Step-by-step explanation:
The radians is just the length of the arc, so if you had a unit circle where the radius was 1, the length of that entire circle would be [tex]2\pi[/tex] since the circumference of any circle is [tex]2\pi r[/tex] except r is 1 so the length is just [tex]2\pi[/tex]. So if you take 1/4 of this you get [tex]\frac{2\pi}{4}[/tex] which can be simplified to [tex]\frac{\pi}{2}[/tex]
Answer:
Step-by-step explanation:
Comments
You need to get the radian measure of the circle.
The radian measure of the entire circle is 2 * pi
To get the radian measure of 1/4 of the circle, just divide by 4.
2 pi / 4 = pi/2
The central angle is = to 1/4 of the circumference of the circle.
So the central angle is also pi/2
Answer: pi/2
Question 5 of 10
Which information would most likely cause a company's stock price to go up?
A. Consumers reduce spending because of a recession.
B. The company releases an innovative car with unique features.
C. The company's charismatic CEO must resign after revelations of
fraud.
D. Congress threatens to break up a large tech company.
SUBMIT
Answer:
B
Step-by-step explanation:
Use your calculator to estimate the value of
log752.
Click on the correct answer.
1.450
1.653
2.031
The value of the given logarithm using calculator is 2.031
Logarithm functionsLogarithm are inverse of exponential functions. Given the following logarithm expression;
log(7)52
This can also be expressed as:
log(7)52 = log52/log7
log(7)52 = 0.5399/0.9804
log(7)52 = 2.031
Hence the value of the given logarithm using calculator is 2.031
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Two points located on JK are A-1,-9) and K(5,3). What is the slope of JK ?
OA -2
OB. -1/2
OC. 1/2
O D. 2
Answer:
D .2
Step-by-step explanation:
3-(-9)
5-(-1)
=3+9
5+1
12
6
= 2
Question 3(Multiple Choice Worth 4 points)
(01.05 LC)
Solve for x: 3
06
06>x>9
00
00>x>3
The value of x from the given equation is ±√10
Solving linear equationsLinear equations are equation that has a leading degree of 1. Given the equation below:
Given the equation below;
x² = 10
Take the square root of both sides
√x² = ±√10
x = ±√10
Hence the value of x from the given equation is ±√10
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You and a friend go to Tacos Galore for lunch. You order two soft tacos and three burritos, and
your total bill is AED 18. Your friend's bill is AED 20.00 for four soft tacos and two burritos.
How much does a soft taco cost?
Answer:
AED 3
Step-by-step explanation:
Let tacos: t
Let burritos: b
1) Set up equations.
2t + 3b = 18
4t + 2b = 20
2) Solve the system of equations using substitution.
2t = 18 - 3b
t = 18/2 - 3b/2
t = 9 - 3b/2
Substitute this into the second equation and simplify.
4(9 - 3b/2) + 2b = 20
36 - 12b/2 + 2b = 20
36 - 6b + 2b = 20
36 - 4b = 20
-4b = 20 - 36
-4b = -16
b = -16/-4
b = 4
3) Substitute the found answer in any one of the two equations.
2t + 3(4) = 18
2t + 12 = 18
2t = 18 - 12
2t = 6
t = 6/2
t = 3
Therefore, a soft taco costs AED 3.
A 2-column table with 9 rows. The first column is labeled x with entries negative 8, negative 6, negative 4, negative 2, 0, 2, 4, 6. The second column is labeled f of x with entries negative 16, negative 8, 0, 8, 16, 32, 64, 128.
Which could be the entire interval over which the function, f(x), is negative?
(–8, –2)
(–8, 0)
(–∞, –6)
(–∞, –4
Answer: (–∞, –6)
Step-by-step explanation:
From the given information, the function is never non-negative over (-8,-6), which is the only subset of the interval that is given.
2.
Generate a frequency table for the following data: 3, 12, 25, 2, 3, 6, 17, 17, 15, 13, 20, 12, 21, 18, 19.
Use the ranges listed in the table:
Range Number of Values Relative Frequency
1 – 5
6 – 10
11 – 15
16 – 20
21 – 25
What is the relative frequency for the range 16 – 20?
0.4
0.33
0.2
.27
The relative frequency for the range 16 - 20 is 0.27.
