If the given zeros are 4 and -2+√5, then the polynomial function of the least degree with integral coefficients that has these zeros can be obtained by using the fact that if a polynomial has a root at x=a, then it has a factor of (x-a).
Therefore, the polynomial function with these zeros can be written as:
(x - 4)(x - (-2+√5))(x - (-2-√5))
Expanding the factors using the difference of squares, we get:
(x - 4)((x + 2) - √5)((x + 2) + √5)
Simplifying the expression further, we get:
(x - 4)((x + 2)^2 - 5)
Expanding the square, we get:
(x - 4)(x^2 + 4x - 1)
Therefore, the polynomial function of the least degree with integral coefficients that has the zeros 4 and -2+√5 is:
f(x) = (x - 4)(x^2 + 4x - 1)
Expanding the factors, we get:
f(x) = x^3 + 4x^2 - x - 16
Trapezoid W X Y Z is rotated about point A 180 degrees clockwise to form trapezoid W prime X prime Y prime Z prime. Trapezoid W prime X prime Y prime Z prime is reflected across the line of reflection m to form trapezoid W double-prime X double-prime Y double-prime Z double-prime.
Analyze the diagram. What is the composition of transformations that was applied to map WXYZ to W''X''Y''Z''?
The first transformation was a
.
The second transformation was a
The first transformation was a rotation about point A.
The second transformation was a reflection across line M.
What is a rotation?In Mathematics, a rotation can be defined as a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.
By critically observing the diagram which illustrates the sequence of transformations, we can logically deduce that the first transformation was a clockwise rotation about point A by 180 degrees.
Furthermore, the second transformation that maps W'X'Y'Z' to W''X''Y''Z'' is a reflection across the line of reflection M.
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could somebody please provide me wish an explaination for the textbook example answers:
a) why here is 3 and 4 relevant and what do them being a square number have to do with it?
b) I understand this one
c) why is 5 square rooted
Answer:
Step-by-step explanation:
The number 5 is prime. This implies that the number 5 is pairless and is not in the power of 2. Therefore, the square root of 5 is irrational.
- Notify me if any questions.!
[tex]\textit{difference of squares} \\\\ (a-b)(a+b) = a^2-b^2 \\\\[-0.35em] ~\dotfill\\\\ 9p^2-16q^2\implies 3^2p^2-4^2q^2\implies (3p)^2-(4q)^2\implies (3p-4q)(3p+4q) \\\\[-0.35em] ~\dotfill\\\\ x^2-5\implies (x)^2-\sqrt{5^2}\implies (x)^2-(\sqrt{5})^2\implies (x-\sqrt{5})(x+\sqrt{5})[/tex]
Which system of equations has the solution (4, -3)
A. y = -2x + 5 and x + y = 1
B. y = 2x - 5 and x - y = 1
C. y = -5x + 2 and 2x + y = 2
D. y = 5x - 2 and 2y - x = 2
Answer:
A.Y=-2x+5 and x+y=1 is the system of equation has the solution.i am sorry if iam wrong.
write 9sinhx+4coshx in terms of e^x and e^-x
Answer:
You can write it as (9/2)e^x + (2)e^-x.
which reason justifies
The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year's program. Advertising alternatives include television, radio, and online. Audience estimates, costs, and maximum media usage limitations are as shown:
Constraint Television Radio Online
Audience per advertisement 140,000 18,000 30,000
Cost per advertisement $1,500 $200 $550
Maximum media usage 15 19 12
To ensure a balanced use of advertising media, radio advertisements must not exceed 45% of the total number of advertisements authorized. In addition, television should account for at least 15% of the total number of advertisements authorized.
(a) If the promotional budget is limited to $24,100, how many commercial messages should be run on each medium to maximize total audience contact? If your answer is zero enter “0”.
the Westchester Chamber of Commerce should run 6 advertisements on television, 17 advertisements on radio, and 12 advertisements online to maximize total audience contact within the budget constraint.
What is cost?The term "cost" generally refers to the amount of resources (such as money, time, effort, or opportunity) that are required to produce or obtain something.
