers, fractions, rational and irrational numbers, decimals, functions, matrices, and vectors, to explain reducing or eliminating physical and abstract values.

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so basically the answer is

Answer:

The dilated image has half the dimensions of the pre-image

So the pre-image is dilated by a scale factor of 1/2 (0.5)

Step-by-step explanation:

The side lengths of the dilated image is related to the preimage by a division of 2

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

The figure

Where we have

Pre-Image = PQRS

Image = P''Q'R'S'

From the figure, we can see that

The side lengths of P''Q'R'S' is half of the side lengths of PQRS

This means that

(x, y) = 1/2(x, y)

Hence, the transformation is (x, y) = 1/2(x, y)

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In order to find the missing numbers, multiply the input number by 4.

The relationship between the input and the output is proportional. Two variables have a proportional relationship when the ratio of the output and the input are constant.

Ratio = output / input

4 / 1 = 4

16 / 4 = 4

28 / 7 = 4

In order to determine the output when the input is 3, multiply 3 by 4: 3 x 4 = 12

In order to determine the output when the input is 6, multiply 6 by 4: 6 x 4 = 24

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The quadratic equation with zeros at -6 and 2 is y² + 4y - 12 = 0. This is in standard form, which is ax² + bx + c = 0, with a = 1, b = 4, and c = -12.

To find the quadratic equation with zeros at -6 and 2, we can start by using the fact that if a quadratic equation has roots x₁ and x₂, then it can be written in the form

(y - x₁)(y - x₂) = 0

where y is the variable in the quadratic equation.

Substituting the given values of the zeros, we get

(y - (-6))(y - 2) = 0

Simplifying this expression, we get

(y + 6)(y - 2) = 0

Expanding this expression, we get

y² - 2y + 6y - 12 = 0

Simplifying this expression further, we get

y² + 4y - 12 = 0

So the quadratic equation with zeros at -6 and 2 is

y² + 4y - 12 = 0

This is the standard form of a quadratic equation, which is

ax² + bx + c = 0

where a, b, and c are constants. In this case, a = 1, b = 4, and c = -12.

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The range of the relation that is represented in the mapping shown in the diagram attached below is: {3, 5, 11, 21}.

If we are given a mapping that represents a relation, the input values (x-values) make up the domain of the relation while the output values (y-values) make up the range of the relation.

In the mapping shown in the diagram attached below, we have the following:

The domain of the relation is: {-1, 0, 1, 2, 3}

The range of the relation is: {3, 5, 11, 21}

Thus, we can conclude that, the range of the relation that is represented in the mapping shown in the diagram attached below is: {3, 5, 11, 21}.

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(c) $16,000 and $24,000, which is derived using the sum-of-the-years-digits method of depreciation.

The sum-of-the-years-digits method is a depreciation method that takes into account the fact that assets are usually more productive in their earlier years and less productive in their later years. To calculate depreciation using this method, you first need to add up the digits of the asset's useful life. In this case, the digits for the four-year life of the machine would be 10 (4+3+2+1). Then, for each year of the asset's life, you multiply the asset's cost by the fraction of its useful life remaining at the beginning of the year. For 2018, the first year of the asset's life, the fraction would be 4/10. Multiplying $45,000 by 4/10 gives you $18,000 in depreciation for 2018. Subtracting that from the original cost gives you a book value of $27,000 at December 31, 2018.

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Answer:

1) 3+4.50x = total cost

2) continuous, because x will be the continuous change depending on the pounds

Step-by-step explanation:

The equation to model the situation is C(w) = 3 + 4.50w, and the domain is continuous because weight (w) can take any real number value for the package.

1. The equation to model this situation can be written as follows:

Total Cost (C) = $3 (Cost of the box) + $4.50 per pound (Weight of the package in pounds)

Let's denote the weight of the package in pounds as "w." The equation is:

C(w) = 3 + 4.50w

2. The domain in this situation is continuous. The weight of the package (w) can take any real number value, and the cost function C(w) is valid for all real values of weight. There are no restrictions or gaps in the possible values of weight, meaning it is continuous.

In summary, the equation to model the situation is C(w) = 3 + 4.50w, and the domain is continuous because weight (w) can take any real number value for the package.

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Answer:

Width can be at least 4.2 in long.

Step-by-step explanation:

The specific solution to the homogeneous recursive relation with the given initial conditions is: an = c1(r1)^n + c2(r2)^n + c3(r3)^n

To solve the homogeneous recursive relation:

an = -3an-1 - 3an-2 - an-3

We first need to find the characteristic equation by assuming a solution of the form:

an = r^n

Substituting this into the recursive relation gives:

r^n = -3r^(n-1) - 3r^(n-2) - r^(n-3)

Dividing both sides by r^(n-3) gives:

r^3 = -3r^2 - 3r - 1

This is the characteristic equation. To solve for the roots, we can use numerical methods or factoring. Factoring this cubic equation is not trivial, so we will use numerical methods.

