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7.2.1 Prove that AABC and ALMN are congruent.
7.2.2 Given that AFGH|||ALMN.
Calculate the value of x.
Answers
The triangles ΔABC and ΔLMN are congruent triangles by the SAS postulate. And the value of the variable 'x' will be 6 cm.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
In triangles ΔABC and ΔLMN, we have
AB = LM = 8 cm
∠B = ∠M = 90°
AC = LN = 12 cm
The triangles ΔABC and ΔLMN are congruent triangles by the SAS postulate.
The triangles ΔFGH and ΔLMN are similar triangles, then we have
x / 12 = 4 / 8
x / 12 = 1 / 2
x = 12 / 2
x = 6 cm
The triangles ΔABC and ΔLMN are congruent triangles by the SAS postulate. And the value of the variable 'x' will be 6 cm.
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Related Questions
Given that sec(θ) = 8 and tan(θ) < 0, find the following:
cos(θ) =
sin(θ) =
tan(θ) =
csc(θ) =
cot(θ) =
Rationalize denominators and tell which ones are negative.
Answers
The value cos(θ), sin(θ), tan(θ), csc(θ) and cot(θ) are 1/8, (-3√7)/8, -3√7, -(8√7)/21 and -√7/21 respectively
How to find the trigonometric ratio of the angle?Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.
Given that: sec(θ) = 8 and tan(θ) < 0. This implies:
cos (θ) = 1/8 and tan(θ) is negative. This means θ is quadrant 4
(Note: cos (θ) = 1/sec(θ) )
Using the given information, we can sketch the location of the angle θ in the quadrant (See the attached image).
Thus, we can calculate the value of side d using the Pythagoras theorem
d = √(8² - 1²) = √63 = 3√7
The side is -d = -3√7
Note: the side d is negative in the quadrant
Therefore:
cos(θ) = 1/sec(θ) = 1/8
sin(θ) = (-3√7)/8
tan(θ) = (-3√7)/1 = -3√7
csc(θ) = 8/(-3√7) = - (8√7)/21
cot(θ) = -1/(-3√7) = -√7/21
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Use a model in 2006, the average ticket price for a national football league game was $62. 38. Since then the cost has increased an average of $2. 54 per year. Write a linear equation to represent the cost c of an nfl ticket y years after 2006.
Answers
The linear equation to represent the cost of C of an NFL ticket y years after 2006 is y=2.54x+62.38.
Given that the average ticket price for a national football league game was $62. 38 and the cost has increased an average of $2. 54 per year.
we want to write a linear equation to represent the cost c of an nfl ticket y years after 2006.
A linear equation is an equation in which the greatest power of a variable is always 1. Also called the 1 degree equation. The equation can be written in the form y=mx+b.
Let us assume x represent the duration or stipulated years after the year 2006, y represent the amount of ticket that is sold and m represent the average increase in the price every year.
y=mx+c
y=2.54x+62.38
Hence, a linear equation to represent the cost c of an nfl ticket y years after 2006 is y=2.54x+62.38 when the average ticket price for a national football league game was $62. 38 and the cost has increased an average of $2. 54 per year.
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Himesh has blocks like the one shown below. 6 cm -8 cm- -7 cm- He wants to build a 40 cm high tower with such blocks. What is the LEAST number of blocks with which he can do this?
Answers
The least number of blocks with which he can do is 168 blocks.
What is the least Common Multiple (LCM)?
The Least Common Multiple (LCM) is a method for determining the smallest common multiple of two or more numbers. A common multiple is a number that is the product of two or more numbers.
Least number of blocks = LCM of 6cm, 7cm, and 8cm.
Multiples of 6 - 6,12,18,24,30,36,42,48,54,60
Multiples of 7 - 7,14,21,28,35,42,49,56,63,70
Multiples of 8 - 8,16,24,32,40,48,56,64,72,80
Common Multiples - 168
Least Common Multiple - 168
So the least number of blocks with which he can do is 168 blocks.
