what is the 20th term of the sequence 1,3,9,27

Answer:

6 and -4

Step-by-step explanation:

Let the first number be n.

Other number= [tex]\frac{-24}{n}[/tex]

Their sum= 2

n + [tex]\frac{-24}{n}[/tex]= 2

[tex]\frac{n^{2-24} }{n}[/tex]= 2

n²-24= 2n

You can solve this problem in either of these 2 ways:

i) Square Completion method:

  n²-2n = 24

  Half of the coefficient= [tex]\frac{2}{2}[/tex] =1

  Its square= 1²= 1

  n²-2n+1= 24+1

      (n-1)²= 25

          n-1= [tex]\sqrt{25}[/tex]

          n-1= ±5

  If n-1= 5,

     n= 5+1

     n= 6

  If n-1= -5,

     n= -5+1

     n= -4

  ∴ the numbers are 6 and -4

ii) Equation Method:

   n²-24= 2n

   n²-2n-24= 0

   a= 1,

   b= -2,

  -b= 2,

   c= -24

   n= -b±[tex]\sqrt{b^{2}-4ac }[/tex]/2a

   n= 2±[tex]\sqrt{-2^{2}-4x1x-24[/tex]/2x1

   n= 2±[tex]\sqrt{4+96}[/tex]/2

   n= 2±[tex]\sqrt{100}[/tex]/2

   n= 2±10/2

   If n= [tex]\frac{2+10}{2}[/tex],

      n= [tex]\frac{12}{2}[/tex]

      n= 6

   If n= [tex]\frac{2-10}{2}[/tex],

      n= [tex]\frac{-8}{2}[/tex]

      n= -4

∴ the numbers are 6 and -4

The quadratic function in standard form of f (x) = x2 - 8x + 23 is  (x) = (x - 4)2 + 7.

The quadratic function given is f (x) = x2 - 8x + 23. To rewrite this function in standard form, we need to complete the square for the x terms. Standard form for a quadratic function is f (x) = a(x - h)2 + k, where (h, k) is the vertex of the parabola.

f (x) = 1(x2 - 8x) + 23

f (x) = 1(x2 - 8x + 16) + 23 - 16

f (x) = 1(x2 - 8x + 16) + 7

f (x) = 1(x - 4)2 + 7

The final answer is f (x) = (x - 4)2 + 7, which is the standard form of the given quadratic function.

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The value of cos J rounded to the nearest hundredth is 0.384.

A mathematical function known as the cosine is used in many branches of mathematics, such as geometry and trigonometry. It is described as the proportion between the hypotenuse and the adjacent side of a right triangle. It is represented by the symbol cos-1 or arc cos and is also known as the inverse cosine or arc cosine.

Using Pythagoras theorem lets find IJ

IJ = [tex]\sqrt{13^2 - 12^2}[/tex]

IJ = √25

IJ = 5

Now,

cos θ = Adjacent side/Hypotenuse

cos J = IJ/HJ

= 5/13

= 0.384

Thus, the value of cos J rounded to the nearest hundredth is 0.384.

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Complete question:

Find the value of cos J rounded to the nearest hundredth, if necessary.

Answer:

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

Given two points:

Find the slope of the line containing these points.

Slope equation:

Substitute coordinates and find the slope:

Answer:

-1/10

Step-by-step explanation:

To find:-

Answer:-

We are here given two points and we are interested in finding out the slope of the line passing through the points. Slope can be calculated by using;

[tex]:\implies \sf \boxed{\pink{\sf m =\dfrac{y_2-y_1}{x_2-x_1}}} \\[/tex]

where ,

Also , we can write the coordinate (-3,-7/2) as (-3,-3.5) .

