9) show ur equation steps ​

Complementary Angles :  ( ∠1 , ∠5 )  , ( ∠2 , ∠6 ) , ( ∠3 , ∠7 ) , ( ∠4 , ∠8 )

Supplementary Angles : ( ∠1 , ∠2 ) , ( ∠2 , ∠4 ) , ( ∠3 , ∠4 ) , ( ∠1 , ∠3 )

Congruent Angles : ( ∠1 , ∠5 )  , ( ∠2 , ∠6 ) , ( ∠3 , ∠7 ) , ( ∠4 , ∠8 )

Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.

Corresponding angles

When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position

Alternate Interior Angles

Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.

Alternate Exterior Angles

The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.

Consecutive Interior Angles

When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles.

Given data ,

Let the parallel lines be represented as m and n

Now , the lines m and n are cut by the transversal line t

So , the angles are

The corresponding angles are ( ∠1 , ∠5 )  , ( ∠2 , ∠6 ) , ( ∠3 , ∠7 ) , ( ∠4 , ∠8 )

The supplementary angles are having a sum = 180°

The supplementary angles are angles in a straight line

So , ( ∠1 , ∠2 ) , ( ∠2 , ∠4 ) , ( ∠3 , ∠4 ) , ( ∠1 , ∠3 ) are supplementary angles

And , ( ∠5 , ∠6 ) , ( ∠6 , ∠8 ) , ( ∠7 , ∠8 ) , ( ∠5 , ∠7 ) are supplementary angles

The congruent angles are having the same measure

So , corresponding angles and alternate interior angles are also congruent angles

Hence , the angles are solved

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From 1976 until 1987, red M&Ms were removed from packets owing to a research associating the food dye used to color them to cancer.

Arithmetic is defined as working with numbers through addition, subtraction, multiplication, and division. Adding two and two to produce four is an example of arithmetic. Arithmetic is a fundamental branch of mathematics that studies the characteristics of classical operations on numbers such as addition, subtraction, multiplication, division, exponentiation, and root extraction. Arithmetic (derived from the Greek word arithmos, "number") relates to the fundamental components of number theory, arts of mensuration (measuring), and numerical computing (that is, the processes of addition, subtraction, multiplication, division, raising to powers, and extraction of roots).

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The x-intercepts or roots of the parabola are the locations where a parabola contacts the x-axis. These are the solutions to the parabola equation where the y-value is equal to zero.

A parabola is an open curve formed by the intersection of a right circular cone with a plane parallel to one of the cone's elements. This is known as the standard form of a quadratic function. A parabola is the graph of a quadratic function that is a U-shaped curve. A parabola is the graph of the equation y=x2 illustrated below. Parabolas are classified into three categories. There are three types of forms: vertex form, standard form, and intercept form. Each type offers a unique important characteristic for the graph. The three major forms from which we graph parabolas are known as standard form, intercept form, and vertex form. Each form will provide you with somewhat different information as well as its own set of pros and downsides.

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In total, there are 252 ways to choose five members without assigning positions, 5 ways to choose five members with assigned positions, and 56 ways to choose five members with two members assigned to a particular position.

a.) The number of ways that the five team members can be chosen without assigning them positions is 10C5 = 252. This is calculated using the formula for combinations, which is n!/(r!(n-r)!), where n is the total number of members and r is the number to choose. In this case, n=10 and r=5, so 10!/(5!(10-5)!) = 252.

b.) The number of ways that the five team members can be chosen with assigned positions is 5!. This is because there are five positions, and each team member must occupy one of the positions. The order of the positions is irrelevant, so there is only one possible combination.

c.) The number of ways that the five team members can be chosen with the two members assigned to position five is 8C5 = 56. This is calculated using the same formula as in part a, but with n=8 since two members are already assigned to position five. 8!/(5!(8-5)!) = 56.

In total, there are 252 ways to choose five members without assigning positions, 5 ways to choose five members with assigned positions, and 56 ways to choose five members with two members assigned to a particular position.

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The largest possible number of red socks in the drawer that is consistent with this data is 990.