What is the frequency of a data set?The frequency of a data set refers to the number of times a data or an event is occurring.
From the given information:
Range Number of values
1 - 5 3
6 - 10 1
11 - 15 4
16 - 20 5
21 - 25 2
Total 15
Relative Frequency = Subgroup frequency/ Total frequency
Relative Frequency for the range 16 - 20:
= 4/15
= 0.27
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Answer:
.27
Step-by-step explanation:
Stephen evaluated (6.34 times 10 Superscript negative 7 Baseline) (4.5 times 10 Superscript 3 Baseline). His work is shown below. Which two statements describe the errors Stephen made?
(6.34 times 10 Superscript negative 7 Baseline) (4.5 times 10 Superscript 3 Baseline). (6.34 times 4.5) (10 Superscript negative 7 Baseline times 10 Superscript 3 Baseline). 28.53 times 10 Superscript negative 4 Baseline. Negative 28.53 times 10 Superscript 4 Baseline. Negative 2.853 times 10 Superscript 3 Baseline.
He changed the sign of the coefficient. A negative exponent does not affect the sign of a coefficient in scientific notation. The sign of the exponent determines the direction the decimal is moved in.
He rewrote Negative 28.53 times 10 Superscript 4 incorrectly; 28.53 times 10 Superscript 4 Baseline = 2.853 times 10 Superscript 5. The exponent is increased to account for the extra place the decimal is moved.
He did not correctly evaluate the exponent. It should be evaluated as (10 Superscript negative 7 Baseline times 10 Superscript 3 Baseline) = 10 Superscript negative 21 since exponents are evaluated using the same operation as the coefficients.
He got the wrong value for the coefficients; 28.53 times 10 Superscript negative 4 is not possible. The coefficients in scientific notation are always greater than 1, but less than 10.
He multiplied the coefficients; he should have added 6.34 and 4.5. The product of powers rule states that coefficients are added.
Steps 4 and 5 describe the errors Stephen made.
Stephen evaluated [tex](6.34\times 10^{-7})(4.5\times 10^3)[/tex].
His work is shown below.
Which two statements describe the errors Stephen made?Step 1 - [tex](6.34\times 10^{-7})(4.5\times 10^3)[/tex]
Step 2 - [tex]=(6.34\times 4.5)(10^{-7} \times 10^3)[/tex]
Step 3 - [tex]=(28.53)(10^{-4})[/tex]
Step 4 - [tex]20.53\times 10^4[/tex]
Error is the step as 4 sign is negative.
So correct step is [tex]=(28.53)(10^{-4})[/tex]
Step 5 - [tex]=(28.53)(10^{-4})[/tex]
Error is the step as there are 4 in place of 3.
So correct step is [tex]=(28.53)(10^{-4})[/tex]
Steps 4 and 5 describe the errors Stephen made.
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What is the relationship between the domain and range of a relation and its inverse?
Answer:
the x-values of the relation are the y-values of the inverse.
Four friends had dinner togethere.
The total cost was $65.60.
The four friends shared the cost eaually between them.
How much did each person pay
Answer:
Your answer is $16.40
Can you see an easy way to work out the value of [tex]\sqrt{ 1^3 + 2^3 + 3^3 + 4^3 + 5^3[/tex] ? if so, describe it.
We have the sum of cubes identity
[tex]a^3 + b^3 = (a + b) (a^2 - ab + b^2)[/tex]
and observing that 1 + 4 = 2 + 3, we have
[tex]1^3 + 4^3 = (1 + 4) (1^2 - 4 + 4^2) = 5 \times 13[/tex]
and
[tex]2^3 + 3^3 = (2 + 3) (2^2 - 6 + 3^2) = 5 \times 7[/tex]
Then
[tex]\sqrt{1^3+2^3+3^3+4^3+5^3} = \sqrt{5\times13 + 5\times7 + 5\times5^2} = \sqrt{5 \times (20 + 25)} \\\\ ~~~~~~~~ = \sqrt{5^2 \times (4 + 5)} = \sqrt{5^2\times9} = \sqrt{5^2\times3^2} = 5\times3 = \boxed{15}[/tex]
Alternatively, we have the well-known sum of cubes formula
[tex]\displaystyle \sum_{i=1}^n i^3 = \frac{n^2(n+1)^2}4[/tex]
The sum under the square root is this sum with [tex]n=5[/tex]. Then
[tex]1^3+2^3+3^3+4^3+5^3 = \dfrac{5^2\times6^2}4 = 225 = 15^2[/tex]
and so the square root again reduces to 15.