So on substituting the respective values, we have;

[tex]:\implies \sf m =\dfrac{-3.5- (-4)}{-3-2} \\[/tex]

[tex]:\implies \sf m = \dfrac{-3.5+4}{-5} \\[/tex]

[tex]:\implies \sf m =\dfrac{0.5}{-5} \\[/tex]

[tex]:\implies \sf m = \dfrac{1}{2(-5)}\\[/tex]

[tex]:\implies \sf m =\dfrac{1}{-10} \\[/tex]

[tex]:\implies \sf \pink{ m =\dfrac{-1}{10}} \\[/tex]

Hence the slope of the line is -1/10 .

\[
 T_{1} \circ T_{2}\left(\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]\right)=\left[\begin{array}{r} 43 x_{1}+2 x_{2} \\ -10 x_{1}+4 x_{2}\end{array}\right]
\]

Let \(T_{1}\) and \(T_{2}\) be linear transformations given by
\[\begin{array}{l}
 T_{1}\left(\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]\right)=\left[\begin{array}{r} 3 x_{1}+6 x_{2} \\ 5 x_{1}-2 x_{2}\end{array}\right] \\
 T_{2}\left(\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]\right)=\left[\begin{array}{r} 8 x_{1}+4 x_{2} \\ 5 x_{1}+2 x_{2}\end{array}\right]
\end{array}\]
A linear transformation is a function that takes two input values and returns two output values in a way that preserves the linear structure of the data. It is described by a matrix that determines the output values from the input values. In the case of \(T_{1}\) and \(T_{2}\), the matrix is
\[
 M=\left[\begin{array}{cc}
   3 & 6 \\
   5 & -2
 \end{array}\right]
\]
and
\[
 M=\left[\begin{array}{cc}
   8 & 4 \\
   5 & 2
 \end{array}\right]
\]
respectively. The two linear transformations can be combined using matrix multiplication, which yields the transformation
\[
 T_{1} \circ T_{2}\left(\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]\right)=M_{1} M_{2}\left(\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]\right)
\]
where
\[
 M_{1}M_{2}=\left[\begin{array}{cc}
   43 & 2 \\
   -10 & 4
 \end{array}\right].
\]
Therefore, the result of applying both transformations to a given input vector is given by
\[
 T_{1} \circ T_{2}\left(\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]\right)=\left[\begin{array}{r} 43 x_{1}+2 x_{2} \\ -10 x_{1}+4 x_{2}\end{array}\right]
\]
This is an example of a linear transformation, where two transformations are combined to produce a single result.

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Answer: what is ur questions?

Step-by-step explanation:

If the length and width of the pen are both whole numbers the possible perimeters for the pen are 98, 52, 38, 32, and 28.

To find the possible perimeters of the pen, we first need to find all the possible length and width pairs that would give us an area of 48 square feet. Since the length and width are whole numbers, we can start by listing out all the factors of 48:

1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Each of these factors represents a possible length or width of the pen, and we can find the other dimension by dividing the area (48) by the first dimension. For example, if the first dimension is 1, then the other dimension is 48/1 = 48. However, we need to make sure that the second dimension is also a whole number.

Using this method, we can find all the possible length and width pairs:

1 x 48, 2 x 24, 3 x 16, 4 x 12, 6 x 8

Now we can calculate the perimeter for each of these pairs. The perimeter is the sum of the lengths of all four sides of the pen. Since the length and width are the same for a square pen, we can use the formula:

perimeter = 2(length + width)

For each pair, we can plug in the values for length and width to get the perimeter:

1 x 48: perimeter = 2(1 + 48) = 98

2 x 24: perimeter = 2(2 + 24) = 52

3 x 16: perimeter = 2(3 + 16) = 38

4 x 12: perimeter = 2(4 + 12) = 32

6 x 8: perimeter = 2(6 + 8) = 28

Therefore, the possible perimeters for the pen are 98, 52, 38, 32, and 28.

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The fully factored form is (m-9)(m-12)(m+2) / [2(m+8)(m-8)].

To subtract the rational expressions and find the answer in its fully factored form, we first need to find a common denominator for the two expressions.

The denominators of the two expressions are (m^(2)-64) and (2m^(2)-128). We can factor both of these to find the common denominator.

