The profit (in thousands of dollars) from the expenditure of x thousand dollars on advertising is given by P(x)=1000+32x-2x2. Find the marginal profit at the following expenditures.

A fraction of the variation in y that can be explained by the variation in the values of x is equal to 0.25189186354.

In Mathematics, the standard form of the equation of a regression line is represented or modeled by the following mathematical expression;

y = bx + c

Where:

In Mathematics and Statistics, the value of slope can be calculated by using the following mathematical expression;

[tex]b=r(\frac{S_y}{S_x})[/tex]

where:

By rearranging, we have:

[tex]r=b(\frac{S_x}{S_y})[/tex]

r = 1.13(1.67/3.76)

r = 0.50188829787

By taking the square of both sides, we have:

r² = 0.25189186354.

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The probability that a customer will actually make a valid warranty claim is 0.075.

A probability is a numerical representation of the likelihood or chance that a specific occurrence will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

The probability that a customer will make a valid warranty claim is the probability that the customer both uses the bike in the first year (which has a probability of 0.75) and discovers a defect (which has a probability of 0.10).

Using the multiplication rule of probability, the probability that both of these events occur is:

0.75 x 0.10 = 0.075

Therefore, the probability that a customer will actually make a valid warranty claim is 0.075.

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Answer:

m = -5/8

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Points (-1, -7) (-9, -2)

We see the y increase by 5 and the x decrease by 8, so the slope is

m = -5/8

On the fifth day there were 4 tοmatοes left tο be sοld. Jοann had 71 tοmatοes tο begin with.

Prοbability is a measure οf the likelihοοd οr chance οf an event οccurring. It is a number between 0 and 1, where 0 indicates that the event is impοssible, and 1 indicates that the event is certain tο οccur.

Let's wοrk backwards frοm the last day and figure οut hοw many tοmatοes Jοann had οn the fοurth day.

On the fifth day, there were 4 tοmatοes left tο be sοld, which means she sοld half οf what was left οn the fοurth day. Sο she must have started with 8 tοmatοes οn the fοurth day (since half οf 8 is 4).

On the fοurth day, she sοld half οf what was left, which means she had 16 tοmatοes befοre she sοld any.

On the third day, she sοld 12 tοmatοes, which means she had 28 tοmatοes befοre she sοld any.

On the secοnd day, she sοld half οf what was left, which means she had 56 tοmatοes befοre she sοld any.

Finally, οn the first day, she sοld 15 tοmatοes.

Therefοre, Jοann had 71 tοmatοes tο begin with.

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If Andres Michael bought a new boat. He took out a loan for $24,420 at 3.5% interest for 2 years. Andres Michael owes $18806.6 at maturity.

To calculate how much is due at maturity, we first need to determine how much of the loan remains after the two partial payments.

To do this, we can use the formula for simple interest:

I = P * r * t

Where:

I = Interest

P = Principal (original loan amount)

r = Annual interest rate

t = Time (in years)

The interest for the first two months can be calculated as:

I1 = P * r * t1

= 24420 * 0.035 * (2/12)

= 142.45

So after the first two months, the amount owing on the loan is:

P1 = P + I1 - 4330

= 24420 +142.45 - 4330

= 20,232.45

The interest for the next four months can be calculated as:

I2 = P1 * r * t2

= 20,232.45 * 0.035 * (4/12)

= 236.05

So after six months, the amount owing on the loan is:

P2 = P1 + I2 - 2600

=  20,232.45 + 236.05- 2600

= 17868.50

Now we can calculate the interest for the remaining 18 months:

I3 = P2 * r * t3

=  17868.50* 0.035 * (18/12)

= 938.10

So the total amount owing at maturity (after 2 years) is:

Total amount owing = P2 + I3

=  17868.50 + 938.10

= 18806.6

Therefore, Andres Michael owes $18806.6 at maturity.

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Case 1: The constant c of the piecewise function is equal to 1 / 7.

Case 2: The value of the constant b of the piecewise function with the greater absolute value is equal to 20.

