You can use calculus to find the maximum value of a parabola by these steps which are given in the solution part.
What is Parabola?A parabola is a U-shaped curve this is drawn for a quadratic function,
To find the maximum value of a parabola using calculus, you can follow these steps:
1. Identify the equation of the parabola in the form "y = ax² + bx + c," where "a," "b," and "c" are constants.
2. Take the derivative of the equation with respect to x.
3. Set the derivative equal to 0 and solve for x. This will give you the value of x at the vertex of the parabola.
Substitute the value of x that you found in step 3 back into the original equation to find the corresponding y-value. This y-value is the maximum or minimum value of the parabola, depending on the value of a. If a is positive, the parabola opens upwards and the y-value is the maximum. If a is negative, the parabola opens downwards and the y-value is the minimum.
For example, suppose you want to find the maximum value of the parabola y = 2x² - 4x + 3. First, take the derivative of the equation: y' = 4x - 4. Set this equal to 0 and solve for x: 0 = 4x - 4, x = 1.
Substituting this value back into the original equation gives us y = 2(1)² - 4(1) + 3 = 2 - 4 + 3 = 1.
Therefore, the maximum value of the parabola is 1.
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consider reordering the letters in the word tennessee. use the technique shown in example 9.5.11 to answer the following questions. (a) if the n's are placed first, how many ways are there to choose positions for them? if the e's are placed second, how many ways are there to choose positions for them? if the s's are placed third, how many ways are there to choose positions for them? if the t is placed fourth, how many ways are there to choose a position for it? so, the total number of ways to reorder the letters in the word tennessee is . (b) imagine placing the letters into positions in a different order. if the e's are placed first, how many ways are there to choose positions for them? if the t is placed second, how many ways are there to choose a position for it? if the s's are placed third, how many ways are there to choose positions for them? if the n's are placed fourth, how many ways are there to choose positions for them? (c) when the method suggested in part (b) is used to find the total number of ways to reorder the letters in the word tennessee, the result is ---select--- when the method of part (a) is used.
Answer:
Step-by-step explanation:
(a) If the n's are placed first, 36 ways are there to choose positions for them. If the e's are placed second, 35 ways are there to choose positions for them. If the s's are placed third, 3 ways are there to choose positions for them. If the t is placed fourth, 1 way is there to choose a position for it.
(b) If the e's are placed first, 126 ways are there to choose positions for them. If the t is placed second, 5 ways are there to choose a position for it. If the s's are placed third, 6 ways are there to choose positions for them. If the n's are placed fourth, 1 way is there to choose position for it.
(c) Part (b) is used to find the total number of ways to reorder the letters in the word tennessee, the result is 36*35*3*1=3780. Part (a) is used to find the total number of ways to reorder the letters in the word tennessee, the result is 126*5*6*1 =3780.
What is permutation of rearranging letters?
A permutation is a (possible) rearrangement of objects. For example, there are 6 permutation of rearranging letters a, b, c: abc, acb, bac, bca, cab, cba. a b c , a c b , b a c , b c a , c a b , c b a .
The total number of ways to reorder the letters in the word "tennessee" is calculated by considering the different ways the letters can be placed first, second, third, and fourth. The number of ways to place the n's first is 9!/(7!2!), the number of ways to place the e's second is 7!/(4!3!), the number of ways to place the s's third is 3!/2!1!, and the number of ways to place the t fourth is 1. When these values are multiplied together, the total number of ways to reorder the letters is 36*35*3*1=3780.
Again placing the letters into positions in a different order. The number of ways to place the e's first is 9!/(4!*5!), the number of ways to place the t second is 5!/(4!*1!), the number of ways to place the s's third is 4!/(2!*2!) and the number of ways to place the n's fourth is 2!/(2!*0!). When these values are multiplied together, the total number of ways to reorder the letters is 126*5*6*1 =3780.
Therefore, the total number of ways to reorder the letters in the word "tennessee" is 3780 in both orders.
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a) 36, 35, 3, 1 ways; b) 126, 5, 6, 1 ways; c) total number of ways to reorder the letters in the word tennessee is 3780 for both a) and b).
(a) If the n's are placed first, 36 ways are there to choose positions for them. If the e's are placed second, 35 ways are there to choose positions for them. If the s's are placed third, 3 ways are there to choose positions for them. If the t is placed fourth, 1 way is there to choose a position for it.
