Matrix A = xd[tex]x^{-1}[/tex] is [tex]\left[\begin{array}{cc}4/\sqrt{17} &2/\sqrt{5} \\1/\sqrt{17} &1/\sqrt{5} \end{array}\right][/tex] [tex]\left[\begin{array}{cc}0 &0 \\0 &-2 \end{array}\right][/tex] [tex]\left[\begin{array}{cc}1/\sqrt{17} &-2/\sqrt{85} \\-1/\sqrt{17} &4/\sqrt{85} \end{array}\right][/tex] .
For the matrix A =
[ 2 -8 ]
[ 1 -4 ]
we need to find x and d such that A = xd[tex]x^{-1}[/tex].
First, we find the eigenvalues of A:
det(A - λI) = (2 - λ)(-4 - λ) - (-8)(1) = λ*λ + 2λ = λ(λ + 2) = 0
So, the eigenvalues are λ1 = 0 and λ2 = -2.
Next, we find the eigenvectors associated with each eigenvalue:
For λ1 = 0:
(A - λ1I)x = 0
[ 2 -8 ] [x1] [0]
[ 1 -4 ] [x2] = [0]
Solving for x gives x = [tex][4,1]^{T}[/tex].
For λ2 = -2:
(A - λ2I)x = 0
[ 4 -8 ] [x1] [0]
[ 1 -3 ] [x2] = [0]
Solving for x gives x = [tex][2,1]^{T}[/tex].
We normalize the eigenvectors to get x1 = [tex][4/\sqrt{17},1/\sqrt{17} ]^{T}[/tex] and x2 = [tex][2/\sqrt{5},1/\sqrt{5} ]^{T}[/tex] .
Now, we can find d:
d = [λ1 0; 0 λ2] = [0 0; 0 -2]
Finally, we can find [tex]x^{-1}[/tex]:
[tex]x^{-1}[/tex] = [tex]\left[\begin{array}{cc}4/\sqrt{17} &2/\sqrt{5} \\1/\sqrt{17} &1/\sqrt{5} \end{array}\right]^{-1}[/tex] = [tex]\left[\begin{array}{cc}1/\sqrt{17} &-2/\sqrt{85} \\-1/\sqrt{17} &4/\sqrt{85} \end{array}\right][/tex]
Therefore, we have:
A = xd[tex]x^{-1}[/tex] = [tex]\left[\begin{array}{cc}4/\sqrt{17} &2/\sqrt{5} \\1/\sqrt{17} &1/\sqrt{5} \end{array}\right][/tex] [tex]\left[\begin{array}{cc}0 &0 \\0 &-2 \end{array}\right][/tex] [tex]\left[\begin{array}{cc}1/\sqrt{17} &-2/\sqrt{85} \\-1/\sqrt{17} &4/\sqrt{85} \end{array}\right][/tex]
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What is the value of exponential 4?
The value of exponential 4 is 4^4, or 256. it means that 4 should be multiplied by itself 4 times.
In mathematics, an exponential is a number that is multiplied by itself a certain number of times. For example, when 4 is used as an exponential, it means that 4 should be multiplied by itself 4 times. This is written as 4^4, or 4 to the fourth power. This means that 4 is multiplied by itself 4 times, resulting in the value of 256.
Exponentials can be used to calculate the power of a number. For example, in the case of 4^4, 4 is the base number and 4 is the exponent. An exponent is the number of times a base number is multiplied by itself. In this case, the base number (4) is being multiplied by itself 4 times, resulting in a value of 256.
In addition, exponentials can be used to solve equations. For example, if we need to solve for x in the equation 4^x = 256, we can use the exponential 4 to determine the value of x. In this case, x = 4 because 4^4 = 256.
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A certain beverage company is suspected of underfilling its cans of soft drink. The company advertises that its cans contain, on average, 12 ounces of soda with standard deviation 0.4 ounces. For the questions that follow, suppose that the company is telling the truth. (a) Can you calculate the probability that a single randomly selected can contains 11.9 ounces or less? If so, do it. If not, explain why you cannot. (b) A quality control inspector measures the contents of an SRS of 50 cans of the company's soda and calculates the sample mean 7. Calculate the mean and standard deviation of the sampling distribution of x for samples of size n = 50. Interpret the standard deviation. (c) What is the shape of the distribution described in part (b)? Justify your answer. (d) The inspector in part (b) obtains a sample mean of x = 11.9 ounces. Calculate the probability that a random sample of 50 cans produces a sample mean amount of 11.9 ounces or less.