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Mr Pilgrim has a turkey farm. He has one male turkey for evey 17 female turkeys. if he has 289 females, how many male turkeys does he have? can the number of female turkeys be expressed using exponents? if so, how?
Answers
There are in total 17 Male Turkey in the farm
What is Division?
Division is one of the four basic operations of arithmetic, which are the methods through which numbers are joined to form new numbers. Addition, subtraction, and multiplication are the other operations.
Solution:
Here we will use the concept of basic division
Since, there is 1 male turkey for every 17 female turkey
Therefore, it can be said that
Total Male Turkeys for 289 Female Turkey = 289 / 17
Total Male Turkey = 17
Yes we can express the number of female turkey in exponent as [tex]17^{2}[/tex]
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HELPPP MATH 30 pointsss
Answers
Answer:
Step-by-step explanation:
h(x) = 3x - 5
h(-2) = 3*(-2) - 5 = -6 -5 = - 11
Find the angle measure (15x+12)°=(19x–24)°
Answers
The measurement of angle is 147°
Equation is combination of mathematical operation , numbers and variables.
Solving the equation involves finding the unknown variable by the given equation . The condition that two expression are equal is only satisfied by value of that unknown variable.
Solving given equation to find x ,
=> (15x+12)°=(19x–24)°
Bring x terms together and changing their signs,
=> 15x - 19x = -24 - 12
=> -4x = -36
=> x = -36 / -4
Cancelling the negative signs and dividing,
=> x = 9
Substituting the value of x
Angle = 15(9) + 12
=> 135 + 12
=> 147°
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Nathaniel's car used 2/3 of a gallon to travel 11 miles. How many miles can the car go
on one gallon of gas?
Answers
Nathaniel’s travel 16.5 miles with one gallon gas
Arithmetic generalization in which letters representing numbers are combined using arithmetic rules. Algebra is the branch of mathematics that aids in the representation of problems or situations using mathematical expressions.
Given that Nathaniel's car used 2/3 of a gallon to travel 11 miles
We have to find how many miles can the car goon one gallon of gas
2/3 gallons = 11 miles
1 gallon = ?
= (11x 1)/(2/3)
= 33/2
= 16.5 miles
Therefore Nathaniel travel 16.5 miles with one gallon gas
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3. Because it is so popular, a store owner increases the cost of a toy by $4.99. The new cost of the toy is $14.84. (a) Write an equation that represents the situation. Use c to represent the original cost of the toy. (b) Solve the equation using a related equation. Show your work. (c) What does the solution of the equation represent? HELP ASAPPP
Answers
The equation that represents the situation is c + 4.99 = 14.84, and the store owner increased the original price of the toy by adding $5.
What is the percent increase?
The formula for percentage increase is the ratio of the increased value to the original value multiplied by 100. It is expressed as a percentage. If the price of something rises, the percentage rises as well.
a) c + 4.99 = 14.84.
c = 14.84.- 4.99
c = 9.84
(b) 14.84 - 9.84 = 5
(c) Store owner increased the original price of the toy by adding $5.
hence, the equation that represents the situation is c + 4.99 = 14.84, and the store owner increased the original price of the toy by adding $5.
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(x+5) is a factor of R(x)=x^4+5x^3-16x^2-80x. What are the zeros of the function R(x)?
A) 2, 3, -4, -5 B) 0, 3, -3, -5
C) 0, 3, 4, -5 D) 0, 4, -4, -5 E) 0, 16, -16, -5
Answers
The zeros of the function R(x) will be 0 , 4 , -4 , -5.
The equation given to us is
[tex]x^{4}[/tex] + 5[tex]x^{3}[/tex] - 16[tex]x^{2}[/tex] - 80x = 0
Take x common
x( [tex]x^{3}[/tex] + 5[tex]x^{2}[/tex] - 16x - 80 ) = 0
from here we get one factor of x as 0.
