The distance between the shortstop and the pitcher calculated as per the given data is 63.6.
Distance between two consecutive bases = 90 feet
Halfway distance between them will be = 45 feets
therefore, halfway distance between first base and second base = 45 feet
and that between second base and third base = 45 feet
So the distance between the shortstop and the pitcher using pythagoras theorem
= >SP² = PQ² + QS²
= 45² + 45²
=4050
SP = 63.6
Therefore , the required distance is 63.36feets.
The Pythagorean Theorem, often known as Pythagoras Theorem, is a crucial concept in mathematics that describes how the sides of a right-angled triangle relate to one another. Pythagorean triples are another name for the sides of the right triangle
In essence, the Pythagorean theorem is used to determine a triangle's angle and length of an unknown side. We can derive the base, perpendicular, and hypotenuse formulas using this theorem.
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Work out the volume of the prism. 6 cm 12 cm 2 cm
Answer:
V = 72 cm³
Step-by-step explanation:
the volume (V) of a prism is calculated as
V = Ah ( A is the area of the triangular face and h is its height )
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
here b = 12 and h = 6
A = [tex]\frac{1}{2}[/tex] × 12 × 6 = 6 × 6 = 36 cm² , then
V = 36 × 2 = 72 cm³
If f(x) + x^2[f(x)]^5 = 34 and f(1) = 2, find f '(1). F '(1) = Use implicit differentiation to find an equation of the tangent line to the curve at the given point. y sin 12x = x cos 2y, (pi/2, pi/4)
To find the derivative of f(x) at x = 1, we can use the formula for implicit differentiation:
d/dx[f(x) + x^2[f(x)]^5] = 0
Substituting the given values, we get:d/dx[f(1) + 1^2[f(1)]^5] = 0
d/dx[2 + 1[2]^5] = 0
Solving for the derivative, we get:d/dx[2 + 1[2]^5] = 0
d/dx[2 + 32] = 0
0 + 32 = 0
Therefore, the derivative of f(x) at x = 1 is 32.
To find the equation of the tangent line to the curve at the given point (pi/2, pi/4), we can use the formula for the slope of a tangent line:
m = f'(x) = d/dx[y sin 12x] / d/dx[x cos 2y]
Substituting the given values, we get:m = d/dx[pi/4 sin 12(pi/2)] / d/dx[pi/2 cos 2(pi/4)]
m = d/dx[pi/4 sin 6pi] / d/dx[pi/2 cos pi/2]
m = 0 / 0
Since the derivative of the numerator is 0 and the derivative of the denominator is 0, the slope of the tangent line is undefined. This means that the tangent line is vertical and parallel to the y-axis.
The equation of the tangent line at the given point is therefore of the form:
x = c
where c is the x-coordinate of the given point, which is pi/2. Therefore, the equation of the tangent line is:
x = pi/2
Note that this is just the equation of a vertical line with an x-intercept at pi/2.
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When archeologists excavate a site, they mark it off with a coordinate grid so that they can easily
identify where artefacts are found and keep a record of the site forever. At the West Kennet Long
Barrow in England, a grave site back to 3600 BCE was found. There are three chambers at the
coordinates (7,9), (17, 33) and (-36,41). It has been said that they form an isosceles triangle with
height twice the length of its base.
Determine whether the statement is true. Justify your answer. Hint: An isosceles triangle has at
least two sides of equal side lengths.
figure abcdef was reflected across the line y = –x to create figure a'b'c'd'e'f'. what are the coordinates of the pre-image of f'?
(C) F = (2, -4) are the coordinates of the pre-image of F'.
What are coordinates?A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.
So, the result of reflecting Figure ABCDEF across y = -x is A'B'C'D'E'F'.
The transformational rule is:
(x, y) ⇒ (-y, -x)
Which means:
(x, y) ⇒ (-y, -x) ⇒ (4, -2)
In contrast:
-y = 4
-x = -2
Solving for x and y as follows:
y = -4
x = 2
Therefore, (C) F = (2, -4) are the coordinates of the pre-image of F'.
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Complete question:
Figure ABCDEF was reflected across the line y = –x to create figure A'B'C'D'E'F'.
On a coordinate plane, a 6-sided figure has points A prime (negative 2, negative 2), B prime (negative 4, 2), C prime (negative 2, 6), D prime (4, 6), E prime (6, 2), and F prime (4, negative 2).
What are the coordinates of the pre-image of F'?
a. (–2, 4)
b. (4, 2)
c. (2, –4)
d. (–4, –2)
The perimeter is less than
or equal to 51 meters.
