Square ABCD has a diagonal AC with the given vertices. Find the coordinates of the remaining vertices.


A(-3, 2) and C(0, 5)

The coordinates are (_,_) and (-3,_)

Square ABCD Has A Diagonal AC With The Given Vertices. Find The Coordinates Of The Remaining Vertices.A(-3,

Answers

Answer 1

∴  Coordinates of B & D are [tex](\frac{9}{2} ,\frac{1}{2} ) & (-\frac{1}{2} ,\frac{4}{2} )[/tex] respectively.

What are coordinates of graph?

Coordinates X and Y axes are present in every graph. Positions on a graph are indicated using coordinates, which are expressed as an ordered pair of numbers.

ABCD is a square with A(-3,2) & C(0,5).

To find out-

The coordinates of B & D

Solution-

Let the coordinates of B=(x,y).

Since ABCD is a square,

[tex]AB=BC=AB^2=BC^2.[/tex]

Using distance formula,

[tex](x-3)^2+(y-2)^2=(x-0)^2+(y+5)^2[/tex]

⟹2x+8y−6=0

⟹x=([tex]\frac{6-8y}{2}[/tex] ) .........(i).

Now, in ΔABC,

[tex]AB ^2+BC ^2=AC ^2[/tex]

[tex](x-3)^2+(y-2)^ 2+(x-0) ^2 +(y+5)^ 2=(3-2) ^2+(0+5) ^2[/tex]

⟹[tex]x^ 2+y ^2 -3x-3y=0.[/tex]

Substituting for x from (i),

[tex](\frac{6-8y}{2} )^2+y ^2 -3(\frac{6-8y}{2} )-3y=0[/tex]

⟹[tex]3y^2-9y+4=0[/tex]

⟹[tex](2y-1)(2y-4)=0[/tex]

⟹[tex]y=( \frac{1}{2},\frac{4}{2} ).[/tex]

Substituting for y in (i),

[tex](x,y)=( \frac{9}{2},\frac{1}{2} ) & (-\frac{1}{2} , \frac{4}{2} )[/tex]Now abscissae of A & C are 3 & 1, respectively.

∴  Abscissa of B will be in between 1 & 3.

So here,  [tex]\frac{9}{2}[/tex] will be the abscissa of B.

 Coordinates of B & D are [tex](\frac{9}{2} ,\frac{1}{2} ) & (-\frac{1}{2} ,\frac{4}{2} )[/tex] respectively.

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Square ABCD Has A Diagonal AC With The Given Vertices. Find The Coordinates Of The Remaining Vertices.A(-3,
Answer 2

The coordinates of the remaining vertices B and D are (0, 2) and (-3, 5) respectively.

What are the coordinates of the vertices?

The unit square precisely refers to the square on the Cartesian plane having four corners.

Since square ABCD has a diagonal with the given vertices A(-3, 2) and C(0, 5), we know that the other two vertices of the square will be B and D, and that all four sides of the square are congruent.

We can use the coordinates of A and C to find the coordinates of B and D.

First, we know that the x-coordinate of B must be the same as the x-coordinate of C because the side BD is parallel to the x-axis.

Therefore, the x-coordinate of B is 0.

Next, we know that the y-coordinate of B must be the same as the y-coordinate of A because the side AB is parallel to the y-axis.

Therefore, the y-coordinate of B is 2.

So, the coordinates of B are (0, 2).

Finally, we know that the x-coordinate of D must be the same as the x-coordinate of A because the side AD is parallel to the x-axis.

Therefore, the x-coordinate of D is -3.

Next, we know that the y-coordinate of D must be the same as the y-coordinate of C because the side CD is parallel to the y-axis.

Therefore, the y-coordinate of D is 5.

So, the coordinates of D are (-3, 5)

Therefore, the coordinates of the remaining vertices B and D are (0, 2) and (-3, 5) respectively.

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Related Questions

consider the case of a binary classification problem in which the response is sampled froma. non-linear complex function which of the following algorithms has the potential to perform the best

Answers

It is used to perform binary classification with a high level of accuracy.