Previous question
a. We cannot calculate the probability, because we do not know the shape of the distribution.
b. The mean and standard deviation of the sampling distribution of x are 12 and 0.0566.
c. The shape of the distribution described in part b is symmetrical.
d. The probability that a random sample of 50 cans produces a sample mean amount of 11.9 ounces or less is 0.0386.
We do not know the shape of the distribution, so we cannot calculate the probability that a single randomly selected can contains 11.9 ounces or less. The question given have not told us that the distribution of individual cans was normal, and we cannot assume it is so; therefore, we cannot calculate its probability.
As given information the mean μx = 12.
And standard deviation σx = σ / √n = 0.4 / √50 = 0.566.
The shape of the distribution described in part b is symmetrical, because the two sides of the distribution are a mirror image of each other. Therefore, it is normal distribution.
Since the sample is large n = 50 and 50 > 30, so by CLT (Central Limit Theorem), the distribution of sample means is approximately normal N(12, 0.0566). So, P(x ≤ 11.9) = normalcdf (0, 11.9, 12, 0.0566) = 0.0386.
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What is the degree of the polynomial 3x² 5x¹ 7?
The degree of the polynomial 3x² 5x¹ 7 is 2.
This can be calculated by examining the highest exponent of the variable in the polynomial. Since the highest exponent is 2, the degree of the polynomial is 2.
Formula: Degree = Highest Exponent of the Variable
To calculate the degree of the polynomial 3x² 5x¹ 7, we first need to examine the highest exponent of the variable. The highest exponent is 2, therefore, the degree of the polynomial is 2.
3x² = 3x2 = 3x2 = Degree = 2
5x¹ = 5x1 = 5x1 = Degree = 1
7 = 7 = 7 = Degree = 0
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Marvin is about to play tag with his friend Paul in a circular field. Paul is away from Joshua, and the field has a diameter of 12m. How far is the distance between the two friends?
Distance between Marvin and Joshua is less or equal to 12 meter.
What is inequality?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Given,
Marvin and Joshua are about to play in a circular field.
Diameter of the field D = 12m
Let distance between two friends is x
Since, Diameter is the longest chord in a circle
Thus, x ≤ D
Distance between two friends ≤ 12 meter.
Hence, Marvin and Joshua are 12 meter or less far away from each other.
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Yesterday, between noon and midnight, the temperature dropped by 29.6°F. If the temperature was -8.6°F at midnight, what was it at noon?
Use the conversions given below to change 63 kg into stones.
Give your answer rounded to 1 dp.
1 kg = 2.2 pounds
1 stone = 14 pounds
Answer:
63kg x 2.2 = 138.6 pounds
138.6 pounds/14 = 9.9 stones
Step-by-step explanation:
Answer:
63kg×2.2=138.6 pounds
138.6 pounds/14=9.9
A rockinghorse has a weight limit of 60 pounds what is 95% of that
Answer: 57
Step-by-step explanation:
1. Multiply 95 and 60
2. You get 5700, then you divide by 100
3. 5700/100 = 57
What is the exponential of 0?
Answer:
The exponential form of 0 is 0.
In simple words, the exponents can said to be the powers of the base. For example, in 2³, the exponent will be 3. If a number is given without any power then its power is 0. The exponential form is simply the number with exponents.
(-6) to the power of -2
Answer: -1/36
Step-by-step explanation:
Answer: - 1/36
Step-by-step explanation: exponet rule a^-b=1/a^
1) Find the Z-score for the data point X given mean μ and
standard deviation o. Round to two decimal places as needed
x=72
μ=63
0=3
The z score when x=72 , μ=63 , 0=3 is z=3
Why is z-score important?Because they allow for a comparison between two scores that do not belong to the same normal distribution, z-scores are significant. They are also employed to determine the likelihood that a z-score will occur inside a normal distribution. A negative z-score indicates that the raw data is smaller than the mean.
What is the z-score formula used for?Because they allow for a comparison between two scores that do not belong to the same normal distribution, z-scores are significant. They are also employed to determine the likelihood that a z-score will occur inside a normal distribution. A negative z-score indicates that the raw data is smaller than the mean.
According to the equation
z=x-u/sigma
we get z=3
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1. During photosynthesis, what is the path or flow of energy among biotic and abiotic parts of an ecosystem?
During photosynthesis, what is the path or flow of energy among biotic and abiotic parts of an ecosystem?