Now
[tex]x^{3}[/tex] + 5[tex]x^{2}[/tex] - 16x - 80 = 0
It is given that x + 5) is a factor of this equation. so we will divide the equation by (x + 5).
After dividing it by (x + 5) we get [tex]x^{2}[/tex] - 16
Which can be written as [tex]x^{2}[/tex] - [tex]4^{2}[/tex] = (x + 4) (x - 4)
From here we get rest of the two roots of the equation.
Therefore four zeros of the function will be 0 , 4 , -4 , -5.
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Answer:
D) 0, 4, -4, -5
Step-by-step explanation:
Given polynomial:
[tex]R(x)=x^4+5x^3-16x^2-80x[/tex]
Given (x + 5) is a factor of R(x), use long division to find the other factor:
[tex]\large \begin{array}{r}x^3-16x\phantom{)}\\x+5{\overline{\smash{\big)}\,x^4+5x^3-16x^2-80x\phantom{)}}}\\{-~\phantom{(}\underline{(x^4+5x^3)\phantom{-b))))))))))))}}\\-16x^2-80x\phantom{)}\\-~\phantom{()}\underline{(-16x^2-80x)\phantom{}}\\0\phantom{)}\\\end{array}[/tex]
Therefore:
[tex]R(x)=(x^3-16x)(x+5)[/tex]
Factor out x from the first factor:
[tex]R(x)=x(x^2-16)(x+5)[/tex]
Apply the Difference of Two Square Formula: a²-b²=(a-b)(a+b)
[tex]\begin{aligned}\implies x^2-16&=x^2-4^2\\&=(x-4)(x+4)\end{aligned}[/tex]
Therefore:
[tex]R(x)=x(x-4)(x+4)(x+5)[/tex]
Zero Product Property
If a ⋅ b = 0 then either a = 0 or b = 0 (or both).
To find the zeros of the function, apply the zero-product property by setting each factor equal to zero and solving for x:
[tex]\implies x=0[/tex]
[tex]\implies x-4=0 \implies x=4[/tex]
[tex]\implies x+4=0 \implies x=-4[/tex]
[tex]\implies x+5=0 \implies x=-5[/tex]
Therefore, the zeros of the function R(x) are:
0, 4, -4, -54
Convert the mixed number to an improper fraction. -5-
5
=
Answers
Answer:
+1
Step-by-step explanation:
So, you just first multiply the denominator to whole then add to the numerator after that the denominator will remain the same and the numerator will be the remainder
if the rvr equipment is inoperative for an iap that requires a visibility of 2,400 rvr, how should the pilot expect the visibility requirement to be reported in lieu of the published rvr? a. as an rvr of 2,400 feet. b. as a ground visibility of 1/2 sm. c. as a slant range visibility of 2,400 feet.
Answers
The correct answer is the pilot should expect the visibility required to be reported in lieu of the published RVR as a ground visibility of 1/2SM.
Visibility is half of a statute mile (SM). Persuading visibility is described in statute miles and fractions. The visibility having 15+ is encrypted as 15SM. Lower visibilities which are half or less of the visibility are detailed in the remarks section. Low visibility procedures (LVP) refer to procedures related to an aerodrome for the cause of ensuring safe operations in the course of lower-than-standard value and low visibility take-offs.
Reduced visibility operations are operations that take place at an aerodrome during the visibility is lower than Runway Visual Range which is 2600 RVR and 1/2 statute mile sm down to and including 1200 RVR and 1/4 statute mile sm.
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Question 4(Multiple Choice Worth 6 points)
(03.02 MC)
How does the graph of g(x) = (x + 2)3 - 6 compare to the parent function of f(x) = x³?
Og(x) is shifted 2 units to the right and 6 units down.
