there are n(n-1)(n-2)/2 simple paths of nonzero length in a tree with n vertices, where two simple paths are regarded as the same if they have the same edges.
In a tree with n vertices, there are (n-1) edges, since a tree is a connected acyclic graph.
To count the number of simple paths of nonzero length in the tree, we can consider each vertex as a starting point for a path and count the number of possible paths from that vertex.
Starting from any vertex, there are at most (n-1) paths that can be formed by moving to any of the neighboring vertices. From each of these neighboring vertices, there are at most (n-2) paths that can be formed by moving to a new neighboring vertex (excluding the vertex that was just visited).
This process can be continued until there are no more vertices to visit. However, to avoid counting the same path twice, we should only consider paths that do not backtrack on themselves.
Therefore, the total number of simple paths of nonzero length in the tree is the sum of all simple paths that start from each vertex:
(number of paths starting from vertex 1) + (number of paths starting from vertex 2) + ... + (number of paths starting from vertex n)
Using the reasoning above, we can see that the number of paths starting from each vertex is at most (n-1) * (n-2), since each path can visit at most (n-2) additional vertices after the starting vertex, and there are at most (n-1) vertices to choose from as the next vertex on the path.
Therefore, the total number of simple paths of nonzero length in the tree is at most n(n-1)(n-2).
However, we have counted each simple path twice (once in each direction), so the actual number of distinct simple paths of nonzero length is half of this maximum value, which is:
n(n-1)(n-2)/2
So, there are n(n-1)(n-2)/2 simple paths of nonzero length in a tree with n vertices, where two simple paths are regarded as the same if they have the same edges.
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Answer for x=
Please
Answer:
53°
Step-by-step explanation:
it’s vertical, verticals are always identical, I think
most people in the united states with a mental disorder in any given 12-month period receive treatment during the same time frame.
Explanation:
Most people with a mental illness in the United States receive care at some point in their lives, but most receive insufficient or inappropriate care. In any given year, fewer than one-third of people with a diagnosable mental illness obtain treatment.
However, according to a study, most people in the United States with a mental disorder in any given 12-month period receive treatment during the same time frame.
According to the National Survey on Drug Use and Health (NSDUH), about one in five adults (18.5%) had a mental illness in 2019. It is said that roughly 22.3 million people aged 18 and above received care for a mental health condition in the preceding year.
Treatment may involve medication, therapy, support groups, or a combination of these methods. The majority of people with mental illness may significantly benefit from these treatments.
As per a study, most people in the United States with a mental disorder in any given 12-month period receive treatment during the same time frame. This statement is true.
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A rental car company charges $74. 90 per day to rent a car and $0. 13 for every mile driven. Tyee wants to rent a car, knowing that:
He plans to drive 175 miles. He has at most $210 to spend. Write and solve an inequality which can be used to determine
�
x, the number of days Tyee can afford to rent while staying within his budget
Tyee can afford to rent the car for at most 2 days while staying within his budget.
Let x be the number of days Tyee can rent the car within his budget.
The total cost of renting the car will be the sum of the daily rental fee and the cost of miles driven:
Total cost = rental fee + (cost per mile x miles driven)
Using the given information, we can write the inequality:
74.90x + 0.13(175)x ≤ 210
Simplifying the expression, we get:
74.90x + 22.75x ≤ 210
97.65x ≤ 210
x ≤ 2.15
Therefore, Tyee can afford to rent the car for at most 2 days while staying within his budget.
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How many hours after the chemical reaction starts are the concentrations of the two products equal?
Responses
0.6
1.0
1.5
2.0
Answer:0.6
Step-by-step explanation: because i got it correct
a car dealership pays $8,350 for a car, they mark up the price by 17.4% to get the retail price. What is the retail price of the car at this dealership
use half angle identity. help
pls
Required value of the given expression is (1+√2)
Given expression is [tex]tan \frac{11\pi}{8} [/tex]
We want to solve it.
