14. One of the classic proofs of the Pythagorean Theorem involves the
diagram below where square ABCD has had points E, F, G, and H located
on its sides such that AE = BF=CG= DH as shown. The proof then
relies on quadrilateral EFGH being a square.

(a) First, explain why EFGH must be a rhombus. Use a paragraph proof
style, but carefully justify all of your statements with reasons.

(b) Give an explanation for why all interior angles of EFGH must be right angles? Explain why this fact in
combination with your proof in part (a) show that EFGH is a square?

The value of x must be between -18 and -6. The solution has been obtained using Triangle inequality theorem.

What is Triangle inequality theorem?

The triangle inequality theorem explains how a triangle's three sides interact with one another. This theorem states that the sum of the lengths of any triangle's two sides is always greater than the length of the triangle's third side. In other words, the shortest distance between any two different points is always a straight line, according to this theorem.

We are given three sides of a triangle as 8, 6 and x+20

Using Triangle inequality theorem,

⇒8+6 > x+20

⇒14 > x+20

⇒-6 > x

Also,

⇒x+20+6 > 8

⇒x+26 > 8

⇒x > -18

Also,

⇒x+20+8 > 6

⇒x+28 > 6

⇒x > -22

From the above explanation it can be concluded that x is less than -6 but greater than -22 and -18.

This means that x must lie between -18 and -6.

Hence, the value of x must be between -18 and -6.

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The area of this triangle in the coordinate plane with coordinates A( 4,5) , B(1,2) and C( 6,2) is equals to the 15 unit². So, option (d) is correct.

The basic formula for the area of a triangle is (1/2) × base × altitude. But we have to calculate the area of a triangle in coordinate geometry. Coordinate geometry is defined as the study of geometry using coordinate points. If coordinates of the triangle are(x₁, y₁), (x₂, y₂), and (x₃, y₃) then the area of the triangle is defined as Area = 1/2[ x₁(y₂ - y₃) + x₂( y₃ - y₁) + x₃(y₁ - y₂) ]

We have a triangle ABC in coordinate plane in above figure. The coordinates of triangle are A( 4,5) , B(1,2) and C( 6,2). Here, x₁ = 4 , y₁ = 5 , x₂ = 1 , y₂ = 2 ,x₃ = 6 , y₃ = 2. So, Area of ∆ABC

= 1/2[ 4( 2 - 2)+ 1( 2 - 5) + 6(5 - 2)

= 0 + (-3) + 18 = 15

Hence, the required area is 15 unit².

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Complete question:

What is the area of this triangle in the coordinate plane? See the above figure.

a)25. 0 units²

b) 27. 5 units²

c) 50. 0 units²

d) 15. 0 units²

Answer:

8 FISHES

Step-by-step explanation:

There are several ways to solve this but lets use proportion cus I feel it's easier. So what you are looking for is simply 100% of the fish they caught.!

So therefore, 75% = 6

100% = (100 × 6) ÷ 75

= 600 ÷ 75

= 8 FISHES

So it will take 945 sec to solve 21 math problem.

As per the data given in the above question are as bellow,

The details provided are as bellow,

Moria solve 15 math question in 20 minutes,

We have to determine how long will it take her to solve 21 math problem?

First taking how much time its take to solve one question ,

So, Total number of question divide the total time we get,

Substitute the value in above equation we get,

=15* 60 =900 Sec

=900/20

=45 sec

So the time taken to solve 21 question will be,

=45*21

=945 sec

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A circle not 100 degrees because 360 is a highly composite number, when a circle is drawn it completes a whole loop making it a 360 degrees.

As you surely well know, we modern people like to divide a circle into 360 wedges that resemble pies. We define the angle at the vertex of each of these wedges as being one degree in size. As you presumably well know, we can measure angles in other ways other in degrees. Angles are also measured in radians and, on a very rare occasion, in the enigmatic gradians used by the military (thus the presence of "deg rad grad" buttons on many calculators).

While the reason the 360 degree convention was chosen is unknown to us, we do know roughly when and where it all began (more on that in a moment). We at least know that it originated a very, very long time ago—around 4,000–5,000 years ago with the Babylonians, the Greeks, and possibly other much older peoples.