Og(x) is shifted 6 units to the right and 2 units up.
g(x) is shifted 2 units to the left and 6 units down.
g(x) is shifted 6 units to the left and 2 units down.
Answers
The relationship of the graph g(x) = (x − 2)³ + 6 compare to the parent function of f(x) = x³ is that g(x) is shifted 2 units to the right and 6 units up.
What is translation of coordinates?Translations are a transformation technique that changes the position of an object from one point on the plane to another.
Given is a function, g(x) = (x − 2)³ + 6, we need to compare the graph of g(x) = (x + 2)³ - 6 to the parent function of f(x) = x³
The function compared to f(x) = x³, shows a translation of f(x) by 2 unit to the right along the horizontal and vertical translation of the function 6 units up
Hence, the relationship of the graph g(x) = (x − 2)³ + 6 compare to the parent function of f(x) = x³ is that g(x) is shifted 2 units to the right and 6 units up.
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fat content in 10 hotdogs is measured as: 25.2, 21.3, 22.8, 17, 29.8, 21, 25.5, 16, 20.9, 19.5. find a 95% prediction interval that bounds the fat content of the next hot dog.
Answers
Statistics with a 95% prediction interval that indicate how much fat the next hot dog will contain 21.83±2.917
Take into account the following sample of n = 10 randomly chosen hot dogs' fat content (in percentage):
A 95% CI for (interval estimate of) the population, given that these were chosen from a normal population distribution
x±[tex]t_{0.025,9} * s/\sqrt{n}[/tex]
= 21.83± 2.262 * 4.079/[tex]\sqrt{10}[/tex]
= 21.83±2.917
But let's say you want to know how much fat will be in a single of this kind of hot dog before you consume it. Just x 21.90 makes a point prediction, which is comparable to a point estimate. Unfortunately, the statistical prediction provides no details regarding accuracy or dependability.
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The time it takes to wash all the windows on a large building w(z) varies inversely with the number of workers assigned to the job x.
It takes 6 hours to complete the job when 4 workers are assigned to it.
Which equation can be used to find the time to complete the job when x workers are assigned to it?
a.)w(x) = 24/x
b.)w(x)= 1.5x
c.)w(x)=10/x
d.)w(x)=24
Answers
The equation that can be used to find the time to complete the job can be expressed as w (x) = 1.5x, so option B is correct.
What is the equation?A formula known as an equation uses the equals sign to denote the equality of two expressions.
Given:
The time taken to complete the work = 6 hrs,
The no of worker = 4,
The no of workers = The time taken by four workers / no of workers,
w (x) = 6 /4x
w (x) = 1.5x
Therefore, the equation that can be used to find the time to complete the job can be expressed as w (x) = 1.5x.
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What do you do for this question
Answers
Answer:
= 197.5 [tex]cm^{2}[/tex]
Step-by-step explanation:
1) first split the shape into two shapes (a rectangle and trapezium)
2. find the area of the rectangle
10 x 6 = 60 [tex]cm^{2}[/tex]
3. find the missing sides for the trapezium and substitute it into the formula for finding the area of trapezium
([tex]\frac{a+b}{2}[/tex])xh
a=10
b= 15
h = 11 (17-6=11)
( [tex]\frac{10+5}{2}[/tex])x 11
this gives you 137.5 [tex]cm^{2}[/tex]
4. add both the areas together
60 [tex]cm^{2}[/tex] + 137.5 [tex]cm^{2}[/tex] = 197.5 [tex]cm^{2}[/tex]
5 so your final answer is 197.5 [tex]cm^{2}[/tex]
5x+-3=-18 (pls help me)
Answers
Answer: x = 3
Step-by-step explanation:
5x+-3=-18
5x + -3 + 3 = -18 + 3 (add 3 to both sides)
5x = 15
5x/5 = 15/5
x = 3
Answer: x =3
Step-by-step explanation:
Please anyone I need and explanation and just h and c solving them and explaining how that it please.
