How do you verify that a dilation is a similarity transformation?

The inverse of f(x) = 3/(x-1) is f^-1(x) = 3/x - 1.

So the correct answer is  f ^ - 1 * (x) = 3/x - 1

The inverse of a function, denoted f^-1(x), is a function that "undoes" the original function. To find the inverse of a function, we need to switch the roles of x and y and then solve for x.

Given the function f(x) = 3/(x + 1), we can find its inverse by:

y = 3/ (x + 1)

Multiply with (x + 1) and divide by y

y(x + 1)/ y = (3/ (x + 1))×(x + 1)/ y

x + 1 = 3/ y

x = 3/ y - 1

Switching the roles of x and y:

y = 3/ x - 1

Thus f^(-1)(x) = 3/ x - 1

It's worth noting that in order for a function to have an inverse function it must be a one-to-one function. This means that for every y value there is only one x value.

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Factor -20 x-5 y, where x+y=4 and x+y=5. Our prime numbers become much, much harder to factor as we add a few extra digits.

When you factor in mathematics, you divide a large number into smaller ones that, when multiplied together, give you the original number. Factorization is the division of an amount into its factors or divisors. The factorization of the integer 12, for instance, might be 3 times 4 or something similar. [tex]N = X^{a} * Y^{b} * Z^{c}[/tex] is used to represent the general factorization formula. In this instance, X, Y, and Z stand for a number's factors. Get a polynomial's GCF (Greatest Common Factor).

GCFs of polynomials should be factored out. By grouping the terms, factor a polynomial with four terms. trinomial of the form, and factor it. The size of our goods and the size of the data we use to check mean that each check takes an average amount of time longer. It is clear from this that factoring the product becomes significantly more difficult when we add a few digits to our prime integers.

Therefore the correct answer is option A)5(4x+y)

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Answer: 37

Step-by-step explanation:

divide the total that she spent over how much each game is (166.50/4.50). this will give you the number of games that she played.

Answer: u = -3

Step-by-step explanation:

   To solve the equation, we will isolate the u variable by simplifying and using inverse operations.

Given:

   4(3u + 5) = 2(2u - 2)

Distribute the 4 and the 2:

   12y + 20 = 4u - 4

Subtract 20 from both sides of the equation:

   12y = 4u - 24

Subtract 4u from both sides of the equation:

   8u = -24

Divide both sides of the equation by 8:

   u = -3

The domain of √ (square root) is all non-negative real numbers.

The domain of a function represents the set of all input values that can be used in the function without resulting in an undefined or meaningless output.

The square root function, represented by √, is only defined for non-negative real numbers. This is because the square root of any negative number is not a real number, it becomes an imaginary number.

This is because in order for the square root to be defined, the radicand (the value inside the square root symbol) must be greater than or equal to zero. Therefore, any real number greater than or equal to zero can be used as the input for the square root function, making its domain all non-negative real numbers.

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a) Using the slope-intercept equation, after 4 years of working at the new company, Nachelle's salary will be $73,000 per annum.

b) After t years of working at the new company, Nachelle's salary will be $57,000 + $4,000(t).

The slope-intercept equation is in the form of y = mx + b.

The slope intercept describes the equation of a straight line, where m is the slope of the line, y and x are the y and x coordinates, and b is its y-intercept.

Initial starting salary per year = $57,000

Annual raise in salary = $4,000

Period = 4 years

Salary after 4 years = $73,000 [$57,000 + $4,000(4)]

Salary after t years = $57,000 + $4,000(t)

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The Trigonometric inequality Sec (x)< cot(x) will hold true in π/2 < x < π.

How can a trigonometric inequality be expressed?

The intervals where the trigonometric inequality sec (x) cot (x) always holds true are what we are looking for.

This can also be expressed as: 1/cos (x) < 1/tan (x)

Now, this is only possible in the fourth quadrant, where cos x is positive and tan (x) is negative, where: π/2 < x < π.

The values for sin, cos, and tan are all positive in the first quadrant.