10 m
8m
8 m
10 m
Solve the inequality
Hamza wants to create a bumper sticker with his design. Bumper stickers usually have a height of 3 1/2 inches. What will the width of his sticker be?
The width of the bumper sticker is 6 1/4 inches .
What is the width of the bumper sticker?In order to determine the width of the bumper sticker, the first step is to determine the relationship between the height of the design and that of the bumper sticker.
The relationship can be determined by dividing the height of the bumper sticker by the height of the design.
Proportion of the heights = 3 1/2 ÷ 2
5/2 ÷ 2
= 5/2 x 1/2 = 5/4 = 1 1/4
Now, multiply the proportion of the heights by the width of the design :
Width of the design = 1 1/4 x 5
5/4 x 5/1 = 25/4 = 6 1/4 inches
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Answer: 6 1/4
Step-by-step explanation: stickers that can be custom screen printed. The most common or average size is probably the 3″ X 11.5″
What is the answer?
Please help
-------------------------------------------------------------------------------------------------------------
Answer: 105 frames
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{25 frames per second, starts at 0 seconds already played 190 frames}[/tex]
Find: [tex]\textsf{Frame count already played when time = -3.4}[/tex]
Solution: In order to find the number of frames that have already played when the time was equal to -3.4 seconds, we must first figure out long the delay is. We can do this by dividing 25 frames per second from 190 frames which gives us that 7.6 seconds passed before we started counting at 0.
Therefore, if we want to look at -3.4 seconds out of -7.6 seconds that means that 4.2 seconds passes after the initial playing to get to -3.4 seconds. Now we can just multiply 4.2 seconds by 25 frames per second which gives us that about 105 frames have played when the time was equal to -3.4
(16-24)-(57-77) divided by (-2)
The answer will be -6 when (16-24)-(57-77) divided by (-2).
What is division?
One of the basic mathematical operations is division, which splits a bigger number into smaller groups with the same number of components. For example, if 20 students need to be divided into groups of five for a sporting event, how many total groups will be created? Dealing with such challenges is made easier by the division operation. In this instance, divide 20 by 5. The result will be 20 x 5 = 4. There will be 4 groups total, each with 5 students. You can verify this number by multiplying 4 by 5 and getting the answer 20, which equals 20.
Here (16-24)-(57-77)/-2
= (-8)-(20)/-2
=12/-2
=-6
Hence the answer will be -6.
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Spin a spinner numbered 1-8 and you land on 8 twice in a row what is the probability?
The probability that you land on 8 twice is 1/64
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
We spin a spinner numbered 1-8 twice
The total sample space can be given by considering all the possible values
Hence the total number of spins are 8*8= 64 spins
The possibility that getting 8 twice is only once possible. As it will be only one pair in all the possible values.
Hence, The total probability is 1/64
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14% of americans like to only cook and 48% of americans like to only shop, while 85% enjoy either cooking or shopping. what is the probability that a randomly selected american enjoys both activities?
The probability that a randomly selected american enjoys both activities is 23 % .
Given :
14 % of americans like to only cook and 48 % of americans like to only shop, while 85 % enjoy either cooking or shopping .
14 % = 0.14
48 % = 0.48
overlapping is 85 % = 0.85
P ( A ) = 0.14
P ( B ) = 0.48
P ( A and B ) = 0.85
we know that,
P ( A or B ) = P ( A ) + P ( B ) - P ( A and B )
= 0.14 + 0.48 - 0.85
= 0.62 - 0.85
= -0.23
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Question 6 If z is a standard normal variable, find the probability. The probability that z is less than 1.13 a. 0.8708 b. 0.8907 c.0.1292 d.0.8485
If z is a standard normal variable, the probability that z is less than 1.13 is given by: A. 0.8708.
What is the standard normal distribution table?In Statistics, the standard normal distribution table is designed and developed to provide only the area to the left of a specified z-score.
Additionally, since z-score (z₁) and z-score (z₂) are generally symmetric about z = 0 and are negatives of one another, then, by symmetry, the area to the right of z-score (z₂) is always equal to the area to the left of z-score (z₁).
This ultimately implies that, the total areas under a standard normal distribution curve in two tails can be determined by calculating the area to the left of z-score (z₁) and multiplying the value by two (2).
From the z-score table, the area to the left of z-score (z₁ = 1.13) is the same as the probability that z is less than 1.13 and this is given by:
Area to the left of z-score (z₁ = 1.13) = 0.8708.
Probability, P(z ≤ 1.13) = 0.8708.
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Select all the coefficients in the simplified form of (4y + 5y2-6) - (5y + 27-2²).