(m^(2)-64) = (m+8)(m-8)

(2m^(2)-128) = 2(m^(2)-64) = 2(m+8)(m-8)

The common denominator is 2(m+8)(m-8).

Now we can rewrite the two expressions with the common denominator and subtract them:

[(m^(2)+4m-12)(2) - (m^(2)+11m+24)(m+8)(m-8)] / [2(m+8)(m-8)]

= [(2m^(2)+8m-24) - (m^(3)+11m^(2)+24m+8m^(2)+88m+192)] / [2(m+8)(m-8)]

= [m^(3)-17m^(2)-104m-216] / [2(m+8)(m-8)]

= (m-9)(m^(2)-8m-24) / [2(m+8)(m-8)]

= (m-9)(m-12)(m+2) / [2(m+8)(m-8)]

So the answer in its fully factored form is (m-9)(m-12)(m+2) / [2(m+8)(m-8)].

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As a result, the formula is (cos 2x - 1) / (2 sin x cos x)

A mathematical expression shows the worth of something by combining numbers, factors, and functions. A mathematical assertion known as an equation involves setting two expressions equivalent to one another.

We can start by using the identity:

cos 2x = cos² x - sin² x

We can rearrange this to get:

cos² x = cos 2x + sin² x

Substituting this into the expression we want to simplify, we get:

(cos² x - sin² x - 1) / (sin 2x)

We can then use the identity:

sin 2x = 2 sin x cos x

Substituting this into the expression, we get:

(cos² x - sin² x - 1) / (2 sin x cos x)

We can simplify the numerator using the identity:

cos² x - sin² x = cos 2x

Substituting this into the expression, we get:

(cos 2x - 1) / (2 sin x cos x)

Therefore, the simplified expression is:

(cos 2x - 1) / (2 sin x cos x)

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The volume of the right square pyramid with the dimensions e = 5m, h = 4m, and s = 6m is 48m³.

Pyramid is a structure with a polygonal base and triangular sides that meet at a point. Pyramids have been used throughout history as tombs, temples and monuments. Many of the most famous pyramids are located in Egypt, such as the Great Pyramid of Giza.

The volume of a right square pyramid is equal to one-third of the base area multiplied by the height. To find the volume of this pyramid, we first need to calculate the base area.
The base area of a square pyramid is equal to the length of one side (s) squared. Since the length of one side of this pyramid is 6m, the base area is 6m x 6m, which equals 36m².
Now that we know the base area, we can calculate the volume of the pyramid. The volume is equal to one-third of the base area multiplied by the height. In this case, the volume of the pyramid is one-third of 36m² multiplied by 4m, which equals 48m³.
Therefore, the volume of the right square pyramid with the dimensions e = 5m, h = 4m, and s = 6m is 48m³.

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The ground distance, given the map distance and the scale, would be 5 kilometers.

If the scale on a map is 1:25,000, it means that one unit of distance on the map represents 25,000 units of distance on the ground. If the map distance is 20 cm, we can find the ground distance as follows:

Convert the map distance from centimeters to kilometers:

20 cm = 0.2 m = 0. 0002 km

Find the ground distance using the scale:

Ground distance = Map distance / Scale

Ground distance = 0. 0002 km / ( 1 / 25,000 )

Ground distance = 0.0002 km x 25,000

Ground distance = 5 km

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The full question is:

The scale on a map is 1:25,000. Calculate the ground distance if the map distance is 20 cm write your answer in kilometers​

Comparing the two probabilities, we can see that the probability of any particular letter being called first (1/5) is five times greater than the probability of any particular number being called first (1/75). This is because there are five letters and only one number will be called first.

Viet's description of the probability of each number being called first can be determined as follows. There are 75 numbers in the set, and each number has an equal chance of being called first. Therefore, the probability of any particular number being called first is 1/75.

Quinn's description of the probability of any particular letter being called first can be determined as follows. There are five letters in the set, and each letter has 15 numbers associated with it. Therefore, the probability of any particular letter being called first is 15/75 or 1/5.