Only positive values for sin are present in the second quadrant.

The tan values in the third quadrant are all positive.

Only positive values for cos are present in the fourth quadrant.

Therefore the inequality Sec(x) < cot(x) will hold true in π/2 < x < π.

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Answer:

31/24 or 1 7/24

Step-by-step explanation:

1 3/8 in an improper fraction is 11/8:

1 times the denominator (8)= 8, add the numerator (3), and get 11

then keep the original denominator

multiply 11/8 by 3 to get 33/24

multiply 1/12 by 2 to get 2/24

now you have the same denominator and can subtract

33/24-2/24= 31/24

The fraction that is bigger than 2/5 and smaller than 2/3 is 8/15.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

Let the fraction be a/b.

2/5 < a/b < 2/3

Now,

a/b

= (2/3 + 2/5) / 2

= (10 + 6) / 30

= 16/30

= 8/15

= 0.533

Thus,

The fraction is 8/15.

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Answer:

x=4

Step-by-step explanation:

3x+14=26

3x=26-14

3x=12

x=12/3

x=4

Answer: x = 4

Let's solve your equation step-by-step:

3x+14=26:

Step 1: Subtract 14 from both sides.

3x+14−14=26−14

3x=12

Step 2: Divide both sides by 3.

3x/3 = 12/3

x=4

Step-by-step explanation:

a line passing through 2 points get a slope just by these 2 points.

all we can do is to verify that the given slope is the same as the slope defined by the 2 points.

the slope is the ratio

y coordinate change / x coordinate change

when going from one point on the line to another.

for our 2 points that gives us

x changes by + 2 (from 2 to 4).

y changes by -2 (from -7 to -9).

the slope is therefore

-2/+2 = -1

the question asks for a slope of -5.

that is a contradiction. there is no line possible to pass through both points and have a slope of -5.

The graph of the function f(x) = 2x² + 2x - 2 is plotted and attached

The graphs of the function is plotted by making a table of value for a number of the x values and the corresponding y values as done below

Using the function the table is created as f(x) = 2x² + 2x - 2

For x = -4, y =  2 * (-4)² + 2 * (-4) - 2 =  22

For x = -2, y =  2 * (--2)² + 2 * (-2) - 2 =  4

For x = 0, y =  2 * (0)² + 2 * (0) - 2 =  -2

For x = 2, y =  2 * (2)² + 2 * (2) - 2 =  10

For x = 4, y =  2 * (4)² + 2 * (4) - 2 =  38

The table of values

x     y

-4   22

-2   4

0    -2

2     10

4    38

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As a result, the answer to the provided linear equation problem is that the iteration runs in an acceptable amount of time and does not rise exponentially.

A linear equation is represented by the algebraic expression y=mx+b. B is the y-intercept, and m is the slope. A "simple formula with 2 factors," where both y and x are variables, is what the previous sentence was referred to as. Calculations with two variables are referred to as "bivariate linear equations." Here are a few illustrations: 2x - 3 = 0; 2y = 8; m + 1 = 0; x/2 = 3; x + y = 2; and 3x - y + z = 3 are the results. A mathematical equation is considered to be linear if its solution has the format y=mx+b, where m stands for the slope and b for the y-intercept.

Here,

Based on how quickly iterations rise as input increases, fair and unreasonable algorithms can be distinguished. Since the algorithm does not grow exponentially, we can infer that it completes in an acceptable amount of time.

assessing the mathematical function that represents the algorithm's growth rate when input is added;

200 = 10k, where k is the proportionality constant.

k = 200/10

k = 20

The function that represents the number of iterations is as a result:

I = input size; n = 20i; represents the number of iterations.

As a result, the answer to the provided linear equation problem is that the iteration runs in an acceptable amount of time and does not rise exponentially.

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A logarithmic curve is a mathematical function.

A logarithmic curve, also known as a logarithmic function, is a type of mathematical function that describes a relationship between a variable x and a variable y in which the logarithm of y is a linear function of x.