ASAP! FIND THE AREA OF THE SECTOR
Answer:
probably B
Step-by-step explanation:
Using the formula pi*r^2, we plug in our values
pi*49=49pi mi^2
but, we still have one more step, as we are calculating for three quarters of a circle, not a full circle.
To find the area for 3/4 of a circle, we just multiply 3/4 by the area of the circle
49pi*3/4=147pi/4
A quick way (though not always accurate) to guess the answer in a multiple choice like this is to see that someone might find the area of the full circle as their final answer, not multiplying by 3/4, so there's a good chance that 49pi mi^2 would be an answer in the multiple choice. since we know that there is a correct answer that is exactly 3/4 of that answer, we can take the ratios of the answers and check if any of them equal 3/4. indeed, after checking a bit, answer B divided by answer A equals 3/4 exactly, and no other answer combination equals 3/4 (D/B is about equal to 4/5). So, we can guess that B is the answer.
Still better to actually do the problem though
74. Real-World Applications
A town's population has been growing linearly. In 2003, the population was 45,000, and the population has been growing by 1,700 people each year. Write an equation, P(t), for the population t years after 2003 .
Answer:
The linear equation modeling the given function is P(t)=1700t+45000.
Step-by-step explanation:
In the question it is given that a town's population has been growing linearly. In 2003, the population was 45000, and the population has been growing by 1700 people each year.
It is required to write an equation P(t), for the population t years after 2003.
To solve this question, substitute the given slope , or change in population in the equation with the initial population . Thus, formulate the equation modeling the given function.
Step 1 of 1
Formulate the equation in the slope-intercept form.
[tex]$$\begin{aligned}&y=m x+b \\&P(t)=1700 t+45000\end{aligned}$$[/tex]
How many solutions does this linear system have?
y = 2/3x+ 2
6x -4y = -10
O one solution: (-0.6, -1.6)
O one solution: (-0.6, 1.6)
no solution
infinite number of solutions?
PLS help fast this is urgent ty
For question 1 option C is the correct answer and for question 2 option A is the correct answer.
We need to find which transformation from the graph of a function f(x) describes the graph of 10f(x).
Here the transformation that describes the graph of g(x) is a vertical dilation of scale factor k = 10 of f(x).
We can start by defining the general vertical dilation.
For a given function f(x), a vertical dilation stretches or contracts the graph vertically, depending on the scale factor k.
And it is written as:
g(x) = k*f(x).
Then here we have:
g(x) = 10*f(x)
It is easy to see that this is a vertical dilation of scale factor k = 10. Therefore, option C is the correct answer.
We need to check from the given options which information is sufficient to prove that quadrilateral ABCD is a parallelogram.
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
Therefore, option A is the correct answer.
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I really need help with this please.
Answer:
y = - 6x + 7.5
Step-by-step explanation:
the perpendicular bisector of BC passes through the midpoint of BC at right angles to BC.
calculate the slope m of BC using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = B (- 2, 1 ) and (x₂, y₂ ) = C (4, 2 )
[tex]m_{BC}[/tex] = [tex]\frac{2-1}{4-(-2)}[/tex] = [tex]\frac{1}{4+2}[/tex] = [tex]\frac{1}{6}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{6} }[/tex] = - 6
the midpoint of BC is the average of the x and y coordinates
midpoint = ( [tex]\frac{-2+4}{2}[/tex] , [tex]\frac{1+2}{2}[/tex] ) = ( [tex]\frac{2}{2}[/tex] , [tex]\frac{3}{2}[/tex] ) = ( 1, 1.5 )
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - 6 , then
y = - 6x + c ← is the partial equation
to find c substitute (1, 1.5 ) into the partial equation
1.5 = - 6 + c ⇒ c = 1.5 + 6 = 7.5
y = - 6x + 7.5 ← equation of perpendicular bisector of BC
Solve this system of equations by
using the elimination method.
