Classify each transformation by its properties.

The possible values of x for the given triangle ABC are 0.75<x<8.

The triangle inequality theorem describes the relationship between the three sides of a triangle. According to this theorem, for any triangle, the sum of lengths of two sides is always greater than the third side.

Given that, m∠A < m∠B < m∠C.

a) From triangle ABC,

BC<AC<AB

2x+3<6x<5x+8

Now, 2x+3<6x

Subtract 2x on both the sides of an inequality, we get

3<4x

Divide 4 on both the sides of an inequality, we get

0.75<x

Here, 6x<5x+8

Subtract 5x on both the sides of an inequality, we get

x<8

So, possible values of x are 0.75<x<8

b) From triangle ABC,

BC<AC<AB

3x+1<4x+8<7x+2

Now, 3x+1<4x+8

Subtract 3x on both the sides of an inequality, we get

1<x+8

Subtract 8 on both the sides of an inequality, we get

-7<x

Here, 4x+8<7x+2

Subtract 4x on both the sides of an inequality, we get

8<3x+2

Subtract 2 on both the sides of an inequality, we get

6<3x

Divide 3 on both the sides of an inequality, we get

2<x

So, possible values of x are -7<x<2

Therefore, the possible values of x for the given triangle ABC are 0.75<x<8.

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The number of nonzero letters that will see Ash and Bea's engraving prices being the same, is  25 letters

The formula for the cost to engrave with Ash, given that the number of letters engraved is x, would be :

= Flat fee + Cost per letter x Number of letters after 21 letters

= 1. 50 + 0. 08 x

The formula for the cost to engrave with Bea, given that the number of letters engraved is x, would be :

= Flat fee + Cost per letter x Number of letters after 15 letters

= 1. 60 + 0. 07 x

Equating these equations together will show the number of letters :

1. 50 + 0. 08 x = 1. 60 + 0. 07 x

0. 08 x - 0. 07 x =  1. 60 - 1. 50

0. 01 x = 1. 10

x = 0. 10 / 0. 01

x = 10 letters

Number of non zero number of letters would be 25 letters :
= 15 + 10

= 25 letters

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The coefficient of Y is 10 in  2y 5.

Any integer or symbol that multiplies the variable of a single term or the terms of a polynomial to represent a constant value is known as a coefficient in mathematics. In some phrases, a letter might be substituted for the usual number. For example, x is the variable and a and b are the coefficients in the formula: ax2 + bx + c.

What is a coefficient?

A coefficient is a quantity or number that is coupled with a variable. Frequently, an integer is multiplied by the variable and written next to it. The variables that don't have a corresponding number are presumed to have a coefficient of 1.

10 is the Y coefficient in 2y 5.

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The best explanation of Irrational Numbers is that , the numbers  that cannot be expressed as a ratio of integers are called as Irrational Numbers .

What are Irrational Numbers ?

The Irrational numbers are the real numbers that cannot be represented in the form of a ratio ([tex]\frac{p}{q}[/tex]) . In other words, the real numbers that are not rational numbers are called as irrational numbers.

For Example : [tex]\pi[/tex] is an irrational number as   [tex]\pi =3.1415925...[/tex] The decimal value in the expansion never stops at any point.

Some Property of Irrational Numbers are :

(i) The Irrational numbers consist of only non-terminating and non-recurring decimals.

(ii) The Irrational Numbers  are real numbers only.

(iii) The Addition, subtraction, multiplication, and division of any two irrational numbers may or may not be a rational number.

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The third side of a triangle, the following formula can be used c² = a² + b² - 2abcos(C)

To calculate the third side of a triangle, first find the lengths of the other two sides and the angle opposite the third side. Then plug these values into the formula above and solve for c.

Where c is the third side of the triangle, a and b are the other two sides, and C is the angle between them.

For example, for a triangle with two sides of length 4 and 6, and an angle between them of 75 degrees, the formula would look like this:

c² = 42 + 62 - 2(4)(6)cos(75)

Solving for c yields a third side length of 8.4.