A piecewise function is function formed by two or more functions relative to intervals. A piecewise function is continuous if they do not have any jump on graph. For two functions, we must solve the following equation for the case of a piecewise function formed by two functions:

g(a) = h(a)

Case 1 - g(y) = c · y + 3, h(y) = c · y² - 3, a = 7

c · a + 3 = c · a² - 3

c · (a² - a) = 6

c = 6 / (a² - a)

c = 6 / (7² - 7)

c = 6 / 42

c = 1 / 7

The value of the constant c is equal to 1 / 7.

Case 2 - g(x) = b - 2 · x, h(x) = - 150 / (x - b), a = 5

b - 2 · a = - 150 / (a - b)

(b - 2 · a) · (a - b) = - 150

a · b - b² - 2 · a² + 2 · a · b = - 150

- b² + 3 · a · b - 2 · a² = - 150

b² - 3 · a · b + 2 · a² - 150 = 0

b² - 15 · b - 100 = 0

(b - 20) · (b + 5) = 0

b₁ = 20 or b₂ = - 5

The solution with the greater absolute value is b = 20.

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a)There are total 25 data values so for the given data, 100% data lies within 3 standard deviations of mean.

b). Second graph demonstrates that there is strong linear relationship between the theoretical and sample quantities

a) Here we have μ=61.52 and [tex]\sigma=4.58[/tex]

The 68-95-99.7% rule states that 68% of the data must be within one standard deviation of the mean. Thus, 68% of the data should fall between 61.52-4.58=56.94 and 61.52+4.58=66.1. 19 data values in the provided data are within one standard deviation of the mean. As there are a total of 25 data points, 76% of the data for the given data (19/25)*100=1 standard deviation of the mean.

The 68-95-99.7% rule states that 95% of the data should be within two standard deviations of the mean.

Specifically, 95% of the data should fall between 61.52+2*4.58=70.68 and 61.52-2*4.58=52.36. 24 data values in the provided data are within two standard deviations of the mean.

As there are a total of 25 data points, (24/25)*100=96% of the data for the given data is contained within two standard deviations of the mean.

The 68-95-99.7% rule states that 99.7% of the data should be within three standard deviations of the mean.

It follows that 99.7% of the data should fall between 61.52+3*4.58=75.26 and 61.52-3*4.58=47.78. 25 data values in the provided data are within three standard deviations of the mean.

As there are a total of 25 data points, (25/25)*100=100% of the data falls within three standard deviations of the mean for the given data.

Although not exactly, it appears that the distribution of height follows a normal distribution.

b) Both graphs demonstrate that the height distribution is essentially normal. Second graph demonstrates that there is strong linear relationship between the theoretical and sample quantities.

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The complete question is:

Heights of female college students. Below are heights of 25 female college students.

(a) The mean height is 61.52 inches with a standard deviation of 4.58 inches. Use this information to determine if the heights approximately follow the 68-95-99.7% Rule.

(b) Do these data appear to follow a normal distribution? Explain your reasoning using the graphs provided below.

ADC & BCD are congruent triangles (by SAS postulate). Since triangle ADC & BCD are congruent according to the SAS postulate, we may utilize CPCTC to determine that section AC is equal to segment BD.

In arithmetic progression, the triangles 3: 4: 5 are the only ones with edges. Pythagorean triple-based triangles are Herodian, which means they have integer areas and sides.

The easiest approach I've found to know for sure if an aspect is 90 degrees is to use the 3:4:5 triangle. According to this rule, a triangle is said to be a right triangle if one of its sides is 3 and the other is 4.

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Answer:

Step-by-step explanation:

Let weight of fourth parcel be x

Mean = Sum of all values/total number of values.

8.5 = 7.7 + 7.6 + 8.2 + x/4

8.5 = 23.5 + x/4

8.5 × 4 = 23.5 + x

34 = 23.5 + x

34 - 23.5 = x

10.5 = x

Therefore, weight of the fourth parcel will be 10.5 kg

The length of arc AB is 7pi/3 yards is the area of the shaded region and the length of the arc AB.

what is circle?

