Answers
So on solving the provided question, we can say that the, here Midsegment theorem has been proved.
How is the midsegment theorem demonstrated?Let's draw a line segment connecting the midpoints of two of the sides of a triangle ABC, say AB and BC. We must demonstrate two things in order to establish the Triangle Midsegment Theorem: DE = (1/2)AC. DE is similar to AC.
DE=EF //Construction
AE=EC //Given, DE is a midsegment
∠AED ≅ ∠CEF // Vertical angles
ΔADE ≅ΔCFE // Side-Angle-Side postulate
∠DAE ≅ ∠FCE // corresponding angles in congruent triangles, (CPCTC)
AB||CF // Converse Alternate Interior Angles Theorem
AD=CF // corresponding sides in congruent triangles, (CPCTC)
AD=DB //Given, DE is a midsegment
CF=DB //(7), (8), the transitive property of equality
DFCB is a parallelogram //two opposite sides of a parallelogram, CF & DB, are equal and parallel
DE||BC //(10), opposite sides of a parallelogram
DF=BC //(10), opposite sides of a parallelogram
DE=EF //(4) corresponding sides in congruent triangles, (CPCTC)
DE= ½DF
DE= ½BC //(12) , (14), substitution
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So on solving the provided question, we can say that the, here Midsegment theorem has been proved.
How is the midsegment theorem demonstrated?Let's draw a line segment connecting the midpoints of two of the sides of a triangle ABC, say AB and BC. We must demonstrate two things in order to establish the Triangle Midsegment Theorem: DE = (1/2)AC. DE is similar to AC.
DE=EF //Construction
AE=EC //Given, DE is a midsegment
∠AED ≅ ∠CEF // Vertical angles
ΔADE ≅ΔCFE // Side-Angle-Side postulate
∠DAE ≅ ∠FCE // corresponding angles in congruent triangles, (CPCTC)
AB||CF // Converse Alternate Interior Angles Theorem
AD=CF // corresponding sides in congruent triangles, (CPCTC)
AD=DB //Given, DE is a midsegment
CF=DB //(7), (8), the transitive property of equality
DFCB is a parallelogram //two opposite sides of a parallelogram, CF & DB, are equal and parallel
DE||BC //(10), opposite sides of a parallelogram
DF=BC //(10), opposite sides of a parallelogram
DE=EF //(4) corresponding sides in congruent triangles, (CPCTC)
DE= ½DF
DE= ½BC //(12) , (14), substitution
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Related Questions
Lesson 13:Find a Sequence
Describe a sequence of reflections, rotations, and translations that takes ABCD onto
A'B'C'D'.
Answers
The sequence of transformation will be;
Rotate 120 degrees Counterclockwise around B, then Translate B to B' and reflect over segment BA.
How to Identify the Transformation?
We want to find the transformation that maps Quadrilateral ABCD onto Quadrilateral A'B'C'D'.
Looking at the given image, the sequence of transformation will be;
Rotate 120 degrees Counterclockwise around B, then Translate B to B' and reflect over segment BA.
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How can you do mental math and solve 2.22 divided by 2 without writing anything down? explain.
Answers
Answer:
1.11
Step-by-step explanation:
There are a total number of 38 possible equally likely outcomes on a roulette wheel. Out of the 38 outcomes, there are 18 odd-numbered outcomes. What's the probability of rolling an odd number
Answers
The probability of rolling an odd number is 9/19.
According to the statement
Total number of possible outcomes = 38
Odd numbered of outcomes = 18
Now we find the probability
Probability = possible outcomes / total outcomes
Probability = 18/38
Probability = 9/19
So, The probability of rolling an odd number is 9/19.
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Answer this please !
Answers
Answer:
6
Step-by-step explanation:
[tex]\frac{y}{2} =x^{2} -7[/tex]
[tex]\frac{a}{2} =2^{2} -7[/tex]
[tex]\frac{a}{2} =-3[/tex]
[tex]a=-6[/tex]
[tex]\frac{b}{2} =1^{2} -7[/tex]
[tex]\frac{b}{2} =-6[/tex]
[tex]b=-12[/tex]
From the calculations above, we learn that line l and the curve intersect at (2, -6) and (1, -12). Next, we will set up a system of linear equations to solve for the slope and the y-intercept of line l.