To solve for c, first square the two side lengths: 42 = 16 and 62 = 36. Then, multiply the two side lengths together and multiply by the cosine of the angle between them: 2(4)(6)cos(75) = 43.9. Finally, add the two squared values together and subtract the result of the multiplication: 16 + 36 - 43.9 = 8.1. Then, take the square root of this result to get the length of the third side: √8.1 = 8.4.

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Answer:

-------------------------------

The width of the space for computer stations is:

Each computer station has a space of:

Answer: x= 96 degrees

Step-by-step explanation:

It we figure out the rest of the angles they would be (the outside ans inside angles are straight angles):

123+153+49+119= 444

Since the total of angles in a pentagon = 540 degrees

540-444 96 degrees

The measure of an angle x will be equal to 96°.

A Pentagon is a two-dimensional geometric shape that consists of five straight sides and five angles. It is a type of polygon, which is a closed shape with three or more sides.

The Pentagon is often used to represent the shape of buildings, monuments, and symbols in architecture and design.

If we figure out the rest of the angles they would be (the outside and inside angles are straight angles):

123+153+49+119= 444

Since the total of angles in a pentagon = 540 degrees

540-444= 96°

Therefore, the measure of an angle x will be equal to 96°.

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The value of 'a' for which the system of equations has a unique solution is a = 4/3.

The given system of equations can be written as:

Ax = 2

6x – 2y = 3

To find the value of 'a' for which the system has a unique solution, we can solve the equations for 'x' and 'y' and equate them.

Solving for 'x' in the first equation, we get:

x = 2/a

Solving for 'y' in the second equation, we get:

y = (3 + 6x)/2

Substituting the value of 'x' in the above equation, we get:

y = (3 + 6(2/a))/2

Equating the two equations, we get:

2/a = (3 + 6(2/a))/2

Multiplying both sides of the equation by 'a', we get:

2 = 3a + 6

Subtracting 2 from both sides of the equation, we get:

3a = 4

Dividing both sides of the equation by 3, we get:

a = 4/3

Therefore, the value of 'a' for which the system of equations has a unique solution is a = 4/3.

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The figure also has a line symmetry for the vertical line x is  5, and a line symmetry for the horizontal line y is 5 .Therefore the figure has both symmetry

A form or item is divided into two equal and symmetrical portions by a line of symmetry. Because it creates a symmetrical split in the figure and the separated pieces look like mirror reflections of one another, we also refer to this line as the axis of symmetry or the mirror line.

An imaginary line that splits a line or shape into two identical parts is called the axis or line of symmetry. The symmetry axis of a parabola will be required of you at higher level mathematics. This u-shaped line on the graph is a parabola.

B) The transformation that maps the figure unto itself are therefore;

1) Rotating the figure 180° about the point (5, 5) which is the center of the figure

2) The figure reflected across the line x = 5 and the figure reflected across the line y = 5

The complete question is : Determine if the figure below has rotational symmetry, line symmetry or both and

describe the transformation that mas the figure onto itself. BE SPECIFIC. You must

name the center of rotation and degree of rotation if it has rotational symmetry or lines of reflection if it has line symmetry

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The percentage increase in project completion time is 26.85%.

Percentage is a relative number that represents the hundredth part of any quantity. One percent (symbolized 1%) is one hundredth part; consequently, 100 percent denotes the complete amount and 200 percent defines twice the supplied amount. percentage. Mathematics percentile is a related topic. A percentage is a fraction of a whole represented as a number between 0 and 100. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent. To calculate a percentage, divide the share of the total by the total and multiply by 100.

Here,

=(137-108)/108*100

=26.85%

The percentage increase in time to complete the project is 26.85%.

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By simple algebra, The number of counters in each box is 2.

Algebra is the study of mathematical symbols and the methods for incorporating them into formulas.

Since algebra is the first math subject most students take where they must deal with variables, complex concepts, and problem-solving abilities, many find it scary.