Comparing the probabilities, we can see that the probability of any particular letter being called first is greater than the probability of any particular number being called first. This is because there are fewer letters (5) than numbers (75), so the probability of selecting a particular letter is higher than the probability of selecting a particular number.

Therefore, Quinn's probability of any particular letter being called first is greater than Viet's probability of any particular number being called first.

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See transcribed text below

TOPIC

7

MID-TOPIC PERFORMANCE TASK

Viet, Quinn, and Lucy are going to play Bingo, using a standard game set. They make some predictions before the game begins. The table shows how the numbers match with the letters B, I, N, G, and O.

Letter

Numbers

B - 1-15

1 -16-30

N-31-45

G- 46-60

O- 61-75

PART A

Viet describes the probability of each number being called first. Quinn describes the probability of any particular letter being called first. Compare the probabilities.

The value of x is equal to 10.

In Mathematics, the basic proportionality theorem states that when any of the two (2) sides of a line segment is intersected by a straight line which is parallel to the third (3rd) side of the line segment, then, the two (2) sides that are intersected would be divided proportionally and in the same ratio.

By applying the basic proportionality theorem to the given triangle, we have the following:

21/(x - 3) = 27/(x - 1)

By cross-multiplying, we have the following:

21(x - 1) = 27(x - 3)

21x - 21 = 27x - 81

27x - 21x = 81 - 21

6x = 60

x = 60/6

x = 10.

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The total percentage of capital contributed by Jacklyn is 30%

The total capital contributed by Sandra, Jaclyn, and Alecia is:

$400 + $600 + $1000 = $2000

To find the percentage of capital contributed by Jacklyn contributed,

Percentage contributed by Jaclyn = (Jaclyn's contribution / Total capital) x 100

= ($600 / $2000) x 100

= 30%

Therefore, Jacklyn contributed 30% of the capital.

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The quadrants that contain all the points found on the linear function -3x + 5y = 15 are given as follows:

The linear function for this problem is defined as follows:

-3x + 5y = 15.

In slope-intercept format, it is given as follows:

5y = 3x + 15

y = 0.6x + 3.

The features of the line are given as follows:

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The remainder is -21 and the quotient is 6a2-18a+21.

Synthetic division is a method for dividing polynomials by monomials. It is a simplified form of the long division of polynomials, and is useful when the divisor is a monomial. The method involves arranging the coefficients of the dividend in a row, and then dividing each term by the divisor .

To determine the quotient and remainder when (2a3+7a2+2a+9) is divided by (2a+3), you can use either long division or synthetic division.

Using long division:

÷2a+3
2a3+7a2+2a+9
-6a2        (2a3 ÷ 2a = 6a2)
-18a        (7a2 ÷ 2a = 3a2 = 18a)
-21        (2a+9 ÷ 2a+3 = -2a+12 ÷ 2a+3 = -21)

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The product  is less than 35.

To analyze this problem without calculating, we can look at the factors involved in the product. The first factor is 7, and the second factor is 5(3)/(4).

The second factor, 5(3)/(4), is less than 5 because it is the product of 5 and a fraction less than 1.

When we multiply 7 by a number less than 5, the result will be less than 35.

Therefore, the product of 7 and 5(3)/(4) is less than 35.

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First, we need to convert 8 yards to inches since the measurement of ribbon needed for one present is given in inches.

1 yard = 36 inches (since 1 yard = 3 feet and 1 foot = 12 inches)

So, 8 yards = 8 x 36 = 288 inches.

To find out how many presents can be wrapped with 288 inches of ribbon, we divide the total length of ribbon by the length needed for one present:

Number of presents = Total length of ribbon ÷ Length of ribbon needed for one present

Number of presents = 288 ÷ 9

Number of presents = 32

Therefore, 32 presents can be wrapped with 8 yards (288 inches) of ribbon.

Hence, the answer is 32 presents.