[tex]-6=2m+b[/tex]
[tex]-12=m+b[/tex]
[tex]-24=2m+2b[/tex]
[tex]18=-b[/tex]
[tex]b=-18[/tex]
[tex]-12=m-18[/tex]
[tex]m=6[/tex]
Therefore, the slope of line l is 6.
Answer:
slope = 6
Step-by-step explanation:
substitute the given points into the equation of the curve to find a and b
(2, a )
[tex]\frac{a}{2}[/tex] = 2² - 7 = 4 - 7 = - 3 ( multiply both sides by 2 to clear the fraction )
a = - 6
then point (2, a ) = (2, - 6 )
(1, b )
[tex]\frac{b}{2}[/tex] = 1² - 7 = 1 - 7 = - 6 ( multiply both sides by 2 )
b = - 12
then point (1, b ) = (1, - 12 )
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, - 6 ) and (x₂, y₂ ) = (1, - 12 )
m = [tex]\frac{-12-(-6)}{1-2}[/tex] = [tex]\frac{-12+6}{-1}[/tex] = [tex]\frac{-6}{-1}[/tex] = 6
The sequence of transformations that can be performed on quadrilateral ABCD to show that it is congruent to quadrilateral GHIJ is a v
Answers
A sporting goods store sells square exercise mats that are m on a side. Find the perimeter and area of the mat.
Answers
The perimeter of the mat is 4m and the area of the mat is [tex]m^{2}[/tex].
What is perimeter of the square?The complete length of a square's boundary is referred to as its perimeter. To get the perimeter of a square, we must add all of its sides.
Perimeter of square = sum of the length of all 4 sides.
In the question side of the mat is m.
Perimeter of the mat = m + m + m + m
= 4m.
Therefore, the perimeter of the mat is 4m.
What is the area of the square?
The total number of unit squares in a square's shape is used to calculate its area.
Area = (Side x Side)
Since, side of the mat is m.
Area of the mat = m x m
= [tex]m^{2}[/tex]
Therefore, the area of the mat is [tex]m^{2}[/tex].
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PLEASE HELP!! This graph shows the bird population of a large lake. Note that the
number of birds at the lake in the month of December is zero. What
does this extreme drop between November and December MOST
likely represent?
Select one:
O a. The beginning of duck hunting season.
O b. A reflection of the migratory nature of the birds at the lake.
O c. An inaccurate collection of data, and so, invalid results.
Od. A reflection of the hibernation patterns of the birds at the
lake.
Answers
The extreme drop in the graph for the number of birds between November and December MOST likely represents a reflection of the migratory nature of the birds at the lake, making option B the right choice.
In the question, we are given a graph showing the bird population of a large lake and are asked the reason for the extreme drop between November and December most likely represent.
Birds migrate in order to shift from low-resource regions to high-resource areas or vice versa. The two main items sought after are food and places to build nests.
Thus, the fall in the graph for the number of birds between November and December represents the migration pattern of birds, in search of new resources.
Hence, the extreme drop in the graph for the number of birds between November and December MOST likely represents a reflection of the migratory nature of the birds at the lake, making option B the right choice.
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Answer: A reflection of the migratory nature of the birds at the lake.
im stuck on this one
Answers
The value of X is 2/3 and -3/2.
According to the statement
we have given equation is 6x^2+5x-6 =0
and we have to find x by the factorization.
Factorization defines the the operation of resolving a quantity into factors.
So, by factorization method the equation is written as
6x^2+5x-6 =0
After forming factors the equation becomes
6x^2+9x-4x-6 =0
3x(2x+3) -2(2x+3) =0
By taking common
(3x-2) (2x+3) = 0
Now equate values equal to 0. and after that the output will get in the form of value of X.
Here the value of x is 2/3 and -3/2
So, the value of X is 2/3 and -3/2.
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Vertical plane R intersects horizontal plane P. Points A, D, and B are on the line of the intersecting planes. Point F is on the top half of plane R. Point G is on the bottom half of plane G. Point C is on the left half of plane P. Point E is on the right half of plane P. Point H is above and to the right of the planes. Point J is below and to the left of the planes. Which statements are true based on the diagram? Check all that apply. Points A, B, and D are on both planes. Point H is not on plane R. Plane P contains point F. Points C, D, and A are noncollinear. The line containing points F and G is on plane R. The line containing points F and H is on plane R.