Now,
[tex] \tan( \frac{11\pi}{8} ) = \tan( \frac{3\pi}{8} + \frac{8\pi}{8} ) \\ = \tan( \frac{3\pi}{8} + \pi ) \\ = \tan( \frac{3\pi}{8} ) [/tex]
Finding [tex] \tan( \frac{3\pi}{4} ) [/tex]
Let,
[tex] \tan(2t) = \tan( \frac{3\pi}{4} ) = - 1[/tex]
Use half angle identity,
[tex] \tan(2t) = \frac{ 2\tan(t) }{1 - {tan}^{2} t} \\ - 1 = \frac{ 2\tan(t) }{1 - {tan}^{2} t} \\ {tan}^{2} t - 2tant - 1 = 0[/tex]
Let,[tex]x = tant[/tex]
So,[tex] {x}^{2} - 2x - 1 = 0[/tex]
Now, [tex]x = 1 \pm \sqrt{2} [/tex]
So,
[tex]tant = tan \frac{3\pi}{8} = 1 \pm \sqrt{2} [/tex]
[tex]tan \frac{3\pi}{8} [/tex] is positive,then required value is 1+√2.
So, option D is the correct answer.
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Last sentence was find the volume of the larger pyramid
a)the ratio of the heights of the pyramids is 5:3. b)the volume of the larger pyramid is 23.04 cm³.
what is volume ?
Volume is a measure of the amount of space that a three-dimensional object occupies. It is usually measured in cubic units, such as cubic meters (m³) or cubic centimeters (cm³). The volume of an object can be calculated using different formulas depending on its shape.
In the given question,
a. Let the height of the smaller pyramid be h₁ and the height of the larger pyramid be h₂. Since the two pyramids are similar, their corresponding linear dimensions are in the same ratio as the areas of their bases. Therefore, we have:
(base area of smaller pyramid)/(base area of larger pyramid) = (linear dimension of smaller pyramid)² / (linear dimension of larger pyramid)²
Since the linear dimension is the height in this case, we can substitute the given ratio of the base areas to obtain:
25/9 = (h₁/h₂)²
Taking the square root of both sides, we get:
h₁/h₂ = 5/3
Therefore, the ratio of the heights of the pyramids is 5:3.
b. Since the volume of a pyramid is proportional to the cube of its height, we have:
(volume of smaller pyramid) / (volume of larger pyramid) = (h₁/h₂)³ = (5/3)³ = 125/27
Substituting the given volume of the smaller pyramid, we get:
108 / (volume of larger pyramid) = 125/27
Solving for the volume of the larger pyramid, we obtain:
volume of larger pyramid = (27/125) * 108 = 23.04 cm³ (rounded to two decimal places)
Therefore, the volume of the larger pyramid is 23.04 cm³.
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Target is selling a speaker for $166.50. It is at Costco for $90. What percentage did
Target markup the speaker?
Answer:
45.6%
Step-by-step explanation:
166.50 minus 45.6% equals 90 dollars
find the area, to the nearest hundredth, of a circle with a circumference of 19 centimeters. use 3.14 for pi
The area of the circle with circumference 19cm is 6.42cm²( nearest hundredth).
What is area of circle?Area of a circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula, A = πr2. Where r is the radius.
The circumference of a circle is given as ;
C = 2πr
C = 9cm
therefore, 9 = 2× 3.14 × r
9 = 6.28r
r = 9/6.28
r = 1.43 cm
Area of circle = πr²
= 3.14 × 1.43²
= 6.42cm²( nearest hundredth)
therefore the area of the circle is 6.42cm²
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For 5 days mr fransico had a total 10. 5 hours of overtime in the office what was his average daily overtime?
Mr. Fransico had average overtime in a day is 2.1 hours.
In mathematics, the central value of a set of data is expressed as the average of a list of data. It is defined mathematically as the ratio of the total number of data points to the number of units in the list. In terms of statistics, the term "mean" also refers to the average of a certain set of numerical data. The average of 2, 3, and 4 is, for instance, (2+3+4)/3 = 9/3 = 3. The center value of 2, 3, and 4 in this instance is 3, thus. Finding the mean value of a bunch of numbers is the definition of average.
For 5 days Mr fransico had a total of 10. 5 hours of overtime in the office
Then the average daily overtime is-
10.5÷5 = 2.1 hours
Hence Mr. Fransico had total overtime in a day is 2.1 hours.
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which would be the expected adult height for a toddler who is 34 inches tall at the 30-month checkup? use numbers only.
The expected adult height for a toddler who is 34 inches tall at the 30-month checkup is around 5 feet 7 inches.
To determine the expected adult height, one must multiply the current height by 1.08. Since 34 inches x 1.08 is equal to 36.72 inches, the expected adult height is 5 feet 7 inches.