Support Vector Machines (SVMs) is a powerful algorithm with the potential to perform best in a binary classification problem with a non-linear complex function. SVMs are based on the concept of maximizing the margin between two classes of data points in the feature space. This is done by solving the optimization problem, which is formulated as a quadratic programming problem.

The formulation of the optimization problem for an SVM model is given by:

minimize W,b

subject to

y_i(w^T x_i + b) ≥ 1,  i = 1,2,…,n

where W is the weight vector, b is the bias, x_i is the ith feature vector, and y_i is the ith class label.

The goal of the optimization problem is to find the weight vector W and bias b such that the distance between the two classes is maximized. This is done by minimizing the objective function, which is the sum  of the weight vector. By solving this optimization problem, we can obtain an optimal hyperplane that separates the two classes. SVMs are powerful algorithms capable of dealing with non-linear complex functions, and can thus be used to perform binary classification with a high level of accuracy.

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Need answer how many hrs week=

Please

Answers

A week has three days, monday \stuesday \swednesday \sthursday \sfriday \ssaturday \ssunday.

The length of a week is ____ days. How many days are there in a week?

A week can be any period of time with 7 days; it is not required to be from Monday through Sunday. Example: The days of Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday, and Monday all add up to a week.

T stands for Tuesday in the alphabetical list of days of the week. W stands for Wednesday. R stands for Thursday. F is for Friday. Saturday is denoted by the letter S.

You're correct about yesterday, today, and tomorrow.

The word "short" is a five-letter phrase that becomes "shorter" when we add the two letters "e,r."

A week has three days, monday \stuesday \swednesday \sthursday \sfriday \ssaturday \ssunday.

The complete question is?

A week has how many ts?

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Work out 194.55 divided by 1.5

Answers

Answer:129.7

Step-by-step explanation:

Literally just used a calculator but if you need explanation lmk

An EMT sees himself as a bit of a rebel, but is highly sociable and is able to keep calm in an emergency. This person would likely score in the lower range of which of the following traits? (A) Psychoticism (B) Neuroticism (C) Extraversion (D) Conscientiousness

Answers

The correct answer is option D, extraversion, neuroticism, and psychoticism

Eysenck's theory of personality is based on three logical attributes namely:  

a) introversion vs. extroversion – Extroversion leads to sociable life , while introversion causes need of being alone and limited interactions

b) neuroticism vs. stability – Neuroticism leads to anxiousness and overactive sympathetic nervous system while  stability leads to emotional stability

c) psychoticism vs. socialization. - psychoticism  leads to independent thinking, and hostility. While socialization leads to co-operative and conventional behaviour.  

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What is the value of x?
Enter your answer in the box.
X =
72 cm
9 cm
bd Reading Of
3x-20
56 cm
Next

Answers

Answer:

9

Step-by-step explanation:

72/9 =8

by the same ratio

56/8 = 7

so 3x-20 = 7

so x = 27/3 = 9

Here are the weights (in pounds) of a sample of 13 male eleventh graders.
148, 140, 159, 141, 151, 156, 173, 167, 160, 159, 146, 174, 170
Send data to calculator
Find the median weight of these students.?
pounds

S

Answers

Weight of the 13 male eleventh graders is 157.23  pounds. Median is the number in the middle, ranked from least to greatest.

Median weight = 148+140+159+141+151+156+173+167+160+159+146+174+170

                                              = 2044/13

                                                 = 157.23

Median :

The value that separates the upper half of a population, a data sample, or a probability distribution from the lower half is known as the median. It could be referred to as "the middle" value for a data set. The value in the middle of a data set is called the median. This means that 50% of the data points have values that are smaller than or equal to the median, and 50% of the data points have values that are higher than or equal to the median. First, you count the number of data points (n) and arrange them in ascending order for a small data set.

How is the Median Calculated?

The middle value in a set of data is called the median. First, arrange the data in ascending order from smallest to largest. Divide the total number of observations by two to get the midpoint value. Round that number up if there are an odd number of observations, and the value in that position is the median. Take the average of the values found above and below that position if the number of observations is even.

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The diagram shows four angles round a point.
a Write an inequality for x.
b Solve the inequality.
c Explain why the angle labelled xº cannot be a right angle.

