what is the value of tan a?

Answer:

Explanation:

The general formula for a permutation is

nPr=n!/n-r!

n=20and r=2, so our equation becomes

20P2=20!/18!=(20×19)=380

Step-by-step explanation:

The greatest amount of sap collected from any one tree is two times.

The maximum amount of sap that can be gathered from a single tree is two times greater than the minimum amount. SAP enables businesses to innovate on anything from cancer therapies to flood mitigation. We support life-saving research and are deeply committed to social responsibility and sustainability. At SAP, we collaborate to create innovations.

Work in a stimulating and rewarding environment by joining us. Minerals and nutrients can be found in tree sap. In the spring, when new buds are growing, a sticky substance that travels through the tree and out onto the branches helps the tree produce energy. Sugars are created as a result of photosynthesis and sent back into the tree, where they serve as sustenance for the tree's growth.

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Correct Question:

The greatest amount of sap collected from any one tree is _____________

The four matches can be sequenced in 1350 different ways, ensuring that each player gets to play at least once.

A sequence is an enumerated collection of things in mathematics where repetitions are allowed and order is important. It includes members, much like a set (also called elements, or terms). A sequence can be formalized as a function from natural numbers (the positions of sequence elements) to the elements at each place. An indexed family, which is a function from any index set, can be thought of as a generalization of the concept of a sequence.

The final matches can be between any two players after we have made sure that every player has played at least one match (except those three matches played)

We can select any two players from a pool of six for the first game =[tex]6_{c_{2} }[/tex]

We can select either of the two players from a total of four for the second match is [tex]4_{c_{2} }[/tex]

We have a choice of two players for the third game.=[tex]2_{c_{2} }[/tex]

Any of the two players from the pool of six can be selected for the fourth match= [tex]6_{c_{2} }[/tex]

P(x) =[tex]6_{c_{2} }[/tex]×[tex]4_{c_{2} }[/tex] ×[tex]2_{c_{2} }[/tex] ×  [tex]6_{c_{2} }[/tex]

P(x) = 15 × 6 × 1 × 15

P(x) = 1350

Therefore, the four matches can be arranged in 1350 different ways, ensuring that each player gets to play at least once.

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The only triangle dimensions that give a right angle triangle are;

3) 15, 36, 39

4) 15, 20, 25

6) 16, 30, 34

We are told that If a triangle has side lengths a, b, and c such that;

a² + b² = c² , then that triangle is a right triangle.

1) Using Pythagoras theorem, we can say that;

15² + 18² ≠ 21²

Thus, this is not a right angle triangle.

2) Using Pythagoras theorem, we can say that;

16² + 20² ≠ 24²

Thus, this is not a right angle triangle.

3) Using Pythagoras theorem, we can say that;

15² + 36² = 39²

Thus, this is a right angle triangle.

4) Using Pythagoras theorem, we can say that;

15² + 20² = 25²

Thus, this is a right angle triangle.

5) Using Pythagoras theorem, we can say that;

16² + 32² ≠ 48²

Thus, this is not a right angle triangle.

6) Using Pythagoras theorem, we can say that;

16² + 30² = 34²

Thus, this a right angle triangle.

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The result after evaluating the expression is: 8

What is equations?

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables.

For this case we have the following expression:

13-0.75w + 8x

We must evaluate for the following values:

w = 12

x = 1/2

Substituting the values we have:

13- 0.75 * (12) + 8 * (1/2) = 8

The result after evaluating the expression is: 8

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this letter in each box that contains the exercise's number. Factoring polynomials can be a tricky process, but it can be done with practice and a few key steps.

