The area of the triangle is A = 10x¹⁰y³
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the triangle be represented as ΔABC
Let the area of the triangle be represented as A
Now , the base of the triangle is = 4x³y
Let the height of the triangle be = 5x⁷y²
And , The area of the triangle = ( 1/2 ) x Length x Base
Substituting the values in the equation , we get
Area of Triangle = ( 1/2 ) ( 4x³y ) ( 5x⁷y² )
On simplifying the equation , we get
Area of Triangle A = 10x¹⁰y³
Hence , the area of the triangle is A = 10x¹⁰y³
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What is the area of the parallelogram?
Answer:
65 m²
Step-by-step explanation:
area of parallelogram = base × height
base = AB = 3 m + 10 m = 13 m
height = 5m
area = 13 m × 5 m
area = 65 m²
Refer to the circle graph below. Suppose there are 300 students at York Middle School. Determine the number of students that have veggies as a snack.
The number of students that have veggies as a snack is equal to 51 students according to the circle graph.
What is a circle graph?A circle graph is also called a pie chart, and it can be defined as a type of graph that is used for the graphical representation of the proportional relationship between each part to a whole, especially by dividing a circle into various sectors or sections.
Given that, there are 300 students at a school, the number of students that have veggies as a snack can be calculated as follows;
Number of students that had veggies = 17/100 × 300
Number of students that had veggies = 0.17 × 300
Number of students that had veggies = 51 students.
Hence, the number of students that have veggies as a snack is equal to 51 students according to the circle graph.
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The complete question is :-
Refer to the circle graph below. Suppose there are 300 students at York Middle School. Determine the number of students that have veggies as a snack. No Snack 12% Fruit. 23% Chips · 18% Cheese 15% Veggies 17% L Cookies 15%
Please answer this question! will give alot of points
Answer: the first question answer is 16.03 ft
the answer for number two is here too hand the way to get this answer
answer: Elijah is standing from the base of the monument 159.14 feet
Step-by-step explanation:
see the attached figure to better understand the problem
In the right triangle ABC
----> by TOA (opposite side divided by the adjacent side)
substitute the given values
solve for AC
therefore
Elijah is standing from the base of the monument 159.14 feet
Answer: Elijah is standing from the base of the monument - 1
And the answer for number 3 is 850.9 feet
On his first birthday, Tomas was 30 inches tall. For the next year, he grew half an inch each month. what equation models his height that year, y, as a function of the number of months, x?
Answer:
y=0.5x+30?
Step-by-step explanation:
You need 2/3 yard of fabric to create a headband. You have 12 feet of blue fabric and 4 feet of yellowfabric. How many headbands can you make with all the fabric
You can make 8 headbands with all the fabric, which is 12 feet of blue fabric and 4 feet of yellow fabric.
To find out how many headbands you can make with all the fabric, you need to convert the fabric measurements to the same unit and then divide by the amount needed for one headband.
First, convert the 12 feet of blue fabric to yards:
12 feet ÷ 3 = 4 yards
Next, convert the 4 feet of yellow fabric to yards:
4 feet ÷ 3 = 1.333 yards
Now, add the two amounts of fabric together:
4 yards + 1.333 yards = 5.333 yards
Finally, divide the total amount of fabric by the amount needed for one headband:
5.333 yards ÷ 2/3 yard = 8 headbands
Therefore, you can make 8 headbands with all the fabric.
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Brent weighed 240 pounds on January 1st. He lost 2 pounds per week by following an exercise plan for w weeks.
Write a function for B, Brent’s weight.
Answer:
B=240-2w
Step-by-step explanation:
.
The Ten Finger calculator company periodically checks random calculators before shipping crates out to customers. On Wednesday, 12 calculators from each of 64 crates of 144 calculators were tested. Two of the tested calculators were found to be defective. Based on this rate of defect, how many total calculators are expected to be defective?
Based on this rate of defect, a total of 256 calculators to be defective in all 64 crates are expected to be defective
What is Proportion ?Mathematically, a proportion is calculated by dividing the number of individuals in a population who have the characteristic of interest by the total number of individuals in the population. For example, if we are interested in the proportion of people in a city who are left-handed, we would count the number of left-handed people in the city and divide it by the total population of the city.
Proportions are commonly used in statistics to describe the prevalence of certain characteristics or outcomes in a population, and they can be used to make comparisons between different populations or subgroups within a population. Proportions are typically expressed as fractions, decimals, or percentages, and they can range from 0 (indicating that none of the population has the characteristic of interest) to 1 (indicating that all of the population has the characteristic of interest).