Answer: c(32

Step-by-step explanation:

Solving a quadratic equation we can see that Jason will hit the water after 6 seconds.

We know that the height of Jason is modeled by the quadratic function:

h = - 16x² + 16x + 480

The water is at h = 0, so we need to solve the quadratic equation:

0 = - 16x² + 16x + 480

If we divide all the right side by 16,we will get:

0 = (- 16x² + 16x + 480)/16

0 = -x² + x + 30

Now we can use the quadratic formula to get the solutions:

[tex]x = \frac{-1 \pm \sqrt{1^2 - 4*(-1)*30} }{2*-1} \\\\x = \frac{-1 \pm 11 }{-2}[/tex]

We only care for the positive solution, which is:

x  = (-1 - 11)/-2 = 6

Jason will hit the water after 6 seconds.

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3 cups of fruit mix is divided equally among 18 items.

Each item will contain 1/6 cup of fruit mix.

First we need to divide the total amount of fruit mix by the number of items.

The total amount of fruit mix is :

8/5 cups of blueberries + 7/5 cups of strawberries

= (8/5 + 7/5) cups

= 15/5 cups

= 3 cups

So, 3 cups of fruit mix is divided equally among 18 items.

To find the fraction of a cup used for each item, we need to divide 3 cups by 18:

Copy code

3 cups ÷ 18 = 1/6 cup

Therefore, each item will contain 1/6 cup of fruit mix.

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P(2) = 73.

To evaluate P(C) using synthetic division and the Remainder Theorem, we will follow the following steps:

Set up the synthetic division table with the value of C on the left and the coefficients of P(x) on the right.

Bring down the first coefficient to the bottom row.

Multiply the value of C by the first coefficient in the bottom row and place the result in the next column.

Add the values in the second column and place the result in the bottom row.

Repeat steps 3 and 4 for the remaining columns.

The last value in the bottom row is the remainder. According to the Remainder Theorem, this is the value of P(C).

Therefore, P(2) = 73.

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The polynomial that need to be added is
(2/5)a^(4) + (-15/4)a^(3) + (1/6)a^(2) + (11/6)a - 3/5 - 5a^(2)b^(2) - 3ab^(2) + 5a^(2)b + 9

To add or subtract polynomials, we need to combine like terms. Like terms are terms that have the same variable and the same exponent.

First, let's add the first two polynomials:

((2)/(5)a^(4)-6a^(3)-(5)/(6)a^(2)+(a)/(2)+1)+((9)/(4)a^(3)+(2a^(2))/(3)+(5)/(3)a-(8)/(5))

= (2/5)a^(4) + (-6 + 9/4)a^(3) + (-5/6 + 2/3)a^(2) + (1/2 + 5/3)a + 1 - 8/5

= (2/5)a^(4) + (-15/4)a^(3) + (1/6)a^(2) + (11/6)a - 3/5

Now, let's subtract the third polynomial from this result:

(2/5)a^(4) + (-15/4)a^(3) + (1/6)a^(2) + (11/6)a - 3/5 - (2a^(2)b^(2)+3ab^(2)-5a^(2)b)

= (2/5)a^(4) + (-15/4)a^(3) + (1/6)a^(2) + (11/6)a - 3/5 - 2a^(2)b^(2) - 3ab^(2) + 5a^(2)b

Finally, let's subtract the last term from this result:

(2/5)a^(4) + (-15/4)a^(3) + (1/6)a^(2) + (11/6)a - 3/5 - 2a^(2)b^(2) - 3ab^(2) + 5a^(2)b - (3a^(2)b^(2)-9)

= (2/5)a^(4) + (-15/4)a^(3) + (1/6)a^(2) + (11/6)a - 3/5 - 5a^(2)b^(2) - 3ab^(2) + 5a^(2)b + 9

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Answer: Let T be the number of true/false questions on the exam, and let M be the number of multiple choice questions on the exam.