(b) If the e's are placed first, 126 ways are there to choose positions for them. If the t is placed second, 5 ways are there to choose a position for it. If the s's are placed third, 6 ways are there to choose positions for them. If the n's are placed fourth, 1 way is there to choose position for it.
(c) Part (b) is used to find the total number of ways to reorder the letters in the word tennessee, the result is 36*35*3*1=3780. Part (a) is used to find the total number of ways to reorder the letters in the word tennessee, the result is 126*5*6*1 =3780.
What is permutation of rearranging letters?
A permutation is a (possible) rearrangement of objects. For example, there are 6 permutation of rearranging letters a, b, c: abc, acb, bac, bca, cab, cba. a b c , a c b , b a c , b c a , c a b , c b a .
The total number of ways to reorder the letters in the word "tennessee" is calculated by considering the different ways the letters can be placed first, second, third, and fourth. The number of ways to place the n's first is 9!/(7!2!), the number of ways to place the e's second is 7!/(4!3!), the number of ways to place the s's third is 3!/2!1!, and the number of ways to place the t fourth is 1. When these values are multiplied together, the total number of ways to reorder the letters is 36*35*3*1=3780.
Again placing the letters into positions in a different order. The number of ways to place the e's first is 9!/(4!*5!), the number of ways to place the t second is 5!/(4!*1!), the number of ways to place the s's third is 4!/(2!*2!) and the number of ways to place the n's fourth is 2!/(2!*0!). When these values are multiplied together, the total number of ways to reorder the letters is 126*5*6*1 =3780.
Therefore, the total number of ways to reorder the letters in the word "tennessee" is 3780 in both orders.
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What is the range of the function 4?
The range is 4.
The range is 4 because y=y can only take on 4 at any point.
What is the median of 50?
The median of the first 50 whole numbers is 24.5.
The midway value in a given set of figures or data is referred to as the median. To get the average value for a given group of integers, three distinct metrics are employed in mathematics.
Non-negative numbers, which can be expressed without fractions, are known as whole numbers.
The first fifty whole numbers are 0,1,2,3,4,5................49
The number of terms in the data, n=50.
Let [tex]n^{th}[/tex] term be denoted by [tex]t_{n}[/tex]
As the number of terms is even, thus the median will be [tex]\frac{t_{\frac{n}{2} } +t_{\frac{n}{2} }+1}{2}[/tex]
Substitute n with 50.
Median = [tex]\frac{t_{\frac{50}{2} } +t_{\frac{50}{2} }+1}{2}= t_{25}+t_{26} /2[/tex]
The 25th term of the sequence is 24.
The 26th term of the sequence is 25.
Thus, median = 24+25/2 = 49/2 = 24.5
Complete question: What is the median of the first 50 whole numbers?
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Astronauts for nasa must measure between 62 and 75 inches tall. Which equation best represents the minimum and maximum heights accepted for nasa astronauts?.
The minimum and maximum heights accepted for NASA astronauts are 62 inches and 75 inches, respectively. These values can be represented by the following equation: 62 <= height <= 75
This equation can be read as "the height must be greater than or equal to 62 inches and less than or equal to 75 inches."
Alternatively, you can represent the minimum and maximum heights using the following inequality:
62 < height < 75
This inequality can be read as "the height must be greater than 62 inches and less than 75 inches."
Either of these equations can be used to represent the minimum and maximum heights accepted for NASA astronauts.
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Why do we check up to the square root of a number to determine if the number is prime?
A number is said to be prime if the integers smaller than its square root cannot divide it, as numbers higher than its square root cannot possibly do so.
what is square root ?A mathematical concept known as a square root is a factor of a number that, when multiplied by itself, equals the original value. For instance, 3 and -3 are the square roots of 9. Starting in the second millennium BC, the Babylonians created effective methods for approximating square roots.
here ,
In other words, if we encounter a number when counting from 2 to sqrt(N), and that number is a factor of N .
then indicates that the number has more than two factors and is thus not a prime number.
Otherwise, if we are unable to locate any factors for N, it is likely that N only has two factors, one and itself, making it a prime number.
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What is 3 5 equivalent to as a fraction?
The fractions equivalent to 3/5 are 6/10, 9/15, 12/20, etc.
Now, According to the question:
Equivalent fractions can be written by multiplying or dividing both the numerator and the denominator by the same number. This is the reason why these fractions get reduced to the same number when they are simplified.