According to given condition :We can start by finding the proportion of defective calculators in the sample of tested calculators. If 2 out of 12 tested calculators were found to be defective, then the proportion of defective calculators in the sample is:
2/12 = 1/6
This means that, on average, we would expect 1 out of every 6 calculators in the population to be defective.
To find the total number of expected defective calculators in all 64 crates, we need to multiply this proportion by the total number of calculators in the population:
(1/6) * (64 crates) * (144 calculators per crate) = 1536/6 = 256
Therefore, we can expect a total of 256 calculators to be defective in all 64 crates.
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Write the ratio 2/5
to 6 as a fraction in simplest form.
Multiply the denominators and numerators together. GCD(12, 5) = 1, keeping the result fraction to the lowest denominator feasible. To put it another way, six times two fifths equals twelve fifths.
What kind of numerator is that?For instance, the fraction bar is the line that separates the digits 4 and 5, and 45 is a fraction. Thus, the numerator is the amount above the fraction bar, and the denominator is the number below the fraction bar. The denominator, or number of pieces out of the total, is represented by a numerator.
A denominator example is what?The top number in a fraction is referred to as the numerator, while the bottom value is referred to as the denominator. 4/5, for instance, is a fraction. In this case, the numerator is 4 and the denominator is 5.
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PLEASE HELP ASAP! THIS IS DUE TONIGHT!!
Question 13 (Essay Worth 12 points)
(Constant of Proportionality, Graphing Proportional Relationships, Real-World Proportional Problems HC)
An ice cream shop serves chocolate milkshakes that are made with ice cream and milk. There is a proportional relationship between the number of scoops of ice cream and the amount of milk needed to make them. For every 1 scoop of ice cream, one-half cup of milk is needed, and for every 5 scoops of ice cream, two and one-half cups of milk are needed.
Part A: Find the constant of proportionality. Show every step of your work. (4 points)
Part B: Write an equation that represents the relationship. Show every step of your work. (2 points)
Part C: Describe how you would graph the relationship. Use complete sentences. (4 points)
Part D: How many cups of milk are needed for 18 scoops of ice cream? (2 points)
The constant of proportion is k = 2. An equation that represent the relation is y = 2x. A graph of the equation y = 2x will show 2 units of x values for y on the y–axis. 9 cups of milk are needed for 18 scoops of ice cream
How to evaluate for the solution of the proportionThe proportional relationship between the number of scoops of ice cream and the amount of milk can be expressed as:
1 scoop of ice cream = 1/2 cup of milk
we evaluate for k the constant of proportion as follows:
1 = k × 1/2
k = 2 {cross multiplication}
if we represent a scoop of ice cream with y and a cup of milk with x, then we can write the equation that represent the relation as:
y = 2x.
In the graph of y = 2x, for every value of x on the x–axis, there are 2 units of x for y on the y–axis, that is when x = 1, y = 2 or x = 3 then y = 6.
For 18 scoops of ice cream, we will evaluate for the amount of cup of milk as follows:
18 = 2x
x = 18/2 {divide through by 2}
x = 9.
In conclusion, he constant of proportion is k = 2. An equation that represent the relation is y = 2x. A graph of the equation y = 2x will show 2 units of x values for y on the y–axis. 9 cups of milk are needed for 18 scoops of ice cream
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what is the name of the length of the straight line drawn from an object’s initial position to the object’s final position?
Displacement is the length of the straight line drawn from an object’s initial position to the object’s final position
The term "displacement" refers to a change in an object's position. It is a vector quantity with a magnitude and direction. The symbol for it is an arrow pointing from the initial position to the ending position. For instance, if an object shifts from position A to position B, its position changes.
If an object moves with respect to a reference frame, such as when a passenger moves to the back of an airplane or a professor moves to the right with respect to a whiteboard, the object's position changes. This change in location is described as displacement.
The displacement is the shortest distance between an object's initial and final positions. Displacement is a vector. It is visualized as an arrow that points from the initial position to the final position, indicating that it has both a direction and a magnitude.
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Florian ran 1.2 miles and walked 4.8 laps around the path at the park for a total distance of 3.6 miles.
Which shows the correct equation and value of x , the distance of 1 lap around the path at the park?
The equation and value of x , the distance of 1 lap around the path at the park is 4.8x + 1.2 = 3.6.
What is 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. LHS = RHS is a common mathematical formula.
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:
Florian ran 1.2 miles and walked 4.8 laps around the path at the park for a total distance of 3.6 miles.