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Answer:

10 seconds

Step-by-step explanation:

create a proportion

450 copies over 15 seconds = 300 copies over 't' seconds

cross-multiply to get:

450t = 4500

t = 10

it will take 10 seconds for Periodical Express to print 300 copies of the Sports Report if they maintain the same printing rate.

What are arithmetic operations?

Arithmetic operations are basic mathematical operations that include addition, subtraction, multiplication, division, and others.

Periodical Express printed 450 copies of The Informer in 15 seconds, which means they printed 450/15 = 30 copies per second.

To find out how long it would take to print 300 copies of the Sports Report, we just need to divide the number of copies by the rate of printing.

So, the calculation is 300 / 30 = 10 seconds

Therefore, it will take 10 seconds for Periodical Express to print 300 copies of the Sports Report, if they maintain the same printing rate.

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Answer:

Step-by-step explanation:

Hello! The slope formula is rise over run, or (y2 - y1)/(x2 - x1).  You can choose either y-coordinate for y2 and y1 and either x-coordinate for x2 and x1.  Since you are given two points already, use those.  The first coordinate in a coordinate pair is always x, and the second coordinate is always y (x, y).  (0, 0) is the origin, or the point where both lines x and y meet up.  The leftmost point is 3 squares below that, and y is a vertical line.  The coordinates of the leftmost point on the line is (0, -3).  The rightmost point on the line is located at the coordinate pair of (1, 0).  Any point located below or left of the origin is negative.  A point below the origin means the y is negative, and a point left of the origin means the x coordinate is negative.  You now have two coordinate pairs, which is all you need to figure out the slope of the line.  Use the formula (y2 - y1)/(x2 - x1) to get your answer.  Substitute the y values in for the first part.  The two y values are 0 and -3.  The two x values are 0 and 1.  You now have (0 - (-3)/(1 - 0).  0 - (-3) = 3 because two negatives make a positive.  You now have 3/1.  If you have to simplify this, then the slope is 3.  Another easy way is shown below:  
Hope this helped you solve slopes!

If the area of the triangle is 120 cm^2, the value of x is equal to 6.

Mathematically, the area of a triangle can be calculated by using this mathematical expression:

Area of a triangle (A) = 1/2 × b × h

Where:

According to Hero's Formula area of triangle by Heron of Alexandria, if a, b, c are the side lengths of a triangle, then, the area of a triangle can be calculated by using this mathematical expression:

Area of a triangle (A) = √[s(s − a)(s − b)(s − c)]

Where:

s = (a + b + c)/2

s = (x + x + 1 + 2x - 1)/2

s = 4x/2

s = 2x

Substituting the parameters into Hero's Formula formula, we have the following;

x√10 = √[2x(2x − x)(2x − x - 1)(2x − 2x + 1)]

x√10 = x√2(x − 1)

√10 = √2(x − 1)

Taking the square of both sides, we have:

10 = 2(x - 1)

10 = 2x - 2

2x = 12

x = 12/2

x = 6.

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To determine their ages, the substitution approach is used.

Joy's age and her brother's age are differed by 10 years.

What is linear system?

It is an system of equation where the maximum power of the variable is consistently 1. a single-dimensional object with no breadth. It consists of an endless number of dots placed side by side.

Given

The combined ages of Joy and her brother total 24.

Joy's older brother is three years older than  twice his age she is.

To locate

Joy's age as compared to that of her brother.

Assume that Joy is x years old and her brother is y.

then in line with the first circumstance.

x + y = 24 ...(1)

And according to the second condition.

2x + 3 = y ...(2)

On solving equations 1 and 2. We get

x + 2x + 3 = 24

            x = 7

Then

y = 2x + 3

y = 17

Then, the difference between Joy's age and her brother's age.

y - x = 17 - 7 = 10

Thus, the difference between Joy's age and her brother's age is 10.