Let r be the number of socks that are red, and t be the total number of socks. We get:

2(r(r-1)+(t − r)(t − r − 1)) = t(t − 1)

Expanding the left hand side and the right hand side,

we get: 4r²-4rt+2t²- 2t = t²- t

And, moving terms, we will get that:

47r²-4rt + t² = t

We notice that the left side is a perfect square.

(2r-t)² = t

Thus t is a perfect square. And, the higher t is, the higher r will be. So, we should set t =44²= 1936

And, we see, 2r- 1936 (+-)44

We will use the positive root, to get that 2r -1936 = 44, 2r =1980, and r = 990

Thoughts about probability began with a question from a French nobleman named Chevalier de Mere to Pascal (1623-1662). He wants to know how the pattern of distributing betting money in a gambling game is if the game has to be stopped before it is finished. This question then became the subject of discussion between Pascal and Fermat (1601-1665), based on this discussion came the theory of probability.

Although the basics of probability initially appeared to explain problems in gambling, in its development, the concept of probability can be applied to various problems such as social problems, engineering, health, biology, industry, transportation, management, accounting, education etc.

Probability is the amount of chance (likely) that an event will occur. The amount of opportunity can be written in the form of a decimal number, fraction or percent.

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Suppose the detector will sound the alarm if more than 2 milligrams of the dye are in your system. It will take 56 minutes for the visit of the doctor

The amount of radioactive dye remaining in your system after t minutes can be modeled as:

A(t) = 11 * (1/2)^(t/20)

where A(t) is the amount of dye remaining after t minutes. We want to find the time t when A(t) = 2 milligrams.

A(t) = 11 * (1/2)^(t/20) = 2

Solving for t:

(1/2)^(t/20) = 2/11

Taking the natural logarithm of both sides:

(t/20) = ln(2/11) / ln(1/2)

Multiplying both sides by 20:

t = 20 * ln(2/11) / ln(1/2)

Using a calculator or logarithm tables, we can estimate t to be approximately 56 minutes. So, your visit to the doctor would take about 56 minutes.

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Check the picture below.

True, If the zero vector is a solution of the system , then the system is homogeneous.

A system of linear equations is considered homogeneous if the zero vector (i.e., the vector with all components equal to 0) is a solution. This means that the system of equations only has the trivial solution of all variables equal to zero, but no non-trivial solutions.

A homogeneous system of linear equations is a system where all the equations have the same form and all the coefficients are proportional to each other. This means that if one equation is multiplied by a constant, the same constant must be multiplied by all the other equations in the system to maintain the homogeneous property.

The zero vector is a solution of a homogeneous system because if all the variables are equal to zero, all the coefficients in the equations are also equal to zero and the equations are satisfied. This is why the presence of the zero vector as a solution is a defining characteristic of homogeneous systems.

In contrast, a non-homogeneous system is a system where the zero vector is not a solution and there are both trivial (zero) and non-trivial (non-zero) solutions. Non-homogeneous systems are solved using different methods compared to homogeneous systems.

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Answer: 14 cupcakes

Step-by-step explanation:

42 divided by 3

The probability that less than four colours will be chosen when the spinner is spun once would be = 0.5. That is option D.

Probability is defined as the expression that show the possible outcome of an event which is likely or unlikely to occur.

The coloured spinner is divided into = 8 colour sections

The number of blue section = 3

The number of red = 1

The number of purple section = 2

The number yellow section = 2

Therefore the probability to select 4 colour when spun once = 4/8 = 1/2 = 0.5

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The solution for the given expression b = √ -1 -2b is b = -1.

An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax^2 + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term. First, there must be a term other than zero in the coefficient of x^2 (a not equal 0) for an equation to be a quadratic equation.

The expression is:

b = √ -1 -2b

Take square on both sides of the equation. The square negates the square root and we have the following expression:

b² = - 1 - 2b

b² + 2b + 1 = 0

The quadratic formula is given as:

x = - b ± √b² - 4ac ÷ 2a

Substituting the value of b = 2, a = 1 and c = 1:

x = -2 ± √4 - 4(1)(1) ÷ 2(1)

x = -2 ÷ 2

x = -1

Hence, the solution for the given expression b = √ -1 -2b is b = -1.