Answers
The true statements are:
Points A, B, and D are on both planes. Point H is not on plane R. Points C, D, and A are noncollinear. The line containing points F and G is on plane R. What is the intersection of 2 planes?If two planes are said to have intersect each other, the intersection will be regarded as a line.
Hence, looking at the image attached, you will see that Points C, D, and A are noncollinear and the line containing points F and G is on plane R.
Note that when a line and a plane are said to intersect each other , the intersection will be a single point, or say a line. So Points A, B, and D are on both planes.
Therefore, option 1, 2, 4 and 5 are correct.
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Answer: option 1 , 2 , 4 , 5
Step-by-step explanation: edge 2022
Is x+2 a factor of the polynomial f(x)=2x^4-3x^2-4x+1?
a. f(2)=0, so (x+2) is a factor.
b. f(-2)=29, so (x+2) is not a factor.
c. f(-2)=0, so (x+2) is a factor.
d. f(2)=13, so (x+2) is not a factor.
Answers
Answer:
B
Step-by-step explanation:
the value of the x should be the same if we want to verify whether x+2 is a factor of f(x)
so if x=-2 ,f(-2) = 29
x+2=0 f(0) = 1
f(0) [tex]\neq[/tex] f(-2) ,so x+2 is not a factor
what it actually means it that if we move the graphic of f(x) to left along to x axis 2 units, the graphic of new one cannot coincide with the original one.
7-2x≥15
solve for inequality
graph the solution
shade the possible solutions
1 -12 13 -4 -42 4
Answers
The solution set of the inequality is x ≤ - 4. The graph of inequality is shown below and the points x = - 4, x = - 12, x = - 42 are part of the solution set.
How to solve an inequality
In this question we must use algebraic axioms and theorems to solve an inequality and graph the solution set with the help of a graphing tool. Now we proceed to present the procedure to solve for x:
7 - 2 · x ≥ 15
7 - 15 ≥ 2 · x
2 · x ≤ - 8
x ≤ - 4
Now we present the graph of the inequality. The points x = - 4, x = - 12, x = - 42 are part of the solution set.
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Is B equal to C in this geometry problem? I just need to know, that and then I can solve the rest.
Answers
In the right angled triangle ACD shown with isosceles triangle ABC and ADC, AB = AC = AD
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A triangle is a polygon that has three sides and three angles. Types of triangles are isosceles, equilateral and scalene.
In the diagram shown:
AB = AC = AD
In the right angled triangle ACD shown with isosceles triangle ABC and ADC, AB = AC = AD
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trying to see what my answer would be
Answers
Answer:
B. [tex]2^{-14}*5^{10}[/tex].
Step-by-step explanation:
Use the power of a power property.
[tex](2^{-7}*5^{5} )^{2}[/tex]
Multiply all the exponents in the parenthesis by 2.
[tex](2^{-7}*5^{5} )^{2}=(2^{-14}*5^{10} )[/tex]
The answer is B. [tex]2^{-14}*5^{10}[/tex].
Hope this helps!
The number of rows in an auditorium can be represented by the function f(x) = 80x. the number of seats in each row can be represented by the function g(x) = x 7. which function represents the total number of seats, h(x) = f(x)g(x)? h(x) = 136x h(x) = 80x2 560x h(x) = 80x 560 h(x) = 80x2 560
Answers
Applying multiplication of functions, the total number of seats in the auditorium is given by:
h(x) = 80x² + 560x.
How polynomial functions are multiplied?They are multiplied applying the distributive property, that is, all the terms are multiplied and then the common terms are added.
In this problem, the functions are given as follows:
f(x) = 80x.g(x) = x + 7.Then the multiplication is:
h(x) = f(x)g(x) = 80x(x + 7) = 80x² + 560x.
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Answer:
The answer is b
Step-by-step explanation:
:)
A parabola is represented by the equation y2 = 5x. which equation represents the directrix?
Answers
The value of the directrix is -5/4.
According to the statement
we have given that the equation of parabola is y2 = 5x. And we have to find that the which equation represents the directrix.