Using a numerical solver, we find that the roots of the characteristic equation are approximately:

r1 = -0.5457

r2 = -1.8475 + 0.5088i

r3 = -1.8475 - 0.5088i

Therefore, the general solution to the homogeneous recursive relation is:

an = c1(r1)^n + c2(r2)^n + c3(r3)^n

where c1, c2, and c3 are constants determined by the initial conditions.

To find these constants, we use the given initial conditions a0 = 1, a1 = -2, and a2 = -1:

a0 = c1(r1)^0 + c2(r2)^0 + c3(r3)^0 = c1 + c2 + c3

a1 = c1(r1)^1 + c2(r2)^1 + c3(r3)^1 = c1(r1) + c2(r2) + c3(r3)

a2 = c1(r1)^2 + c2(r2)^2 + c3(r3)^2 = c1(r1)^2 + c2(r2)^2 + c3(r3)^2

We can write this system of equations in matrix form:

[ 1  1  1 ][ c1 ]   [ a0 ]

[ r1 r2 r3][ c2 ] = [ a1 ]

[r1^2 r2^2 r3^2][ c3 ]   [ a2 ]

Using Gaussian elimination or a similar method, we can solve for the constants c1, c2, and c3. The solution is:

c1 = (a0 - a1r2/(r2-r1) - a2(r3+r2)/(r3-r1))/(r1^2 - r2r1 - r3r1 + r2*r3)

c2 = (a0 - a1 - c1)/(r1-r2)

c3 = a0 - c1 - c2

Therefore, the specific solution to the homogeneous recursive relation with the given initial conditions is:

an = c1(r1)^n + c2(r2)^n + c3(r3)^n

where c1, c2, and c3 are determined by the above formulas.

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Answer:

Step-by-step explanation:

The slope of a line given two points can be found by using the formula

\(m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\\)

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(-1,8) and (3,-4)

The slope is

\(m = \frac{ - 4 - 8}{3 - - 1} = \frac{ - 12}{4} = - 3 \\ \)

We have the final answer as

Hope this helps you

If i think about this question right i think its (3x+15)

Step-by-step explanation:

Answer:

(3x + 5) + (x +3) = 180 sum of angles on a

straight line

3x + 5 + x + 3 = 180

3x + x + 5 + 3 = 180

4x + 8 = 180

4x = 180 - 8

x = 172/4

x = 43

PQR = 3x + 5 = 3(43) + 5 = 129 + 5 = 134

180-74=106-48=58/2=29=x. x=29. You would type in "29" (excluding the quotation marks) as your answer.

Special Product are the result of binomials being multiplied, or simplified further, and can be solved with ease using the First Last Inner Outer method. this product is not a special product.

Special Product (a+b) (a+b) = aa + ab + ab + bb = \(a^{2} + 2ab + b^{2}\).

we can use this formula anytime we are multiplying a binomial of the form a + b.

Factor as a Difference of Squares

factoring:  \(81a^{2} b^{4} - c^{6}\) = \((3^{4}a^{2} . b^{4}) - c^{6}\)

A difference of two perfect squares, \(A^{2} - B^{2}\) can be factored into

\((A+B)(A-B)\\A^{2} - AB + BA - B^{2}\\ A^{2} - AB + AB -B^{2}\\ A^{2} -B^{2}\)

AB = BA is he commutative property of multiplication from the expression.

-AB+BA equal zero and is therefore eliminated from the expression.

81 is the square of 9

\(a^{2}\) is the square of \(a^{1}\)

\(b^{4}\) is the square of \(b^{2}\)

\(c^{6}\) is the square of \(c^{3}\)

Factorization is \((9ab^{2}+c^{3}) . (9ab^{2}-c^{3} )\)

Factoring: \((9ab^{2}+c^{3})\)

A sum of perfect cubes, \(a^{3} + b^{3}\) can be factored into :\((a+b).(a^{2}-ab+b^{2})\\a^{3}-a^{2}b+ab^{2}-b^{2}a+b^{3}\\ a^{3}+(a^{2}b-ba^{2})+(ab^{2}-b^{2}a)+b^{3}\\ a^{3}+b^{3}\)

9 is not a cube(Binomial can not be factored as the difference of two perfect cubes)

Factoring: \((9ab^{2}-c^{3} )\)

A difference of two perfect cubes, \(a^{3} - b^{3}\) can be factored into

\((a-b).(a^{2}+ab+b^{2})\\a^{3}+a^{2}b+ab^{2}-ba^{2}-b^{2}a-b^{3}\\ a^{3}+(a^{2}b-ba^{2})+(ab^{2}-b^{2}a)-b^{3}\\ a^{3}-b^{3}\)

9 is not a cube(Binomial can not be factored as the difference of two perfect cubes)

Hence, 81a2b4 - c6 this solution deals with factoring binomials as the sum or difference of cubes.