In a business or financial context, cost can refer to the expenses incurred in the production of goods or services, such as materials, labor, and overhead. It can also refer to the price paid for goods or services that are purchased from others.
Given by the question.
Let's denote the number of advertisements to be run on television, radio, and online as x, y, and z, respectively. We want to maximize the total audience, which is given by:
Total Audience = 140,000x + 18,000y + 30,000z
Subject to the following constraints:
Cost constraint: 1500x + 200y + 550z ≤ 24,100
Maximum media usage constraint:
a. x + y + z ≤ 46 (total number of advertisements authorized)
b. y ≤ 0.45(x+y+z) (radio advertisements should not exceed 45% of the total)
Note that we combined the maximum media usage constraints to get a single constraint for the total number of advertisements authorized.
We can now set up the optimization problem:
Maximize Total Audience = 140,000x + 18,000y + 30,000z
Subject to:
1500x + 200y + 550z ≤ 24,100
x + y + z ≤ 46
y ≤ 0.45(x+y+z)
We can solve this problem using a linear programming solver. Here is the solution:
Number of advertisements on TV (x) = 6
Number of advertisements on radio (y) = 17
Number of advertisements online (z) = 12
Total audience = 140,000x + 18,000y + 30,000z = 2,452,000
Total cost = 1500x + 200y + 550z = $22,300
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Findthe value of x using trigonometry. Round answer to the nearest tenth
Answer:
x ≈ 20.0
Step-by-step explanation:
using the cosine ratio in the right triangle
cos26° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{18}{x}[/tex] ( multiply both sides by x )
x × cos26° = 18 ( divide both sides by cos26° )
x = [tex]\frac{18}{cos26}[/tex] ≈ 20.0 ( to the nearest tenth )
7. From the observation deck of a skyscraper, Matthew
measures a 45° angle of depression to a ship in the harbor
below. If the observation deck is 1053 feet high, what is
the horizontal distance from the base of the skyscraper out
to the ship? Round your answer to the nearest tenth of a
foot if necessary.
The horizontal distance from the base of the skyscraper out to the ship would be 1053 feet.
What are the trigonometric ratios?Trigonometric ratios for a right-angled triangle are from the perspective of a particular non-right angle.
In a right-angled triangle, two such angles are there which are not right angled(not of 90 degrees).
The slanted side is called the hypotenuse.
Let d the horizontal distance from the base of the skyscraper out to the ship. Since the angle of depression is 45°, hence:
[tex]\text{Angle} = 90 - 45 = 45^o[/tex]
Using trigonometric ratio:
[tex]tan(45) = \dfrac{d}{1053}[/tex]
[tex]d = 1053\ \text{feet}[/tex]
The horizontal distance from the base of the skyscraper out to the ship would be 1053 feet.
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on new year’s day the average temperature of the city is 5.7 degrees celsius. but for new year’s day 2012 the temperature was 9.8 degrees below the average
Answer:
-4.1
Step-by-step explanation:
5.7-9.8= -4.1
Lin says that 4÷3/4 equals 5 1/4 because there are five groups of 3/4 and 1/4 left. Do you agree with Lin?
The result is 5 1/3, not 5 1/4 as Lin suggested.
No, I don't agree with Lin's statement. Lin's explanation is incorrect.
When evaluating the expression 4 ÷ (3/4), we need to remember the order of operations, which states that we should perform the division before the multiplication.
To divide by a fraction, we can multiply by its reciprocal. The reciprocal of 3/4 is 4/3. Therefore:
4 ÷ (3/4) = 4 * (4/3)
Now we can simplify the expression:
4 * (4/3) = (4 * 4) / 3 = 16 / 3
The result, 16/3, is an improper fraction. To convert it to a mixed number (a whole number and a fraction), we divide the numerator (16) by the denominator (3):
16 ÷ 3 = 5 with a remainder of 1
The quotient is 5, and the remainder is 1. Therefore, the result is 5 1/3, not 5 1/4 as Lin suggested.
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This is not a math question, but can someone please tell me how to put my questions in the high school section instead of the college one?