The calculation for adult height is an approximation. Factors such as nutrition, genetics, and gender play a role in final height.
It is important to note that this calculation is just a guide and the actual adult height may differ from the predicted adult height.
To get a more accurate estimation of the expected adult height, it is recommended to have multiple height checks throughout childhood and take into account growth patterns.
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diego wants to package all 48 brownies and 64 cookies so that each bag has the same combination of items. how many bags can he make, and how many of each will be in each bag? determine at least one way to package both items.
Diego can make 56 bags with each bag containing 8 brownies and 12 cookies.
To package both items, he can divide the items into groups of 8 brownies and 12 cookies. He will then make 56 of these groups, ensuring each bag contains 8 brownies and 12 cookies.
Diego has 48 brownies and 64 cookies to package. To make the same combination of items in each bag, he needs to group the items into groups of 8 brownies and 12 cookies.
This can be done by dividing the 48 brownies into 6 groups of 8, and the 64 cookies into 5 groups of 12. He then needs to combine these two groups together, making 56 total bags.
Each of these bags will contain 8 brownies and 12 cookies. This is one way of packaging both items so that each bag has the same combination.
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The closing stock prices for a particular social media company follows an unknown distribution with a mean of $150 and a standard deviation of $25. An investor is looking to find the likelihood of the closing stock price falling above the average. After randomly selecting n=52 closing stock prices from the social media company, use a calculator to find the probability that the sample mean is between $155 and $160.
Rounded to three decimal places.
Rounded to three decimal places, the probability that the sample mean is between $155 and $160 is 0.072.
To find the probability that the sample mean is between $155 and $160, we will use the Central Limit Theorem. The Central Limit Theorem states that the distribution of the sample mean (with a large enough sample size) will be approximately normally distributed with the same mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
Mean of the sample distribution: μ = $150
Standard deviation of the sample distribution: [tex]σ/√n = $25/√52 ≈ $3.46[/tex]
Now, we'll calculate the z-scores for $155 and $160:
[tex]Z1 = (155 - 150) / 3.46 ≈ 1.445[/tex]
[tex]Z2 = (160 - 150) / 3.46 ≈ 2.890[/tex]
Using a z-table or calculator, we can find the probability for each z-score:
[tex]P(Z1) ≈ 0.9259[/tex]
[tex]P(Z2) ≈ 0.9981[/tex]
Now, we can find the probability between the two z-scores:
[tex]P(1.445 < Z < 2.890) = P(Z2) - P(Z1) = 0.9981 - 0.9259 = 0.0722[/tex]
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An airplane is 5,000 ft above ground and has to land on a runway that is 7,000 ft away as shown above. Let x be the angle the pilot takes to land the airplane at the beginning of the runway. Which equation is a correct way to calculate x?
The fourth equation which is tan x = [tex]\frac{7000}{5000}[/tex] is the correct way to calculate x. This has been obtained by using trigonometry.
What is trigonometry?
Trigonometry is the study of right-angled triangles, which includes the sides, angles, and connections of each triangle.
We are given that the airplane is 5,000 ft above ground and has to land on a runway that is 7,000 ft away with an angle x.
Since, we are not given the hypotenuse so, we will use tan θ.
We know that in trigonometry, tan θ is calculated as the ratio of the opposite side to the adjacent side.
So,
tan x = [tex]\frac{7000}{5000}[/tex]
Hence, the fourth equation is the correct answer.
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The complete question has been attached below
Números que multiplicados me den 24 y sumados me den -11
The two numbers that multiply to give 24 and add to give -11 are -3 and -8.
How do we get these numbers?To find these numbers, you can use a system of equations. Let x and y be the two numbers. Then we have:
xy = 24 (because the two numbers multiply to give 24)x + y = -11 (because the two numbers add to give -11)We can use the second equation to solve for one of the variables in terms of the other. For example, we can solve for x:
x + y = -11
x = -11 - y
We can then substitute this expression for x into the first equation:
xy = 24
(-11 - y)y = 24
Expanding and rearranging, we get:
y^2 + 11y + 24 = 0
This is a quadratic equation that we can solve using factoring or the quadratic formula. Factoring, we get:
(y + 3)(y + 8) = 0
So either y + 3 = 0 or y + 8 = 0. This means that y can be -3 or -8. Substituting each of these values into x = -11 - y, we get:
If y is -3, then x is -11 - (-3) = -8
If y is -8, then x is -11 - (-8) = -3.