We know that the general equation of parabola is
(y - k)2 = 4a(x - h) -(1)
and given parabola equation is
y2 = 5x. -(2)
After comparing the both equations we get k=0 and h=0
And the formula to find the directrix is
x = h - a
Substitute the values of h and a in it then
x = 0-5/4
x = -5/4.
Here the directrix is -5/4.
So, The value of the directrix is -5/4.
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telephone poll administered by a computer randomly generating numbers to call, found that 68% of Americans in the sample of 2000 were in favor of legalizing recreational marijuana use. Thus, almost 70% of Americans favor legalizing recreation marijuana use.
Answers
The method that was used to arrive at the approximate population probability is called; a reasonable statistical generalization
What is statistics generalization?Statistical generalization is a concept that involves inferring the results from a sample and applying it to a population. Carrying out this means that the sample must be selected randomly and be representative of the population.
Now, in this case, we see that the sample gave a probability of 68% to represent those were in favor of legalizing recreational marijuana use.
Now, since the conclusion was approximated to 70% to reflect the probability of the population then we can say that a reasonable statistical generalization was utilized.
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The dot plots below show the scores for a group of students who took two rounds of a quiz:
Two dot plots are shown one below the other. The title for the dot plot on the top is Round 1 and the title for the bottom plot is Round 2. Below the line for each dot plot is written Score. There are markings from 5 to 9 on the line at intervals of one. There are 2 dots above the mark 5, 3 dots above the mark 6, 4 dots above the mark 7, and 1 dot above the mark 8. For the bottom dot plot there are 6 dots above the mark 6, 2 dots above the mark 8, and 2 dots above the mark 9.
Which of the following inferences can be made using the dot plot?
A. The range of each round is the same.
B. There is no overlap between the data.
C. Round 1 scores were higher than round 2 scores.
D. Round 2 scores were lower than round 1 scores.
Answers
The inference that can be made from the dot plot is the range of each round is the same.
What is the inference that can be made?A dot plot is a graph that shows the frequency of a number using dots. The greater the number of dots above a number, the greater its frequency.
Range is the difference between the largest number and smallest number.
Range of round 1 = 8 - 5 = 3
Range of round 2 = 9 - 6 = 3
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URGENT!, will mark brainiest!
Use the box plots comparing the number of male pets and number of female pets attending doggy daycare each day for a month to answer the questions. Two box plots shown.
The top one is labeled Males. Minimum at 1, Q1 at 3, median at 10.5, Q3 at 14, maximum at 21, and a point at 30.
The bottom box plot is labeled Females. Minimum at 0, Q1 at 15, median at 18, Q3 at 21, no maximum shown
Part A: Estimate the I Q R for the males' data. (2 points)
Part B: Estimate the difference between the median values of each data set. (2 points)
Part C: Describe the distribution of the data and if the mean or median would be a better measure of center for each. (4 points)
Answers
For the males' data, we can logically deduce the following data elements:
Upper quartile (Q₃) = 14Lower quartile (Q₁) = 2Mathematically, the male IQR can be calculated by using this formula:
IQR = Q₃ - Q₁
IQR = 14 - 2
Male IQR = 12.
Next, we would find the difference between the median values:
Note: The median of male's data is equal to 10 while median of female's data is equal to 18.
Difference, d = 18 - 10
Difference, d = 8.
The distribution of data.The male's data has an outlier probably due to sampling technique used while the female's data doesn't have an outlier. Thus, the median would be a better measure of center for the male's data and the mean being a better measure of center for the female's data.
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Answer: s
Step-by-step explanation:
The label on a bag of chocolates states that there are 0.384 pounds of chocolates.
The actual weight of the chocolates is 0.3798 pounds.
How much lighter are the chocolates than stated on the label?
Answers
Answer:
Answer:The chocolate are 0.0042 lighter than the stated on the label
PLEAZE HELP IM STUCK PLS
Answers
Answer:
[tex]T_{23}=-153[/tex]
Step-by-step explanation:
[tex]T_{23}=a+(n-1)d\\[/tex]
[tex]=a+(23-1)d=a+22d[/tex]
Now [tex]a=-21[/tex] and
[tex]d=-27-(-21)\\=-6[/tex]
So [tex]T_{23}==21+((22)6\times-1)[/tex]
[tex]=-153[/tex]
A research center poll showed that 85% of people believe that it is morally wrong to not report all income on tax returns. What is the probability that someone does not have this belief? The probability that someone does not believe that it is morally wrong to not report all income on tax returns is (Type an integer or a decimal.)