Answers

For the given figure, The value angle x is 55 ° . A) x + x + 30 + 2x < 360; x < 82.5°.

C) The figure does not permit any right angles of 90 degrees that correspond to the mathematical norms involving opposite angles and angles of a turn. This means that x is not a right angle.

1) Interpreting the question we'll be asking:

In the diagram, a point is surrounded by four angles.

A) Construct a difference for x.

B) Addressing the inequality

C) Describe the reasons why the angle is not a straight angle.

2) In response to each query, we shall have:

A) x + x + 30 + 2x < 360

4x < 360 - 30

4x < 330

x < 82.5,

B) x + 2x + x + 30 + 2x = 360

6x = 360 - 30

6x = 330

x = 55

C) A right angle is one that measures 90 degrees; in the problem at hand, x cannot be straight because, in that case, the total of the values shown in the figure would exceed 360, which would be an incorrect representation of the mathematical principles governing opposite angles and angles of a turn.

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Gabriel is deciding between two landscaping companies for his place of business. Company A charges $45 per hour and a $250 equipment fee. Company B charges $55 per hour and a $200 equipment fee. Let AA represent the amount Company A would charge for tt hours of landscaping, and let BB represent the amount Company B would charge for tt hours of landscaping. Write an equation for each situation, in terms of t,t, and determine the interval of hours, t,t, for which Company A is cheaper than Company B.

Answers

The linear functions for each situation are given as follows:

Company A: 45x + 250.Company B: 55x + 200.

The interval of hours for which Company A is cheaper than Company B is given as follows:

x > 5.

How to model the linear functions?

The linear functions are modeled in slope-intercept format, as follows:

y = mx + b.

In which:

The slope m represents the cost per hour.The intercept b represents the equipment fee.

Hence the functions are defined as follows:

Company A: 45x + 250.Company B: 55x + 200.

Company A will be cheaper when:

45x + 250 < 55x + 200

10x > 50

x > 5.

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Solve the following system of equations. Enter the y coordinate of the solution. Round your answer to the nearest tenth. 5x+ 27= 21 -2x+6y=-34

Answers

The solution to the system of equations is x = ( -6/5 ) and y = -6.1

What is an Equation?

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

Let the second equation be represented as B

Now , the value of A is

5x + 27 = 21   be equation (1)

Now , the value of B is

-2x + 6y = -34   be equation (2)

On simplifying the equations , we get

Subtracting 27 on both sides of the equation , we get

5x = -6

Divide by 5 on both sides of the equation , we get

x = -6/5

Substitute the value of x in equation (2) , we get

-2 ( -6/5 ) + 6y = -34

12/5 + 6y = -34

Subtracting 12/5 on both sides of the equation , we get

6y = -34 - 2.4

6y = -36.4

Divide by 6 on both sides of the equation , we get

y = -6.067

y = -6.1

Hence , the value of y is -6.1

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Find the volume of the solid of revolution generated when the region in the first quadrant bounded by the graphs of y = x2 +1, y = 5, and the y-axis is revolved about the line x = -3. a. 8πb.12πc. 20π d. 40π

Answers

When the area in the first quadrant bordered by x=0, y=1, x=y4, and y=10 is rotated about the line y=10, the solid's volume is 11π/3

What is meant by volume?Every three-dimensional item takes up space in some way. The volume of this area is what is used to describe it. The area occupied within an object's three-dimensional bounds is referred to as its volume. The object's capacity is another name for it. Volume is a mathematical term that describes how much space in three dimensions is occupied by an object or a closed surface. The measurement of volume is done in cubic units, like m3, cm3, in3, etc.Volume is a measurement of how much room a thing occupies. To put it another way, just as height and width are terms used to describe size, volume is a measurement of the size of an object.