A -1
B. 4
C. 5
D. 6
E. 33
The coefficient of x² in simplified form is 5
What is coefficient ?
A coefficient in mathematics is a multiplicative factor in a polynomial term, a series term, or an expression. It is typically a number, but it can also be any expression. They may also be referred to as parameters if the coefficients are variables in and of themselves.
a symbol or number that multiplies another symbol or number (used as a mathematical variable). The coefficient of x in the phrase 3x is 3, and it is a number that represents a quality (such as the metal's coefficient of expansion) of a substance or device.
(4y + 5y² - 6) - (5y + 27 - 2²)
4y + 5y² - 6 - 5y - 27 + 4
5y² - 1y - 29
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Which of the following quadratic equations has roots 3, 5? a)`x^2-15x+3=0` b)`x^2-8x+15=0` c)`x^2+3x+5=0` d)`x^2+8x-15=0`
The quadratic equation (B) x²-8x+15=0 has the required roots 3 and 5.
What is a quadratic equation?ax2 + bx + c = 0 is a quadratic equation or a second-order polynomial equation with a single variable.
The algebraic's theorem guarantees that it is a second-order polynomial equation, hence it must have at least one solution.
The answer might be straightforward or challenging.
x2 - 5x - 3x + 15 = 0 are the roots of the quadratic equation x2 - 8x + 15 = 0.
x(x-5)-3(x-5)
(x-3)(x-5)=0
x = 3, 5
So, the correct answer is x² - 8x + 15 = 0.
Therefore, the quadratic equation (B) x²-8x+15=0 has the required roots 3 and 5.
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in the simek and o'brien study, a novice golfer had to sink four consecutive putts before going to the next step. this exemplifies:
In the Simek and O'Brien study, progressive overload was used by requiring the novice golfer to sink four consecutive putts before moving on to the next step. Progressive Overload.
Progressive overload is the gradual increase of stress placed on the body during physical activity. By requiring the novice golfer to sink four consecutive putts before moving on to the next step, the study is increasing the difficulty of the task and placing additional stress on the body.
Progressive overload is an effective and essential technique for improving physical performance. It involves gradually increasing the intensity of the activity or exercise, which places additional stress on the body and forces it to adapt and become stronger. In the Simek and O'Brien study, progressive overload was used by requiring the novice golfer to sink four consecutive putts before moving on to the next step. This increased the difficulty of the task and allowed the golfer to gradually improve their performance. By gradually increasing the difficulty of the task, the study was able to effectively use progressive overload to improve the golfer's performance.
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Solve the following system of equations using substitution
-3x+6y=12
2y=x+4
From the equation, 0 = 0. Therefore, the system of equation has infinite number of solutions.
How to solve system of equation?System of equation can be solved using different method such as elimination method, graphical method and substitution method.
Let's use substitution method to solve the system of equation as follows;
-3x + 6y = 12
2y = x + 4
x = 2y - 4
Hence, let's substitute the value of x in equation(i)
-3(2y - 4)+ 6y = 12
-6y + 12 + 6y = 12
-6y + 6y = 12 - 12
0 = 0
Therefore, the system of equations has infinite solutions.
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Priya invests a sum of money at an interest rate of 8% per year.
At the end of one year, the interest she receives is 1800 rupees.
Work out the value of Priya’s investment at the end of one year.
The value of Priya's investment at end of the year is Rs. 24300.
Simple Interest:The formula for simple interest is given by
Simple interest, I = PTR/100Where, P = Principal amount, T = Time period, and R = Rate of interest
And the formula for the Amount at end of the time period is given by
Amount, A = P + IHere we have
Priya invests a sum of money at an interest rate of 8% per annum
The interest that she gained after 1 year = 1800 Rs.
Let P be the principal amount i.e Priya's investment
Then calculate Simple interest on P at 8% for 1 year
As we know Simple interest = PTR/100
Interest on P = P(1)(8)/100 = 0.08P
From the given data, interest at end of the year = Rs. 1800
=> 0.08P = 1800
=> P = 1800/0.08
=> P = 22500
The amount that Priya invested = Rs. 22500
As we know Amount = Principal amount + interest
= Rs. 22500 + Rs. 1800
= Rs. 24300
Therefore,
The value of Priya's investment at end of the year is Rs. 24300.
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Which equation choice could represent the graph shown below?
By analizying the zeros on the graph, we conclude that the equation that could represent the graph is:
y = (x + 5)²*(x - 3)²
Which equation choice could represent the graph?On the graph, we have a polynomial.