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The  height of the pyramid is 6cm

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Given that Six square-based pyramids fit exactly onto the six faces of a cube of side 4 cm.

The volume of the object formed is 256 cm³.

We need to find the  height of each of the pyramids.​

The total volume can be calculated as

Total volume= cube volume+6 one pyramid volume

cube volume=4³=64

pyramid volume=1/3.4²h=16/3h

64+6.16h/3=256

64+32h=256

Subtract 64 on both sides

32h=256-64

32h=192

Divide both sides by 32

h=6

Hence, the  height of the pyramid is 6cm

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From the graph of the system of equations y = 3x - 8 and 6x - 2y = 10, there is no solution

An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.

The standard form of a linear equation is:

Ax + By = C

Where A, B and C are constants

The slope intercept form of a linear equation is:

y = mx + b

Where m is the slope and b is the y intercept

The slope of the line passing through points (x₁, y₁) and (x₂, y₂) is:

m = (y₂ - y₁) / (x₂ - x₁)

Given the system of equations:

y = 3x - 8        (1)

and:

6x - 2y = 10     (2)

From the graph of the equations, there is no solution

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Option A is a correct representation of the graph of the function,

g(x) = -1/3f(x).

When two parallel lines intersect, a two-dimensional coordinate plane called the cartesian plane is created. The horizontal line is the X-axis, while the vertical line is the Y-axis. If the sign of x is positive, the coordinate point (x, y) in the Cartesian plane indicates that the point is on the right of the origin; otherwise, it indicates that the position is on the left of the origin.

Given the graph of the function,

f(x) is the shape of a parabola so the graph is of a quadratic function.

and given g(x) = -1/3f(x)

graph of f(x) is on coordinates (0, 0), (1, 1), and (-1, 1)

so the function is f(x) = x²

so g(x) should lie in coordinates (0, 0), (1/3, -1/3), and (-1/3, -1/3)

the shape of g(x) will be the same as f(x), but due to the negative sign, the shape will be in opposite quadrants.

and g(x) is 1/3 time f(x) so the shape will evolve more as compared to g(x),

so the graph of Option A only follows the required condition.

Hence option A is correct.

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Answer: The last one; is the one closest to the keyboard.

Step-by-step explanation: Its D because after I looked at the range, I looked at the median, which is 22, and D is the only one that had that as its median. I hope this helped!

A polynomial that represents the area of the soccer field is 40x² + 240x + 200

What is polynomial?

A polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

The area (A) of the rectangular pitch is calculated as

A = lb ( l is the length and b the breadth )

  = (10x + 10)(4x + 20)

Each term in the second factor is multiplied by each term in the first factor, that is

10x(4x + 20) + 10(4x + 20) ← distribute both parenthesis

= 40x² + 200x + 40x + 200 ← collect like terms, thus

A = 40x² + 240x + 200 ← in standard form

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The points will  meet x when it is folded are C or E

A point is a location of an object by taking reference of origin, In general case we consider it at (0,0), At the origin value of both the coordinate position is considered as Zero, In simple words point indicates how much it is above or below from the coordinate axes.

Vertical distance from the x axis is known as y coordinate and horizontal distance from the y axis is known as x coordinate.

Given that,

A green colored Net,

After folding x point will  meet the points = ?

When we start folding,

First step,

Side ABCD and DEFG will be folded,

C and E will meet with each other

Second Step,

Side ABCD and AGHI will be folded,

B and I will meet with each other

Third step,

Side DEFG and AGHI will be folded,

F and H will meet each other

Fourth step,

Upper portion AHI will cover the upper portion BCF of the box

X will at position of C or E

Hence, the X will meet C or E

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The student that has the half piece of paper with the greater area is blake.

Find the area that its outer surfaces possess. Sum of all those surfaces' area is the surface area of the considered object.

Given;

Tyler and Blake have rectangular pieces of paper with the same length and same width

Tyler cuts his paper horizontally through the middle

Blake cuts his paper along a diagonal

Now,

Let the length and breadth be y

Tylers half area= y*y/2=y^2/2

Blakes half area=1/2* [tex]\sqrt{3}[/tex]y*[tex]\sqrt{3}[/tex]y/2

=3y^2/4

Therefore, blakes piece of paper has more area.