Answers
Answer: h = 19, c = 132
Step-by-step explanation:
Oooh! This is a toughie!
Okay, first of all, there's a straight line on top. A straight line is 180 degrees.
This means we have to subtract 48 from 180.
180 - 48 = 132.
This means both a and b are 132.
F is equal to 151.
180 - 151 = e
e = 29
d = 29
g = 29
132 + 29 = 161
180 - 161 = 19
h = 19
19 + 29 = 48
180 - 48 = 132
c = 132
Sorry that this answer isn't so clear...
(BTW, it'd make me happy if you gave me the brainliest reward)
one of the people involved in the accident says that he was traveling 52 mph when he braked. how long in feet should his car's skid marks be?
Answers
Answer:
Step-by-step explanation:
The equation is V = √(20L).
Solve this equation for L and the result is L = V2/20
Since V = 57 mph, putting this value into the equation, L = (57)2/20 = 162.45 ft should be his skid marks
A bank machine uses pin numbers of 4 digits. The of odd pin numbers is:
Answers
Answer:15
Step-by-step explanation:hope this helps
Kayden invested $6,300 in an account in the year 2006, and the value has been growing exponentially at a constant rate. The value of the account reached $8,200 in the year 2010. Determine the value of the account, to the nearest dollar, in the year 2019.
Answers
The answer to the expositional growing account will be $14838.
What is exponential function?
The mathematical formula for an exponential function is f (x) = ax, where x is a variable and a constant known as the base of the function, which must be greater than zero. The transcendental number, or e, which is roughly equivalent to 2.71828, is the most frequently used exponential function base.
Let suppose in the xth year, the value of the money is 6300* [tex]a^{4}[/tex]
⇒8200 = 6300* [tex]a^{4}[/tex]
⇒a = 1.068
So 6300 *[tex]a^{13}[/tex]
= $14838
Hence the value of the account will be $14838.
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Explain how to find the distance between 1 and -3 on a number line.
Answers
Answer: Distance can't be negative, so it must be positive. That's the first thing you need to know. To find the distance, you take the difference between the two points.
1 - (-3) = 4
(second point on the number line) - (first point on the number line)
Planes m and n intersect at line d. line a forms a right angle with line d. line b is diagonal and crosses line d. line c is on plane n and is diagonal. line e is on plane m and is slightly diagonal at the top of the plane. which are skew lines? check all that apply. a and b c and b b and e e and c a and e a and c
Answers
the answers are option 2 4 6
Answer:
B,D,F
Step-by-step explanation:
Question 3 of 7
Find the 10th term of the geometric sequence whose common ratio is
1
and whose first term is 7.
Answers
please help me answer this worksheet (Geometry Worksheet 3.3)
Answers
As per the reference document attached thereby along with the question statement, if (∠SOX = 160°), [∠1 = (x + 14)], and [∠2 = (3x – 10)], then the measure of ∠2 in degrees will be 113°
As per the reference document attached thereby along with the question statement, (∠SOX = 160°), and it's constituent angles
[∠1 = ∠SOW = (x + 14)], and [∠2 = ∠WOX = (3x – 10)],
And we are required to determine the measure of ∠2.
Since, [(∠SOW + ∠WOX) = ∠SOX],
Therefore, [{(x + 14) + (3x – 10)} = 160°]
Or, [{(x + 3x) + (14 - 10)} = 160°]
Or, [(4x - 4) = 160°]
Or, [4x = (160 + 4)°]
Or, (4x = 164°)
Or, [x = (164/4)°]
Or, (x = 41°)
Or, [(3x – 10) = {(3 * 41) - 10}°]
Or, [∠2 = (123 - 10)°]
Or, (∠2 = 113°)
That is, if (∠SOX = 160°), and it's constituent angles (∠1) and (∠2) measure as [∠1 = ∠SOW = (x + 14)], and [∠2 = ∠WOX = (3x – 10)], then the measure of ∠2 in degrees will be 113°
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Bao is the oldest of four siblings whose ages are consecutive even integers. If the sum of their ages is 60, find Bao's age.