The general form of a logarithmic function is y = logb(x), where b is the base of the logarithm, and x and y are real numbers. The base of the logarithm can be any positive number, but the most common bases used are 10 (common logarithm) and e (natural logarithm).

The graph of a logarithmic function is a curve that starts at negative infinity and increases gradually as x increases. The slope of the curve becomes closer to zero as x increases, and it is undefined for x=0 or x<0.

Logarithmic functions are often used in many areas of science, engineering, and mathematics to model real-world phenomena that exhibit exponential growth or decay, such as population growth, radioactive decay, sound levels and more.

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The graph of the inequality system is attached. The coordinate of a point in the solution set is (-1, 2).

In order to graph the system of inequalities graphically, consider the equation of each inequality.

y = x – 1

y = x - 4

Choosing a few values of x, plot the graph for each equation. Shade the area bounded by the line based on the inequality. If the inequality is less than, shade the area right to the line and if the inequality is greater than, shade the area left to the line. Hence, y < x – 1 is represented by red area and y > x – 4 is represented by blue area. The overlapping shaded area contains the coordinates that represent the solution of the inequality system. The coordinate of a point in the solution set is (-1, 2).

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Answer:

-24

Step-by-step explanation:

2(6)(-2)

Answer:

The answer is Terrestrial planets

Each child's real height falls between 1.60 and 1.28, with the tallest child's height difference at 0.32 and the smallest child's height difference at 0.04 respectively.

a) The ranges that each child's actual height falls within is ;

Here, Daisy is 1.28 meters short while Isaac is 1.56 meters tall at his tallest.

b) The largest height difference between the tallest and shortest child is 1.60-1.28 =0.32m , while the smallest height difference is 1.60-1.56 = 0.04meters.

A number's possible range of values before being rounded or truncated is known as an error interval. Inequalities are frequently used to express error intervals as a range having a lower bound and an upper bound.

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A given set of expressions are known as equivalent expression if and only if the result after evaluating those expression is the same number.

Example,

3 + 2 = 5

4 + 1 =  5

5 + 0 = 5

These three are equivalent as because the sum of all of them is same , i.e., 5.

An equivalent expression is an expression which consists of variables, coefficients, constants, and mathematical functions such as addition, subtraction, multiplication, and division.

In general, if two objects are identical, they are then called as identical.

These expressions are also known as duplicates of each other though they look different but they are same.

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Answer:

5.6

Step-by-step explanation:

56% = 0.56

5.6 > 56%

In order to find the hypotenuse of the triangle

We need to find the other sides of a right triangle

Length of the 1st side of a right triangle is connected with a square with area 144[tex]cm^{2}[/tex]

Hence in order to find the side we

[tex]\sqrt{144} = side[/tex]

[tex]12 = side[/tex]

Length of the second side is connected to a small square with area 25[tex]cm^{2}[/tex]

[tex]\sqrt{25} = side[/tex]

[tex]5 = side[/tex]

Now we can find the hypotenuse of a right triangle with the phytogorean theorem

[tex]a^{2}+ b^{2} = c^{2}[/tex]

[tex]12^{2}+ 5^{2} = c^{2} \\169 = c^{2}[/tex]

[tex]\sqrt{169}= c[/tex]

[tex]13 = c[/tex]

Hence , the hypotenuse of a right triangle is 13cm

Answer:

1:11

Step-by-step explanation:

We know

There are 25 tables that seat 4 people

First, we find the total number of tables by taking

25 + 30 = 55 tables

Then we find the ratio of tables that seat 4 people to the total number of tables by

5 / 55 = 1/11 = 1:11

So, the ratio is 1:11

The product of (2x-3y)(2x+3y) is 4x^2-9y^2.

the solution of the question is as follows,

Product = (2x-3y)(2x+3y)

Product =2x(2x+3y)-3y(2x+3y)

Product = 2x(2x)+2x(3y)-3y(2x)-3y(3y)

{using distributive property of multiplication}

Product = 4x^2 +6xy - 6xy -9y^2

solving 6xy-6xy=0,

Product = 4x^2 - 9y^2

4x^2-9y^2 is the product of (2x-3y)(2x+3y).

distributive property of multiplication

This property states that  multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together. The multiplication of (a - b)(a + b) is equal to a^2 - b^2. This result is used as an identity.