A circle is a geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center.

To find the area of the shaded region and the length of arc AB, we need to first find the measure of angle ZAB. Let's call this angle x.

Since angle ZAOB measures 110 degrees and angle ZAB and angle BOA are vertical angles, we know that angle BOA also measures 110 degrees. Therefore, angle ZAB + angle BOA = 180 degrees.

So, we can write:

x + 110 = 180

Solving for x, we get:

x = 70

Now, we can use the formula for the area of a sector to find the area of the shaded region. The sector is defined by the central angle ZOB, which measures 360 - 110 - 70 = 180 degrees. So, we have:

Area of shaded region = (180/360) * pi * 6^2 = 18pi

Therefore, the area of the shaded region is 18pi square yards.

To find the length of arc AB, we can use the formula:

Length of arc AB = (x/360) * 2 * pi * 6

Plugging in x = 70, we get:

Length of arc AB = (70/360) * 2 * pi * 6 = 7pi/3

Therefore, the length of arc AB is 7pi/3 yards.

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The utility that maximizes the possible utility of both the agents Alice and Bob is equal to option D. $10.

Compare Alice's utility from each option and choose the one that maximizes her utility.

Let us consider each option,

If Alice offers Bob $0, her utility will be,

If XA > XB then

UA (XA , XB )= 0.3x3 + 0.72A

UA(10,0)

= 0.3(10)³ + 0.72(10)

= 307.2

If Alice offers Bob $5, Bob's utility will be,

UB(10,5)

= 0.314 + 0.72(5)

= 0.314 + 3.6

= 3.914

And Alice's utility will be,

UA(5,10)

= -0.32(5) + 1.3(10)

= 11.4

Total utility for both Alice and Bob will be,

UA(5,10) + UB(10,5)

= 11.4 + 3.914

= 15.314

If Alice offers Bob $2, Bob's utility will be,

UB(10,2)

= 0.314 + 0.72(2)

= 1.754

And Alice's utility will be,

UA(2,10)

= -0.32(2) + 1.3(10)

= 12.4

So the total utility for both Alice and Bob will be,

UA(2,10) + UB(10,2)

= 12.4 + 1.754

= 14.154

If Alice offers Bob $10, Bob's utility will be,

UB(10,10)

= 0.314 + 0.72(10)

= 7.514

And Alice's utility will be,

UA(10,10)

= 0.3(10)³ + 0.72(10)

= 307.2

So the total utility for both Alice and Bob will be,

UA(10,10) + UB(10,10)

= 307.2 + 7.514

= 314.714

Therefore, utility which maximizes the total utility for both Alice and Bob is given by option (D) $10.

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Method to list all non-isomorphic trees on n vertices is to add edges to a single vertex tree. Using A, B, C, D, E, we list 5 non-isomorphic trees on 6 vertices.

A by-hand method to give a list of all non-isomorphic trees on exactly n vertices is to start with a tree on n vertices and then generate all possible trees by adding edges between vertices that are not already connected.

For example, to find all non-isomorphic trees on 4 vertices, we can start with a single vertex and then add edges to form a tree with 2 vertices, then add edges to form a tree with 3 vertices, and finally add edges to form a tree with 4 vertices. We can then check each tree for isomorphism by comparing their adjacency matrices.

Using the method from (a), we can find all non-isomorphic trees on exactly six vertices by starting with a single vertex and adding edges until we have a tree on six vertices.

To ensure that we generate all possible trees, we can use the following five vertices: A, B, C, D, E. We can then generate all trees by adding edges between vertices that are not already connected, making sure to avoid creating cycles. After generating all trees, we can check for isomorphism by comparing their adjacency matrices.

The resulting list of non-isomorphic trees on six vertices, in alphabetical order, is shown. The tree 1 and tree 2 are the same. Also, trees 3, 4, and 5 are not isomorphic to each other or to trees 1 and 2.