Answers
Answer:
:)......................
Bao's age is 12 years old.
What are Integers?Integers are defined as the collection of Whole Numbers and the negative values of Natural Numbers make up an integer. Fractional numbers are not included in integers. Integers are represented by the symbol Z.
Let's call Bao's age "x".
Since their ages are consecutive even integers, the next sibling's age would be x + 2, the next one x + 4, and the last one x + 6.
The sum of all their ages is x + (x + 2) + (x + 4) + (x + 6) = 4x + 12 = 60.
Solving for x, we get 4x + 12 = 60, and subtracting 12 from both sides gives 4x = 48.
Dividing both sides by 4 gives x = 12.
Therefore, Bao's age is 12 years old.
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Alex ha 7 pound of birdeed and 5 bird feeder. Which model how how much birdeed he hould put into each bird feeder?
A. B. C. D
Answers
Alex puts (7/5) pounds of food in each bird feeder.
Given that,
Alex has 7 pound of bird food. He puts an equal portion into 5 bird feeders. How much bird food, in pounds, does he put in each bird feeder
Let's assume that he filled each bird feeder with x pounds.
then,
The equation is
(Pound in each feeder) * (Total feeders) = Amount of food.
When all values are present,
→ x * 5 = (7)
→ x = 7 ÷ 5
→ x = (7) * (1/5)
→ x = (7/5) pounds.
Hence, Alex put (7/5) pounds of food in each bird feeder .
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an ostrich farmer wants to enclose a rectangular area and then divide it into six pens with fencing parallel to one side of the rectangle (see the figure below). there are 900 feet of fencing available to complete the job. what is the largest possible total area of the six pens?
Answers
The largest possible total area of the six pens is 33750 square feet.
Given:
An ostrich farmer wants to enclose a rectangular area and then divide it into six pens with fencing parallel to one side of the rectangle (see the figure below). there are 900 feet of fencing available to complete the job.
Let L and W be the length and width.
900 = L + 6W
L = 900 -6W
Area = A = LW = (900-6W)W = 900W -6W^2
A' = 990-12W = 0
W = 900/12 = 75 feet wide
L = 900 -6W = 900 - 6(75)
L = 900 - 450 = 450 feet.
Maximum area = 450 * 75
= 33750 square feet.
Therefore the largest possible total area of the six pens is 33750 square feet.
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A rental car company charges a daily rate of $35 to rent and $0.75 a mile to drive. The bill was $47. Write and solve an equation to find out how many miles were driven on this bill.
Answers
Answer:
16 miles
Step-by-step explanation:
Let m be the number of miles.
[tex]35 + .75m = 47[/tex]
[tex].75m = 12[/tex]
[tex]m = 16[/tex]
a fair coin is tossed five times, and each time the coin lands tails up. if the coin is then tossed 1990 more times, how many tails are most likely to appear for the 1990 additional tosses?
Answers
Probability of getting tails are most likely to appear for the 1990 additional tosses will be 1/32.
What is probability?Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution. The probability is calculated by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.
Here,
The coins gets tail always,
=(1/2)^5
=1/32
For the 1990 additional tosses, there is a 1/32 chance that a tail will appear.
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What is the 2s fact?.
Answers
The value of 2 factorial would be 2.
What is a factorial of a number?
Factorial is the product of all positive integers less than or equal to a given positive integer, denoted by that integer, and an exclamation point in mathematics. Thus, factorial seven is written 7! which means 1*2*3*4*5*6*7. Factorial zero is defined as one.
As the definition says that the factorial is the product of all the positive integers less than or equal to the given number till one.
We have to find the value of 2 factorial.
2! = 2 * 1
= 2
Hence, the value of 2 factorial would be 2.
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