x - 5y = 16
4x - 2y = -8
( , )
Answer:
[tex]x = - 4[/tex]
[tex]y = - 4[/tex]
Step-by-step explanation:
Looking at these equations, we can see neither x or y have the same coefficient. Therefore, we need to multiply or divide, to make either the x or the y the same. It's less of a hassle to make the Xs the same, so let's do that. Taking the top equation and multiplying it by 4, we get:
[tex]4x - 20y = 64[/tex]
Now let's subtract the top equation from the bottom equation, leaving us with a third equation:
[tex] - 18y = 72[/tex]
Divide 72 by -18 to get
[tex]y = - 4[/tex]
Now let's substitute into our first equation to find X:
[tex]x + 20 = 16[/tex]
Leaving us with:
[tex]x = - 4[/tex]
Now let's substitute into the second equation to check our solution is correct:
[tex] - 16 + 8 = - 8[/tex]
This is correct, so the answer is X and Y are both equal to -4
You have 73 trading cards. Your cousin says that
you have 7 less than half the cards he has. You
say you have 33 more than one-fourth the cards
he has. Can you both be right?
Using proportions, it is found that both can be right, as the amounts found from each operation are the same.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Considering you have 73 cards, and your cousin says that you have 7 less than half the cards he has, his amount is found as follows:
0.5x - 7 = 73
0.5x = 80
x = 160.
Then, one-fourth of his amount is:
(1/4) x 160 = 40.
33 more than this is:
33 + 40 = 73.
Both operations have results (73,160), hence the both can be right.
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What is the coefficient of the last term in the binomial expansion of (x 1)9? 0 1 9 10
The coefficient of the last term in the binomial expansion is 1.
Given term is (x + 1)⁹.
The algebraic expansion of a binomial's powers is expressed by the binomial theorem or binomial expansion. The process of expanding and writing terms that are equal to the natural number exponent of the sum or difference of two terms is known as binomial expansion.
The binomial expansion formula for (a + b)ⁿ= ⁿC₀(aⁿb⁰)+ⁿC₁(aⁿ⁻¹b¹)+ⁿC₂(aⁿ⁻²b²)+ⁿC₃(aⁿ⁻³b³)+...............+ⁿCₙ(a⁰bⁿ)
Here, a = x, b = 1 and n = 9.
Substituting the values in the formula,
⁹C₀(x⁹{1}₀)+⁹C₁(x⁹⁻¹{1}¹)+⁹C₂(x⁹⁻²{1}²)+⁹C₃(x⁹⁻³{1}³)+......+⁹C₉(x⁰{1}⁹)
The last term is ⁹C₉(x⁰{1}⁹)
The coefficient of the last term = ⁹C₉ = 1.
Hence, the coefficient of the last term in the binomial expansion of (x+1)⁹ is 1.
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What is the value of x? (There should be an image)
Answer:
22
Step-by-step explanation:
A research scientist wants to know how many times per hour a certain strand of bacteria reproduces. The mean is found to be 7.6 reproductions and the population standard deviation is known to be 2.2. If a sample of 707 was used for the study, construct the 90% confidence interval for the true mean number of reproductions per hour for the bacteria. Round your answers to one decimal place.
The confidence interval for the true mean number of reproductions per hour is (7.5,7.7)
Given mean of 7.6 , standard deviation of 2.2, n=707 and 90% confidence level.
We have to find the confidence interval for the true mean number of reproductions per hour for the bacteria.
α=0.90
μ=7.6
σ=2.2
m=707
α/2=0.45
We have to calculate z value for the p value of 0.45 which is z=1.64.
Margin of error=z*μ/[tex]\sqrt{n}[/tex]
=1.64*2.2/[tex]\sqrt{707}[/tex]
=0.13
Lower level=mean -m
=7.6-0.13
=7.47
after rounding upto 1 decimal
=7.5
Upper level= mean +m
=7.6+0.13
=7.73
after rounding upto 1 decimal
=7.7
Hence the confidence interval is (7.5,7.7) for the true mean number of reproductions per hour.
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What z-score value separates the highest 70% of the scores in a normal distribution from the lowest 30%
-0.5244 will separates the highest 70% of the scores in a normal distribution from the lowest 30%
Normal Distribution is bell shaped and symmetrical in nature.
We use standard normal to find probabilities of normal distribution.