Given,

counter in Box A = 6y+2

counter in Box b=4y+6

Since there are the same amount of counters in both boxes.

hence

6y+2=4y+6

6y-4y=6-2

2y=4

y=2

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Using substitution method to solve the system of linear equation, the girls have tp sell 700 flower arrangement.

A system of linear equations is a collection of two or more linear equations that use the same set of variables. The solution of the system is the set of values for the variables that satisfy all of the equations in the system.

To solve this problem, we have to set our variables as;

Let;

The equations can be written as;

5x + 6y = 500 ...eq(i)

x + y = 200 ...eq(ii)

From equation ii,

x = 200 - y ...eq(iii)

Put eq(iii) into eq(i)

5(200 - y) + 6y = 500

1000 - 5y + 6y = 500

1000 + y = 500

y = -500

Put y = -500 into eq(ii)

x - 500 = 200

x = 700

From the solution, it shows they couldn't sell any candy and had to sell 700 flower arrangement.

Kindly find the attached graph below

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A book cost $2.00.

In Maths, a variable is an alphabet or term that represents an unknown number or unknown value or unknown quantity. The variables are specially used in the case of algebraic expression or algebra. For example, x+9=4 is a linear equation where x is a variable, where 9 and 4 are constants.

Variables may be classified into two main categories: categorical and numeric. Each category is then classified in two subcategories: nominal or ordinal for categorical variables, discrete or continuous for numeric variables.

Given the no of books purchased by

Alana =4

Petra =2

Angus = 16

So, the total price of 4 books of Alana =$4

Total price for Petra = $2

Total price of Alana and Petra =4x+2x

=6x

Total price for Angus = 16x

But given Angus received a discount  of $15

So price post discount = 16x- 15

According to the question

16x-15 = 6x +5

Adding 15 both sides

16x +15-15 = 6x + 5+15

16x= 6x+20

Subtracting 6x both sides

16x - 6x = 6x - 6x + 20

10x = 20

i.e x=2

Cost of one book = $2

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Answer:

slope is 2 ,, y intercept is 5

Step-by-step explanation:

y=mx+c

m represents slope

c represents y intercept

The new income is new income.

Generally, To find the new income of the man, we can use the formula: New Income = Original Income + Increase in Income

Since the ratio of increase in income is 7:8, we can assume the original income to be 7x and the new income to be 8x.

The increase in income is given as Rs. 4500 per month, so we can set up the equation as:

8x = 7x + 4500

By solving for x, we get that

x = 4500.

Therefore, the new income of the man is

8x = 8 * 4500

= Rs. 36000 per month.

b)

The ages of the two sisters are in the ratio 7:5. If the elder sister is 15 years 9 months old, we can assume her age in months to be

15*12 + 9 = 189 months.

Let's assume x be the age of younger sister in months.

So, according to the ratio 7:5, we can set up the equation as:

x = (5/12)*189

By solving this equation we get

x= 78.75 months, which is roughly 6 years and 6 months.

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A log 10 transformation is a mathematical operation that is used to change the scale of a variable in a data set. The log 10 transformation is applied to the variable by taking the base-10 logarithm of each value in the data set. The result of this operation is a new variable that is on a different scale than the original variable.

The log 10 transformation is commonly used in statistics and data analysis to normalize data that is on a large scale, such as data that spans several orders of magnitude. By applying the log 10 transformation, the data is transformed into a more manageable scale that is easier to work with and analyze.

The log 10 transformation can also be used to stabilize the variance of a variable, this is particularly useful when the data is positively skewed. The log 10 transformation can also be useful for data that has a multiplicative relationship, for example, population growth or stock prices.

It is important to note that the log 10 transformation can only be applied to data that is positive and greater than zero because the logarithm of zero or a negative number is not defined.

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50 cm is the required perimeter of shape B.

A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter.

A circle's or an ellipse's circumference is referred to as its perimeter.

There are numerous uses in real life for perimeter calculations.

We must sum up the lengths of the rectangle's four sides in order to get its perimeter.

So, according to the given figures:

Shape A's circumference is 60 cm.

Let x cm be the length of each square.