The first step is to identify if the polynomial is a prime or a composite. A prime polynomial cannot be factored, while a composite polynomial can be factored into two linear factors. Then, look for two numbers that can be multiplied together to give the constant term, and two numbers that add together to give the coefficient of the x-term. Once you have identified these numbers, factor out the greatest common factor and then separate the remaining terms into two binomials. Finally, use the distributive property to factor the binomials and simplify. The answers are: A. (x+2)(x+3) E. (x+1)(x+6) D. (x+4)(x+5) U. (x+4)(x+3) C. (x+2)(x+6) R. (x+1)(x+15) S. (x+1)(x+12) N. (x+3)(x+5) I. (x-3)(x+5) W. (x-5)(x+3) T. (x-3)(x-5) F. (x+7)(x-4) K. (x+4)(x-7) H. (x-7)(x-4) L. (x-11)(x+3) B. (x-3)(x+11)

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The simplified form can be written as -

7.8y + 1.4z

We have the following expression -

6(0.7y + 0.8z) − 4z − 6(−0.1z − 0.6y)

We have -

6(0.7y + 0.8z) − 4z − 6(−0.1z − 0.6y)

(6 x 0.7y + 6 x 0.8z) - 4z + 6 x 0.1z + 6 x 0.6y

4.2y + 4.8z - 4z + 0.6z + 3.6y

7.8y + 4.8z - 3.4z

7.8y + 1.4z

Therefor, the simplified form can be written as -

7.8y + 1.4z

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The given coordinates represent a function and at f(-7) equals to 9.

We have the following coordinates -

(-7, 9) (-4, 10) (2, 6) (-6, 3)

Yes, these coordinates represent a function as a unique value of [x] has only one value of [y]. At x = -7, we can write -

f(-7) = 9

Therefore, the given coordinates represent a function and at f(-7) equals to 9.

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A. y = - (4/3)x + 4. y = - (4/3)x - 1 has No solution.

B. y = 4x - 5. y = - 2x + 7 has one solution.

C. 2x + 3y = 8. 4x + 6y = 17 has No solution.

D. y = 5x - 15. y = 5(x - 3) has Infinitely many solutions.

Graphical solutions of a system of equations are a way of finding the intersection points of all the equations given.

We are given graph each system of equations, If they intersect at one point they have one solution, if they are parallel to each other they have no solution and if they are coinciding with each other they have infinitely many solutions.

y = - (4/3)x + 4.

y = - (4/3)x - 1.

These are parallel lines no solution thus we have;

y = 4x - 5.

y = - 2x + 7.

These lines intersect at (2, 3) one solution thus we have;

2x + 3y = 8

4x + 6y = 17.

They are parallel to each other thus we have;

y = 5x - 15.

y = 5(x - 3).

These are coinciding lines, if we distribute the terms hence infinitely many solutions.

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The random variable x's mean and standard deviation are 8 and 2, respectively. W=7+ 4x is the formula for the random variable w. The mean of w is E(W) =39

A dataset's mean is calculated by dividing the sum of all values by the total number of values. The term "average" is frequently used to describe it because it is the most widely used central tendency metric.

Divide the entire number of values by the total number of numbers to find the average. A mean is the term used to describe the mathematical average of a set of two or more data values. Average is also referred to as mean or arithmetic mean.

The mean is the average value of the data. It's easy to calculate: just add up all the numbers, then divide by the total number of numbers. Or, to put it another way, it is equal to the sum divided by the quantity.

The mean is then determined as follows:

E(W) = E (7 + 4X)

This results

E(W) = 7 + 4 E (X)

We thus have:

E(W) = 7 + 4 x 8

E(W) =39

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Standard deviation = 8 and mean = 39.

What is standard deviation?

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean (also known as the anticipated value) of the collection.

Given, the formula for mean is E(W) = 7 + 4(X)

∴ E(W) = 7 + 4E(X)

Mean, E(X) equals to 8, hence substituting in the above equation, we get,

E(W) = 7 + 4×8

⇒E(W) = 39

Since, E(W) = 7 + 4(X)

Var(W) = Var(7) + Var(4X)

Since, Var(constant)=0,

Var(W) = Var(4X)

Var(W) = 4²×Var(X), where Var(X)=σₓ²

⇒ Var(W) = 16×σₓ², where σₓ²=2²

⇒ Var(W) = 16×4

⇒ Var(W) = 64

Standard Deviation (SD) = √64 = 8

Thus, standard deviation = 8 and mean = 39.