Fig 1 represents Graph of standard normal
and Fig 2 is % points Table for standard normal distribution.
From % points Table the value separates the highest 70% of the scores in a normal distribution from the lowest 30% is 0.5244 since 30% lies left side from 0 it will be negative
⇒ value separates the highest 70% of the scores in a normal distribution from the lowest 30% is -0.5244
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For the following exercises, solve the inequality and express the solution using interval notation.
71. |3x − 2 | < 7
Answer:
In interval notation, the solution of |3 x-2|<7 is [tex]$-\frac{5}{3} < x < 3$[/tex] or [tex]$\left\{-\frac{5}{3}, 3\right\}$[/tex].
Step-by-step explanation:
The given absolute value function is |3 x-2|<7.
It is required to solve the inequality and express the solution using interval notation. -B<x-A<B and solving them separately for x
Step 1 of 3
Given absolute value equation is |3 x-2|<7.
It can be written as -7<3 x-2<7.
To solve for the equality, 3x-2=7 and
[tex]$$3 x-2=-7$$[/tex]
First, solve the equation 3x-2=7, then add 2 on both sides.
[tex]$$\begin{aligned}&3 x=7+2 \\&3 x=9\end{aligned}$$[/tex]
Step 2 of 3
Simplify 3x=9 further, by dividing each side with 3 .
[tex]$$\begin{aligned}&\frac{3 x}{3}=\frac{9}{3} \\&x=3\end{aligned}$$[/tex]
Step 3 of 3
Similarly, 3x-2=-7
From the above term 3x-2=-7,
Add 2 on each side.
[tex]$$\begin{aligned}&3 x=-7+2 \\&3 x=-5\end{aligned}$$[/tex]
Simplify $3 x=-5$ further, by dividing each side with 3 .
[tex]$$\begin{aligned}&\frac{3 x}{3}=-\frac{5}{3} \\&x=-\frac{5}{3}\end{aligned}$$[/tex]
Therefore, the solution is [tex]$-\frac{5}{3} < x < 3$[/tex] or [tex]$\left\{-\frac{5}{3}, 3\right\}$[/tex]
inverse of y = 2x squared
The inverse of the given function is y = [tex]\rm \sqrt {x/2}[/tex].
What is a Function ?A function is a mathematical statement used to relate a dependent and an independent variable.
The function given is
y = 2x²
To find the Inverse of a function ,
The x and y are interchanged and the function is again written in terms of x
Here
x = 2y²
y² = x/2
y = [tex]\rm \sqrt {x/2}[/tex]
Therefore the inverse of the given function is y = [tex]\rm \sqrt {x/2}[/tex].
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Find the probability of picking 4 consonant and 1 vowels when 5 letters are picked (without replacement) from a set of alphabet tiles
The required probability is 0.45
We have total 26 letters in english, of which 21 are consonants and 5 are vowels.
According to the question, we have to select 5 of them of which 4 will be consonants and 1 will be vowel.
Suppose we want to have the vowel in the first selection, so the probability of picking a vowel is equal to the quotient between the number of vowels and the number of total number of letters.
So the probability is 5/26
Now, a letter has been selected, so in the set, we have 25 letters left.
In the next 4 selections, we must select consonants.
In the second selection the probability is 21/25
In the third selection the probability is 20/24
In the fourth selection the probability is 19/23
In the last selection the probability is 18/22
So, the probability is (5/26)×(21/25)×(20/24)×(19/23)×(18/22)
Now, remember that we take that the vowel must be in the first place, but it can be in any five places, so if we add the permutations of the vowel letter we have,
P = 5×(5/26)×(21/25)×(20/24)×(19/23)×(18/22) = 0.45
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On a coordinate plane, quadrilateral Q R S T has points (0, 2), (negative 4, 0), (0, negative 3), and (4, 0).
The rule for the dilation of quadrilateral QRST to the image Q'R'S'T' is DO,0.5(x, y) → (0.5x, 0.5y).
What are the coordinates of Q', if Q(0, 2)?
(, )
By applying the definitions of rigid transformation ((x, y) → (0.5 · x, 0.5 · y)) and dilation, we conclude that the coordinates of Q'(x, y) are (0.1).