As, we know the number of them (4.8) would be multiplied by the variable (x). We also know that 1.2 is the constant.
So, the equation can be framed as
4.8x + 1.2 = 3.6
4.8x = 2.4
x = 0.5
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The question attached here seems to be incomplete the remaining portion is given below:
3.6 x + 1.2 = 4.8; x = 1 mile
4.8 x + 1.2 = 3.6; x = 1 mile
3.6 x + 1.2 = 4.8; x = 0.5 mile
4.8 x + 1.2 = 3.6; x = 0.5 mile
5 x = negative 58
How many 90 hours in a week ?
There are 168 hours in a week. Therefore, there are approximately 0.536 weeks in 90 hours.
Time conversion is the process of converting a given amount of time from one unit of measurement to another. It involves using conversion factors to change the numerical value of the time while keeping the duration constant.
For example, converting a duration from hours to minutes involves using a conversion factor of 60 minutes per hour. To convert, you multiply the number of hours by 60 to get the equivalent duration in minutes.
To get this answer, you can divide the number of hours (90) by the total number of hours in a week (168):
90 hours ÷ 168 hours/week = 0.536 weeks (rounded to three decimal places)
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For each blank you will type a letter for example blank 1 = a
The two rectangles are not similar because the scale factor is not the same.
What is the similarity?Two objects are said to be comparable if they have the same shape. Therefore, two figures are said to be comparable in mathematics if they share the same shapes, lines, or angles.
If two figures have three sides similar then they will be similar by side-by-side property which is written as SSS.
Given dimension of the rectangle is 2 cm and 4 cm. The dimension of the second rectangle is 6 cm and 4 cm.
The scale factor for the two sides should be,
6 / 2 = 3
4 / 4 = 1
Since the scale factor is not constant so the rectangles are not similar.
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Question 3 help please
(0, 6) and (1, 2) is the solutions to the given system of equation. Option A is correct.
Solving system of equationGiven the following system of equation
y = x^2 - 5x + 6
y = -4x + 6
Equating both equations, we will have:
x^2 - 5x + 6 = -4x + 6
Collect the like terms
x^2 - 5x + 6+4x - 6 = 0
x^2 - x = 0
x^2 = x
x = 0, 1
If x = 0
y = -4(0) + 6
y = 6
One of the solution is (0, 6)
If x = 1
y = -4(1) + 6
y = 2
The other solution will be (1, 2)
The solution to the given system of equation will be (0, 6) and (1, 2).
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x - 1/3 = 6
Give your answer as an improper fraction.
Answer:
19/3 (6 1/3)
Step-by-step explanation:
What is the surface area?
What is the Volume?
Answer:
Surface Area is the space occupied by a two-dimensional flat surface is called the area.
Total surface area is the area including the base(s) and curved part(s).
Calculating Surface Area:
To find the surface area of a shape, we need to find the measurement (in this case, centimeters) of each face/side and add them together.
Volume:
The amount of space an object/3D shape occupies. (Ex: A circle does not have volume, a sphere, however, does.)
Calculating Volume:
Volume = the length times the width times the height. (Volume = length x width x height)
What is the constant of proportionality in the table below?
x 5 10 6 9 2
y 15 30 18 27 6
1/3
5
3
15
Answer:
1/3
Step-by-step explanation:
constant proportionality = x/y
x1/y1 , x2/y2 , x3/y3 , ....
5/15 , 10/30 , 6/18 , 9/27 , 2/6
= 1/3 , 1/3 , 1/3 , 1/3 , 1/3
since in all the cases x/y = 1/3 ,
Therefore, the contant proportionality in the given table is 1/3
Hope it's helpful..
The graph of y = 3x - 4 is shown
Consider the solutions of y>3x-4 then day each point to the appropriate bin
The solutions of y > 3x - 4 are (-5,-3), (-3,4), (0,0) and (0, -4)
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
The given equation of the graph is y>3x-4.
We have to check each of the ordered pair is a solution or not.
(-5, -3)
Plug in the values ion inequality
-3>3(-5)-4
-3>-15-4
-3>-19
(-5, -3) is the solution of y>3x-4.
(-3, 4)
4>-9-4
4>-13, So (-3, 4) is the solution of y>3x-4.
(-4, 0)
0>-12-4
0>-16, So (-4, 0) is the solution of y>3x-4.
(0, 0)
0>-4 So (0, 0) is the solution of y>3x-4.
(1, -7)
-7>-3-4 So (1, -7) is not the solution of y>3x-4.
(1, 1)
1>3-4
1>-1, so (1, 1) is not the solution of y>3x-4.