Remember that the degree of the polynomial is related to the zeros of the polynomial. Here we can see that we have two double zeros, one at x = -5 and other at x = 3
We know that are double zeros because the curvature of the polynomial changes there.
Then the equation will be something like:
y = (x + 5)²*(x - 3)²
So that is the correct option, top right.
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The coordinates of the endpoints A B are given. A (7,6) and B (-9,-6). Point K is located on AB so that AK= 3/1. What is the x-coordinate of point K?
The x-coordinate of the point K that divides AB in 3:1 will be -5.
What is the section of the line?Let A (x₁, y₁) and B (x₂, y₂) be a line segment. Then the point P (x, y) divides the line segment in the ratio of m:n. Then we have
x = (mx₂ + nx₁) / (m + n)
y = (my₂ + ny₁) / (m + n)
The directions of the endpoints A and B are given. A (7,6) and B (- 9,- 6). Point K is situated on the Stomach muscle with the goal that AK: KB = 3/1.
Then the x-coordinate of the point K is given as,
x = (mx₂ + nx₁) / (m + n)
x = [3(-9) + 1(7)] / (3 + 1)
x = (- 27 + 7) / 4
x = - 20 / 4
x = - 5
The x-coordinate of the point K that divides AB in 3:1 will be -5.
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a bag contains different colored beads. the probability of drawing two black beads from the bag without replacement is 335, and the probability of drawing one black bead is 310. what is the probability of drawing a second black bead, given that the first bead is black?
The probability of drawing a second black bead, given that the first bead is black, is 1/3 or 0.33.
The probability of drawing two black beads from a bag without replacement is given as 335. The probability of drawing one black bead is also given as 310. To calculate the probability of drawing a second black bead, given that the first bead is black, we can use the formula P(B2|B1) = P(B1 and B2) / P(B1). The probability of drawing one black bead is P(B1) = 310. The probability of drawing the two black beads is P(B1 and B2) = 335. Therefore, P(B2|B1) = 335 / 310 = 1/3 = 0.33.
The probability of drawing two black beads from a bag without replacement is given as P(B1 and B2) = 335. This means that, out of all the possible combinations of beads in the bag, 335 of them contain two black beads. The probability of drawing one black bead is given as P(B1) = 310. This means that, out of all the possible combinations of beads in the bag, 310 of them contain one black bead. To calculate the probability of drawing a second black bead, given that the first bead is black, we can use the formula P(B2|B1) = P(B1 and B2) / P(B1). The probability of drawing one black bead is P(B1) = 310. The probability of drawing two black beads is P(B1 and B2) = 335. Therefore, P(B2|B1) = 335 / 310 = 1/3 = 0.33. This means that the probability of drawing a second black bead, given that the first bead is black, is 1/3 or 0.33.
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50 POINTS Giselle wants to buy the newest book in her favorite series. She has some money saved but does not want to
use all her savings on the book. Giselle’s grandma offers to pay some of the cost of the book for every weed she
pulls in her grandma’s garden.
The graph shows the cost to Giselle for the purchase of the book after pulling x weeds in her grandma’s garden.
Select True or False to describe each statement.
(2 points for each correct answer = 10 points)
SELECT True or False
Answer:
true false false true true
greatest comman factor comman factor x^2+5x
The greatest common factor of x² + 5x is x. The greatest common factor of x² + 5x is the largest number or expression that can divide evenly into both x² and 5x.
To find the greatest common factor, you can use the prime factorization method.
This involves expressing each term as the product of its prime factors. For example, x² can be written as x × x, and 5x can be written as 5 × x.
The prime factors of x² are x and x, and the prime factors of 5x are 5 and x. The greatest common factor is the product of the common prime factors, which in this case is just x. Therefore, the greatest common factor of x² + 5x is x. The greatest common factor of x² + 5x is the largest number or expression that can divide evenly into both x² and 5x.
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50 POINTS DUE TODAY, Giselle wants to buy the newest book in her favorite series. She has some money saved but does not want to use all her savings on the book. Giselle’s grandma offers to pay some of the cost of the book for every weed she pulls in her grandma’s garden. The graph shows the cost to Giselle for the purchase of the book after pulling x weeds in her grandma’s garden.
Select True or False to describe each statement.
Answer:
Step-by-step explanation:
Based on the graph, it appears that Giselle's grandma is offering to pay for a certain percentage of the cost of the book for every weed that Giselle pulls in her garden. The more weeds Giselle pulls, the more money her grandma will contribute, which will reduce the amount that Giselle has to pay for the book. This can be a good way for Giselle to save money on the book without using all of her savings.
1. True, the graph's beginning represents cost before she picks any weeds.
2. False, the graph shows that the cost for he goes into the negatives, showing that she is still able to earn more money from picking weeds.