We using,

V = π ∫|(f(x) - d) 2 - (g (x) - d) 2|dx Integrating from a to b

For this case, a = 0, b = 1, g(x) = 1, f(x) = x1/4

Simplifying the equation,

V = π∫|(x1/4 - 10) 2 - (1 - 10) 2dx = π∫|x1/2 - 20x1/4 + 100 - 81|dx

= π[(2/3) x 3/2 - 20(4/5) x 5/4 + 19x] evaluated from at 1 and 0

= π|(2/3 -16 +19) = 11π/3

The complete question is?

find the volume of the solid obtained by rotating the region in the first quadrant bounded by x=0, y=1, x=y^4 about the line y=10

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Select the correct answer.
Choose the system of inequalities that best matches the graph below.
y
O B.
O А. У <
um All rights reserved
C
4
-2-10
4 5 6
4
y > 42 - 4
y ≤ 4
y ≤ x +4

Answers

The set of inequality that most closely resembles the graph below is called [tex]$y \leq \frac{2}{3} x-3$[/tex] , [tex]$y < -x$[/tex] .

What is the system of inequality ?

Two or more inequalities in one or more variables make up a system of inequalities. When a problem has a variety of possible solutions and those solutions are subject to several constraints, systems of inequalities are used. Inequality in income, gender, health care, and social class are some of the most prominent examples of social inequality.

At position five, there is an open circle with a right arrow. As a result, the compound inequality can be solved, for instance, by the numbers 0 and 6, but not by the number 4. An expression that doesn't contain the equals sign (=) is called an inequality. ,, >, and are the most widely used inequality symbols. Addition, subtraction, multiplication, and division are the four operations kinds that are performed on linear inequalities.

Therefore the correct answer is option B ) [tex]$y \leq \frac{2}{3} x-3$[/tex] , [tex]$y < -x$[/tex] .

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A graph the shows y= -3/2x - 2

Answers

The graph of the given equation is given at end.

A graph is a graphic depiction or diagram that displays data in an organized manner. The points on a graph are typically used to depict the relationships between two or more things.

Determine the slope and y-intercept first, then put the equation in y-intercept (y=mx+b) form to get the equation of a graphed line. The y-to-x change ratio is known as the slope. The two locations you locate on the line should be connected by a sloping triangle.

Common graph types include line graphs, bar graphs, pie charts, scatter plots, and histograms. Graphs are an excellent tool for visualizing data and presenting statistics. An example of displaying numerical data is with a bar graph or chart.

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A number is between 26 and 31. It has prime factors of 2 and 7. What is the​ number?

Answers

Answer:28

Step-by-step explanation:

Trick: just check if it's divisible by both numbers

If we know that a 3 by 3 matrix B is known to have eigenvalues 0, 1 and 2, find each of the following, or explain why more information is needed to find the answer: (a) The rank of B. (b) The determinant of BTB. (c) The eigenvalues of BTB. (d) The eigenvalues of (B?+1)-!

Answers

a) The rank of B can be determined by looking at the eigenvalues of B. Since the eigenvalues of B are 0, 1, and 2, the rank of B is 3.

b) The determinant of BTB can be found by multiplying the eigenvalues of B together. Since the eigenvalues are 0, 1, and 2, the determinant of BTB is 0.

c) The eigenvalues of BTB can be found by taking the square of the eigenvalues of B. Since the eigenvalues of B are 0, 1, and 2, the eigenvalues of BTB are 0, 1, and 4.

d) More information is needed to find the eigenvalues of (B?+1)-!. We need to know the components of B in order to solve this equation.

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PLEASE HELP! Find the slope of the secant line between x= 3 and x= 8 for the function f(x) = [tex]\sqrt{16x-47}[/tex]. (Enter your answer in either exact notation of round to four decimal places.

Answers

The slope of the secant line between x = 3 and x = 8 for the function [tex]f(x) = \sqrt{16x - 47}[/tex] is given as follows:

8/5.

How to obtain the slope of the secant line?

The secant line intersects the function f(x) at the coordinates x = 3 and x = 8.

The numeric value for the function at each of these points is given as follows:

x = 3: [tex]f(x) = \sqrt{48 - 47} = 1[/tex].x = 8: [tex]f(x) = \sqrt{128 - 47} = \sqrt{81} = 9[/tex]

Given two points, the slope of a line is calculated as the change in y divided by the change in x, hence:

m = (9 - 1)/(8 - 3)

m = 8/5.