(2, 2)
2>6-4
2>2, so (2, 2) is not the solution of y>3x-4.
(4, 2)
2>12-4, so (4, 2) is not the solution of y>3x-4.
Hence, (-5,-3), (-3,4) , (0,0) and (0, -4) are the solutions of y > 3x - 4.
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What are the Factors of 192?
Answer: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192
Step-by-step explanation:
To find all the factors of a number, multiply all the prime factors of the number in all possible solutions.
SOLVE FOR X AND Y PLEASE AND THANKS
Measures of angles, x = 93° and y = 97°
What is cyclic quadrilateral?A cyclic quadrilateral is a quadrilateral with all four vertices on a circle. Also called an inscribed quadrilateral. A circle consisting of all vertices around a polygon is known as the circumcircle.
Given,
Interior angles of quadrilateral
= x° , y° , 83°
Arc angles on the center of circumcircle are 64° and 122°.
angle made by chord on the center is twice to the angle made on the circumference of the circle
64° + 122° = 2x
186° = 2x
x = 186°/2
x = 93°
In cyclic quadrilateral,
Sum of opposite interior angles is 180°
y + 83° = 180°
y = 180° - 83°
y = 97°
Hence, measure of angles x and y are 93° and 97° respectively.
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Please help asap!!!!!
Answer:
s = 9
Step-by-step explanation:
A = s^2
81 = s^2
√81 = s
s = 9
simplify the fraction
6jk/8k
Answer: 0.75j or 3/4j
Step-by-step explanation:
Use the figure shown for Items 1-4.
In the figure, m IJL= 0.5 m JIK.
The statements that must be true are
A. KL = 15
B. JL bisects overline IK
D. JL is the perpendicular bisector of overline IK .
2. JL = 15 units
3. angle IJK = 90
angle JKI = 45
angle kW = 45
How to find the value of xThe value of x is solved by the information given in the problem
IL = LK
3x = 2x + 5
solving for x
3x - 2x = 5
x = 5
angle IJL = 0.5 angle JIK,
< JIL = < KJL base angles of isosceles triangle
< JIL + < LJI + 90 = 180
< LKJ + < KJL + 90 = 180
equating both
< JIL + < LJI + 90 = < LKJ + < KJL + 90
< JIL + < LJI = < LKJ + < KJL
and < JIL = < KJL
hence < LJI = < LKJ
we can therefore say that
< JIL = < LJI = < LJK = < JKL = 45 degrees
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Celine's Cupcakes recorded how many cupcakes it recently sold in each flavor. carrot cupcakes 8 pumpkin cupcakes 1 lemon cupcakes 6 Considering this data, how many of the next 20 cupcakes sold would you expect to be lemon cupcakes?
Number of lemon cupcakes in next 20 cupcakes sold is 1.33.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Given;
carrot cupcakes 8 pumpkin cupcakes 1 lemon cupcakes 6
Now,
For 20 cupcakes
Let the number of lemon cupcakes be x
8+6+1=1lemon
15=1lemon
20=1*20/15lemon
=4/3lemon
Therefore, by algebra the answer will be 1.33lemons
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What is the z-score for a 98% confidence interval?
Using a standard normal distribution table, we can find the closest value to 0.99, which is 2.33. Therefore, the z-score for a 98% confidence interval is 2.33.
To calculate the z-score for a 98% confidence interval, we can use a standard normal distribution table or a calculator with a built-in z-score calculator. To calculate the z-score for a 98% confidence interval, we can use the following formula:
z = invNorm(1 - (1 - confidence level) / 2)
Where "invNorm" is the inverse normal distribution function, and "confidence level" is the level of confidence expressed as a decimal. For a 98% confidence level, we have:
z = invNorm(1 - (1 - 0.98) / 2)
z = invNorm(0.99)
Using the table, we can find the z-score corresponding to a cumulative area of 0.98 by looking up the closest value to 0.98 in the table.
invNorm(0.98) = 2.33.
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Given f of x is equal to 1 over the quantity x minus 4 end quantity and g of x is equal to the square root of the quantity x plus 4 end quantity comma what is the domain of f (g(x))?.
The domain of f(g(x)) = (-infinity, -4) U [-4, 4) U (4, infinity).
To find the domain of f(g(x)), we first need to find the domain of g(x) and then the domain of f(x).
The domain of g(x) is the set of all real numbers x such that x + 4 >= 0. So, g(x) is defined for all x >= -4.
To find the domain of f(x), we need to exclude the values of x for which f(x) is not defined. In this case, f(x) is not defined for x = 4. Hence, the domain of f(x) is all real numbers except 4, i.e., (-infinity, 4) U (4, infinity).