Let us understand the two ways in which we can make equivalent fractions:
Multiply the numerator and the denominator by the same number, or,Divide the numerator and the denominator by the same number.Hence, the equivalent fractions for 3/5 are:
(3/5) × (2/2) = (3 × 2) / (5 × 2) = 6/10
(3/5) × (3/3) = (3 × 3) / (5× 3) = 9/15
(3/5) × (4/4) = (3 × 4) / (5 × 4) = 12/20
Thus, 6/10, 9/15, 12/20 are equal to 3/5,
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I need help with this
The value of the function (f o g )(11) is -1
How to find the value of the given function?Applying composite function formula,
(f o g )(x) = f [g (x)]
Here ,f(x) = [tex]\sqrt{x} - 3[/tex]
g (x ) = x - 7
(f o g )(x) =f [x - 7 ]
=[tex]\sqrt{x-7} -3[/tex] --(1)
Substitute x = 11 in the given function in (1)
[tex](f o g )(11) =\sqrt{11-7} -3\\(f o g )(11) =\sqrt{4} - 3\\(f o g )(11) = 2 -3 = -1[/tex]
The value of the function (f o g )(11) is -1
What is a composite function?A composite function is a function whose values are obtained by applying one function to an independent variable.Then using the result to apply the second function, and the domain of which is made up of the independent variable values for which the output of the first function falls within the domain of the second. The composition of functions is a particular instance of the composition of relations, and it is sometimes also indicated by °.Therefore, all characteristics of composition of relations, including associativity, are also characteristics of composition of functions. However, composition of functions differs from multiplication of functions ,if it is defined at all and has a number of distinct characteristics, most notably that it is non-commutative.So, option 2 is correct .To learn more about composite function, refer:
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Rosie ran directly toward her home at a constant velocity for 78 seconds. In one-third of that time, she ran 52 meters. What was Rosie's velocity?
The velocity of Rosie when running is 2 meters per second
How to determine the velocity of Rosie?From the question, we have the following parameters that can be used in our computation:
Time = 1/3 of 78 seconds
Distance covered = 52 meters
The velocity can be calculated using the following equation
Velocity = Distance covered/Time
Substitute the known values in the above equation, so, we have the following representation
Velocity = 52/(1/3 * 78)
Evaluate the quotient
Velocity = 2
Hence, the velocity is 2 meters per second
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What additional information is needed to show that △ ABC ≅ △ DEF by SSS?
SSS congruence of triangles is proved when all three sides of considered two triangles are congruent(that is, of equal measures).
What is SSS congruence of triangles?If two considered triangles have corresponding side pairs congruent(for all three sides), then both the triangles are congruent. This proof of congruence is triangle is done by SSS congruence of triangles (Side Side Side congruence)
Since it is given that the sides CB and FE are congruent, and since it is given that sides AB and DE are congruent too.
Thus, for SSS congruence of both considered triangles, we need the third side pair of the given triangles to be congruent too.
Thus, we need the line segment DF congruent to the line segment AC.
We can write it symbolically as:
[tex]$\overline{D F} \cong \overline{A C}$[/tex] (remember that order doesn't matter here. This can be written as [tex]$\overline{A C} \cong \overline{D F}$[/tex] .)
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What makes similar shapes similar?
The property scale factor make the similar shapes similar one.
The term shape in math refers the outline or the boundary of an object.
Here we need to find the property that makes the similar shape similar.
As per the definition of shape we have identified that the shape has the following property, they are listed as,
=> Length
=> Breadth
=> height.
All these are collectively called scaling factor,
Based on these values we have take the two similar shapes such as similar triangles, similar rectangles, similar square, are the shapes whose dimensions are in equal or common ratio but the size or length of their sides vary.
Therefore the common ratio is called the scale factor.
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Is for the next 2 min please help
Answer:
Step-by-step explanation: 44/59 = 0.74576271186 so that means the answer is around 74.5% or 74.6%
Why is it called linear function?
A linear function is a type of function that can be expressed in the form of a linear equation with one or more variables.
The equation is written as y = mx + b, where m is the slope and b is the y-intercept. The slope is the rate at which the line rises or falls and the y-intercept is the point where the line crosses the y-axis. The slope and y-intercept of a linear function are constants, meaning that the line does not curve or change direction. This is why it is called a linear function.