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how many different numbers can be represented in a 4 byte integer. (note that this is not the same as the above question.)

Answers

The range, based on the solution, is between -2,147,483,648 and 2,147,483,647.

Describe range:

When the sample maximum as well as minimum are subtracted, the range of a collection of data seems to be the difference between the greatest and lowest values. It uses the same units as the data to express itself.

Why is math range?

The distance between the greatest and smallest data sets in some kind of a set of numerical data is known as the range. The average of the greatest and smallest data points is the middle.

According to the given information:

1 byte has 8 bits,

so 4 bytes have 32 bits.

Each bit can have 2 distinct states, so we have 2³² distinct combinations of bits (in 4 bytes) which correspond to 2³² distinct whole numbers.

Normally,

the range is 0 to 4,294,967,295 but if you want to allow negatives,

the range is -2,147,483,648 to 2,147,483,647

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the polynomial 1-x x^2-x^3 \ x^{16}-x^{17} may be written in the form a 0 a 1y a 2y^2 \a {16}y^{16} a {17}y^{17}, where y

Answers

The polynomial[tex]1-x x^2-x^3 \ x^{16}-x^{17}[/tex] can be written in the form [tex]a0 + a1(x+1) + a2(x+1)^2 + ... + a16(x+1)^{16} + a17(x+1)^{17}[/tex] where y = x + 1 and a1's are constants.

a polynomial can be written in the form

[tex]a0 + a1x + a2x^2 + a3x^3 + ... + anx^n[/tex]

where a0, a1, a2, ..., an are constants (also known as coefficients) and x is the variable.

In this case, we are given a polynomial in the form [tex]1-x x^2-x^3 \ x^{16}-x^{17}[/tex] and we want to express it in the form [tex]a0 + a1y + a2y^2 + ... + a17y^{17}[/tex], where y = x + 1 and a1's are constants.

By substituting y = x + 1 into the polynomial, we get:

[tex]1 - (x + 1) + (x + 1)^2 - (x + 1)^3 + ... + (x + 1)^{16} - (x + 1)^{17}[/tex]

Each term in this polynomial is a function of y, which is in turn a function of x.

We can then match the coefficients a0, a1, a2, ..., a17 with the corresponding powers of y in the polynomial, i.e, a0 = 1, a1 = -1, a2 = -1, a3 = 0, ..., a16 = -1, a17 = -1, and we get the polynomial

It's important to note that the value of a1's are constants, meaning that they are not dependent on the variable x.

Did you mean: The polynomial [tex]1-x x^2-x^3 \ x^{16}-x^{17}[/tex] may be written in the form [tex]a 0 a 1y a 2y^2 \a {16}y^{16} a {17}y^{17}[/tex], where y = x + 1 and a1's are constants?

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[tex]-\frac{11}{48} +\frac{1}{72} -\frac{3}{16}[/tex]

Answers

Answer:

[tex]\frac{-29}{72}[/tex]

Step-by-step explanation:

use a calculator

write the equation of an ellipse with center at (2, 1), one vertex at (2, -4), and one focus at (2, -2)

Answers

An ellipse is defined as the set of all points such that the sum of the distances between the point and the two foci is constant. The equation of an ellipse can be represented in the standard form as:

(x-h)^2/a^2 + (y-k)^2/b^2 = 1

where (h, k) is the center of the ellipse, a is the distance from the center to a vertex, and b is the distance from the center to the focus.

Given that the center of the ellipse is at (2, 1), one vertex is at (2, -4), and one focus is at (2, -2), we can use this information to find the values of a and b, and represent the equation of the ellipse:

a = distance from center to vertex = |1 - (-4)|/2 = 2.5

b = distance from center to focus = |1 - (-2)|/2 = 1.5

The equation of the ellipse is:

(x-2)^2/2.5^2 + (y-1)^2/1.5^2 = 1

which can also be written as:

(x-2)^2/6.25 + (y-1)^2/2.25 = 1

This equation represents the ellipse with center at (2, 1), one vertex at (2, -4), and one focus at (2, -2)

prove mr. greedy that it is enough to work on 2 edges to find your circumcenter by providing a 2 columns proof of the circumcenter theorem

Answers

The proof of the circumcenter theorem states that given three points A, B and C, drawing lines AB and AC or AB and BC and finding the perpendicular bisector of the corresponding segment will intersect at the circumcenter of triangle ABC.