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Answer:

7

Step-by-step explanation:

Experimental probability is based on the actual results of an experiment (gathered by experimenting repeatedly).  

It is calculated by dividing the recorded number of times an event happens by the total number of trials in the actual experiment:

[tex]\boxed{\textsf{Experimental Probability} = \dfrac{\textsf{Number of times an event happens}}{\textsf{Total number of trials}}}[/tex]

As the number of trials increases, we would expect for the experimental probability to get closer to the theoretical probability.

Given:

The experimental probability of drawing a short straw is:

[tex]\implies \sf P(short\;straw)=\dfrac{35}{50}=\dfrac{7}{10}[/tex]

If Laura conducts 10 further trials of the experiment, based on the results in the table, the number of additional trials that will have a result of a short straw being drawn is:

[tex]\begin{aligned}\implies \textsf{Additional trials (short straw)} &=\sf experimental\;probability \times number\;of\;trials\\&= \sf \dfrac{7}{10} \times 10\\&= \sf 7\end{aligned}[/tex]

The value of sin (x - y) of the triangles is -33/65

Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles

Given: sin x = 3/5 and cos y = 5/13.  Both triangles are in quadrant 1

(Consider the image attached)

For triangle with angle x

adjacent = √(5²-3²)  = 4

cos x = 4/5 (adjacent/hypotenuse)

For triangle with angle y

opposite = √(13²-5²)  = 12

sin y = 12/13 (opposite/hypotenuse)

Using the trigonometric identity:

sin(x-y) = sinxcosy - sinycosx

sin(x-y) = (3/5)×(5/13) - (12/13)×(4/5)

sin(x-y) = 3/13 - 48/65

sin(x-y) = -33/65

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The three beat frequencies possible with tuning forks are-

f1 = 9 Hz; f2 = 3Hz; f3 = 5Hz

The three beat frequencies are -

f1= 262 - 254 = 9 Hz

f2 = 257 - 254 = 3Hz

f3 = 262 - 257 = 5Hz

Thus, the possible beat frequencies of the turning fork are found.

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Answer:

8

Step-by-step explanation:

(4/5)/(1/10)

To solve, flip the second fraction, and instead of dividing, multiply:

(4/5)/(1/10) = (4/5) * (10/1)

Multiply straight across:

(4/5) * (10/1) = (4 * 10)/(5 * 1) = 40/5

SImplify. Divide:

40/5 = 8

8 is your answer.

Hope it helps

Step-by-step explanation:

how to simplfy the fifth root

The derivative of the given function sin(xy)=3x−2y is obtained as;

dy/dx =  3sec(xy)/x - y/x

The given equation is-

sin(xy) = 3x − 2y

Be sure to account for both sides of this argument.

d/dx(sin(xy)) = d/dx(3x − 2y)

Differentiate the equation's left side.

Set the left side equal to a right side to reform the equation.

x.cos(xy).y' + y.cos(xy) = 3

Solve for y'.

y' = 3sec(xy)/x - y/x

Thus, replace y' with dy/dx

dy/dx =  3sec(xy)/x - y/x

Thus, the derivative of the given function sin(x y)=3x−2y is obtained as;

dy/dx =  3sec(xy)/x - y/x

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All of the following equations have the same solution except x + 6.5 = 6.3   , the correct option is (c) .

In the question ,

four equations are given ,

we have to select the option that has a different solution form the given options .