When calculating linear functions, the equation is used to identify the slope and the y-intercept. The slope and y-intercept are then used to plot the points on a graph. A linear equation has the form y = mx + b, where m is the slope and b is the y-intercept. The slope indicates the rate of change of the function and the y-intercept indicates the point where the line crosses the y-axis. To find the slope of a linear function, the equation is solved for m, which is the rise over run. To find the y-intercept, the equation is solved for b, which is the y-value when x = 0. Once the slope and y-intercept are determined, the points can be plotted on a graph and the linear equation can be written.
In summary, a linear function is a type of function that can be expressed in the form of a linear equation. The equation of the linear function is used to identify the slope and y-intercept, which are then used to plot the points on a graph. Linear functions can be used to model many real-world situations and to solve for x and y values for any given point.
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Your couing ay 5,953 round to 5,053 when rounded to the nearet hundred. If your couin correct ? Explain
No , cousin is not correct because when 5,953 is rounded to the nearet hundred the value should be 6000 .
Given :
What is rounding to the nearest hundred ?
Rounding a number to the nearest hundred means to write down the multiple of 100 that is nearest to the number .
if the hundred value number is less than 5 then we must round to the lowest value .if the hundred value number is greater than 5 then we must round to the highest near value .so here given number = 5,953
so here the number 53 is greater than 50 .
We round the number up to the nearest hundred if the last two digits in the number are 50 or above.
so the number after rounded = 6000
so his cousin is incorrect .
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You want to put $2,500 in a simple interest account. It has a 4% annual interest rate. How long must you invest that money to earn $500 in interest?
A) 1.25 years
B) 2.5 years
C) 5 years
D) 20 years
Answer:c
Step-by-step explanation:
Answer: C) 5 years
Step-by-step explanation:
Formula for the simple interest is: I = P * r * t, where: I = $500, P = $2,500, r = 0.04 and t stays for the number of the years. 500 = 2,500 * 0.04 * t; 500 = 100 * t; t = 500 : 100; t = 5.
Which is an example of a sequence?
3,7,11,15 is an example of sequence since we can see a pattern is previous and next term.
What are the name of four type of sequences?Arithmetic sequence
Geometric sequence
Harmonic sequence
Fibonnaci numbers.
Is sequence a set?In contrast to a set, the same items might appear more than once in a sequence at various points, and unlike a set, the order is important. A sequence can be described formally as a function from natural numbers (the positions of the sequence's elements) to the items at each of those positions.
A sequence is a list of elements that has been arranged in a certain way. For instance, the sequence 3, 7, 11, 15,... is a sequence because it follows a pattern where each term is created by adding 4 to the term before it.
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A recipe that yields 30 servings calls for 3/4 cup flour. You want to prepare only 10 servings. After scaling the recipe to yield 10 servings, how much flour will you need?.
The number of servings that can be made from 3 / 4 cups, the number of cups of flour needed for 10 servings is 1/4 cups.
Given :
First the number of servings that can be made per cup :
= Number of servings / Number of cups
= 30 / 3/4
= 30 * 4 / 3
= 120 / 3
= 40 servings
To get 10 servings therefore, you would need:
= Number of servings needed / Number of servings per cup
= 10 / 40
= 1/4 cups
Hence the flour will be needed is 1/4 cup is needed.
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A certain math test has a mean of 50 and a standard deviation of 12. the teacher wants to convert the scores to a new scale using the transformation x*=65+0.6x. what are the new mean and standard deviation?
a) mean=50, standard deviation=7.2
b) mean=95, standard deviation=7.2
c) mean=95, standard deviation=12
d) mean=95, standard deviation=72.2
e) mean=77, standard deviation=12
Answer:
(b) mean=95, standard deviation=7.2.
Step-by-step explanation:
To find the new mean and standard deviation, we first need to apply the transformation to the original mean and standard deviation.
The new mean is given by: x*=65+0.6x
Substituting in the original mean of 50, we get: x*=65+0.6(50) = 95
The new standard deviation is given by: s*=0.6s
Substituting in the original standard deviation of 12, we get: s*=0.6(12) = 7.2
Therefore, the new mean and standard deviation are (b) mean=95, standard deviation=7.2.
How to compute 1sd 2sd 3sd?
The average degree of variability in the dataset is represented by the standard deviation. It reveals the average deviation of each statistic from the mean.