Translated question "Numbers that multiply to give me 24 and add to give me -11"
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which of the following is true of a meta-analysis? in a meta-analysis, there is an manipulation of variables. in a meta-analysis, random assignment is required. in a meta-analysis, only a certain amount of studies can be used. in a meta-analysis, we can look for gaps in the research, based on a statistical analysis.
In the following question, among the given options, The statement "In a meta-analysis, there is a manipulation of variables" is false. hence meaning that the rest of them are stated to be true.
In A meta-analysis is a statistical technique for synthesizing the findings of multiple studies. It involves combining the results from multiple studies, analyzing them, and presenting a summary of the overall evidence. It does not involve manipulating variables or performing a random assignment. In a meta-analysis, any amount of studies can be used, and researchers can look for gaps in the research, based on a statistical analysis.
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g the sequence is decreasing and bounded below by 0. explain in clear english (briefly) why this means it must have a limit.
Since the sequence is always decreasing and cannot go below the lower bound, it becomes increasingly closer to the lower bound, and thus converges to a limit.
A sequence is said to be decreasing if each term is smaller than the previous one, and bounded below if there exists a lower bound such that no term in the sequence is smaller than this bound. In this case, the sequence is decreasing and bounded below by 0.
When a sequence is both decreasing and bounded below, it must have a limit because the terms cannot continue to decrease indefinitely, as they cannot go below the lower bound (in this case, 0). This means that as we progress through the terms of the sequence, the difference between consecutive terms will decrease and eventually approach a constant value.
The limit of a sequence is a value that the terms of the sequence approach as they get closer and closer to the end. In this situation, the limit is the smallest possible value that the sequence can approach, without going below the lower bound.
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WHAT IS THE ANSWER
I NEED HELP ASAP
Answer: yes, yes, no
Explanation: In order for a figure to be a triangle, the two smallest sides must add up to be larger than the biggest side. The reason why the last one isn't a triangle is because 6+8 EQUALS 14 and is not greater than 14.
Can someone please help me answer these I’m gonna have a lot of these on my test I just need help answering this one and if you could please try to explain it to me to that would be great
The formula for percent from the board can be expressed this way:
The total number of students that like pineapple pizza * 100.
The total number of students
A (i). The part is the number of students that like pineapple pizza which is 5.
(ii). The whole is the total number of students namely; 7 + 12+ 5 + 3 + 6 = 33.
(iii). Plugging the part and whole into the equation, we will have: 5/33 * 100
(iv). Final answer is = 15.15%
What is a percentage?A percentage is a mathematical expression that is aimed at calculating the proportion of a given quantity out of 100. In the question, we are requested to find what proportion of students like pineapple pizza.
To get the answer, we first have to determine the number of students that like pineapple pizza which is 5 according to the table. Next, we get the sum of students which is 33. The percentage will then get the fraction and multiply the result by 100. The final answer is 15.15%.
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a large bag contains marbles of different colors. there are 10 red marbles, 5 blue marbles and 7 yellow marbles. when selecting 3 marbles without replacement, find the probability of selecting 3 red marbles
A large bag contains marbles of different colors. there are 10 red marbles, 5 blue marbles and 7 yellow marbles. when selecting 3 marbles without replacement, the probability of selecting 3 red marbles is 1/54.
The probability of selecting 3 red marbles is 1/54.What is a probability?
Probability refers to the likelihood or chance of an occurrence. The probability of an event occurring is the ratio of the number of favourable outcomes to the total number of possible outcomes.
A fraction or a decimal is used to express it.The total number of marbles in the bag is 10 + 5 + 7 = 22 marbles.
There are ten red marbles in the large bag, so the number of ways to select 3 red marbles from ten red marbles is:
[tex]10C_3 = (10 \times 9 \times 8) / (3 \times 2 \times 1) = 120[/tex]
There are 22 marbles in the bag, therefore, the total number of ways to pick 3 marbles from 22 is:
[tex]22C_3 = (22 \times 21 \times 20) / (3 \times 2 \times 1) = 1540[/tex]
Hence, the probability of choosing 3 red marbles out of the 22 marbles in the bag without replacement is:120/1540 = 1/54
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scores on an iq test are normally distributed with a mean of 100 and a standard deviation of 15. what is the z-score for an iq score of 122?
The z-score for an IQ score of 122 is 2.