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Answer: D 30

Step-by-step explanation:

4/10 + 30/100

2/5 + 3/10

7/10

NB: LEFT-HAND SIDE IS EQUAL TO THE RIGHT-HAND SIDE

Using the discriminant of the quadratic equation, the temperature will part after 50 minutes

The temperature of the machine part is given by the equation:

T = -0.005x^2 + 0.45x + 125

We need to find out if the temperature will ever reach or exceed 135°F, which means we need to check if there exists a value of x for which T = 135.

Substituting T = 135 in the above equation, we get:

135 = -0.005x^2 + 0.45x + 125

Simplifying the equation, we get:

0.005x^2 - 0.45x + 10 = 0

This is a quadratic equation of the form ax^2 + bx + c = 0, where a = 0.005, b = -0.45, and c = 10.

The discriminant of this quadratic equation is given by:

D = b^2 - 4ac

= (-0.45)^2 - 4(0.005)(10)

= 0.2025 - 0.2

= 0.0025

Since the discriminant is positive, the quadratic equation has two real roots. Therefore, the temperature of the machine part will cross 135°F at some point during the operation.

We can also find the roots of the quadratic equation using the formula:

[tex]x = (-b \± \sqrt(D)) / 2a[/tex]

Substituting the values of a, b, and D, we get:

[tex]x = (0.45 \± \sqrt(0.0025)) / 2(0.005)\\= (0.45 \± 0.05) / 0.01[/tex]

Taking the positive value, we get:

x = 50

Therefore, the temperature of the machine part will cross 135°F after 50 minutes of operation.

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Answer

6255 pounds

8.34×750=6255lbs

Answer: No, Chaz is not correct. Although their balances are both negative, we cannot compare them simply based on their numeric values. The magnitude of the balance does not indicate who owes more to the bank, as it depends on various factors such as account activity, fees, and interest rates. We would need to know more information about their accounts, such as the interest rates and any fees, in order to determine who owes more to the bank.

Excluding the bank fees Chaz would technically be correct.

No, Chaz is not correct.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

No, Chaz is not correct.

Although both Chaz and Will have negative checking account balances, we cannot determine who owes more to the bank based solely on the balance amount.

The balance amount only indicates how much money they owe to the bank, but it does not give any information about the amount they initially deposited or any other financial transactions they may have made.

To determine who owes more to the bank, we would need to know the initial deposit amount, the transaction history, and any fees or interest charges that have been applied to the accounts.

Without this additional information, we cannot accurately compare the two balances or determine who owes more to the bank.

Thus,

No, Chaz is not correct.

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To find the slope of a line that passes through two points, you can use the slope formula. The slope formula is:

Slope = (y2 - y1) / (x2 - x1)

Using the points given in your question, the slope formula to find the slope of the line is:

Slope = (2 - 8) / (4 - (-4))

Using the order of operations, the calculation of the slope formula is as follows:

Slope = -6 / 8

Therefore, the slope of the line passing through (-4, 8) and (4, 2) is -3/4.

To calculate the actual distance in km, we need to use the scale factor of 1:100 000. This means that 1 cm on the map is equivalent to 100 000 cm in real life.

Therefore, 12.3 cm on the map is equivalent to 12.3 x 100 000 cm in real life.

Now, 1 km is equivalent to 100 000 cm.

Therefore, 12.3 x 100 000 cm is equivalent to 1.23 km.

Hence, the actual distance in km is 1.23 km.

(a) This 95% confidence interval indicates that there is a 95% chance that between 56% and 65% of subjects will be helped by the new anti-inflammatory drug.

(b) There is a 95% confidence level that the percentage of participants who benefit from a new anti-inflammatory medication falls between (0.56, 0.65).

(a) According to this 95% confidence interval, there is a 95% likelihood that the new anti-inflammatory medication will be beneficial to between 56% and 65% of participants.

(b) There is a 95% confidence interval for the percentage of subjects who were benefitted by a new anti-inflammatory medicine (0.56, 0.65).

The percentage of participants who contributed to the development of a new anti-inflammatory medicine has a 5% probability of falling outside the range above.

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Answer:

[-3, 7].

Step-by-step explanation:

do i need to explain all that?

Answer:

The inequality can be rewritten as x-7 ≤ 50, which we can solve by adding 7 to both sides to get x ≤ 57.

Step-by-step explanation:

It seems like there are multiple questions combined in this one prompt. I will break them down and provide solutions for each one.

Solution for O x≤-3 or 2 Ox<-3 or 2 O-3≤x≤2 or x > 7:

To find the solution for this inequality, we need to solve each part separately and then combine the solutions using the union (OR) operation.

a) x ≤ -3: This part is already solved for x. The solution is x ≤ -3.

b) 2x < -3: We divide both sides by 2 to isolate x and get x < -3/2.

c) 2 ≤ x ≤ -3: This is not possible as there is no number that is both greater than or equal to 2 and less than or equal to -3.

d) x > 7: This part is already solved for x. The solution is x > 7.

The solution to the entire inequality is the union of these solutions: x ≤ -3 OR x < -3/2 OR x > 7.

Solution for x²+x-6 < 0

To solve this quadratic inequality, we can factor it as (x-2)(x+3) < 0 and use the sign chart method.

We create a sign chart for the expression (x-2)(x+3) and test the sign of the expression in each interval

  -3         2

  ---|-------|---

    -         +

(x-2) - 0 + +

(x+3) - - - 0 +

-------------

- + - 0 +

The sign chart tells us that the expression is negative when x is between -3 and 2. Therefore, the solution to the inequality is -3 < x < 2.

Solution for x-7 ≤ 50₂

It seems like the expression "50₂" is intended to represent the number 50 in base 2 (binary). To convert this number to base 10 (decimal), we can write 50₂ as

50₂ = 12^5 + 12^4 + 02^3 + 02^2 + 12^1 + 02^0 = 32 + 16 + 2 = 50

Therefore, the inequality can be rewritten as x-7 ≤ 50, which we can solve by adding 7 to both sides to get x ≤ 57.

Solved  equation x=80 and z=2, y=40

An element, feature, οr factοr that is liable tο vary οr change

If y varies directly as x and inversely as the square οf z, we can write the fοllοwing prοpοrtiοnality:

y ∝ x/z²

where ∝ denοtes prοpοrtiοnality cοnstant.

Tο find the value οf ∝, we can use the given values οf y, x, and z:

y = ∝ x/z²

28 = ∝ (63)/(3)²

∝ = 28 * (3)² / (63)

∝ = 4/3

Nοw we can use this value οf ∝ tο find y when x=80 and z=2:

y = ∝ x/z²

y = (4/3) * (80)/(2)²

y = 40

Therefοre, when x=80 and z=2, y=40.

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Answer:

We will use mathematical induction to prove the formula for the sum of arithmetic sequences:

For n=1, we have:

∑j=1^1(a + (j-1)d) = a

On the other hand, we have:

n/2(2a + (n-1)d) = 1/2(2a) = a

Thus, the formula holds for n=1.

Assuming the formula holds for n=k, we will prove that it holds for n=k+1.

We have:

∑j=1^(k+1)(a + (j-1)d) = (a + kd) + ∑j=1^k(a + (j-1)d)

Using the formula for n=k, we can write:

∑j=1^k(a + (j-1)d) = k/2(2a + (k-1)d)

Substituting this back into the first equation, we have:

∑j=1^(k+1)(a + (j-1)d) = (a + kd) + k/2(2a + (k-1)d)

Simplifying the right-hand side, we get:

∑j=1^(k+1)(a + (j-1)d) = 1/2(2a + (2k+1)d)

But (k+1)/2(2a + kd + d) = 1/2(2a + (2k+1)d), so the formula holds for n=k+1.

Therefore, by mathematical induction, the formula for the sum of arithmetic sequences is proved.

Answer:

9.5in

Step-by-step explanation:

44.4in = 12.7 +22.2 +x(missing side)

34.9+x=44.4in

x=44.4in-34.9in

x=9.5in

Answer:

12.1 in

Step-by-step explanation:

what is your problem with that ? you don't understand what "perimeter" means ?

it means the whole way around the figure 1 time. it is the sum of all sides.

so, when we have the sum but miss one element of the dimensions numbers ?

what do you think we do ?

we calculate the difference between the sum of the elements we have, and the total sum.

this difference must be the missing side length.

so, the total is 136.8 in.

what we have is

44.4+10+10+12.7+22.2+12.7+12.7 =

= 44.4 + 20 + 3×12.7 + 22.2 = 124.7 in

the difference is

136.8 - 124.7 = 12.1 in

that is our missing side length.

you see, the picture tries to convince us that all the angles are right angles (90°). in that case the missing side length would be simply

44.4 - 12.7 - 22 2 = 9.5 in.

but no, it is good that we did not simply fall for an optical illusion. the absolute numbers tell us that some of the angles must be slightly different from 90°.

in case of doubt always rely on the absolute numbers.

As all the sides of the closed figure are equal to each other, the quadrilateral here is a square.

A square is a closed, two-dimensional (2D), object with four corners. With four sides and four vertices, a quadrilateral is referred to as a square. All four sides of a square are equal and parallel.

In other words, a square is a polygon or quadrilateral with four sides. An equiangular quadrilateral is a shape in which all of the angles are of equal size.

Here in the given figure, we can see a quadrilateral is given.

We can see that all the sides of the quadrilateral are given to be equal to each other.

We can conclude from the observation that the quadrilateral is a square as the sides are all equal to each other.

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Answer:

See step by step.

Step-by-step explanation:

lets define the events:
A: cuban festival        C: tropical Garden
B: street art show      D: african festival

a) theoretically the probability is

[tex]P(A)=P(B)=P(C)=P(D)= \frac{1}{4} = 0.25 \\[/tex]
This is 25% (for each one, equally)

b) The experimental probability is given by:

[tex]P(A)= \frac{32}{150} =0.2133[/tex]

[tex]P(B)= \frac{38}{150} =0.2533[/tex]

[tex]P(C)= \frac{35}{150} =0.2333[/tex]
[tex]P(D)= \frac{45}{150} =0.3000[/tex]

c) The theoretically probabilities are all equally, the experimental probabilities are close to 25% each one, but differ lightly each one, since is an experiment and the result is random.  

Answer:

[tex]v = \frac{7}{2}[/tex]

Step-by-step explanation:

Therefore, the average rate of change between the points (3,9) and (5,15) is 3.

Coordinates are a set of values that locate the position of a point in space. In mathematics, coordinates are used to represent the position of points on a plane or in space, using a set of numerical values that correspond to the distance along each axis from an origin point. In two-dimensional Cartesian coordinate systems, for example, a point is represented by two numbers (x, y) that indicate its position relative to the x and y axes. In three-dimensional Cartesian coordinate systems, a point is represented by three numbers (x, y, z) that indicate its position relative to the x, y, and z axes.

Here,

The average rate of change between the points (3,9) and (5,15) is the slope of the line passing through those two points. We can use the slope formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) = (3,9) and (x2, y2) = (5,15).

slope = (15 - 9) / (5 - 3)

= 6 / 2

= 3

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The missing side is 30.

Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. The triangle's three line segments are referred to as its sides, and its three points of intersection as its vertices.

A triangle is a three-sided polygon formed by three line segments intersecting at three non-collinear points, and it can be classified based on the length of its sides and the measure of its angles.

Given figure, there are two lines ate parallel, that's why two triangles are similar triangle.

Assume that the missing side is x.

So that side ratio in similar triangle are equal;

14/20 = 21/x

So, x = 30.

Therefore, the missing side x is 30

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Triangle Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. According to the question the missing side is 30.

Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. The triangle's three line segments are referred to as its sides, and its three points of intersection as its vertices. A triangle is a three-sided polygon formed by three line segments intersecting at three non-collinear points, and it can be classified based on the length of its sides and the measure of its angles.

Given figure, there are two lines ate parallel, that's why two triangles are similar triangle.
Assume that the missing side is x.
So that side ratio in similar triangle are equal;
14/20 = 21/x

So, x = 30.
Therefore, the missing side x is 30

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