Explain the term standard deviation?Empirical principle
If your frequency distribution follows a normal distribution, the standard deviation and mean combined might help you determine where the majority of the values are located.
The 68-95-99.7 rule, often known as the empirical rule, reveals your values to you:
Nearly 68% of scores are within one deviation of the mean, nearly 95% are within two standard deviations, and nearly 99.7% are within three standard deviations.Thus, the standard deviation is a less trustworthy indicator of variability for non-normal distributions and should be combined with other metrics like range or interquartile range.
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How do you solve for x and y using substitution?
In substitution method we have to put the the value of one variable from one equation to the other equation. Then we solve the equation and can find the value of variable x and y.
In the given question we have to explain how we can solve for x and y using substitution.
In the Substitution method we find the value of one variable in term of other variable from the one equation then we put the value of that variable in other equation. After putting the value of that variable in other equation, equation converts into the similar variable. Then after solving we can easily find the value of one variable. After finding the value of one variable we put the value of that variable in first equation. By this we can find the value of both variable.
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Can Someone Help Me Please
Answer:
63 with 3 left over
Step-by-step explanation:
381/6=63.5
63x6=378
378+3=381
What does associative property look like?
The associative property looks like a + (b + c) = (a + b) + c.
According to the associative property, if 3 numbers are added or multiplied then the grouping of numbers does not change the final result.
The associative property is applicable in addition as well as in multiplication.
According to the associative property in addition - when 3 numbers, say a, b, and c are being added then their sum will not change even if the grouping of numbers is changed. It can be presented as:
(a + b) + c = a + (b + c)
According to the associative property in multiplication - when 3 numbers, say a, b, and c are being multiplied then their product will not change even if the grouping of numbers is changed. It can be presented as:
(a × b) × c = a × (b × c)
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For each set of numbers find the mean (average).
6, 12, 10, 8
Answer:
9
Step-by-step explanation:
add all the numbers: 6+12+10+8=36
then divide by the amount of numbers there are: 36/4=9
help what is the answer to this picture?
WX is a segment bisector
WX is a perpendicular bisector
W is the midpoint of a segment in the diagram
A cuboid has a lateral surface of 260 cm and a height of 10 cm. The dimensions of the base are: one is 3 cm smaller than the other. Instruction: First, we find the perimeter of the base of the cuboid as a ratio of the side surface to the height. (260cm2: 10cm=26 cm.) Then we write the equation x+x-3+x+x-3=26cm, where with x we marked one of the sides, we find the sides
Answer:
A cuboid is a 3-dimensional shape with six rectangular faces, four of which are the sides or lateral faces, and the other two are the base and the top. To solve the problem, we can first find the perimeter of the base of the cuboid by dividing the lateral surface area by the height. In this case, the perimeter of the base is 26 cm.
To find the dimensions of the base, we can set up an equation using the given information. Let x be one of the sides of the base, and let y be the other side. Since one of the sides is 3 cm smaller than the other, we can write the equation as:
x + x - 3 + x + x - 3 = 26 cm
We can simplify the equation by combining like terms:
4x - 6 = 26 cm
Next, we can solve the equation by adding 6 to both sides and then dividing by 4:
4x = 32 cm
x = 8 cm
Therefore, the dimensions of the base of the cuboid are 8 cm x 11 cm (since one side is 3 cm smaller than the other). The perimeter of the base is 26 cm, and the height of the cuboid is 10 cm.
Step-by-step explanation:
a number has three distinct digits, the sum of the digits equals the products of the digits. how many three digit numbers satisfy this condition?
Only one three digits number 111 would satisfy this condition.
Let the three digits be x, y and z. Since the sum of the digits is equal to the product of the digits, we can write x + y + z = xyz
Simplifying the equation, we get x + y + z - xyz = 0
This is a quadratic equation in the form ax2 + bx + c = 0 where a = 1, b = 1 and c = -xyz
To solve this equation, we use the quadratic formula: x = [-b ± √(b2 - 4ac)]/2a
In this case, x = [-1 ± √(1 - (-4 * 1 * (-xyz))]/2
Since xyz must be a positive integer, the only solution is when the square root of 1 - (-4 * -xyz) is 0
This means xyz must be 1, so x + y + z = 1 + y + z = 3
Since x, y and z are all distinct digits, the only possible solution is when x = 1, y = 1 and z = 1, giving the solution 111.