Part(a) the equation is 7.5x = 1.5

simplifying further ,

we get ,

x = 1.5/7.5 = 0.2

Part(b) the equation is x/5 = 0.04

simplifying further ,

we get ,

x = 5*0.04 = 0.2

Part(c) the equation is x + 6.5 = 6.3

simplifying further ,

we get ,

x = 6.3 - 6.5 = -0.2

Part(d) the equation is -1.8 + x = -1.6

simplifying further ,

we get ,

x = -1.6 + 1.8 = 0.2

Therefore , the equation that is having a different solution (x = -0.2) is (c) x + 6.5 = 6.3   .

The given question is incomplete , the complete question is

All of the following equations have the same solution except _____.

(a) 7.5x = 1.5

(b) x/5 = 0.04

(c) x + 6.5 = 6.3

(d) -1.8 + x = -1.6

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a) The formula for the area of the triangle is given as follows:

Area = 0.5 x base x height.

b. The length of the base is given as follows: 6.3 units.

c. The length of the height is given as follows: 5 units.

d. The area of the triangle is given as follows: 15.75 units squared.

The area of a triangle is calculated as half the multiplication of the triangle's base by the triangle's height, as follows:

Area = 0.5 x base x height.

The vertices for the right triangle in this problem are given as follows:

(-4, -1), (2,1), (2,6).

Hence the base of the triangle is of:

[tex]B = \sqrt{(2 - (-4))^2 + (1 - (-1))^2} = 6.3[/tex]

The height is given as follows:

6 - 1 = 5.

Which means that the area of the triangle is of:

Area = 0.5 x 5 x 6.3 = 15.75.

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The four equations' coefficients of x can only take two values, thus if one of those values is m, the other solution will be -1/m.

A relation between different terms on either side of the equal sign is described by a straightforward equation.

Simple equations also follow one or a mixture of the four arithmetic computations of addition, simple arithmetic, multiplication, and division.

There are three primary versions of the set of equations: point-slope form, standard form, or slope-intercept form.

So, Shannon's error would be:

In a rectangle, the adjoining sides are perpendicular to one other, whereas parallel runs between the opposing sides.

The slope of parallel lines is equal, and the slope, of a line perpendicular to some other line with a slope, m, is -1/m , thus the slopes of the central axis should be equal, which also gives:

Two sets of systems of equations with equal slopes should make up the equation: B. Y = -x + 6 and Y = -x - 5 are a pair.

Therefore, the slopes of the other two lines are -1/-1 = 1 and the equations of the other two lines are y = x - 4 and y = x - 5 correspondingly.

Therefore, the four equations' coefficients of x can only take two values, thus if one of those values is m, the other solution will be -1/m.

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Correct question;
Shannon says that the lines y=-3x-4,y=-(1)/(3)x+6,y=-4x-5, and y=(1)/(4)x-5 could represent the sides of a rectangle. Explain Shannon's error.

The value of AC is 22.5

The property of three parallel lines and their transversals is used to solve this sum. The property explains that if the ratio of the corresponding intercepts made on any other transversal by the same parallel lines is the same as the ratio of the intercepts made on a transversal formed by three parallel lines.

XY ║seg AC

2AX = 3BX

XY = 9

Since, 2AX =3BX

∴ AX÷ BX = 3÷2

AX + BX÷ BX = 3+2÷2

AB ÷ BX = 5÷2

Δ BCA ~  ΔBYX (SAS test of similarity)

( The SAS similarity test determines whether two triangles are similar if the ratio of the lengths of two sides of one triangle equals the ratio of the lengths of two sides of another triangle, and the included angles are equal.)