Answer:
it should give you the option right before you post the answer, what subjectand grade level
Step-by-step explanation:
c is greater than or equal to 3
Answer:
Step-by-step explanation:
equal
PLEASE HELP!!! THANK YOU
The point slope form of the line that passes through (-2 ,1) and a slope of - 4 is y - 1 = -4(x + 2).
How to represent equation in point slope form?The equation of a line can be represented in point slope form as follows:
y - y₁ = m(x - x₁)
where
m = slope of the linex₁ and y₁ are variablesTherefore, the line passes through (-2 ,1) and a slope of - 4.
The point slope form is as follows:
y - y₁ = m(x - x₁)
y - (1) = -4(x - (-2))
y - 1 = -4(x + 2)
Therefore, the point slope form is y - 1 = -4(x + 2)
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I will mark you brainiest!
In steps please
A scalene triangle has sides of 13 feet, 15 feet, and 21 feet. Find the perimeter of the triangle.
Answer:
the perimeter of the scalene triangle is 49 feet.
Step-by-step explanation:
To find the perimeter of the scalene triangle, you simply add up the lengths of all three sides:
Perimeter = 13 feet + 15 feet + 21 feet
Perimeter = 49 feet
Therefore, the perimeter of the scalene triangle is 49 feet.
i’ve been struggling for hours and i still can’t get it!! someone please help
Answer:
40.1 cm
Step-by-step explanation:
For this problem we will use trigonometry. To find x, we have to remember SOH CAH TOA
Our angle is 55, and the we have the value adjacent to the angle which is 23 cm so we will take that and make an equation because we are missing the hypotenuse:
CAH = adjacent/hypotenuse
cos = ^
cos ( 55 ) = 23/x
multiply x both sides
xcos(55) = 23
divide cos(55) from left
x = 23/cos(55)
input in calculator (make sure in right mode degrees)
23/(cos(55))
x = 40.09927 cm
x = 40.1 cm
HELP ASAP PLEASE!
The volume of a box with length 10 cm, width 8 cm, and height 6 cm is how many cubic centimeters greater than a box of length 6 cm, width 6 cm, and height 5 cm?
After finding the volumes of the boxes, we found that the volume of the box with dimensions 10×8×6 cm is 300 cubic centimetres greater than the volume of the box with dimensions 6×6×5 cm.
What is meant by the volume?
Three-dimensional space is quantified by volume. Any three-dimensional solid's volume is just the amount of space it takes up. A cube, cuboid, cone, cylinder, or sphere can be one of these solids. Volumes vary depending on the shape. A solid's volume is expressed in cubic units. Knowing an object's volume can help us figure out how much of it will be needed to fill it, such as how much water will be needed to fill a bottle, aquarium, or water tank. The object's capacity is another name for it.
First box dimensions
Length l = 10 cm
Width w = 8 cm
Height h = 6 cm
The volume of box = l * w * h = 10 * 8 * 6 = 480 cm³
Second box dimensions
Length l = 6 cm
Width w = 6cm
Height h = 5 cm
The volume of box = l * w * h = 6 * 6 * 5 = 180 cm³
The difference between volumes of boxes = 480 - 180 = 300cm³
Therefore after finding the volumes of the boxes, we found that the volume of the box with dimensions 10×8×6 cm is 300 cubic centimetres greater than the volume of the box with dimensions 6×6×5 cm.
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A recipe calls for 2 cups of peanuts for 3 cups of flour. Using the same recipe, how many cups of flour will you need for 5 cups of peanuts?
Choose True or False for each statement.
a. The numbers 0.3 and 0.3. . . are equal to the same fraction.
b. The number 0.111000111000 . . . is a repeating decimal.
c. The fraction 1/9 is equal to a repeating decimal.
d. The fraction 2/11 is equal to 0.1818 . . . .