The total length of shape A's free bounds is equal to 12x.

Consequently, 12x = 60.

x = 5 cm

Currently, the length surfaces of form B equal 10x.

Shape B's perimeter equals 10x.

= 10(5)

= 50 cm

Therefore, 50 cm is the required perimeter of shape B.

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Correct question:
Shape A and Shape B are each made from 5 identical squares.

The perimeter of shape A is 60cm. Work out the perimeter of Shape B

To know if a triangle is a 30-60-90 triangle, you must check if the triangle's angles measure 30°, 60°, and 90°. Additionally, the sides of a 30-60-90 triangle will have a specific ratio. The longest side of the triangle is always double the length of the shortest side, and the side opposite the 60° angle is always the square root of 3 times the shortest side.

1. Measure the angles of the triangle.

2. Check if the angles measure 30°, 60° and 90°.

3. Measure the sides of the triangle.

4. Check if the longest side is double the length of the shortest side and if the side opposite the 60° angle is the square root of 3 times the shortest side.

To know if a triangle is a 30-60-90 triangle, you must check if the triangle's angles measure 30°, 60°, and 90°. Additionally, the sides of a 30-60-90 triangle will have a specific ratio. The longest side of the triangle is always double the length of the shortest side, and the side opposite the 60° angle is always the square root of 3 times the shortest side.

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The dimensions of the flag are:

length = 19 feet and width = 10 feet

Let 'l' be the length of the flag and 'w' be the width of the flag.

The length of the flag is 9 feet longer than the width.

So, we get an equation

l = 9 + w                ............(1)

The flag has a perimeter of 58 feet.

We know that the formula for the perimeter of rectangle:

P = 2(l + w)             ..............(2)

Here, P = 58 feet

Substitute the value of P in equation (2)

58 = 2(l + w)                

29 = (9 + w) + w                      ..........(from (1))

29 - 9 = 2w

2w = 20

w = 10

Substitute this value in equation (1),

l = 9 + 10

l = 19 feet

Therefore, length = 19 ft and width = 10 ft

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From set theory, A and B: {4, 6} A or B: {2, 3, 4, 5, 6, 8} B's complement is 1, 2, 7, and 8.

Basic set theory describes these various kinds of sets as follows: Finite set: There are only a finite number of elements. A set with an infinite number of elements. A set that is empty has no elements. A singleton set consists of just one element.

The elements that appear in both A and B at the same time are referred to as A and B.

From 1 to 8, the even numbers are 2, 4, 6, and 8.

The numbers 3, 4, 5, and 6 are in that order.

Look for the components that are the same in both sets.

A and B: {4, 6}

The union of the two sets is either A or B.

Combine the components from both sets.

A or B: {2, 3, 4, 5, 6, 8}

All the components that are absent from B make up its complement.

Except for the event elements, write all of the sample space's components.

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The value of x in the triangle LMO is 38°

An equation shows how two or more numbers and variables are related to each other.

∠KLO + ∠OLM = 180° (sum of angle in straight line)

134 + ∠OLM = 180°

∠OLM = 46°

∠OML + ∠OMN = 180° (sum of angle in straight line)

∠OML + 84 = 180°

∠OML = 96°

∠OLM + ∠OML + ∠LOM = 180° (angle in a triangle)

46 + 96 + x = 180

x = 38°

The value of x is 38°

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The correct answer is option c as DE/AE=BC/AC

In Mathematics, a slope of a line is the change in y coordinate with respect to the change in x coordinate. The net change in y-coordinate is represented by Δy and the net change in x-coordinate is represented by Δx. Where “m” is the slope of a line. So, tan θ to be the slope of a line.

Given here ΔADE ≈ΔABC and thus  DE/AE=BC/AC

but tanθ = DE/AE=BC/AC where tan θ is the slope of the line thus both the lines have identical slopes.