Column 1:

1. Given three points A, B and C, draw lines AB and AC.

2. A bisector of angle BAC is the perpendicular bisector of segment AC.

3. The perpendicular bisector of segment AC intersects line AB at the circumcenter of triangle ABC.

Column 2:

1. Given three points A, B and C, draw lines AB and BC.

2. A bisector of angle ABC is the perpendicular bisector of segment BC.

3. The perpendicular bisector of segment BC intersects line AB at the circumcenter of triangle ABC.

The proof of the circumcenter theorem states that given three points A, B and C, drawing lines AB and AC or AB and BC and finding the perpendicular bisector of the corresponding segment will intersect at the circumcenter of triangle ABC. Therefore, it is enough to work on two edges to find the circumcenter.

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Which sign makes the following statement true?
1/4 _____ 5/16

Answers

Answer:

2. <

Step-by-step explanation:

To compare these two fractions we can first find them a common denominator. A common denominator between 4 and 16 is 16.

To get from 16 from 4 we multiply by 4 so we do the same to the numerator, changing 1/4 to 4/16.

5/16 already has a denominator of 16 so we can leave that one as is.

4/16___5/16

In this form it is obvious that 5/16 is the larger fraction because 5 is larger than 4, meaning that 5/16 is larger than 1/4.

A rectangular prism measures 7” x 7” x 4” what is the surface area?

Answers

The surface area of a rectangular prism is calculated by adding up the area of all its faces. To calculate the surface area of a rectangular prism, you can use the formula: 2(lw + lh + wh) where l represents the length, w represents the width and h represents the height.

In this case, the rectangular prism measures 7" x 7" x 4", so the surface area can be calculated as: 2(7" x 7" + 7" x 4" + 4" x 7") = 2(49" + 28" + 28") = 2(105") = 210 square inches.

It is important to note that the surface area is a measure of the total area of all the faces of a three-dimensional object, and it is always a positive value. Also, it is measured in squared units, in this case square inches, since all the measurements provided are in inches.

I hope this helps :)

Answer:

210 square

Step-by-step explanation:

just because

FILL IN THE BLANK When multiplying matrices, multiply the elements in each ____ of the first matrix time the corresponding elements in each column of the second matrix.

Answers

The answer to the problem is: row

The picture shows two ladders propped against
facing walls. The end of the first ladder is 5m
above the base of the second wall. The second
ladder is 5m above the base of the first wall.
5m
Can you work out at what height the
ladders cross?
Are you surprised that we don't need to know
the distance between the two walls?
5m
5m
10m

Answers

By using Triangles ABC and ADC given in image, Ladders will cross at 10/3 m above the ground.

What are triangles?

Triangles are polygons in geometry that have three sides and three vertices. This figure is two-dimensional and has three straight sides. A triangle is a three-sided polygon. A triangle's three angles added together equals 180°. A single plane contains the triangle. The triangle is classified into six forms based on its sides and angles.

A triangle is categorized into three categories based on its sides, namely:

Scalene Triangle - Each side has a distinct length.

Isosceles Triangle - A triangle with two sides of equal length and one side of a different length.

Equilateral Triangle - A triangle has three sides that are of the same length.

A triangle is categorized into three categories based on its angles, namely:

Acute Angle Triangle - A triangle with all of its angles smaller than 90°.

Obtuse Angle Triangle - A triangle with one of its angles larger than 90°.

Triangle with a Right Angle - A triangle with one of its angles equal to 90°.

Now,

As shown in image  that the angles ∠BAD and ∠ADC are alternate angles, and therefore equal. Likewise, angles ∠ABC and BCD are also alternate and therefore equal.

∠BEA and ∠CED are opposite, which means that they are equal. You can see these equal angles in the image.

This means that the triangles ABE and DCE have the same angles as each other, and are therefore similar.