∴ BA ÷ BX = AC ÷ XY ( Corresponding sides)

∴ 5÷ 2 = AC ÷ 9

∴ AC = 22.5

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Answer:

(4) (-1,6)

Step-by-step explanation:

f(x) = x² - 3x + 4

1) (0,4) ==>x=0 and f(x)=4

4 = 0² - 3(0) + 4

4 = 0 + 4

4 = 4 ==> true X

2) (1.5,1.75)==> x=1.5 and f(x)=1.75

1.75 = (1.5)² - 3(1.5) + 4

1.75 = 2.25 - 4.5 + 4

1.75 = 2.25 - 0.5

1.75 = 1.75 ==> true  X

3) (5,14)

14 = (5)² - 3(5) + 4

14 = 25 - 15 + 4

14 = 10 + 4

14 = 14  ==> true X

4) (-1,6)

6 = (-1)² - 3(-1) + 4

6 = (|-1|)² - (-3) + 4  ==> the square of a negative number is equal to the square

                              of the absolute value of that number since the square of

                             a real number is always positive

6 = (1)²+ 3 + 4  ==> subtracting a negative number is equivalent to adding

                          the positive number

6 = 1 + 3 + 4

6 = 4 + 4

6 = 8  ==> false √√

Hence, the answer is (4) (-1,6).

The table that contains only viable solutions if b represents the number of books he orders and w represents the total weight of the books, in ounces is the second table on the image given at the end of the answer.

The variables for this problem are given as follows:

To obtain the viable solutions, we must consider the input variable. The number of books is a countable amount, meaning that it can only assume non-negative integer values.

Thus the first table is incorrect, as it contains a negative amount of books, and the second table is the one that contains only viable solutions in the context of this problem.

The table is given by the image shown at the end of the answer.

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[tex]~~~~~~~~~~~~\stackrel{\textit{\LARGE Sydney}}{\stackrel{\textit{payments at the beginning of the period}}{\textit{Future Value of an annuity due}}}[/tex]

[tex]A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]\left(1+\frac{r}{n}\right) \\\\ \qquad \begin{cases} A=\textit{accumulated amount} \\ pmt=\textit{periodic payments}\dotfill & 100\\ r=rate\to 0.8\%\to \frac{0.8}{100}\dotfill &0.008\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &10 \end{cases}[/tex]

[tex]A=100\left[ \cfrac{\left( 1+\frac{0.008}{12} \right)^{12 \cdot 10}-1}{\frac{0.008}{12}} \right]\left(1+\frac{0.008}{12}\right) \\\\\\ A=100\left[ \cfrac{\left( \frac{1501}{1500} \right)^{120}-1}{\frac{1}{500}} \right]\left(\frac{1501}{1500}\right) \implies {\Large \begin{array}{llll} A \approx 12497.05 \end{array}}[/tex]

The standard error for the estimate of the proportion of all persons aged 65 and over with osteoarthritis is 0.0092.

The subset chosen from the larger set to make assumptions is known as a random sample. Standard Error can be defined as the term that measures the accuracy of the sample distribution which represents the population.

We know that,

                   Standard Error   =   √ ( P ( 1 - P ) / n )    → 1

As per the given question,

Substitute the values in 1,

Standard Error ( SE )   =   √ ( P ( 1 - P ) / n )

                                    =   √ ( 0.115 ( 1 - 0.115 ) / 1200 )

                                    =   √ ( 0.115 ( 0.885 ) / 1200 )

                                    =   √ ( 0.101775 / 1200 )

                                    =   √ ( 0.0000848125)

Standard Error ( SE )   =   0.0092093702   ≅   0.0092

Therefore, 0.0092 is the standard error for the estimate of the proportion of all persons aged 65 and over with osteoarthritis.

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The time Austin had left to solve part two will be 25 minutes.

It is important to note that an equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, Austin's final exam in math had two parts. He had a total of 50 minutes to complete the entire exam.

Since he spent 25 minutes on Part one of the exam, the time he had left to solve part two will be:

t = 50 - 25

t = 25

The time is 25 minutes.

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Answer:

$385 discounted by 30% the final price would be $269.50

$385 discounted by 20% the final price would be $308.00

$385 discounted by 10% the final price would be $346.50

Step-by-step explanation:

Answer:

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

The selling price is $385.