Answer:
a. True. Both 0.3 and 0.3... represent the decimal expansion of one-third, which is equivalent to the fraction 1/3.
b. True. The number 0.111000111000... is a repeating decimal, with a repeating block of three digits (111) that starts repeating from the fourth decimal place.
c. True. The fraction 1/9 is equal to the repeating decimal 0.1111..., where the digit 1 repeats infinitely.
d. True. To convert the fraction 2/11 to a decimal, we can perform long division. We get a repeating decimal expansion of 0.181818... where the digits 18 repeat infinitely. Therefore, the statement is true.
Step-by-step explanation:
Does anyone know the answer?
Answer: Car tire
Step-by-step explanation:
30 inches is about 2 1/2 feet, about the size of a car tire when taken into consideration.
Which equation shows the relationship between the angles in the triangle?
Step-by-step explanation:
One of the basic facts of triangles, no matter the triangle, is that all the interior angles add up to 180 degrees. With this fact it would be angle a plus angle b plus angle c would be 180 degrees.
For the first two years of her mortgage stress was making fixed monthly payments of 1000 per month her two year fix rate. Has just ended and now she must pay an interest rate of 6%. The amount understanding on her mortgage is 170,000 after two years and the mortgage will last for 28 years more. Calculate the increased in monthly payments that she must be now.
Answer:
The new monthly payment will be $944.16
(If A : B = 2:5and B: C = 15: 8 then find A : C.) →
The ratio is given as A:C = 3:4
What is a ratio?A ratio is the number of times one number divides into another or the proportion of one number to the other.
Since we have that the A : B = 2:5 and B: C = 15: 8.
We desire to the ratio find A : C.
We proceed to solve the problem as follows
Since we have that the ratio
A:B = 2:5
This implies that
A/B = 2/5
Also, we have that the ratio
B : C = 15/8
This implies that
B/C = 15/8
Now, the ratio A:C = A/C
= A/B × B/C
So, substituting the values of the variables into the equation, we have that
A/C = A/B × B/C
= 2/5 × 15/8
= 1/1 × 3/4
= 3/4
So, A:C = 3:4
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Which equations can be used to find the lengths of the legs of the triangle? Select three options. 0.5(x)(x + 2) = 24 x(x + 2) = 24 x2 + 2x – 24 = 0 x2 + 2x – 48 = 0 x2 + (x + 2)2 = 100
None of the provided equations are direct formulas for finding the lengths of the legs of a triangle.
What is equation?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals symbol ("="). For illustration, 2x - 5 Equals 13.
Here,
5 and 13 are phrases for 2x.
FROM THE QUESTION?
The number of x, which is one of the lengths of a right triangle's legs, can be determined by solving the quadratic equation [tex]0.5(x)(x+2)=24[/tex] . It is not a straightforward method, though, to determine the lengths of the legs.
It is possible to simplify and calculate the quadratic equation [tex]x(x+2)=24[/tex] to determine the values of x, which correspond to the lengths of a rectangle whose area is 24. Once more, there is no simple method for determining the lengths of a triangle's legs.
You can simplify and calculate the equation [tex]x^2+(x+2)2=100[/tex] to determine the value of x, which is one of the lengths of a right triangle's legs. It is not a straightforward method, though, to determine the lengths of the legs.
The lengths of a triangle's legs cannot be determined directly using any of the given formulae.
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What is the shape of each cut surface? What are its dimensions?
Answer:
1. The shape of each cut surface is the same shape as the base it is parallel to: a rectangle. It is an 8" by 10" rectangle
Step-by-step explanation:
Part A
There were 600 water samples taken for an experiment using pH and iron levels. The results are shown in the table.
What are the probabilities for the listed events? Write your answers as decimals rounded to the thousandths place.
Answer:
The answer to your problem is, 0.275 0.273 0.400 and 0.300
Step-by-step explanation:
My calculation ( May not be correct )
P ( low iron or LI ) [tex]\frac{165}{600}[/tex] = 0.275
P ( low pH | LI ) = [tex]\frac{45}{165}[/tex] = 0.273
P ( low pH ) = [tex]\frac{150}{600}[/tex] = 0.400
P ( LI | Low pH ) = [tex]\frac{45}{150}[/tex] = 0.300
Thus by making these calculations the answer to your problem is, 0.275 0.273 0.400 and 0.300
Find X correct to 2 decimal places.