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Step-by-step explanation:

hope you can see the awful green

Answer:

13.14cm

Step-by-step explanation:

lets start by finding the length of AD

90 + 65=155...........180-155= 25

x/sin 25= 7/sin 90

xsin90=7sin 25

x= 2.96cm=AD

Now lets find DC

we shall find DB first;

x/sin65=7/sin90

xsin90=7sin65

x=6.34cm...=DB

Now lets use Pythagoras theorem to find DC

12²-6.34²=√103.80

DC=10.18cm

Add AD and DC

2.96+10.18= 13.14cm

AC=13.14cm

The standard deviation of assembly time (in minutes) is approximately .33.

The standard deviation of a uniform distribution of assembly time is calculated using the following formula:

σ = √((b-a)^2 / 12),

where a is the lower boundary of the range of assembly time (6 minutes) and b is the upper boundary of the range of assembly time (10 minutes).

Substituting a = 6 and b = 10 into the formula yields:

σ = √((10-6)^2 / 12)

σ = √(16/12)

σ = √(1.33)

σ = .33

Therefore, the standard deviation of assembly time (in minutes) is approximately .33.

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The solution is the given triangles are similar to each other due to S-S-S rule.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

From the given figure we get,

triangle ABC & HIJ

we get,

AC = 2* HI

AB= 2*IJ

BC = 2* HJ

so, the scale factor = 2

Hence, The solution is the given triangles are similar to each other due to S-S-S rule.

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Answer:

[tex]f^{-1}(x)=\sqrt[4]{x}+2 \qquad \textsf{for $x \geq 0$}[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=(x-2)^4[/tex]

The domain of the given function is restricted:  

Therefore, the range of the given function is also restricted:  

To find the inverse of a function, swap x and y:

[tex]\implies x=(y-2)^4[/tex]

Rearrange the equation to make y the subject:

[tex]\implies \sqrt[4]{x}=y-2[/tex]

[tex]\implies y=\sqrt[4]{x}+2[/tex]

Replace y with f⁻¹(x):

[tex]\implies f^{-1}(x)=\sqrt[4]{x}+2[/tex]

The domain of the inverse of a function is the same as the range of the original function.  Therefore, the domain of the inverse function is restricted to {x : x ≥ 0}.

Therefore, the inverse of the given function is:

[tex]f^{-1}(x)=\sqrt[4]{x}+2 \qquad \textsf{for $x \geq 0$}[/tex]

After 15 hours there will be 1.875 grams of the radioactive tellurium.

We know that the half-life of a radioactive kind of tellurium is 3 hours.

This means that for any quantity A of that radioinuclei, after 3 hours we will have half of that amount.

Then we can write the exponential equation:

M(x) = A*(1/2)^(x/3h)

Here we start with A= 60 grams, and after 15 hours we will have:

M(15h) = 60g*(1/2)^(15h/3h)

M(15h) = 60g*(1/2)^(5) = 1.875 g

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In a convex hexagon, if the area of the hexagonal region is 2116 (√2 + 1), then the value of AB is 46.

A convex hexagon is a hexagon in which all of the inner angles and all of the vertices have to be smaller than 180 degrees. There are both regular and irregular convex hexagons. Inside a convex hexagon, there are no angles. More specifically, no internal angle will exceed 180 degrees. Any internal angle which exceeds 180 degrees is concave.

Let the side length be x.

So, the diagonal BF = √(AB^2 + A F^2) = √(x^2 + x^2) = x√2.

Then, the areas of the triangles AFB and CDE in total equals (x^2 / 2) * 2, and the area of the rectangle BCEF equals x * x√2 = x^2 √2.

Now, let the equation be:

2116 (√2 + 1) = x^2√2 + x^2

And by simplifying the above equation, we will get:

2116 (√2 + 1) = x^2 (√2 + 1)

2116 = x^2

By taking root both sides, then it will be:

x = 46

Hence, the value of AB is 46.