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Answer:

-6

Step-by-step explanation:

Hello!

Since we are finding f(-1) we put -1 in for x

2(-1)^2 + 8(-1)

Follow PEMDAS

2 * 1 + 8(-1)

2 * 1 + -8

2 + -8 = -6

The answer is -6

Hope this helps!

Answer:

1:5

Step-by-step explanation:

The number of arrangements for the world's societies is vast and ever-changing, making sociology a fascinating and dynamic field to study.

Sociology is the arrangement of the world's societies into different forms. The arrangement of societies can be looked at in many different ways, and there is no one right answer.

However, the most commonly recognized arrangement of the world's societies is based on their level of economic development, cultural differences, and political structures.

These arrangements can be divided into five categories: hunting and gathering, pastoral, agricultural, industrial, and post-industrial.

Each category represents a different stage of societal development and is characterized by specific cultural, economic, and political features.

Furthermore, the arrangement of societies is not just based on a single factor but is instead influenced by a complex interplay of economic, political, and cultural factors.

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Answer:

30 i think

Step-by-step explanation:

Answer:

the city at a lower altitude would have a colder climate

The percent change in height after the second bounce would be:

Percent change = [(h_2 - h_1) / h_1] * 100%

The expression \(25(0.93)^x\)represents the height of the ball after x bounces. To find the percent change in height after each bounce, we need to calculate the ratio of the change in height to the original height and express it as a percentage.

Let's denote the height after the first bounce as h_1, the height after the second bounce as h_2, and so on.

The percent change in height after the first bounce is given by:

Percent change = [(h_1 - original height) / original height] * 100%

Using the given expression, we can substitute x = 1 to find h_1:

h_1 = \(25(0.93)^1\) = 23.25

Therefore, the percent change in height after the first bounce is:

Percent change = [(23.25 - original height) / original height] * 100%

To find the percent change after subsequent bounces, we can continue this process. For example, after the second bounce:

h_2 = \(25(0.93)^2\)

And the percent change in height after the second bounce would be:

Percent change = [(h_2 - h_1) / h_1] * 100%

You can repeat this process for each subsequent bounce to find the percent change in height after each bounce using the given expression.

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Answer:

In cooking (recipes).

Step-by-step explanation:

If the serving size for a recipe is not adequate for the number of people you are serving, you will have to convert the amounts(measurements) of the ingredients to suit your needs. You will do this by first creating a ratio defining the relationship between the serving size of the given recipe to the number of people needed to be served. For example, if a recipe serves 4 people, and you need to serve 8, your ratio would simplify to 1/2. This means you must proportionally relate this ratio to the individual amounts of each ingredient.

Answer:

236

Step-by-step explanation:

we are to solve for f(g(2)

that means, solve for g(2) first, then place it in f

g(2) = x^3 + 1

= 2^3+1

= 8+1 = 9

f(g(2) = f(9) since g(2) = 9

f(9)= 3x^2-7

3*9^2-7

3*81-7

243-7

236

Answer:

236 is the answer

Step-by-step explanation:

The augmented matrix for the system of equations calculator that represents the given system of linear equations.

To write the augmented matrix for a system of linear equations, you need to identify the coefficients of the variables and the constants of each equation involved in the system. Augmented matrices are mathematical representations of systems of equations with variables. Each column of the matrix corresponds to a variable, while each row corresponds to an equation. The last column of the matrix is made up of the constant terms of the equations. The result is a matrix that contains all the information needed to solve the system of equations. The augmented matrix for a system of equations calculator is shown below.

The augmented matrix for the system of equations calculator is given as follows:

The augmented matrix for the system of equations calculator can be obtained by writing down the coefficients of the variables and the constants of each equation involved in the system as follows:

3x + 2y + 5z

= 4 4x - 3y + 2z

= 7 2x + 7y - 6z

= 8

Writing down the coefficients of the variables and the constants of each equation involved in the system in a matrix form, we get Augmented matrix = 3 2 5 | 4 4 -3 2 | 7 2 7 -6 | 8

The above is the augmented matrix for the system of equations calculator that represents the given system of linear equations.

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