As we see the first option is cheaper:

x = -2 and y = -10 is the solution of the equations y = 8x +6 and 10x - 5y = 30.

What is Substitution method to solve equations?

The method of substitution involves three steps: Solve one equation for one of the variables. Substitute (plug-in) this expression into the other equation and solve. Resubstitute the value into the original equation to find the corresponding variable. he substitution method is the algebraic method to solve simultaneous linear equations.

Given Equations :

y = 8x +6

10x - 5y = 30

A) Solve equation [1] for the variable  y

    [1]    y = 8x + 6

B)  Plug this in for variable  y  in equation [2]

  [2]    -5•(8x+6) + 10x = 30

  [2]     - 30x = 60

C)  Solve equation [2] for the variable  x

  [2]    30x = - 60

  [2]    x = - 2

D)  By now we know this much :

   y = 8x+6

   x = -2

E)  Use the  x  value to solve for  y      y = 8(-2)+6 = -10

Solution : {y,x} = {-10,-2}

Hence , x = -2 and y = -10 is the solution of the equations y = 8x +6 and 10x - 5y = 30.

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Answer: E

Step-by-step explanation:

Hence, the three side length of two triangles are same so they are congurent.  

What is the congurency?

Two shapes are congruent if they are the same (shape and size)- in other words, if the lengths of the sides and the angles are the same.

It is often useful to know when two triangles are congruent.

Here given coordinates of the triangle [tex]FGH[/tex] and triangle [tex]JKL[/tex] are

[tex]F(-5, 10), G(-2, 2), H(-9, -7), J(0, -5), K(9, 2), L(-8, -2)[/tex].

So, the distance formula is

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Distance between [tex]FG[/tex]  is

[tex]d=\sqrt{(-2-(-5))^2+(2-10)^2}\\\\d=\sqrt{(-2+5)^2+(2-10)^2}\\\\d=\sqrt{(3)^2+(-8)^2}\\\\d=\sqrt{9+64}\\\\d=\sqrt{73}[/tex]

Distance between [tex]GH[/tex]  is

[tex]d=\sqrt{(-9-(-2))^2+(10-(-7))^2}\\\\d=\sqrt{(-9+2)^2+(10+7)^2}\\\\d=\sqrt{(-7)^2+(-9)^2}\\\\d=\sqrt{49+81}\\\\d=\sqrt{130}[/tex]

Distance between [tex]HF[/tex]  is

[tex]d=\sqrt{(-5-(-9))^2+(10-(-7))^2}\\\\d=\sqrt{(-5+9)^2+(10+7)^2}\\\\d=\sqrt{(4)^2+(17)^2}\\\\d=\sqrt{16+289}\\\\d=\sqrt{305}[/tex]

Distance between [tex]JK[/tex]  is

[tex]d=\sqrt{(9-0)^2+(2-(-5))^2}\\\\d=\sqrt{(9)^2+(2+5)^2}\\\\d=\sqrt{(9)^2+(7)^2}\\\\d=\sqrt{81+49}\\\\d=\sqrt{130}[/tex]

Distance between [tex]KL[/tex]  is

[tex]d=\sqrt{(-8-9)^2+(-2-2)^2}\\\\d=\sqrt{(-17)^2+(-4)^2}\\\\d=\sqrt{289+16}\\\\d=\sqrt{305}[/tex]

Distance between [tex]LJ[/tex]  is

[tex]d=\sqrt{(0-(-8))^2+(-5-(-2))^2}\\\\d=\sqrt{(8)^2+(-5+2)^2}\\\\d=\sqrt{(8)^2+(-3)^2}\\\\d=\sqrt{64+9}\\\\d=\sqrt{73}[/tex]

Since, [tex]FG[/tex]≅[tex]LJ-GH[/tex]≅[tex]JK-HF[/tex]≅[tex]KL[/tex]

Hence, the three side length of two triangles are same so they are congurent.  

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