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Answer:

  more than 110

Step-by-step explanation:

You want to know the number of $6 tickets that must be sold to pay for the $660 cost of a school play and make a profit.

The profit is the difference between revenue and cost. The revenue from the sale of n tickets will be 6n. We want the profit to be positive, so we want ...

  6n -660 > 0 . . . . . . positive profit

  n -110 > 0 . . . . . . divide by 6

  n > 110 . . . . . . add 110

More than 110 tickets must be sold to make a profit.

__

Additional comment

Sale of exactly 110 tickets will cover the cost, but there will be no profit.

Yes it is possible to make the prediction about Ramiro's School but not completely.

It is possible to use the information from Ramiro's sample to make predictions about the school-wide results, but it is important to note that the sample may not be fully representative of the entire population of students at the school. There may be sampling biases or other factors that affect the results.

With that said, based on the information provided, we can calculate the proportion of students in Ramiro's sample who use the library in a certain way, and then use that proportion to estimate the number of students at the school who use the library in that way.

For example, if Ramiro's sample shows that 40 out of the 60 people he surveyed use the library to study, we can estimate that approximately 40/60 = 67% of the school's students use the library to study. We can then use this proportion to estimate that approximately 540 x 67% = 361 students at the school use the library to study.

It's important to note that these predictions are based on sample data and they may not be accurate. To make more accurate predictions, a larger, more representative sample would be needed.

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On solving the provided question, we can say that - the function value will be [tex]g(x) = -3 + 12x + 15[/tex] and

The topic of numbers, formulae and associated structures, forms and the areas where they exist, quantities and their variations, and spaces where they exist are all included in the field of mathematics. An association between a collection of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs and outputs, where each input has a single, specific outcome. A domain and a codomain, or scope, are assigned to each function. Typically, f is used to represent functions (x). input is x. Four different sorts of functions are available. Based on the following items: One-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.

Here,

[tex]y =a(x-x1)(x-x2),[/tex] y equals a(x-5)(x+1)

g(x) = -3(x-5)(x+1)

[tex]g(x) = -3(x-5)(x+1)[/tex]

g(x) = -3 + 12x + 15

y-intercept of g(x) is (0,15)

Therefore , the solution to the given problem of the equation comes out be  y-intercept of g(x) is (0,15).

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Answer:

Step-by-step explanation:

6

The number of packages of 5 wheels can be made from the 30 wheels is 6.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, a model car maker puts 5 wheels in each kit. A machine makes 30 wheels at a time.

Now, number of packages of 5 wheels

= 30/5

= 6

Therefore, the number of packages of 5 wheels can be made from the 30 wheels is 6.

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Answer:

Step-by-step explanation:

The mean of 4 5 6 7 8

there are 5 numbers in sequence, you can solve at a glance by looking at the number in the middle, or add the numbers and divide them by their number, in any case the answer will be 6

4 5 6 7 8    (6 is central)

or

(4 + 5 + 6 + 7 + 8) : 5 =

30 : 5 =

6

a) The data on the y-axis: the numbers of people in each salary category.

b) The data on the x-axis: salaries

c) The distribution of salaries is skewed to the right.

We know that a histogram is a graph in which the x-axis is a quantitative variable split into bins, and the y-axis is the frequency.

For given distribution of salaries for individuals, the Y-axis would have the frequency i.e., the numbers of people in each salary category.

And x-axis would have income, because this is out quantitative variable of interest.

consider the following histogram.

We can observe that the graph of distribution of salaries is skewed to the right, because most income data are positively skewed. There would be a substantial number of individuals at or near the lowest salary level, but some people make a tremendously high salary.

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A. Commutative property of addition

B. Distributive property

C. Commutative property of addition

D. Associative property of multiplication