Bonnie spent a total of $77.77 on new clothes at a clothing store. She Brought 1 pair of sandals, 2 T-Shirts for 11.49 each, 1 pair for $32 The Tax on the purchase was 4.40. How Much did Bonnie pay for the pair of sandals
The total cost of a pair of sandals is given by the equation A = $ 18.39
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the cost of pair of sandals be represented as A
Now , the equation will be
The total amount spent by Bonnie = $ 77.77
The cost of one shirt = $ 11.49
So , the cost of 2 shirts = 2 x 11.49 = $ 22.98
And , the cost of 1 pair = $ 32
The total tax on the purchase = $ 4.40
So , the cost of pair of sandals A = total amount spent by Bonnie - cost of 2 shirts - cost of 1 pair - total tax on the purchase
Substituting the values in the equation , we get
The cost of pair of sandals A = 77.77 - 22.98 - 32 - 4.40
On simplifying the equation , we get
The cost of pair of sandals A = $ 18.39
Hence , the total cost of sandals is $ 18.39
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Marhall and Vickie are alepeople who earned the ame amount thi week, although Vickie made 6 more ale than Marhall. Marhall earn a bae of $186 plu $15 per ale. Vickie earn a bae of $48 plu $18 per ale. How many ale did Marhall make thi week?
Marhall made 9 ales this week, earning a base of $186 plus $15 per ale. Vickie earned a base of $48 plus $18 per ale. Since both of them earned the same amount, we can set up the equations
Marhall made 9 ales this week.
Step by explanation
We can use an equation to solve this problem.
Let x = number of ales Marhall made
Marhall's Earnings = 186 + (15 x)
Vickie's Earnings = 48 + (18 x)
Since both of them earned the same amount, we can set up the equations and solve for x:
186 + (15 x) = 48 + (18 x)
15x = 138
x = 9
Therefore, Marhall made 9 ales this week.
Marhall made 9 ales this week, earning a base of $186 plus $15 per ale. Vickie earned a base of $48 plus $18 per ale.
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The graph shows the location of the entrance to a state park each unit on the graph represents 1 km Rodrigo uses the graph to locate a waterfall the waterfall is located 3 km to the left and 4 km down from the park entrance Rodrigo says we ordered pair for the waterfall is three, nine use the drop-down menus to explain Rodrigo
The location of the waterfall on the graph will be (3,1). Instead of going down down, Rodrigo goes 4 units upward direction.
What are the coordinates of a point?
Coordinates are a pair of integers (Cartesian coordinates), or sporadically a letter and a number, that identify a certain place on a grid, also referred to as a coordinate plane. The x-axis (horizontal) and y-axis are the two axes that make up a coordinate plane (vertical).
Given that the location of the entrance is at (6,5).
To reach the waterfall, you need to go 3 km to the left and 4 km down from the park entrance.
The x-coordinate decreases to the left side of a point and increases to the right side of a point.
The y-coordinate decreases to a downward point and increases upward a point.
The x-coordinate of the waterfall is 6 - 3 =3
The y-coordinate of the waterfall is 5 - 4 = 1.
The coordinate that represents the location of a point is (3,1).
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Which of the following is the solution of the equations: 2x+3y=3, 3x+2y=7
The solution of the equations: 2x+3y=3, 3x+2y=7 is x =0 and y =1.
Equation:
An equation is a mathematical formula containing two algebraic expressions on either side of an equal sign (=). It shows the equivalence relation between the formula written on the left and the formula written on the right. In any formula, L.H.S = R.H.S (left side = right side). We can solve equations to find the values of unknown variables that represent unknown quantities. If a statement doesn't have an equals sign, it means it's not an equation. considered to be an expression.
According to the question:
Given in the question:
2x+3y=3 --------------------------------------- (1)
3x+2y=7 ---------------------------------------- (2)
Multiplying Equation (1) by 3 and (2) by 2, we get:
6x + 9y = 9 --------------------------------- (3)
6x + 4y = 14 --------------------------------- (4)
Now,
Subtracting equation (4) from (3)
5y = 5
⇒ y = 1
Now, putting y = 1 in equation (1) we get:
2x + 3 × 1 = 3
⇒ 2x + 3 = 3
⇒ x = 0
Therefore, x =0 and y=1.
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WILL MARK BRAINLEST 40 POINTS Simplify three fifths times the quantity 1 plus the square root of 16 end quantity squared minus the quantity five minus two end quantity cubed.
−18
−12
36
42
The value of the expression is -5.84
How to find the value?The question is mathematically expressed as follows
The question reads: three fifths times the quantity 1 plus the square root of 16 end quantity squared minus the quantity five minus two end quantity cubed
[(3/5*1 + √16)]² - (5-2)³
Simplify the brackets first
This implies that
(3/5 + 4)² - (3)³
Simplify further to have
[(3+20)/5]² - 27
⇒(23/5) -27
Simplify to get
529/25 - 27
= 21.16 - 27
=-5.84
Therefore the expression gives -5.84
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A tenant’s monthly rent of $675 will be increased by 3% every year. To the nearest cent, what will be the tenant’s monthly rent in 3 years?