Answers
The probability that someone does not believe that it is morally wrong to not report all income on tax returns is = 0.15
For given question,
A research center poll showed that 85 percent of people believe that it is morally wrong to not report all income on tax returns.
so, the probability that someone have this belief is P = 0.85
We know that in probability,
p = 1 - q
where;
p is probability of success
q is probability of failure.
Thus the probability that someone does not have this belief would be,
= 1 - P
= 1 - 0.85
= 0.15
Therefore, the probability that someone does not believe that it is morally wrong to not report all income on tax returns is = 0.15
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Mike and hallie are going to a movie. together they bring $60 in cash. hallie brings three times as much cash as mike does. let m be the amount of money mike brings and let h be the amount of money hallie brings. create a system of equations that models the information given in this problem and solve it to determine how much each brought to the movie.
Answers
Mike brought $15 and Hallie brought $45 to the movie
There are many ways to define an equation. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
The value of the variable that makes the equation a true statement is the solution to the equation.
We have to find how much money Mike and Hallie brought to the movie.
Let the money Brought by Mike be $ m and by Hallie be $ h.
Mike and hallie are going to a movie. together they bring $60 in cash
m + h = $ 60.............(1)
Hallie brings three times as much cash as mike does
h = 3 m.......... (2)
Pur the value of h from equation (2) in equation (1)
m + 3 m = $ 60
4 m = $ 60
m = $ 60/4
m = $ 15
put this value of m in equation (2)
h = 3(15)
h = $ 45
Hence we created a system of equations that models the information given in this problem and Mike brought $15 and Hallie brought $45 to the movie
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You measure 46 textbooks' weights, and find they have a mean weight of 77 ounces. Assume the population is normally distributed with a standard deviation of 12.2 ounces. Based on this, construct a 99% confidence interval for the true population mean textbook weight. Give your answers correct to at least two decimal places. Lower Limit = Upper Limit =
Answers
Using the z-distribution, the 99% confidence interval for the true population mean textbook weight is (72.37, 81.63).
What is a z-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.In this problem, we have a 99% confidence level, hence[tex]\alpha = 0.99[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.
The other parameters are given as follows:
[tex]\overline{x} = 77, \sigma = 12.2, n = 46[/tex]
Hence the lower and upper bound of the interval are given, respectively, by:
[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 77 - 2.575\frac{12.2}{\sqrt{46}} = 72.37[/tex][tex]\overline{x} + z\frac{\sigma}{\sqrt{n}} = 77 + 2.575\frac{12.2}{\sqrt{46}} = 81.63[/tex]More can be learned about the z-distribution at https://brainly.com/question/25890103
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Adding and Subtracting Decimals
16.5 + 2.147=
Free Brainliest for 2 answers
REPETING: 2 ANSWERS
Answers
Answer: 14.353 or 18.647
Step-by-step explanation:
Hi.
Subtracting:
16.5 - 2.147 = 14.353
Adding:
16.5 + 2.147 = 18.647
Which of the following graphs has x-intercepts of -1 and 2?
Answers
Answer:
this graph has an x-intercept values of -1 and 2
PLEASE HELP quickly
Answers
Answer:
C. Radius or diameter must be known.
Step-by-step explanation:
The radius or diameter must be known so you can use the formula.
Hope this helps!
Solve this for me anyone?
Answers
Answer:
52 degrees
Step-by-step explanation:
Really easy, i learned it this summer
1. 180-128=52
2. 3=52 cus alternate interior angles
Andrei wants to fill a glass tank with marbles, and then fill the remaining space with water. www represents the volume of water andrei uses (in liters) if he uses nnn marbles. w=32-0.05nw=32−0.05nw, equals, 32, minus, 0, point, 05, n what is the volume of each marble?