3.True, from 0 weeds to 5 weeks picked you can see the price change from $18 to $17.
4. True, once she picks 90 weeds she earns the exact amount of money needed to buy the book.
5. False, she would need to pull 90 weeds in order to not spend her own money.
Please help me!!!!
Simplify the expression completely.
2 (2.5 -|-6|)
The value fo the numerical expression 2 × (2.5 -|-6|) will be negative 7.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expression is given below.
⇒ 2 × (2.5 -|-6|)
We know that the value inside the mode is always positive, then the expression is written as,
⇒ 2 × (2.5 -|-6|)
⇒ 2 × (2.5 - 6)
Simplify the expression, then the value of the expression is given as,
⇒ 2 × (2.5 - 6)
⇒ 2 × (- 3.5)
⇒ - 7
The value fo the numerical expression 2 × (2.5 -|-6|) will be negative 7.
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Find the Amount (A) (Principal Rs 50000 Time = 7 years interest = 3%.
Answer: Rs 60500
Step-by-step explanation:
Principal = Rs 50000 = p
Time = 7 years = t
Simple interest rate = 3% = r
Interest = p*t*r/100
using above formula,
50000*7*3/100=10500
So, final amount = principal + interest = 50000+10500 = Rs 60500
Which of the following Cannot be the sides of a triangle class 7? (a) 4,5,6
(b) 3,4,5
(c) 2,3,4
(d) 1,2,3
These can not be the sides of a Triangle.
What is a triangle and the response?
Triangles are a particular kind of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here.
Three-sided polygons include triangles. Three triangle angles added together equal 180 degrees.
Property of triangle
Sum of any two sides > third Side
4 , 5 , 6
4 + 5 > 6 , 4 + 6 > 5 , 5 + 6 > 4
3 , 4 , 5
3 + 4 > 5 , 3 + 5 > 4 , 4 + 5 > 3
2 , 3 , 4
2 + 3 > 4 , 2 + 4 > 3 , 3 + 4>2
1 , 2 , 3
1 + 2 = 3
Sum of 1 & 2 is not greater than 3
Hence, these can not be the sides of a Triangle.
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Expectation of Product of Random Variables Proof From the definition of the expected value, the expected value of the product of two random variables is E(X . Y) = EErr-r2 . P(X=Y =r2) where the sum is over all possible values of r1 and r2 that the variable X and Y can take on_ Using the definition above formally prove that if the events X = r1 and Y =r2 are independent (for any r1 and r2) , we have E(X . Y) = E(X) . E(Y). Now; if you have two random variables X and Y and Y=aI+c, show that if E[X2] # E[XJ? , then E(X . Y) # E(X) . E(Y). If you roll a die 6 times in a rOW what is the expected value of the product of the 6 outcomes?
Look to the photo and you will find the answers there ✔️
start from left to right
I need this answer i dont think this is the right anwser please help
Answer: 11 ft.
Step-by-step explanation:
Start by listing the variables that you have.
-Total Area=1,848; lot a 33ft wide, 42ft long; lot b xft wide, 42ft long.
- so, our equation looks like 1,848=(33x42)+(42x)
-multiply 33x42=1,386
-subtract 1,386 from both sides to get 462.
-equation should look like 462=42x
-divide by 42 to 11
PLEASE HELP ME 100 points if u do pls don't plagiarize the answer look at the image
Answer:
The given graph is not a direct variation.
Step-by-step explanation:
A direct variation occurs when the rate of change between any two points on a graph is always the same. In this sense, direct variation only occurs when a graph is linear. The given graph is parabolic; its equation is [tex]y = x^2[/tex]. Therefore, it does not exhibit direct variation, as the slope between consecutive points continually changes.
If you want to prove this claim, show that the slope changes between the given points: the rate of change from (2,4) to (3,9) is greater than the rate of change from (0,0) to (2,4).
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Which of the following is not a criterion for congruence of ∆ s a SAS B ASA C SSA D SSS?
(C) SSA is not a requirement for triangle congruence.
What is the congruence of triangles?
Two triangles are said to be congruent if all three corresponding sides and all three corresponding angles have the same size.
We can move, flip, twist, and turn these triangles to produce the same effect.
When relocated, they are parallel to one another.
Two triangles are congruent if they satisfy all five conditions for congruence.
Right angle-hypotenuse-side (RHS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and side-angle-side (SSS) are the four terms (RHS).
We know that SSA is not the criteria for the congruence of the triangles.
Therefore, (C) SSA is not a requirement for triangle congruence.
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