How to apply rigid transformations on a point
Herein we must apply a rigid transformation into a given point to determine an image. Rigid transformations are transformations applied on a geometric locus such that Euclidean distance is conserved. Dilations are a kind of rigid transformations such that:
(x, y) → (k · x, k · y), for k > 0
If we know that Q(x, y) = (0, 2) and k = 0.5, then the coordinates of Q' are:
Q'(x, y) = (0.5 · 0, 0.5 · 2)
Q'(x, y) = (0, 1)
By applying the definitions of rigid transformation ((x, y) → (0.5 · x, 0.5 · y)) and dilation, we conclude that the coordinates of Q'(x, y) are (0.1).
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Answer: Q' = (0,1)
Step-by-step explanation: just did it on edge
Members of a baseball team raised $1780.50 to go to a tournament. They rented a
bus for $1151.50 and budgeted $37 per player for meals. Determine the number of
players the team can bring to the tournament.
Answer: 17 players
Step-by-step explanation: 1780.50-1151.50=629, 629/37 = 17
The number of players the team can bring to the tournament is 17.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
As per the given,
Budget = $1780.50
Fixed cost (bus rent) = $1151.50
Variable cost = $37 per player.
For n number of players.
Total cost = 1151.50 + 37n
Total cost ≤ total budget
1151.50 + 37n ≤ $1780.50
37n ≤ 629
n ≤ 17
Hence "The number of players the team can bring to the tournament is 17".
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Theo is using this spinner to predict the favorite movie genre of randomly chosen students in his school.
A spinner with 5 sections labeled action, drama, sci-fi, horror, comedy.
If Theo spins the spinner 60 times, how many times should he expect it to land on “Action”?
Theo should expect the spinner to land on "Action" 12 times.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
Given: A spinner with 5 sections labeled action, drama, sci-fi, horror, and comedy.
Theo spins the spinner 60 times.
We need to find the number of times, out of 60, the spinner lands on "Action".
Here, a total number of outcomes= 5
A number of favorable outcomes = 1
So, the probability that the spinner lands on "Action" = 1/5
Theo spins the spinner 60 times.
So, the number of times the spinner lands on "Action"
= 1/5 x 60 = 12
Hence, Theo should expect the spinner to land on "Action" 12 times.
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INTEGERS A frog starts at 0 on a number line. It jumps 100 units to the right then jumps 200 units to the left. It then jumps 199 units to the right followed by 198 units to the left, and then 197 units to the right followed by 196 units to the left. The frog continues to move in alternate directions. Each movement is 1 unit less than the previous movement.
Where on the number line is the frog after 10 moves?
On the number line after 10 moves frog is at the integer -96.
Given that, a frog starts at 0 on a number line.
It jumps 100 units to the right then jumps 200 units to the left=+100-200=-100 (2 moves).
It then jumps 199 units to the right followed by 198 units to the left =-100+199-198=-99 (2 moves).
It then jumps 197 units to the right followed by 196 units to the left =-99+197-196=-98 (2 moves).
It then jumps 195 units to the right followed by 194 units to the left =-98+195-194=-97 (2 moves).
It then jumps 193 units to the right followed by 192 units to the left =-97+193-192=-96 (2 moves).
Hence, on the number line after 10 moves frog is at the integer -96.
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Triangle H L I is shown. Line segment J K is drawn near point L to create triangle J L K.
If △HLI ~ △JLK by the SSS similarity theorem, then StartFraction H L Over J L EndFraction = StartFraction I L Over K L EndFraction is also equal to which ratio?
StartFraction H I Over J K EndFraction
StartFraction H J Over J L EndFraction
StartFraction I K Over K L EndFraction
StartFraction J K Over H I EndFraction
The correct option is to show that the ratios HL/JL = IL/KL = HI/JK are equivalent. Option A is correct.
Similarity theorem of trianglesFor two triangles to be similar, the ratio of the measure of similar sides of the triangle must be equal to a constant known as a scale factor.
From the given figures, the expression that can be used to prove that the triangles are similar is as shown;
HL/JL = IL/KL = HI/JK
Hence the correct option is to show that the ratios HL/JL = IL/KL = HI/JK are equivalent
Learn more on similar triangles here; https://brainly.com/question/11920446
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I can Confirm A is correct
Step-by-step explanation: