Answers
The length of XZ is 5.5 m.
What is the length of XZ?
The length of side XZ is calculated by applying the following cosine and sine rule.
If the length of WY is 7 m, then ∠WYZ is calculated as follows;
cos Y = (z² + w² - y² ) / (2zw)
where;
Y is ∠WYZy is the length of the side opposite angle YZ is the length of the side opposite angle Zw is the length of the side opposite angle Wcos Y = ( 7² + 5.1² - 3² ) / ( 2 x 7 x 5.1 )
cos Y = 0.9245
Y = cos⁻¹ (0.9245)
Y = 22.4⁰
The value of ∠WYX is calculated as follows;
cos Y = (x² + w² - y² ) / (2xw)
cos Y = ( 7² + 5² - 4.8² ) / ( 2 x 7 x 5)
cos Y = 0.728
Y = cos⁻¹ (0.728)
Y = 43.28⁰
The value of ∠ZYX = 43.28⁰ + 22.4⁰ = 65.68⁰
The length of XZ is calculated by using the following cosine rule.
|XZ|² = |XY|² + |ZY|² - (2 x |XY| x |XY|) cos Y
|XZ|² = 5² + 5.1² - (2 x 5 x 5.1 ) x cos (65.68)
|XZ|² = 30
|XZ| = √30
|XZ| = 5.5 m
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Related Questions
8x=__when x= 3
pls tell me
Answers
Answer:
24
Step-by-step explanation:
are used to represent an unknown quantity in a mathematical expression.
Answers
Answer:
Variables
Step-by-step explanation:
A variable is a quantity that can be changed and is not fixed. Variables are essential as they form a major algebra component. We usually use “x” and “y” to express an unknown integer.
could you please help me thank you and I think the values of X might be wrong thank you .
and I am sorry for a little bit of points it's because I don't have a lot I only have one hundred.
Answers
The area of the triangle is 5√11 cm².
What are angles?
A point where two lines meet produces an angle.
The breadth of the "opening" between these two rays is referred to as a "angle". It is depicted by the figure.
Radians, a unit of circularity or rotation, and degrees are two common units used to describe angles.
By connecting two rays at their ends, one can make an angle in geometry. The sides or limbs of the angle are what are meant by these rays.
The limbs and the vertex are the two main parts of an angle.
The common terminal of the two beams is the shared vertex.
According to our question-
b = base of the triangle = 2(√6² - 5²) = 2(√36 - 25) = 2√11 cm
h = height of the triangle = 5 cm
area of the triangle = 1 / 2 × 2√11 × 5
area of the triangle = 5√11
area of the triangle = 5√11 cm²
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Find the range of the data set: 10, 18, 21, 28, 12, 20. A. 10 B. 12 C. 18 D. 20
Answers
Answer:
18
Step-by-step explanation:
The range of the data set is 18, which is calculated by subtracting the smallest value (10) from the largest value (28).
A circus has 15 performers, of which 5 are clowns. What is the probability that a randomly selected performer will be a clown?
Write your answer as a fraction or whole number
Answers
the probability of selecting a clown is 1/3, which is the answer to the problem.
The probability of an event happening is defined as the number of favorable outcomes divided by the total number of possible outcomes.
In this case, the total number of performers is 15, and the number of clowns is 5. Therefore, the probability of selecting a clown is:
P(clown) = number of clowns / total number of performers
= 5 / 15
= 1/3
Probability is a branch of mathematics that deals with the study of random events and their likelihood of occurrence. It is defined as the measure of the likelihood or chance of an event occurring.
The probability of an event is expressed as a number between 0 and 1, where 0 means that the event is impossible, and 1 means that the event is certain to happen. An event with a probability of 0.5 (or 50%) is considered to be equally likely to happen or not happen.
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Students in the high school choir sing one of four voice parts.
sopranos 5
altos 22
basses 8
tenors 5
What is the probability that a randomly selected singer will be a soprano?
Answers
The probability of selecting a soprano is 0.125 or 12.5%.
What distinguishes a probability from an odds ratio?The percentage of times you anticipate seeing a certain occurrence across many trials is the chance that it will happen. Probabilities are always in the 0 to 1 range. The probability of an event happening divided by the likelihood that it won't happen is how odds are calculated.
Probability 0 is equivalent to chances 0. Odds less than 1.0 are represented by probabilities between 0 and 0.5. The chances of 1.0 are the same as a probability of 0.5. Consider it like this: 50% of the time, a coin will land on its head. The chances are "50:50," which translates to 1.0.
The total number of singers are:
5 + 22 + 8 + 5 = 40
Now, the probability of selecting a soprano is:
P(soprano) = 5 / 40
P(soprano) = 1/8 or 0.125
Therefore, the probability of selecting a soprano is 0.125 or 12.5%.
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(14) If z1 = 2-3i and z2=3+i, find
(a) z1
Answers
a) 2 - 3i.
Given that z1 = 2-3i and z2=3+i. We are to find a) z1. Let's learn the concept of complex numbers and solve the problem. The complex number is a combination of a real number and an imaginary number expressed as a + bi, where a and b are real numbers, and i is an imaginary number. The given complex numbers are,z1 = 2-3iz2 = 3+i(a) z1. To find z1, it is already given as 2-3i. Therefore, the answer is 2 - 3i. Hence, a) z1 is 2 - 3i.
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Do what the photo says.
Answers
The area of the composite figure is 186.5 m².
How to find the area of a composite figure?The figure above is a composite figure. A composite figure is a shape that has two or more shapes in it.
Hence, the area of the composite figure is the sum of the whole individuals area of the shapes.
The composite figure can be divided into rectangles, square and quarter circle.
area of the composite figure = area of rectangle + area of square + area of quarter circle
area of the composite figure = 8 × 9 + 6 × 6 + 1 / 4 × 3.14 × 10²
area of the composite figure = 72 + 36 + 1 / 4 × 3.14 × 100
area of the composite figure = 108 + 314 / 4
area of the composite figure = 108 + 78.5
area of the composite figure = 186.5 m²
Therefore, the composite figure with different shapes has an area of 186.5 metres squared.
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Mixes two varieties of saffron X and y the ratio 3:8 if the cost of X is rupees 154 per g and that of y is rupees 121 per gram at what price should he sell the mixture make a profit of 25%
Answers
The seller should sell the mixture at Rs. 162.5 per gram to make a profit of 25%.
Let's assume that the quantity of variety X in the mixture is 3x and the quantity of variety Y is 8x. Therefore, the total quantity of the mixture will be 3x + 8x = 11x.
The cost of variety X is Rs. 154 per gram. Therefore, the cost of 3x grams of variety X will be 3x × Rs. 154 = Rs. 462x.
Similarly, the cost of variety Y is Rs. 121 per gram. Therefore, the cost of 8x grams of variety Y will be 8x × Rs. 121 = Rs. 968x.
The total cost of the mixture will be the sum of the costs of the individual varieties:
Total cost = Rs. 462x + Rs. 968x = Rs. 1430x
To make a profit of 25%, the selling price of the mixture should be 1.25 times the cost price:
Selling price = 1.25 × Total cost
= 1.25 × Rs. 1430x
= Rs. 1787.5x
Therefore, the selling price of the mixture should be Rs. 1787.5x to make a profit of 25%. To find the price per gram of the mixture, we need to divide this selling price by the total quantity of the mixture:
Price per gram of mixture = Selling price / Total quantity
= Rs. 1787.5x / 11x
= Rs. 162.5 per gram (approx.)
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Which statement is not true about the absolute value of -6?
It equals the absolute value of 6.
It can be expressed as |-61.
It describes the distance between -6 and 0 on the number line.
It describes the distance between 6 and -6 on the number line.
My Progress
Done →
out express written consent of Curricu
Answers
Answer:6
Step-by-step explanation:
Absolute value is just how many units, it is away from 0.
Decrease £14132.77 by 14.5%
Give your answer rounded to 2 Dp
Answers
Answer:
900
Step-by-step explanation:
because 14132.77/14.5%
Draw a number line and show the following numbers. positive proper fractions with a denominator of 6
Answers
The fraction 1/6 is closer to 0, while the fraction 5/6 is closer to 1.
What does the denominator represent?A horizontal bar between two numbers and, on occasion, the symbol "/" can be used to identify a fraction. The term "fractional bar" refers to this bar or symbol. The "denominator" is the number below the fractional bar, while the "numerator" is the number at the top.
Indeed, the following number line displays positive proper fractions with the denominator 6:
0 1 2 3 4 5
|------------|------------|------------|------------|------------|
0 1/6 1/3 1/2 2/3 5/6
The complete numbers are represented by tick marks, while the fractions are displayed in between. The fractions 1/6 and 5/6 are closer to the numbers 0 and 1, respectively.
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Suppose that, for a certain mathematics class, the scores are normally distributed with a mean of 75 and a standard deviation of 8. The teacher wishes to give A's to the top 5% of the students and F's to the bottom 5%. The next 15% in either direction will be given B's and D's, with the other students receiving C's. Find the bottom cutoff for receiving an A grade.
Answers
The bottom cutoff for receiving an A grade is 88.16.
What is the statistical application of the empirical rule?A statistical concept known as the empirical rule, often called the 68-95-99.7 rule, asserts that for a normal distribution: Around 68% of the data falls within one standard deviation of the mean.
The data is within two standard deviations of the mean for around 95% of the time. The data is within three standard deviations of the mean for about 99.7% of the time.
To find the bottom cutoff we need to find 5% of the students that score higher.
Using the z-score for 5% distribution we have:
z = 1.645
Formula for converting a z-score to a raw score:
z = (x - μ) / σ
x = z * σ + μ
x = 1.645 * 8 + 75
x = 88.16
Hence, the bottom cutoff for receiving an A grade is 88.16.
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Carmen buys candy that costs 7 $ per pound. She will spend more than 56$ on candy. What are the possible numbers of pounds she will buy?
Use p for the number of pounds Carmen will buy.
Write your answer as an inequality solved for p.
write as an Inequality
Answers
We can say that after answering the offered question Hence, p > 8 is the equation inequality expressing the range of feasible values for p.
What is equation?An equation is a mathematical statement that proves the equality of two expressions connected by an equal sign '='. For instance, 2x – 5 = 13. Expressions include 2x-5 and 13. '=' is the character that links the two expressions. A mathematical formula that has two algebraic expressions on either side of an equal sign (=) is known as an equation. It depicts the equivalency relationship between the left and right formulas. L.H.S. = R.H.S. (left side = right side) in any formula.
Let's use the letter "p" to indicate how many pounds Carmen will spend.
Candy is $7 for every pound.
Carmen's sweets expenditure is expressed as follows:
Cost per pound times the weight of the candy purchased is 7p.
Carmen will undoubtedly spend more than $56 on sweets, therefore we may say:
More than $56 was spent on candy
Using the following equation in place of the amount spent on candy:
7p > $56
When we multiply both sides by 7, we get:
p > 8
So, any figure more than 8 is a possibility for the amount of pounds Carmen will purchase. We can express this as follows:
p > 8
Hence, p > 8 is the inequality expressing the range of feasible values for p.
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answer the question below
Answers
The time it takes to empty the tank is given as follows:
1.85 minutes.
How to obtain the volume of a cylinder?The volume of a cylinder of radius r and height h is given by the equation presented as follows, which the square of the radius is multiplied by π and the height.
V = πr²h.
The parameters for this problem are given as follows:
r = 0.7 ft, as the radius is half the diameter.h = 3 ft.Hence the volume of the cylinder in ft³ is given as follows:
V = π x 0.7² x 3
V = 4.62 ft³.
Oil is drained at a rate of 2.5 ft³ per minute, hence the time it takes to drain the oil is given as follows:
4.62/2.5 = 1.85 minutes.
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The volume, in cubic centimetres, of a rectangular box can be modelled by the polynomial expression 2x3−11x2−41x+140. Determine an equation to represent the area of the base of the box if the height, in centimetres, is given by 2x−5. [APP 3 marks]
Answers
The equation for area of the base of the box will be x² - 6x + 28.
What is Volume ?
In physics and mathematics, volume is a measure of the amount of three-dimensional space occupied by an object or a region. It is often measured in cubic units, such as cubic meters, cubic centimeters, or cubic feet.
The volume (V) of a rectangular box is given by the product of its length (l), width (w), and height (h):
V = lwh
Given that the volume is modelled by the polynomial expression 2x³- 11x² - 41x + 140, we can write:
V = 2x³ - 11x² - 41x + 140
And since the height is given by 2x - 5, we can substitute this expression into the formula for volume:
V = lwh = (lw)(2x - 5)
So we need to find an equation for the area of the base (lw). We can do this by rearranging the formula for volume:
lw = V / (2x - 5)
Substituting the expression for V, we get:
lw = (2x³ - 11x² - 41x + 140) / (2x - 5)
We can simplify this expression by polynomial long division or synthetic division, which gives:
lw = x² - 6x + 28
Therefore, the equation for the area of the base of the box is:
A = x² - 6x + 28, where A is the area in square centimeters, and x is the length in centimeters.
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Using the graph answer the following questions What is the slope of the function What is the y intercept of the function What is the slope intercept form of the function?
Answers
Answer: what's the queston?
Step-by-step explanation:
Answer:
um question ?
Step-by-step explanation:
The ratio of boys to girls is 4to3 how many boys are there
Answers
The ratio of boys to girls is 4:3 boys are there of 5 boys were more than girls.
Most of the explanations for ratios and proportions use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. The foundation for understanding the numerous concepts in mathematics and science is provided by the two key notions of ratio and proportion.
We apply the concepts of ratio and proportion every day, for example, while dealing with money in business or when preparing any meal, etc. Students occasionally struggle to understand the difference between ratio and proportion.
Formula used:
No. of Object= Total No of abject. x Given ratio/Sum of ratios
No. of Boys = 35 x 4 /7
No. of Boys = 140 / 7
No of Boys = 20
And No. of Girls = 35 x 3/7
No. of Girls = 105 /7
No. of Girls = 15
Final answer:
No. of boys - No. of girls
20-15= 5
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Which sign makes the statement true?
Answers
Answer: <
It is "<" because 8 1/2 as a decimal is 8.50 and the other decimal is 8.375. 8.50 is greater than 8.375.
Your welcome!
=^..^=
Answer:<
Step-by-step explanation:
8.375= [tex]8\frac{375}{1000} =8\frac{3}{80} \\[/tex]
1/2=40/80
40/80>3/80
so,
create an art work from home in any theme that will alllow you to aply youre learnings on angle pairs and lines. The art work should be made of composed od corguent traingles
Answers
u have to pay me to do it for you thanks
what is the value of v100
Answers
Step-by-step explanation:
I'm sorry, but I cannot provide a specific answer to this question without additional context. The value of v100 could refer to many different things depending on the context.
If you could provide more information about what v100 represents or what it pertains to, I would be happy to try and help you with your question.
please address those questions please type
1, You have 7 identical cookies to distribute to 4 kids.
a, How many ways can you distribute the cookies?
2, how many three colors flag can you make with the colors white, red and blue.
Answers
The sοlutiοn οf the given prοblem οf unitary cοmes οut tο be 1.20 and 2.27 .
What is an unitary methοd?By cοmbining the infοrmatiοn οbtained using this nanοsectiοn technique with all variable additiοnal data frοm twο individuals whο used a specific strategy, the task can be cοmpleted. Simply put, this mean that, if the desired οutcοme materialises, either the specified entity will be knοwn οr, actually, the cοlοur frοm bοth enοrmοus prοcesses will be skipped. Fοr fοrty pens, a refundable charge οf Rupees ($1.01) might be required.
Here,
There are several apprοaches tο the issue οf giving 4 children each 7 identical cοοkies, but οne pοpular strategy is tο use a stars and bars strategy.
Cοnsider 7 stars as the 7 biscuits and 3 bars as the 3 partitiοns separating the 4 children. Then, any cοnfiguratiοn οf stars and bars represents a pοtential cοοkie dispersal.
=> (10 + 3) chοοse 3 = 120 / 6 = 7 + 3 chοοse 3 = 20
The fοur children can therefοre share the cοοkies in 20 variοus ways. The number οf ways tο create a three-cοlοr flag is as fοllοws because we have three cοlοur οptiοns and can repeat cοlοurs in variοus ways:
=> 3 x 3 x 3 = 27
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Complete question:
An object with a mass of 7.5kg accelerates 8.3m/s2 when an unknown force is applied to it. What is the amount of force
Answers
Answer: The amount of force (F) can be calculated using Newton's second law of motion, which states that force is equal to mass times acceleration:
F = m*a
where F is the force, m is the mass, and a is the acceleration.
Plugging in the given values, we get:
F = 7.5kg * 8.3m/s^2
F = 62.25 N
Therefore, the amount of force applied to the object is 62.25 Newtons.
Step-by-step explanation:
3 A cake is made of three round layers. The diameters and heights are in the ratio 5:3:2 The cake's bottom layer has a diameter of 30cm and a height of 10cm. Work out the following, giving your answers to the nearest whole number. cm (1 mark ) a
Answers
The diameter of the middle layer is 18 cm and the height is 9 cm. The diameter of the top layer is 12 cm and the height is 5 cm.
The ratios of the diameters and the heights are 5:3:2. Therefore, to calculate the diameters and heights of the other two layers, we need to take the bottom layer's diameter and height as our reference values.
The diameter of the bottom layer is 30 cm and the height is 10 cm.
To find the diameter and height of the middle layer, we multiply the bottom layer's values by 3/5 and then 3/2 respectively. So, the diameter of the middle layer is (30 x 3/5) cm = 18 cm and the height is (10 x 3/2) cm = 9 cm.
To find the diameter and height of the top layer, we multiply the bottom layer's values by 2/5 and then 1/2 respectively. So, the diameter of the top layer is (30 x 2/5) cm = 12 cm and the height is (10 x 1/2) cm = 5 cm.
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Pay your bills: In a large sample of customer accounts, a utility company determined that the average number of days between when a bill was sent out and when the payment was made is 30 with a standard deviation of 3 days. Assume the data to be approximately bell-shaped.
Between what two values will approximately 68% of the numbers of days be?
Answers
Approximately 68% of the customer accounts have payments made between 23 and 37 days.
How the mean and standard deviation is related: The formula for calculating the standard deviation uses the mean.
In actuality, we cannot determine a sample's standard deviation without first knowing what the sample means.
We want to calculate what two values will approximately 68% of the number of days be.
For a bell-shaped distribution, we can apply the 68-95-99.7 rule, which states that approximately 68% of the data will fall within 1 standard deviation from the mean.
Then, for a mean of 30 and a standard deviation of 7, we can calculate the two values as:
[tex]X_1=u+z_1.n=30-1.7=30-7=23\\X_2=u+z_2.n=30+1.7=30+7=37,[/tex]
Approximately 68% of the customer accounts have payments made between 23 and 37 days.
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Simplify the expression
Answers
Answer:
2 Is the Ans
Step-by-step explanation:
As per the Picture....
PLS HELP! I WILL MAKE U BRAINLIST! LATE WORK
Answers
Step-by-step explanation:
to graph a line always find 2 points out has to go through. that means the points' coordinates make the equation true.
I usually start with x = 0.
point 1 of equation 1 is then
y = -2×0 + 6 = 6
(0, 6)
point 1 of equation 2 is then
y = (3/2)×0 - 1 = -1
(0, -1)
then I pick a value for x that makes the handling of any fractions easier. like in our case x = 2.
point 2 of equation 1 is then
y = -2×2 + 6 = -4 + 6 = 2
(2, 2)
point 2 of equation 2 is then
y = (3/2)×2 - 1 = 3 - 1 = 2
(2, 2)
oh, so I have found the intersection point right away (point 2 of both equations).
so, let's pick a different point 2 for equation 1, like x = 4
y = -2×4 + 6 = -8 + 6 = -2
(4, -2)
with these 4 points you define the 2 lines, and you have the intersection point at (2, 2).
Writing Suppose the relationship between x and y is proportional. When x is 29, y is 275. 5. Find the constant of proportionality of y to x. Use the constant of proportionality to find x when y is 408. 5. Use pencil and paper. Explain how you can tell a relationship that is proportional from a relationship that is not proportional
Answers
If x and y have a proportional relationship, we may write: y = kx where k is the proportionality constant. To calculate k, we may utilise the supplied data point (x=29, y=275.5) and plug .
The following values into the equation: 275.5 = k(29) (29) When we solve for k, we get: k = 275.5/29 ≈ 9.5 As a result, the proportionality constant is 9.5. We can utilise this constant to obtain x for y=408.5 by plugging y=408.5 and k=9.5 into the equation and solving for x: 408.5 = 9.5x x = 408.5/9.5 ≈ 43 As a result, when y equals 408.5, x is around 43. By charting the data and seeing if the points fall on a straight line flowing through the origin, we may determine if a connection is proportional (0,0). If the points are lost.
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A population of values has a normal distribution withμ=178andσ=75.2. You intend to draw a random sample of sizen=48. Find the probability that a sample of sizen=48is randomly selected with a mean between182.3and 198.6.P(182.3×M<198.6)=Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exactz-scores orzscores rounded to 3 decimal places are accepted.
Answers
The probability that a sample of size n=48 has a mean between 182.3 and 198.6 is approximately 0.9474.
The central limit theorem: what is it?The behaviour of sample means and sums in sizable random samples is described by the central limit theorem, a statistical concept. It asserts that regardless of how the underlying population is distributed, as the sample size grows, the distribution of the sample means and sums will converge to a normal distribution. This theorem is crucial because it enables us to extrapolate population parameters from sample data. Because sample means and variances are simpler to gather and evaluate, we may use them to estimate population means, variances, and other characteristics. Several study fields, including the social sciences, the natural sciences, and business, frequently employ the central limit theorem.
Given that the sample size n = 48.
The mean between 182.3and 198.6 is calculated using the central limit theorem.
The sample mean is given as:
Z = (M - μ) / (σ / √(n))
Substituting the values we have:
Z = (198.6 - 178) / (75.2 / √(48)) - (182.3 - 178) / (75.2 / √(48))
Z = 1.62
Now, Z-score less than 1.62 is approximately 0.9474.
Hence, the probability that a sample of size n=48 has a mean between 182.3 and 198.6 is approximately 0.9474.
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Can some on solve this?
Answers
The length οf the missing side is 10 cm.
What is a triangle?A triangle is a clοsed, twο-dimensiοnal geοmetric shape that has three straight sides and three angles. It is οne οf the mοst basic shapes in geοmetry and is used extensively in mathematics, science, and engineering.
Tο sοlve fοr x, we can use the Pythagοrean theοrem which states that in a right triangle, the square οf the hypοtenuse (the side οppοsite the right angle) is equal tο the sum οf the squares οf the οther twο sides.
In this case, we can see that the hypοtenuse is 10 cm and οne οf the οther sides is x cm. The remaining side is then (10 - x) cm (since the triangle is isοsceles).
Applying the Pythagorean theorem, we get:
x² + (10 - x)² = 10²
x² + 100 - 20x + x² = 100
2x² - 20x = 0
2x(x - 10) = 0
So x = 0 or x = 10. However, x cannot be 0 since it would not form a triangle. Therefore, the only valid solution is x = 10.
Therefore, the length of the missing side is 10 cm.
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