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a cone with a radius of 4.96 and a volume of 102
The volume of a cone is given by the formula:
V = (1/3) * π * r² * h
Where V is the volume, r is the radius, and h is the height.
In this case, we know the radius (4.96) and the volume (102), so we can use the formula to solve for the height.
Substituting the known values into the formula, we get:
102 = (1/3) * π * (4.96)² * h
Dividing both sides by (1/3) * π * (4.96)², we get:
h = 102 / [(1/3) * π * (4.96)²]
Substituting in the value for π, we get:
h = 102 / [(1/3) * 3.14 * (4.96)²]
Which simplifies to:
h = 102 / [(1/3) * 3.14 * 24.1952]
Which simplifies to:
h = 102 / (0.7853 * 24.1952)
Which simplifies to:
h = 102 / 19.1268
Which is approximately 5.33.
Therefore, the estimated height of the cone is approximately 5.33.
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Answer:
Step-by-step explanation:
The volume of a clone = 1/3 × π × r^2 × h
Volume, v = 102
Radius r = 4.96
r^2 = 4.96^2 = 24.6016
Approximately = 24.6
π = 3.142
v = 1/3 x π x r^2 x h
Cross multiply
3v = π x r^2 x h
h = (3 x 102) / 24.6 x 3.142
h = 3.959 cm
I hope this was helpful
You ask 50 of your classmates if they have any siblings. Complete the two-way frequency table to show the results of the survey.
Girls of 25 says Yes, 10 boys say No. 30 total Students say No, 45 girls total, with a total of 60 Students
What meant by mathematical expression ?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
An expression that uses numbers, variables, or both is a mathematical expression. The equal symbol is never used in expressions. Here are a few phrases as examples. A mathematical statement stating the equality of two expressions is known as an equation.
Given,
5 boys tell yes and total boys and girls tell yes is 30 by simplifying
no of girls tell yes =30 - 5= 25
no of girls tell no =20
overall total boys tell no = 15-5=10
The no of boys tell no =10
So total no of boys and girls tell no = 20+10=30
total no of girls tell yes and no =60-15=45
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Find the 87th term of the arithmetic sequence -19, -13, -7…
Answer:
497
Step-by-step explanation:
a(87) = -19+(87-1)6
a(87)=-19+(86)6
a(87)=-19+516
a(87)=497
I used the arithmetic formula which is an=a1+(n-1)d.....
What type of set is X?
A set X is a subset of set Y (Written as X ⊆ Y) if every element of X is an element of set Y.
What is a set ?A set is represented by a capital letter symbol and the number of elements in the finite set is represented as the cardinal number of a set in a curly bracket {…}.
A set has many types, such as;
Empty Set or Null set: It has no element present in it.Example: A = {} is a null set.
Finite Set: It has a limited number of elements.Example: A = {1,2,3,4}
Infinite Set: It has an infinite number of elements.Example: A = {x: x is the set of all whole numbers}
Equal Set: Two sets which have the same members.Example: A = {1,2,5} and B={2,5,1}: Set A = Set B
Subsets: A set ‘A’ is said to be a subset of B if each element of A is also an element of B.Example: A={1,2}, B={1,2,3,4}, then A ⊆ B
Universal Set: A set which consists of all elements of other sets present in a Venn diagram.Example: A={1,2}, B={2,3}, The universal set here will be, U = {1, 2,3}
A set X is a subset of set Y (Written as X ⊆ Y) if every element of X is an element of set Y.
Example : − Let, X = { 1, 2, 3, 4, 5, 6 } and Y = { 1, 2 }. Here set Y is a subset of set X as all the elements of set Y is in set X. Hence, we can write Y ⊆ X.
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How do you complete the proof?
From the proof below, we have been able to prove that IK bisects ∠HIJ by CPCT postulate
How to complete the proof of congruent angles?Congruent angles are defined as angles that have equal measure.
Now, we are given that;
IK bisects ∠HKJ
HK ≅ JK
Thus, since IK bisects ∠HKJ, then it means that by definition of angle bisector that;
∠HKI = ∠JKI
Now, we are also told that HK ≅ JK.
Now, by reflexive property of congruence, we can say that IK is congruent to itself.
Thus, we now have 2 congruent sides and an include angle and as such both triangles are congruent by SAS Congruency postulate.
Thus, we can conclude that ∠HIK = ∠JIK by CPCT which states that Corresponding parts of Congruent Triangles are congruent.
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