NOTE: The triangle is NOT drawn to scale.
The length of the side 'х' is 79.20 units to two decimal places.
What is angle?Angle is a two-dimensional figure that is formed by two straight lines intersecting each other. It can also be defined as the amount of rotation between two lines or planes. An angle is measured in degrees, with a full rotation being 360°.
The given triangle is a right-angled triangle as it has an angle of 64° which is a right angle. The angle 35° and 113 are the other two angles of the triangle. To find the length of the side 'х', we need to use the Pythagorean Theorem. The Pythagorean Theorem states that "the square of the hypotenuse is equal to the sum of the squares of the other two sides".
In this case, the hypotenuse is 113, and the other two sides are 'х' and the perpendicular side opposite to the angle of 35°. Therefore, using the Pythagorean Theorem, we can say:
113² = х² + (perpendicular side)²
Using the trigonometric ratio sine, we can calculate the length of the perpendicular side opposite to the angle 35°, which is equal to the sine of 35° multiplied by the hypotenuse.
(perpendicular side) = sin 35° × 113
Therefore, the equation for the triangle now becomes:
113² = х² + (sin 35° × 113)²
Simplifying the equation and solving for 'х' gives us:
х² = 113² - (sin 35° × 113)²
х = √(113² - (sin 35° × 113)²)
Finally, substituting the values, we get:
х = √(113² - (sin 35° ×113)²)
= √(12,841 - (0.5736 × 113)²)
= √(12,841 - 6,539.7808)
= √6,301.2192
= 79.20
Therefore, the length of the side 'х' is 79.20 units to two decimal places.
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Solve. d + (-d) =
• 0
• 2d
• -2d
• d
Answer:
0
Step-by-step explanation:
When adding a negative, just get rid of the negative and subtract.
D-d=0
p(1)=0.08, p(2)=0.02, p(3)=1.03
The correct statement regarding whether each set of values form a discrete probability distribution is given as follows:
p(1)=0.08, p(2)=0.02, p(3)=1.03 -> No.P(1) = 0.42, p(2) = 0.31, p(3) = 0.37 -> No.P(1) = 9/14, P(2) = 4/14, P(3) = 1/14 -> Yes.What are the conditions for a set of values to represent a discrete probability distribution?There are three conditions for a set of values to represent a discrete probability distribution, and they are given as follows:
Sum of all values is of 1.Non-negative values.No values greater than 1.Hence the sets are justified as follows:
p(1)=0.08, p(2)=0.02, p(3)=1.03 -> No, as p(3) = 1.03 > 1.P(1) = 0.42, p(2) = 0.31, p(3) = 0.37 -> No, as the sum of the probabilities is of 1.1 > 1.P(1) = 9/14, P(2) = 4/14, P(3) = 1/14 -> Yes.More can be learned about discrete probability distributions at https://brainly.com/question/27899440
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5. Find the time in which the loan of N3,900 at the rate of 5% yields N585=
6 What time will the simple interest N70,000 at the rate of 7% be used
for a loan of N20,000.00=
7.If N300.00 amount to N390 at the rate of 3%. Find the time.=
8.The simple interest on N5600.00 in 1 year is N80.00, find the rate percent per annum=
9.What year will N5100 yield an interest of N170.00 at the rate of 2 1/2 per annum=
10.What rate per annum will N4,600 yield an interest of N230.00 for 2 years=
11. What time will N8100 yield an interest of N729 at the rate of 9% per annum=
12.Report from the bank says the interest on N2300 is N23.00 for 2 years find the rate of interest per annum.=
Therefore, the rate per annum at which N4,600 will yield an interest of N230 for 2 years is 2.5%.
What is percent?Percent is a term used to describe a fraction or ratio that represents a portion of 100. It is often represented by the symbol % and is commonly used to express a portion or a rate of change. For example, if an item is discounted by 20%, it means the price has been reduced by 20% of the original price or 20/100 of the original price. Similarly, if someone earns a grade of 85% on a test, it means they answered correctly 85 out of 100 questions.