This is calculated by subtracting the mean (100) from the score (122) and dividing by the standard deviation (15). So, 122-100=22, 22/15=2.
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Find the side of a square whose diagonal measures 15v2 cm
15 is area of Side of Square .
What is a square, exactly?
All four of the sides and all four of the angles make up the regular quadrilateral known as the square. The square's angles are 90 degrees away from each other or at right angles. In addition, the square's diagonals are equally spaced and split at a 90-degree angle.
Length of diagonal of Square =15√2 cm-------------(1)
Let side of Square = a cm
So, Length of Diagonal
By Using Pythagorean Theorem
= √a² + a²
= a√2 ........................(2)
Equating (1) and (2)
a√2 = 15√2
a = 15
cancelling root 2 from both sides.
a = 15
Side of Square= 15 cm
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The complete question is -
Find the side of a square whose diagonal is of the given measure. Given = 15√2 cm.
this question pertains to a standard 52-card deck (52 total cards, 4 suits each with 13 possible values: ace, two, king, etc). you draw two cards at random with replacement. what is the probability that at least one card is a spade?
The probability of drawing at least one spade when drawing two cards with replacement from a standard deck of cards is approximately 0.26%.
When drawing two cards at random with replacement from a standard 52-card deck, there are 4 possible outcomes for the first card being a spade and 4 possible outcomes for the second card being a spade.
However, there is also 1 possible outcome where both cards are spades, which would be counted twice if we add the outcomes for the first and second cards separately. Therefore, the total number of outcomes where at least one card is a spade is 4 + 4 - 1 = 7.
The total number of possible outcomes when drawing two cards with replacement is 52 x 52 = 2,704.
Therefore, the probability that at least one card is a spade when drawing two cards with replacement is:
P(at least one spade) = 7 / 2,704 ≈ 0.0026
So, the probability that at least one card is a spade is approximately 0.0026 or 0.26%.
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Find the area of the regular octagon.
Answer:
48 square centimeters
Step-by-step explanation:
[tex] \frac{1}{2} (4)(8)(3) = 48[/tex]
Alex used his grandmother’s recipe to make 11 3/7 pounds of granola. If he fills as many bags as he can with 2 2/3 pounds of granola in each bag, how many pounds will he have left over?
A 16/21 pound
B 2 20/21 pounds
C 4 2/7 pounds
D 8 16/21 pounds
The number of pounds that he will have left over from 11 3/7 pounds is 4 2/7
How many pounds will he have left over?To find out how many bags of granola Alex can fill, we need to divide the total amount of granola he made by the amount of granola in each bag.
We can convert 11 3/7 pounds to an improper fraction:
11 3/7 pounds = 80/7 pounds
Also, we have
2 2/3 pounds = 8/3 pounds
Now we can divide the total amount of granola by the amount in each bag:
(80/7) ÷ (8/3)
To divide fractions, we invert the second fraction (change it to its reciprocal) and multiply:
(80/7) × (3/8)
Simplifying, we get:
(80 x 3) / (7 x 8) = 30/7
Divide
(80 x 3) / (7 x 8) = 4 2/7
Hence, the bags is 4 2/7
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when player a played football, he weighed 204 pounds. how many standard deviations above or below the mean was he?
Player A's weight was 0.208 standard deviations below the mean weight of the football team.
To calculate the standard deviation, we first need to calculate the mean weight of the football team
Mean weight = (sum of all weights) / (number of team members)
(174+176+178+184+185+185+185+185+188+190+200+202+205+206+210+211+211+212+212+215+215+220+223+228+230+232+241+241+242+245+247+250+250+259+260+260+265+265+270+272+273+275+276+278+280+280+285+285+286+290+290+295+302) / 52
= 225.5 pounds
Now we can calculate the standard deviation using the following formula:
Standard deviation = sqrt((sum of (x - mean)^2) / N)
Where x is the weight of a team member, N is the total number of team members.
We can simplify this formula by calculating the variance first:
Variance = (sum of (x - mean)^2) / N
So we have
Variance = ((174-225.5)^2 + (176-225.5)^2 + ... + (302-225.5)^2) / 52
= 10764.35
Now we can calculate the standard deviation
Standard deviation = sqrt(Variance)
= sqrt(10764.35)
= 103.76
To find out how many standard deviations above or below the mean Player A's weight was, we can use the following formula
Z-score = (x - mean) / standard deviation
Where x is Player A's weight, mean is the mean weight of the team, and standard deviation is the standard deviation we just calculated.