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The solutions to the system of equations are x = 4 and y = -6

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the first equation be represented as A

Now , the value of A is

2y = -3x  

Divide by 2 on both sides of the equation , we get

y = ( -3/2 )x   be equation (1)

Let the second equation be represented as B

Now , the value of B is

y = -2x + 2   be equation (2)

Substituting the value of y from equation (1) in equation (2) , we get

( -3/2 )x = -2x + 2

Adding 2x on both sides of the equation , we get

2x - ( 3/2 )x = 2

( 4x - 3x ) / 2 = 2

x/2 = 2

Multiply by 2 on both sides of the equation , we get

x = 4

Substitute the value of y in equation (1) , we get

y = ( -3/2 ) 4

y = -3 ( 2 )

y = -6

Therefore , the value of x and y is 4 and -6 respectively

Hence , the equations are solved

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The process to graph an absolute value piecewise function is explained below .

Let us consider the Absolute value function as :

y = | x -2 | ;

this absolute function can be written in piecewise wise form as :

⇒ [tex]y =\begin{array}{cc} \{ & \begin{array}{cc} -x+2 & x < 2 \\ x-2 & x\geq 2 \end{array}\end{array}[/tex]  ;

this piecewise function means that the main function divides into two pieces ,

for any input value that is less than 2 , the function"-x+2" will be used , and

for any input value greater than or equal to 2, the function "x-2" , will be used ;

for example : if x = 3 , then ⇒ y = 3 - 2 = 1  ;

and is x = 1 , then ⇒ y = -1 +2 = 1 ;

the points to be plotted are (3,1) and (1,1) .

The graph of this absolute value piecewise function is shown below .

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Answer:

B(-9) = 432

Step-by-step explanation:

B(x) = 4x² - 12x

B(-9) = 4(-9)² - 12(-9)

B(-9) = 4(81) + 108

B(-9) = 324 + 108

B(-9) = 432

Answer:

432

Step-by-step explanation:

B(x) = - 9

Replacing the value of x in the equation,

4x² - 12x

= 4 * (-9)² - 12 * (-9)

= 4 * 81 + 108

= 324 + 108

= 432

_________

hope this helps!

Answer:

78 Tigers

Step-by-step explanation:

1440=270+15x

1170=15x

78=x

Chunking is a good way to introduce your child to some of the more basic concepts of division, and once they have come to terms with this they can then move onto the short method of division.

Now, According to the teaching Ideas:

We have four basic arithmetic operations i.e., addition, subtraction, multiplication, and division. Amongst these four operations, the division is one of the major operations we use in our daily activities. It is the process of splitting a large group into equal smaller groups. For example, divide 25 by 5. Division fact for this example will be, 25 ÷ 5 = 5.

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The number of silverfish employees put in the aquarium is 11.

The ratio is defined as a comparison of two quantities of the same unit to determine how much of one quantity is contained in the other. Ratios are divided into two sorts.

The first is a part-to-part ratio, and the second is a part-to-whole ratio. The part-to-part ratio expresses the relationship between two distinct entities or groupings.

Given that,

The ratio of the number of g total number of fish in the aquarium = 6: 11

Let us assume that the total number of silverfish employees put in the aquarium is x

So, The total number of fish = 6+11 = 17 out of which 11 are silverfish.

Complete question: A pet store employee put only silverfish and goldfish in an aquarium. The ratio of the number of g total number of fish in the aquarium was 6 to 11. Which number could be the number of silverfish employees put in the aquarium?

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The square root function is translated so that the endpoint is located at (-7,7), [tex]g(x)= \sqrt{x+7} +7[/tex]  and this can be determined by using the transformation.

The square root parent function is translated so that the endpoint is located at (-7,1).

The following steps can be used to determine the equation that represents this new function:

                       [tex]f(x) =\sqrt{x}[/tex]

[tex]g(x)= \sqrt{x+7} +7[/tex]

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Answer:

The answer is -88.

Step-by-step explanation:

We can substitute the given values into the expression to find its value:

mnp + (-n)

= (5)(8)(-2) + (-8)

= -80 + (-8)

= -88

So, the value of the expression mnp + (-n) if m = 5, n = 8, and p = -2 is -88.

I would greatly appreciate Brainliest.
Have a nice day.