Answer:
$735.75
Step-by-step explanation:
The equation is:
A = P(1 + rt)
We know
P = $675
r = 3% = 0.03
t = 3 years
Let's solve
A = 675(1 + 0.03 x 3)
A = 675( 1.09)
A = $735.75
A current flows at 5 mph. A boat can travel 20 mi downstream in the same amount of time it can go 12 mi upstream. What is the speed of the boat in still water?
If a current flows at 5 mph. A boat can travel 20 mi downstream in the same amount of time it can go 12 mi upstream. The speed of the boat in still water is 20mph.
How to find the speed?Boat speed x mph
Current speed 5 mph
Against current x - 5 mph
With current x + 5 mph
Distance against current 12
Distance with current 20
Time = same equate the time against with time with current
t=d/r
12 /(x- 5)= 20 /(x+ 5)
12 ×(x+ 5 )= 20 ×(x- 5 )
12 x + 60= 20 x -100
12 x -20 x = -100 + -60
-8x = -160
x = -160/-8
x= 20 mph
Therefore the speed of the boat in still water is 20mph.
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What is the 15th digit of pi
Darren randomly selected fifty 10th grade students at his high school and asked how they normally get to school. The results are shown in the
table.
Mode of
Number of
Transportation Students
Bus
38
Car
Walk
Which inferences can be made from the results? Choose all correct statements.
Approximately 3% of the 10th graders at Darren's school take
car.
E
Approximately 18% of the 10th graders at Darren's school walk.
C. Approximately 18% of all the students at Darren's school walk.
D. Approximately 38% of the students at
Darren's school ride the bus.
Approximately 76% of the 10th
graders at Darren's school ride the bus.
B} Approximately 18% of the 10th graders at Darren's school walk.
E} Approximately 76% of the 10th graders at Darren's school ride the bus. Options B and E are correct options
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
Total students = 50
Number of students in bus = 38
Number of students in car = 3
Number of students in Walk = 9
Percentage student go to school by bus = 36 / 50 × 100% = 76%
Similarly,
Percentage students go to school by car = 6%
Percentage of students who go to school by walk = 18%
From the above calculation, the Correct options,
B} Approximately 18% of the 10th graders at Darren's school walk.
E} Approximately 76% of the 10th graders at Darren's school ride the bus.
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.
answer?????????????????
Which expressions have a product of 10? Options A. 5/14x14, B. 5/6 x14, C. 3/5 x 20, 2/3 x 15. Please help this assignment is due tomorrow
The expressions that have a product of 10 are:
Option B: 5/6 x 14 = (5/6) * 14 = (514)/6 = 70/6 = 10
Option C: 3/5 x 20 = (3/5) * 20 = (320)/5 = 60/5 = 12
Option A: 5/14 x 14 = (5/14) * 14 = (514)/14 = 70/14 = 5
Option D: 2/3 x 15 = (2/3) * 15 = (215)/3 = 30/3 = 10
So options B and D have a product of 10.
Why is 45 a prime number?
No, the given statement 45 is a prime number is false statement as 45 represents the composite number.
As given in the question,
Given number is equal to :
45
Prime numbers represents such numbers which is having only two factors one and the given number itself.
Prime numbers does not get exactly divided by any other integer.
Factors of 45 are equals to :
1, 3, 5, 9, 15, 45
It represents 45 has more than two factors.
And number 45 exactly get divided by 3, 5, 9, 15 .
So it is not a prime number rather it represents the composite number.
Therefore, the given statement 45 is a prime number is false statement as 45 is a composite number.
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John is driving around town. When he reaches the gas station, he notes that he has traveled 11 miles. He reaches home 2 hours later and notes that he has traveled 30 miles. If d represents the distance and t represents the time, in hours, John has traveled since the gas station, which of the following equations can be used to model this situation?
The correct equation for this given situation is,
⇒ d = 9.5t + 11
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
John is driving around town. When he reaches the gas station, he notes that he has traveled 11 miles.
And, He reaches home 2 hours later and notes that he has traveled 30 miles.
Now, Let d represents the distance and t represents the time, in hours
So we get;
Let the equation which model this situation,
⇒ d = a t + b
Where a and b are constant.
Let the gas station is the starting point.