So we have
Z-score = (204 - 225.5) / 103.76
= -0.208
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The given question is incomplete, the complete question is:
Following are the published weights (in pounds) of all of the team members of Football Team A from a previous year.
174, 176, 178, 184, 185, 185, 185, 185, 188, 190, 200, 202, 205, 206, 210, 211, 211, 212, 212, 215, 215, 220, 223, 228, 230, 232, 241, 241, 242, 245, 247, 250, 250, 259, 260, 260, 265, 265, 270, 272, 273, 275, 276, 278, 280, 280, 285, 285, 286, 290, 290, 295, 302
median = 241
the first quartile = 205.5
the third quartile = 272.5
Assume the population was Football Team A. When Player A played football, he weighed 204pounds. How many standard deviations above or below the mean was he?
Question 20
After months of negotiations, Jabu's annual salary was increased by 6. 35% to R330 000. Determine his
previous monthly salary and the monthly increase he will be getting.
Original salary of R20 955. 00, with an increase of R6 545. 00 per month.
[2] Original salary of R25 858. 02, with an increase of R1 641. 98 per month
(3) Original salary of R27500. 00, with an increase of R1 746. 25
per
month.
14] Original salary of R25 858. 02, with an increase of R1 746. 25 per month.
Jabu's Monthly salary is of R27500.00, with an increase of R1 746.25 per month. Jabu's monthly increase is R1 746.25. The correct answer is option 3.
To find Jabu's previous monthly salary, we can use the formula:
Previous monthly salary = (Annual salary / 12)
Since Jabu's new annual salary is R330 000, his previous annual salary would be:
Previous annual salary = (New annual salary / 1.0635) = (R330 000 / 1.0635) = R310 020.10
Therefore, Jabu's previous monthly salary would be:
Previous monthly salary = (Previous annual salary / 12) = (R310 020.10 / 12) = R25 835.01
To find the monthly increase, we can subtract Jabu's previous monthly salary from his new monthly salary:
Monthly increase = (New monthly salary - Previous monthly salary) = (R27 618.38 - R25 835.01) = R1 783.37
Therefore, Jabu's monthly increase is R1 746.25 (rounded to the nearest cent).
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x-2
A. 44 in
B. 48 in
C. 52 in
D. 64 in
X
X
x-2
The figure above consists of five congruent rectangles. If the total area of the figure is 75in¹, what
is its perimeter?
The perimeter of the figure, given the rectangles and the total area, can be found to be 48 inches
How to find the perimeter ?The total area is 75 in² which means that the areas of all 5 rectangles add up to 75 in². We can use this to solve for x to be:
5 × ( x × ( x - 2 )) = 75 in²
5 × ( x² - 2x ) = 75 in²
x² - 2x = 15 in²
(x - 5)(x + 3) = 0
x - 5 = 0 or x + 3 = 0
x = 5 or x = -3
Dimensions of a rectangle cannot be negative so x is equal to 5.
The perimeter is then:
= ( x - 2 ) + x + ( x - 2 ) + x + (x - 2 ) + x + ( x - 2 ) + x + (x - 2 ) + x + ( x -2 ) + x
= ( 5 - 2 ) + 5 + ( 5 - 2 ) + 5 + (5 - 2 ) + 5 + ( 5 - 2 ) + 5 + (5 - 2 ) + 5 + ( 5 -2 ) + 5
= 48 inches
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A population of a town increases by 7% every year. If its population today is 40,000, what is its population in 3 years?
A = 40,000(1 + 0.07)^3
A = 40,000(1.07)^3
A = 47,676.08
Therefore, the population of the town in 3 years will be approximately 47,676.
Use the given information to prove the following theorem.
Answer: two right-angled triangle, equilateral triangle
Step-by-step explanation:
It is a combination of two right-angled triangle or it is an equilateral triangle.
Explanation:
You want to prove a point P on the perpendicular bisector of segment YZ is equidistant from Y and Z.
Statement . . . . Reason1. PX is the perpendicular bisector of YZ . . . . given
2. angles at X are right angles . . . . definition of perpendicular
3. YX = XZ . . . . definition of bisector
4. PX = PX . . . . reflexive property of congruence
5. ∆PXY ≅ ∆PXZ . . . . LL congruence theorem
6. YP ≅ ZP . . . . CPCTC