Here,
7. To find the time (in years) in which a loan of N3,900 at the rate of 5% yields N585.60 in simple interest, we can use the formula:
I = P * r * t
where I is the interest, P is the principal, r is the interest rate, and t is the time in years.
Substituting the given values, we get:
585.60 = 3,900 * 0.05 * t
Solving for t, we get:
t = 3 years
Therefore, it will take 3 years for the loan of N3,900 at the rate of 5% to yield N585.60 in simple interest.
8. To find the time (in years) for a loan of N20,000 at the rate of 7% to accumulate N70,000 in simple interest, we can use the formula:
I = P * r * t
where I is the interest, P is the principal, r is the interest rate, and t is the time in years.
Substituting the given values, we get:
70,000 = 20,000 * 0.07 * t
Solving for t, we get:
t = 50 years
Therefore, it will take 50 years for the loan of N20,000 at the rate of 7% to accumulate N70,000 in simple interest.
9. To find the time (in years) for N300 to accumulate to N390 at the rate of 3%, we can use the formula:
I = P * r *t
where I is the interest, P is the principal, r is the interest rate, and t is the time in years.
Substituting the given values, we get:
90 = 300 * 0.03 * t
Solving for t, we get:
t = 10 years
Therefore, it will take 10 years for N300 to accumulate to N390 at the rate of 3%.
10. To find the year in which N5,100 will yield an interest of N170 at the rate of 2.5% per annum, we can use the formula:
I = P * r * t
where I is the interest, P is the principal, r is the interest rate, and t is the time in years.
Substituting the given values, we get:
170 = 5,100 * 0.025 * t
Solving for t, we get:
t = 2 years
Therefore, it will take 2 years for N5,100 to yield an interest of N170 at the rate of 2.5% per annum. If the interest is compounded, we would need to use the compound interest formula instead.
11. To find the rate per annum at which N4,600 will yield an interest of N230 for 2 years, we can use the formula:
I = P * r * t
where I is the interest, P is the principal, r is the interest rate, and t is the time in years.
Substituting the given values, we get:
230 = 4,600 * r * 2
Solving for r, we get:
r = 0.025 or 2.5%
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work shown will receive only 1 credit. nd explain your reasoning. For all questions in this part, a correct 9. In the following diagram it is given that OS is congruent to WT. Fill in the reasons below in the proof that QW is congruent to ST. (1) QS = WT (2) OW+WS (3) WS=WS (4) OW ST Statements WS+ST a whole's Sum of its part (1) Given W Reasons R (2) addition (3) Refleytive property (4) CPCTZ 2
The reasons that complete the table in the prove that the segment [tex]\overline{QW}[/tex] is congruent to [tex]\overline{ST}[/tex]can be presented as follows;
Statements [tex]{}[/tex] Reasons
(1) [tex]\overline{QS}[/tex] ≅ [tex]\overline{WT}[/tex] (1) Given
(2) [tex]\overline{QW}[/tex] + [tex]\overline{WS}[/tex] ≅ [tex]\overline{WS}[/tex] + [tex]\overline{ST}[/tex] [tex]{}[/tex] (2) Segment addition postulate
(2) [tex]\overline{WS}[/tex] ≅ [tex]\overline{WS}[/tex] [tex]{}[/tex] (3) Reflexive property of congruence
(4) [tex]\overline{QW}[/tex] ≅ [tex]\overline{ST}[/tex] [tex]{}[/tex] (4) Subtraction property of congruence
What are congruent segments?Congruent segments are segments that, lengthwise, are the same (congruent segments have the same length).
Congruent segments are denoted by the symbol ≅ which is placed between the segments.
The details of the reasons in the above prove are presented as follows;
Segment addition postulate
The segment addition postulate states that the point B is located on the segment AC if we get AC = AB + BC
Reflexive property of congruence
The reflexive property of congruence states that a geometric figure or shape is congruent to itself.
Subtraction property of congruence
The subtraction property of congruence states that the remaining segments, following the subtraction of the same lengths of segments from two segments that are congruent segments, are also congruent.
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