So, at gas station t = 0 , d = 11
Hence,
⇒ 11 = 0 × a + b
⇒ b = 11
When he reaches home 2 hours later notes that he has traveled 30 miles.
And, with substituting with b = 20
⇒ 30 = 2 × a + 11
⇒2a = 30 - 11 = 19
⇒ a = 19/2 = 9.5
So, We get the equation,
⇒ d = 9.5t + 11
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Solve for X. M<1= (x+13)
M<2=39
M<3=(5x+4)
On solving the provided question, we can say that using properties of triangle, the value of x is 7.
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
By using the property of triangle,
The exterior angle of the triangle is the sum of opposite two angle of the triangle.
Hence,
64 + 8x = 18x - 6
10x = 70
x = 7
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Which doesn't belong and
why?
64
289 81 363 121
The number 363 does not belong to the set.
What is Square Root?Square root of a number is the value such that the value when multiplied to itself two times gives the original number.
It is denoted by the symbol √.
For example, square root of 16 is 4 since 4 × 4 = 16
The given numbers are 64, 289, 81, 363 and 121.
The numbers 64, 289, 81 and 121 is a perfect square of integers.
64 = 8²
289 = 17²
81 = 9²
121 = 11²
But 363 is not a perfect square of any integer.
Hence the number which is odd in the list is 363.
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A car is traveling at a rate of 40 mph. What is the speed in feet per min
Answer:3520.000
Step-by-step explanation:
ft/min =mph * 88.00000
ft/min =40 * 88.00000
ft/min =3520.000
What does 2x² mean?
A quadratic equation is a second-degree equation, meaning it contains at least one squared term.
what is quadratic equation ?A quadratic polynomial in a single variable is x ax2+bx+c=0, which is a quadratic equation. a 0. The fact that this polynomial is of second order guarantees that it has at least one solution according to the Fundamental Theorem of Algebra. Solutions could be straightforward or difficult. A quadratic equation is one that has four variables. This suggests that at least one word in it has to be squared. One of the common formulas for solving quadratic equations is "ax2 + bx + c = 0." where the undefined variable "X" is represented by the numerical coefficients or constants a, b, and c.
given
2x2-7x = 0.
As we already know, a quadratic equation is a second-degree equation, meaning it contains at least one squared term.
Regarding comparing the quadratic equation in standard form with the equation 2x27x=0
ax ²+bx+c=0:
We get a=2, b=7, and c=0.
The equation 2x27x=0 is therefore a quadratic equation.
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A study finds that out of every 400 babies born in the world, 20 have some kind of major birth defect. What is the simplest way to assign random numbers to conduct a simulation based on this statistic?
Select the correct choice below and fill in the answer boxes to complete your choice.
Fill in the question mark for the answer you choose
A. Use 1 digit numbers 0-9, let 0- ? Represent babies born with birth defects and #?-? Represent babies born without a major defect
B. Use 1 digit numbers 0-9, let 0- ? Represent babies born with birth defects, #?-? Represent babies born without a major defect, and skip #?-9.
C. Use 2 digit numbers 00-99, let 00-?? represent babies born with birth defects and #??-?? Represent babies born without a major defect.
D. Use 2 digit numbers 00-99, let 00-?? represent babies born with birth defects, #??-?? Represent babies born without a major defect, and skip #??-99
This is equal to 0.04 plus 1.96 into root over 0.04 into 0.96 divided by 400 point. This is equal to 0.059, which is equal to 5.9 percent. Therefore, double 0 to 5.9 percent represent babies born with defect.
What is the Justification for the above?According to one research, 28 out of every 400 kids born in the globe suffer some form of serious birth problem. To execute a simulation based on this data, the easiest approach to assign random numbers is to use 00-06 (7%) to identify the newborns with birth abnormalities.
It is to be noted that:
The sum total of births is: 400
The sum of defective babies = 28
Hence, the fraction or ratio of this is:
28/400
= 7/100
= 7%.
The implication here is that that 07-99 (93%) will represent the babies without birth defects.
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Does anyone know how to find this out?? Thank you so much!
The solution set is (A) TV/RS = TQ/ RQ.
What is the similarity of the triangle?
If the measures of the corresponding sides of two triangles are proportional then the triangles are similar. Likewise if the measures of two sides in one triangle are proportional to the corresponding sides in another triangle and the including angles are congruent then the triangles are similar.
We have given,
Triangle QRS and triangle QTV are similar,
ΔQRS ≈ ΔQTV
If the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle inscribed by the two sides in both the triangle are equal, then two triangles are said to be similar.
so, TV/RS = TQ/ RQ
Therefore, The solution set is (A) TV/RS = TQ/ RQ.
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