Then, the total number of points Manuel can earn on the exam is:

3T + 4M

We know that Manuel needs more than 82 points on the exam to get an A in the class. Therefore, we can write the following inequality:

3x + 4y > 82

where x is the number of true/false questions Manuel gets correct, and y is the number of multiple choice questions Manuel gets correct.

Step-by-step explanation:

The point that would be included in the region shaded to show the half-plane greater than the line is the point that lies above the line.

In order to determine which point is included in the region shaded to show the half-plane greater than the line, we can use the following steps:
1. Identify the equation of the line.
2. Plug in the x and y values of the point into the equation of the line.
3. If the result is greater than the constant term in the equation of the line, then the point is included in the region shaded to show the half-plane greater than the line.

For example, if the equation of the line is y = 2x + 1, and the point is (2,5), we can plug in the x and y values into the equation:
5 = 2(2) + 1
5 = 5

Since the result is equal to the constant term in the equation of the line, the point (2,5) is included in the region shaded to show the half-plane greater than the line.

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To find the coordinates of point R after the reflection and translation, we would need to know its original coordinates in the figure QRST. Then we could apply the above rules to get its new coordinates.

What are coordinates ?

Coordinates are numerical values that specify the position or location of a point in a given space. In mathematics, coordinates are often expressed as ordered pairs or triplets of numbers, which correspond to the distances of the point from a set of fixed reference points or axes.

Without seeing the figure QRST, it is not possible to give the exact coordinates for point R after the reflection and translation. However, we can use some general knowledge about the effects of reflection and translation on the coordinates of a point.

When a figure is reflected across the x-axis, the x-coordinates of all its points remain the same, but the y-coordinates are negated. That is, if a point has coordinates (x, y) before the reflection, its coordinates after the reflection will be (x, -y).

When a figure is translated down by 3 units, the y-coordinates of all its points are decreased by 3. That is, if a point has coordinates (x, y) before the translation, its coordinates after the translation will be (x, y - 3).

Therefore, to find the coordinates of point R after the reflection and translation, we would need to know its original coordinates in the figure QRST. Then we could apply the above rules to get its new coordinates.

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According to the inequality, Christopher would need to purchase 35 + 10s 75 sets of spoons to ensure that the restaurant has enough of them.

According to analysts, inequality promotes political dysfunction and slows down economic progress. Because wealthy households typically spend a smaller proportion of what they earn than do poorer households, concentrated earnings lower the amount of demand for goods and services. The economy may suffer if low-income families have fewer possibilities.

There are already 355 spoons available, but the eatery needs at least 75. Each set that is for sale includes 10 spoons.

Let s be the representation of each set. It will be demonstrated by:

35 + (10 × s) ≥ 75

35 + 10s ≥ 75

Collect like terms

10s ≥ 75 - 30

10s ≥ 45

Divide

s ≥ 45/10

s ≥ 4.5

The restaurant must have at least 5 sets.

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Answer: 10s + 355 >=755

s>=42

Step-by-step explanation:

Total 3 hours of labor were required to fix the computer.

To find the number of hours of labor required to fix the computer, we can use the following equation:

Total cost = Cost of parts + (Cost of labor per hour × Number of hours of labor)

We can rearrange this equation to solve for the number of hours of labor:

Number of hours of labor = (Total cost - Cost of parts) ÷ Cost of labor per hour

Plugging in the given values:

Number of hours of labor = ($190 - $115) ÷ $25

Number of hours of labor = $75 ÷ $25

Number of hours of labor = 3 hr

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The value of x and y in the line segment are 6 and 6.5 units repsectively.

The lines are three parallel lines cut by two transversal lines. The transversal lines that cut across the parallel lines have same length at intervals .

Using the information in the diagram let's find the value of x and y in the diagram.

Therefore,

2x + 1 = x + 7

2x - x = 7 - 1

x = 6 units

Therefore,

3y - 8 = y + 5

3y - y = 5 + 8

2y = 13

divide both sides by 2

y = 13 / 2

y = 6.5 units

Therefore,

x = 6 units

y = 6.5 units

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