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Although part of your question is missing, you might be referring to this full question: In a convex hexagon ABCDEF, all six sides are congruent, ∠A and ∠D are right angles. And ∠B, ∠C, ∠E and ∠F are congruent. The area of the hexagonal region is 2116 (√2 + 1). Find AB.

The trigonometric form of the complex number is,  

-6+ i (-6) = 6√2( cos5pi/4 + i sin 5pi/4)

In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit and satisfying the equation {\displaystyle i^{2}=-1}; every complex number can be expressed in the form a + bi, where a and b are real numbers.

here, we have,

the complex number which we get from the given graph is,

-6+ i (-6)

so, a = -6

    b = -6

i.e. z = √a^2+b^2

        =6√2

so, we know,

The trigonometric form of a complex number:

z = |z| (cosα +i sinα)

now, cosα = a/|z|

                 = -1/√2

and, sinα = b/|z|

              = -1/√2

so, solving we get,

α = 5pi/4

i.e. -6+ i (-6) = 6√2( cos5pi/4 + i sin 5pi/4)

Hence, The trigonometric form of the complex number is,  

-6+ i (-6) = 6√2( cos5pi/4 + i sin 5pi/4)

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There are 120 possible ways for two tables and 90 ways for 3 tables.

If we split the six people into 4/1/1, there will be (6 4) ways to select the 4 people sitting together, and 3! ways to arrange them at their table, so this gives (6 4)(3!)=15(6)=90 possibilities.

If we split the six people into 3/2/1, we will get (6 3) ways to select the 3 people sitting together, 2! ways to arrange them at their table, and (3 2) ways to select the 2 people sitting together, so this gives (6 3)⋅2⋅(3 2)=20(2)(3)=120 possibilities.

Finally, there are 120 possible ways for two tables and 90 ways for 3 tables.

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A graph of the system of linear inequalities is shown in the image attached below.

In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:

In this exercise, we would use an online graphing calculator to plot the given system of linear inequalities y > -x + 5 and y ≤ 3x -4 as shown on the graph attached below. Based on the graph (see attachment), we can logically deduce that the solution to the given inequality is the shaded region, with a point of intersection at the ordered pair (2.25, 2.75) in quadrant I.

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a) The proportion of the population that is less than 18 is 0.3085.

b) The probability that a randomly chosen value is greater than 25 is 15.39%, which is not equal to 2.6667 as stated in the question.

a) To find the z-score corresponding to the value of 18, we can use the standard normal formula:

z = (18 - mu) / sigma

Where mu is the mean and sigma is the standard deviation of the population.

To find the proportion of the population that is less than 18, we can use the cumulative distribution function (CDF) of the standard normal distribution.

The CDF gives us the proportion of the population that is less than a given value.

For a standard normal distribution, we can use a standard normal table or a calculator to find the CDF.

Using the standard normal table, or a standard normal calculator,

we find that the CDF of the standard normal distribution at z = -0.6309 is 0.3085.

So, the proportion of the population that is less than 18 is 0.3085.

b) To find the z-score corresponding to the value of 25, we can use the standard normal formula:

z = (25 - mu) / sigma

Using a standard normal calculator or table,

we find that the z-score for 25 is 1.0538.

The proportion of the population that is greater than 25 is 1 - the CDF of the standard normal distribution at z = 1.0538.

Using a standard normal calculator or table, we find that the CDF of the standard normal distribution at z = 1.0538 is 0.8461.

So, the proportion of the population that is greater than 25 is 1 - 0.8461 = 0.1539.

To find the probability that a randomly chosen value is greater than 25, we can multiply 0.1539 by 100% to get 15.39%.

Therefore, the probability that a randomly chosen value is greater than 25 is 15.39%, which is not equal to 2.6667 as stated in the question.

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The solution is, A. m + n, must also be even .

A number that is divisible by 2 and generates a remainder of 0 is called an even number. Examples of even numbers are 2, 4, 6, 8, 10, etc. For example, assume you have ten chocolates. These chocolates may be divided into two groups, each having five chocolates. So, ten is an even number.

here, we have,

given that,

If 3(m + n) is even

so, we get,

3(m + n) is divisible by 2.

i.e. m+n is must ne divisible by 2.

Hence, The solution is,  A. m + n, must also be even .

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