Hence, The correct answer is option c)  ΔADE ≈ΔABC thus DE/AE=BC/AC Therefore the slope of AD is the same as the slope of AB

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Answer:

see explanation

Step-by-step explanation:

under a counterclockwise rotation about the origin of 90°

a point (x, y ) → (- y, x ) , then

C (1, 9 ) → C' (- 9, 1 )

D (4, 9 ) → D' (- 9, 4 )

E (0, 3 ) → E' (- 3, 0 )

The inverse of the function is {(5, 3), (8, 2), (5, 1), (3, 0)} and it is not a function

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

((3,5), (2,8), (1.5), (0.3))

The above ordered pairs can be represented a

(x, y)

This means that the inverse function is

(y, x)

So, we have the following expression

(y, x) = {(5, 3), (8, 2), (5, 1), (3, 0)}

Also, the inverse is not a function

This is so because the x value 5 has different y values 3 and 1

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The point (2, 3) lies in the first quadrant.

Quadrant

The axes of a two-dimensional Cartesian system divide the plane into four infinite regions, called quadrants, each bounded by two half-axes.

These are often numbered from 1st to 4th and denoted by Roman numerals: I (where the signs of the (x; y) coordinates are I (+; +), II (−; +), III (−; −), and IV (+; −).

Cartesian system

The Cartesian coordinate system uses a horizontal axis that is called the x-axis and a vertical axis called the y-axis. Equations for lines in this system will have both the x and y variable.

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The volume of the composite solid round to the nearest tenth is 83.7 inches³.

Volume of a three dimensional shape is the space occupied by the shape.

There are 2 hemispheres and a cylinder in the given composite solid.

Volume of hemisphere =  [tex]\frac{2}{3}[/tex] π r³, where r is the radius.

Volume of the cylinder = π r² h, where r is the radius and h is the height.

Here r = 2 inches and

h = 8 - 4 = 4 inches

Volume of hemisphere = [tex]\frac{2}{3}[/tex] π × 2³

                                      = [tex]\frac{16}{3}[/tex] π

There are two hemispheres.

Volume of two hemispheres = 2 × [tex]\frac{16}{3}[/tex] π =  [tex]\frac{32}{3}[/tex] π

Volume of the cylinder = π r² h

                                      = π × 2² × 4

                                      = 16 π

Volume of the composite Solid = [tex]\frac{32}{3}[/tex] π + 16 π

                                                    = [tex]\frac{80}{3}[/tex] π

                                                    = 83.7 inches³

Hence the volume of the composite solid is 83.7 inches³.

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The difference is quartiles 3 - quartiles 1 = 2.05 - 1.79 = 0.26

The first quartile (Q1) is the 25th percentile of a dataset, which separates the lowest 25% of the data from the rest. The third quartile (Q3) is the 75th percentile of a dataset, which separates the lowest 75% of the data from the highest 25%. To find the difference between Q1 and Q3, you would subtract Q1 from Q3.

In this specific dataset, you would need to sort the values first in increasing order:

1.61, 1.75, 1.79, 1.84, 1.96, 2.09, 2.11

The first quartile (Q1) is the median of the lowest half of the dataset, which is 1.79

The third quartile (Q3) is the median of the upper half of the dataset, which is 2.05

so the difference is Q3 - Q1 = 2.05 - 1.79 = 0.26

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The phrase that is identical to 7(d - 4) in option B is -4(d+ 7). A mathematical expression is a statement that contains a minimum of two numbers .

A mathematical expression is a phrase having a minimum of two numbers or variables and at least one mathematical operation. This mathematical operation may be addition, subtraction, multiplication, or division. An expression's basic components are as follows: Expression is (Number/Variable, Math Operator, Number/Variable). A mathematical expression is a statement that contains a minimum of two numbers or variables and at least one mathematical operation. Let's learn how to write expressions. A number is 6 more than half of another number, and that other number is called x. In a mathematical expression, this statement is represented as x/2 + 6.

given

The correct response is 4 less than 7, since 4 is less than 7.

Thus, 7-4=3 could be considered.

The first section of 7–4 appears to be answer B.

The phrase that is identical to 7(d - 4) in option B is -4(d+ 7).

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