Answers
Using linear function concepts, it is found that the volume of each marble is of 0.05 liters.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The linear function that gives the volume of water, when n marbles are inserted into the tank, is given by:
w = 32 - 0.05n
The slope of -0.05 means that for each marble inserted, there are 0.05 liters less for water, hence the volume of each marble is of 0.05 liters.
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Answer:
.05 liters
Step-by-step explanation:
The number of bicycles parked in the parking area on 11 days are listed
below:
27, 34, 35, 48, 48, 66, 75, 85, 85, 96, 99
Find the 50th percentile, 25th percentile, and 75th percentile.
Answers
Answer:
the 50th percentile = 66
The 25th percentile = 35
The 75th percentile = 85
Step-by-step explanation:
We have 11 numbers ,so we are dealing with an odd set of values.
Also ,we notice that the numbers are already in order.
then
the 50th percentile of the set 27, 34, 35, 48, 48, 66, 75, 85, 85, 96, 99
is the 6 number in the list [ 6 = (11+1)/2 ]
Which is 66.
The 25th percentile (the median) of the set 27, 34, 35, 48, 48
is the 3rd number [ 3 = (5+1/)2 ]
Which is 35.
The 75th percentile (the median) of the set 75, 85, 85, 96, 99
is the 3rd number [ 3 = (5+1/)2 ]
Which is 85.
There are n cities in a OneWayCountry (country in which every road is a One-Way road). Every pair of cities is connected by exactly one direct one-way road. Show that there exists a city which can be reached from every other city either directly or via at most one other city.
Answers
The cities such that this path is [tex]C_{1}[/tex] → [tex]C_{2}[/tex] → [tex]C_{3}[/tex] . . . → [tex]C_{n}[/tex]. Now, if all roads are going towards [tex]c_{n}+1[/tex], then add [tex]c_{n}+1[/tex] at the end of this path. Otherwise, let [tex]C_{i}[/tex] be the first city in this path such that there is a road from [tex]C_{i}[/tex]-1 to [tex]c_{n}+1[/tex] and from [tex]c_{n}+1[/tex] to [tex]C_{i}[/tex]. Place [tex]c_{n}+1[/tex] between [tex]C_{i}[/tex]−1 and [tex]C_{i}[/tex] to get the desired path.
What is mathematical induction method?Mathematical Induction is a technique of proving a statement, theorem or formula which is thought to be true, for each and every natural number n. By generalizing this in form of a principle which we would use to prove any mathematical statement is 'Principle of Mathematical Induction'.
The question says that between any two cities X and Y, either there’s an
one-way road from X to Y or from Y to X, but not both. Then show that
there is a path from some city A which visits all the cities exactly once.
This problem is very similar to the Football league problem #7 in Homework 1. This problem can be modeled as a directed graph in which cities
are represented as vertices and there’s an edge from vertices X to Y if
there’s a road from cities X to Y. And then, our goal is to find a path
in this graph which visits every vertex in the graph.
The rest of the solution is very similar to the argument in Problem 7 of
homework 1. We use induction of number of cities, say n.
As a base case, if n = 2, there are only two cities X and Y and the path
is simply the edge between X and Y.
For induction hypothesis, assume that the statement is true for any set
of n cities. That is’ for any set of n cities, we can find a path which visits
all the cities exactly once.
Let’s prove the statement for n + 1 cities. Leave out n + 1 th city (say,
[tex]c_{n}+1[/tex]) and for the remaining n cities, by induction hypothesis, we can find a path which visits all these n cities exactly once. Let us label the cities such that this path is [tex]C_{1}[/tex] → [tex]C_{2}[/tex] → [tex]C_{3}[/tex] . . . → [tex]C_{n}[/tex]. Now, if all roads are going towards [tex]c_{n}+1[/tex], then add [tex]c_{n}+1[/tex] at the end of this path. Otherwise, let [tex]C_{i}[/tex] be the first city in this path such that there is a road from [tex]C_{i}[/tex]-1 to [tex]c_{n}+1[/tex] and from [tex]c_{n}+1[/tex] to [tex]C_{i}[/tex]. Place [tex]c_{n}+1[/tex] between [tex]C_{i}[/tex]−1 and [tex]C_{i}[/tex] to get the desired path.
To learn more about induction hypothesis from the given link :
https://brainly.com/question/24672369
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