This means:

AE/ED=AB/DC=5m/10m=1/2

Therefore AE=1/3AD

This means E is 1/3 of the way up from the floor to D, so is at a height of 10/3m=3 1/3m

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Use the result of Example 6 to compute arctan 0.2 correct to five decimal places.

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The value of  [tex]tan^{-1}(0.2)[/tex] = -0.19739 + ... i.e. [tex]tan^{-1} (0.2)= (0.2) - \frac{(0.2)^{3} }{3} +\frac{(0.2)^{5} }{5} -\frac{(0.2)^{7} }{7}+...[/tex]

The power series of  [tex]tan^{-1}(x)[/tex] obtained in example 6 is called the Gregory's series. The Gregory series is an infinite series of fractions or rational numbers

                       

After the Scottish mathematician James Gregory (1638-1675) who had anticipated some of Newton's discoveries we have shown that  the Gregory's series is valid when -1 < x < 1.

But it turns out (although it isn't easy to prove) that it is also valid when:

x = 1 or ≠ 1.

According to Example 6, The radius of convergence of the series for

[tex]1/(1 +x^{2} )[/tex]  is 1, the radius of convergence of this series for [tex]tan^{-1}(x)[/tex] is also 1.

                          [tex]tan^{-1} x = x - \frac{x^{3} }{3} +\frac{x^{5} }{y} -\frac{x^{7} }{y} +....[/tex]  

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f(x+1)=3x2+4x-2 find the function

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Hhytcffvyvuvuuvuvuuvuvuvyvcd dfnhffx fn jyyfc Th bgg ghk

if trace of a matrix is postive and determinant is positive does it mean eigen values are all positive?

Answers

To have the determinant negative, at least one Eigenvalue has to be negative but the reverse of this statement may or may not be true.

If we add all the diagonal elements of the square matrix, we get the trace of the given matrix.

Eigenvalues is a scalar that associates with a set linear equation described as -

(A - λ I) X = 0

If we take the product of all the eigenvalues of a matrix, we'll get the determinant of the matrix. If we consider a case in which the trace of the matrix is +ve, and its determinant is -ve, then at least one or an odd no. of Eigenvalues must be negative, since their product has to be positive when we solve for the determinant of the matrix

Therefore, to have the determinant negative, at least one Eigenvalue has to be negative but reverse may or may not be true.

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The scale factor is _______________ the original figure

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Answer: A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller). Therefore, The scale factor would be 1/2

Write a general expression for the electric potential V at any point on the y-axis inside the triangle in terms of Q,l , and y.

Answers

The electric potential V at any point on the y-axis inside the triangle can be expressed in terms of the charge Q, the length of the triangle l, and the distance y from the origin. The expression is V(y) = (Q/2l)y - (Q/2l)(2l-y) = (Q/l)(y - l).

The electric potential V at any point on the y-axis inside the triangle can be expressed in terms of the charge Q, the length of the triangle l, and the distance y from the origin. To find the expression, first note that the total charge of the triangle is Q, and the electric potential at the origin is 0. The distance from the origin to the top corner of the triangle is 2l. The electric potential at the top corner of the triangle is then equal to the total charge of the triangle divided by the length of the triangle, or Q/2l. The electric potential at any point on the y-axis is then equal to the total charge of the triangle divided by the length of the triangle times the distance from the origin to the point, minus the total charge of the triangle divided by the length of the triangle times the distance from the top corner of the triangle to the point. This gives the expression V(y) = (Q/2l)y - (Q/2l)(2l-y) = (Q/l)(y - l).

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which of the following sampling strategies makes it difficult to discern what sub-population the sample represents?

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Convenience sampling represents the sub-population of the sample strategies.

Convenience sampling is defined as a type of non-probability sampling that involves the sample being drawn from that part of the population that is close to hand and is a type of sampling that is most useful for pilot testing.

Convenience sampling can be used by almost anyone and has been around for generations. One of the reasons that it is most often used is due to the numerous advantages it provides

Expedited data collection, Ease of research, Ready availability, Cost-effectiveness.

Bias, Power is the disadvantages of convenience sampling.

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