The tangent formula is thus written as follows:

tan θ = (opposite side) / (adjacent side)

where "opposite side" refers to the side that is across from angle x and "adjacent side" refers to the side that is right next to it.

The tangent (tan) function is discussed in the tangent formulas. Let's assume a right-angled triangle where x is the acute angle.

The tangent formulas are trigonometric formulas that describe the tangent function. One of the six trigonometric functions, the tangent function, also known as "tan," is the ratio of the opposite side to the adjacent side.

Numerous trigonometric identities and formulas can be used to obtain numerous tangent function-related formulas.

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An exponential function is a mathematical function that models a relationship between a variable (in this case, t) and a constant multiplied by the power of another variable (in this case, y). The general form of an exponential function is y = ab^t, where

In this specific scenario, we are told that in 1997, the population of a city was 220,000 people and that each year since then, the population has grown by 6.2%. We can use this information to find the values of a and b in the exponential function.

The initial value, a, is simply the population of the city in 1997, which is given as 220,000.

To find the value of b, we need to determine how much the population increases each year as a proportion of the current population. We are told that the population grows by 6.2% each year. This means that if the population is currently P, the population will be (1 + 0.062)P the next year. We can write this as P(1.062) as the growth factor b.

So, combining the values of a and b, we have:

y = 220,000 * (1.062)^t

This equation tells us that the population of the city, y, is equal to the initial population of 220,000 multiplied by the growth factor of 1.062 raised to the power of t, where t is the number of years since 1997. This equation expresses the relationship between population and time.

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Answer:

268268268 + 424424424 = 692692692

So there are 692692692 cans of food

692692692 - 242424 × x = 0

x = Amount of boxes used

x = 2857.36021186...

The rounded answer is 2857.

Without the price floor, the equilibrium price is $0.15, and the equilibrium quantity is 200 billion pounds of milk.

Consumer surplus is calculated as the difference between the maximum price a consumer is willing to pay for a good and the price they actually pay. With an equilibrium price of $0.15, the consumer surplus can be calculated by calculating the area between the demand curve and the price line at $0.15.

The producer surplus can be calculated using an equilibrium price of $0.15 by calculating the area between the supply curve and the price line at $0.15. The producer surplus is the triangular area between the two prices and the supply curve, which intersects the price axis at $0.05.

The sum of the consumer and producer surpluses is the total surplus. Without the price floor, the consumer and producer surpluses would be different than they are now. The total surplus would also differ, reflecting changes in consumer and producer behavior.

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The value of x is 16.2degrees

Two angels whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.

Given;

(x+14), (9x-4)

Now,

According to supplementary angles;

(x+14)+ (9x-4)=180

10x+18=180

10x= 180-18

10x= 162

x= 16.2

Therefore, in these angles the value of x will be 16.2degree

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Answer:

C

Step-by-step explanation:

Rectangle Area = Length x Breadth

6.12 = Length x 1.8

Therefore, Length = 3.4m

To solve the equation 2x + 3y = 10 we need to plot the graph for the equation by calculating the intercepts for the same.

Here we see that we are given the equation

2x + 3y = 10

Since we do not have any other equation we will solve this by plotting it on a graph by the intercepts.

Intercepts of both the x and y axes are obtained by equating the other to 0.

Hence to get the x-intercept, we need to equate y to 0

Hence we get

2x = 10

or, x = 5

Hence for the y-intercept, we equate x to 0 to get

3y = 10

or, y = 10/3

By plotting these points and drawing a line through them we will get the graph for the equation.

Now to obtain a unique solution, we need to follow similar steps for the other equation and the intersecting point will give us the solution.

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Complete Question

How to solve 2x + 3y = 10?

The rectangular coordinates for (4.5, -30 degrees) are (3.9, -2.3), which is option B.

What is rectangle ?

A rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal; or a parallelogram containing a right angle.

To find the rectangular coordinates for a point in a plane given its polar coordinates, use the following formula:

x = r * cos(θ)

y = r * sin(θ)

Where (r, θ) are the polar coordinates and (x, y) are the rectangular coordinates.