Therefore, the domain of f(g(x)) is the set of all real numbers x such that g(x) is defined and g(x) belongs to the domain of f(x). This means that f(g(x)) is defined for all x >= -4, except x = 4.
So, the domain of f(g(x)) = (-infinity, -4) U [-4, 4) U (4, infinity).
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[tex]4.03 x 10x^{6}[/tex]
The simplified form of the given expression 4.03x + 10x⁶, is [tex]x(4.03x + 10x^5)[/tex]
What is an expression?An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.
Given that an expression 4.03x + 10x⁶
We need to simplify it,
4.03x + 10x⁶
Applying the exponent rule: [tex]a^{b+c}=a^ba^c[/tex]
[tex]x^6=x^5x[/tex]
[tex]=4.03x+10x^5x[/tex]
Factor out common term x,
[tex]=x\left(4.03+10x^5\right)[/tex]
Hence, the simplified form of the given expression 4.03x + 10x⁶, is [tex]x(4.03x + 10x^5)[/tex]
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Which of the following statement(s) about multiple regression analysis is FALSE?A. Multiple regression analysis allows you to analyze more than one dependent (Y) variable at a time.B. Multicollinearity occurs when the X variables are highly correlated with the Y variable in multiple regression.C. Multicollinearity occurs when two or more of the X variables are highly correlated with one another.D. Both A and B are false statements.E. All of the statements above are false.
Multiple regression analysis analyze more than one dependent variable at a time and multicollinearity occurs when the X variables are highly correlated with the Y variable in multiple regression are false. Correct option is D.
The statement (A) that "Multiple regression analysis allows you to analyze more than one dependent (Y) variable at a time" is false. In multiple regression, there is only one dependent variable (Y) that is being predicted by a combination of independent variables (X).
The statement (B) that "Multicollinearity occurs when the X variables are highly correlated with the Y variable in multiple regression" is also false.
Multicollinearity occurs when two or more independent variables (X) are highly correlated with each other, which can cause problems in accurately estimating the effect of each independent variable on the dependent variable.
The statement (C) that "Multicollinearity occurs when two or more of the X variables are highly correlated with one another" is true.
Therefore, the correct answer is (D) "Both A and B are false statements."
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There is a 30% chance an avocado is
perfectly ripe by tomorrow (not over-ripe
or under-ripe). If it is perfectly ripe
tomorrow there is a 40% chance it is still
perfectly ripe the next day. If it is not
perfectly ripe tomorrow there is a 60%
chance it is perfectly ripe by the next day.
What is the probability it is not perfectly
ripe on both days? Answer form 0.00
Answer:
Step-by-step explanation:6
Can someone help? I need to know what the answers are for this. it’s trig btw!
The missing length of the geometric system of right triangles is equal to 15.833 centimeters.
How to find the missing length in a system of 10 right triangles
Herein we find the case of a geometric system formed by ten right triangles, whose missing length can be found by means Pythagorean theorem and trigonometric functions, whose definitions are shown below:
Pythagorean theorem
r = √(x² + y²)
Trigonometric function
cos θ = x / r
Where:
θ - Angle, in degrees.x - Leg adjacent to angle, in centimeters.y - Leg opposite to angle, in centimeters.r - Hypotenuse, in centimeters.Now we proceed to determine the missing length:
First triangle:
x = 8 / cos 28°
x = 9.061
x' = 9.061 - 2.5
x' = 6.561
Second triangle
x = (6.561 + 3.6) · cos 11°
x = 9.974
x' = 9.974 - 2
x' = 7.974
Third triangle
x = √[(7.974 + 2.9)² - 3.8²]
x = 10.188
x' = 10.188 - 1
x' = 9.188
Fourth triangle
x = (9.188 + 3.2) · cos 43°
x = 9.060
x' = 9.060 - 1
x' = 8.060
Fifth triangle
x = (8.060 + 1) / cos 30°
x = 10.462
Sixth triangle
x = (10.462 + 3.2 + 1.9) · cos 19°
x = 14.714
Seventh triangle
x = (14.714 - 4.8 - 1.1) / cos 46°
x = 12.688
Eighth triangle
x = √[(12.688 + 1.7)² + 3.2²]
x = 14.740
Ninth triangle
x = (14.740 - 2.73) · cos 22°
x = 11.135
x' = 11.135 - 2.24
x' = 8.895
Tenth triangle
x = (8.895 + 6.9) / cos 4°
x = 15.833
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