For the point (4.5, -30 degrees), have:

r = 4.5

θ = -30 degrees = -30 * (π / 180) radians

x = r * cos(θ) = 4.5 * cos(-30 * (π / 180)) = 3.9

y = r * sin(θ) = 4.5 * sin(-30 * (π / 180)) = -2.3

So, the rectangular coordinates for (4.5, -30 degrees) are (3.9, -2.3), which is option B.

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The rectangular coordinates for (4. 5, -30 degrees) are (3.9, -2.3).

The rectangular coordinates for (4.5, -30 degrees) can be found using the following formula:

x = r * cos(θ)

y = r * sin(θ)

where r is the magnitude (or distance from the origin) and θ is the angle in radians.

In this case, r = 4.5 and θ = -30 degrees = -30 * (π/180) radians.

So:

x = 4.5 * cos(-30 * (π/180)) = 4.5 * cos(-π/6) = 4.5 * sqrt(3)/2

y = 4.5 * sin(-30 * (π/180)) = 4.5 * sin(-π/6) = -4.5 / 2

Therefore, the rectangular coordinates are (x, y) = (4.5 * sqrt(3)/2, -4.5 / 2), which is approximately (3.9, -2.3).

Option B (3.9, -2.3) is the right response as a result.

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2x(6x2 + 4x − 3) × (2x − 3)(5x + 6)

= (2x)2(6x2 + 4x − 3)(5x + 6)

= 12x3(5x + 6) + 8x2(5x + 6) − 6x(5x + 6)

= 60x4 + 48x3 − 45x2 − 36x

The equation that represent Ivan having is: 150+ 5x and Uma having is:  45 + 20x

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

To solve this problem, we have to state the equation using the information of the problem:

Information about the problem:

Writing the equation according to the information gave, we have:

y(Ivan) = 150+ 5x

y(Uma) = 45 + 20x

Where:

The relationship between the No. weeks passed and the amount earned is: linear and direct because when the number of weeks increases (x), the amount earned (y) will decrease.

The "y" variable is the dependent variable, because it will change according to the number of weeks passed (x).

The "x" variable is the independent variable, because it doesn't depend on any other value, just the number of weeks passed.

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In the biological sciences, exponential functions are frequently employed to simulate the evolution of a certain quantity over time, such as population number. Experimental data graphs are often created with the quantity on the y-axis and the time on the x-axis.

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth. You will find the formulas, rules, characteristics, charts, deviations, exponentially series, and examples of exponential functions in this article.

Depending on the exponential function, an exponential curve might increase or decrease. A quantity should have either exponential growth or exponential decay if it regularly increases or decreases by a predetermined percentage.

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Data points plotted below the line y=x (also known as the line of best fit) indicate that the observed value is less than the predicted value.

What exactly is a math graph?

A math graph is a visual representation of mathematical data or concepts. It typically uses Cartesian coordinates (x, y) to plot points, lines, and shapes that help to illustrate mathematical relationships. Graphs can be used to represent many types of mathematical information, including functions, equations, data sets, and geometric shapes. They are commonly used in fields such as science, engineering, economics, and statistics to analyze and understand complex information. Graphs are also an important tool for conveying mathematical ideas and results in a clear and understandable way.

This could be due to measurement errors, outliers, or other factors that are not accounted for in the model used to generate the line of best fit. It's important to note that the location of data points relative to the line of best fit can provide insight into the underlying pattern or relationship between the variables being studied, but further investigation is needed to determine the specific cause of the discrepancy.

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We can find no solution by the condition; if (a₁/a₂) = (b₁/b₂) ≠ (c₁/c₂), then there will be no solution.

A linear equation in two variables is a type of equation in the form ax + by + c = 0 where a, b, c ∈ R, a, and b ≠ 0. A linear equation with no solution is named an inconsistent pair of linear equations.

Suppose the pair of linear equations is in two variables, x and y.

a₁x + b₁y + c₁ = 0

a₂x + b₂y + c₂ = 0

Where a₁, b₁, c₁, a₂, b₂, c₂ are all real numbers.

Note that, a₁² + b₁² ≠ 0, a₂² + b₂² ≠ 0

If (a₁/a₂) = (b₁/b₂) ≠ (c₁/c₂), then there will be no solution.

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