Determine the quotient and remainder when (2a^(3)+7a^(2)+2a+9) is divided by (2a+3). Use long division or synthetic division

The correct solution to the equation is (20 - 24)/6

From the question, we have the following parameters that can be used in our computation:

6(x + 4) = 20.

There are many different expressions that can represent a correct solution to an equation

These expression depends on the specific equation and context.

Open the bracketss

So, we have

6x + 24 = 20

Collect the like terms

6x = 20 - 24

Divide both sides by 6

So, we have the following representation

x = (20 - 24)/6

Hence, the correct expression in the equation solution is (20 - 24)/6

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Answer:

x = -4 + √15 and x = -4 - √15.

Step-by-step explanation:

To solve for x in the equation (x + 4)^2 = 15 using square roots, we can take the square root of both sides of the equation, remembering to include both the positive and negative square root:

(x + 4)^2 = 15

Taking the square root of both sides:

±(x + 4) = √15

Now we can isolate x by subtracting 4 from both sides of the equation:

x + 4 = ±√15

x = -4 ±√15

Therefore, the solutions to the equation (x + 4)^2 = 15 are x = -4 + √15 and x = -4 - √15.

Therefore , the solution of the given problem of unitary method comes out to be the religious gathering thus had 144 more males than girls.

To finish the job using the unitary method, multiply the measures taken from this microsecond variable section by two. In a nutshell, when a wanted thing is present, the characterized by a group but also colour groups are both eliminated from the expression unit technique. For instance, 40 changeable-price pencils would cost Inr ($1.01). It's conceivable that one nation will have complete control over the strategy used to achieve this. Almost all living things have a unique trait.

Here,

Find out how many people and kids are attending the event first.

There were 3 kids for every 4 people. We can thus divide the overall population by the sum of the ratios as follows:

=> 4 + 3 = 7

Adult population

=> (4/7) x 560 = 320

Children's number

=> (3/7) x 560 = 240

Now that we know that the majority of the kids were males,

Number of boys:

=> (4/5) * 240 = 192.

By deducting the number of male children from the total number of children, we can calculate the number of girl children:

48 is the number of girls out of 240 total kids.

There are 192 male children and 48 girl children, which equals 144.

The religious gathering thus had 144 more males than girls.

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In analysis the results are a) 0.017,  b) 0.1515, c) punctual probability, and d) Outcome is improbable.

Probability is a way to gauge how likely something is to happen. Several things are difficult to forecast with absolute confidence. With it, we can only make predictions about the likelihood of an event happening, or how likely it is.

a)Sd(Y) = (226) = 15.033 .

Let's call Z the approximation, we conclude:

X = [tex]\frac{Z-452}{15.033}[/tex]

With reference, that would be 0.017.

b) P(Y ≥ 467) is just 0.1515, a low number. This means that it 467girls from 904 births is a pretty high number.

c) Calculating a punctual probability will likely provide a low figure due to a large number of potential outcomes.

d) The results appear to be relatively successful. We thus estimate that getting a comparable or better outcome is improbable.

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Answer:

enter the step by step answer u did and then add the number the match and enter them in the box and u shall be done

Step-by-step explanation:

a polynomial function completely multiplied out with real coefficient  that has the given zeros is f(x) = x³-x²-16x+16

To find a polynomial function with the specified zeros that is fully multiplied out with real coefficients, we can use the fact that if a polynomial has a zero at x = a, then (x-a) is a factor of the polynomial. Therefore, we can write the polynomial as a product of its factors:

(x-1)(x+4)(x-(3+1)) = (x-1)(x+4)(x-4)

Now, we can multiply out the factors to get the polynomial in standard form:

(x-1)(x+4)(x-4) = (x²+3x-4)(x-4) = x³+3x^(2)-4x-4x²-12x+16 = x³-x²-16x+16

Therefore, the polynomial function completely multiplied out with real coefficients that has the given zeros is:

f(x) = x³-x²-16x+16

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The domain and range of the function are respectively, (-6, 6) & (0, 6).

The domain of a function is the set of all input values (independent variable) for which the function is defined and produces a valid output (dependent variable).

The range of a function is the set of all possible output values of the function. It represents the set of all possible values of the dependent variable.

Given that,

The graph of the function,

As we know from the definition of the graph,

the domain is all the possible values of the function for which it gives definite value so it can be seen in the graph,

function gives definite value only in the interval (-6, 6)

The range is all the outputs for the input value of  domain

and it can be seen in the graph,

the output values are in the range of (0, 6)

Therefore, the domain and range are respectively (-6, 6) & (0,6)

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The exact value of \( \tan \left(\arccos \frac{2}{3}\right) \) is:
\( \tan \left(\arccos \frac{2}{3}\right) = \frac{\sin \left(\arccos \frac{2}{3}\right)}{\cos \left(\arccos \frac{2}{3}\right)} = \frac{\frac{\sqrt{5}}{3}}{\frac{2}{3}} = \frac{\sqrt{5}}{2} \).

1) The exact value of \( \sin ^{-1}\left(\sin \frac{5 \pi}{3}\right) \) is \( \frac{\pi}{3} \).
2) The exact value of \( \tan \left(\arccos \frac{2}{3}\right) \) is \( \frac{\sqrt{5}}{2} \).
Explanation:
1) We know that \( \sin \frac{5 \pi}{3} = \sin \left(\frac{5 \pi}{3} - 2\pi\right) = \sin \left(\frac{5 \pi}{3} - \frac{6 \pi}{3}\right) = \sin \left(-\frac{\pi}{3}\right) = -\sin \frac{\pi}{3} = -\frac{\sqrt{3}}{2} \).
So, we have:
\( \sin ^{-1}\left(\sin \frac{5 \pi}{3}\right) = \sin ^{-1}\left(-\frac{\sqrt{3}}{2}\right) = -\frac{\pi}{3} \).
But, since the range of the inverse sine function is \( \left[-\frac{\pi}{2}, \frac{\pi}{2}\right] \), we need to find an angle in this range that has the same sine value.
We know that \( \sin \frac{\pi}{3} = \frac{\sqrt{3}}{2} \), so \( \sin \left(\pi - \frac{\pi}{3}\right) = \sin \frac{2\pi}{3} = \frac{\sqrt{3}}{2} \).
Therefore, the exact value of \( \sin ^{-1}\left(\sin \frac{5 \pi}{3}\right) \) is \( \frac{\pi}{3} \).
2) We know that \( \cos \left(\arccos \frac{2}{3}\right) = \frac{2}{3} \), and we need to find the value of \( \tan \left(\arccos \frac{2}{3}\right) \).
Using the Pythagorean identity, we have:
\( \sin ^2 \left(\arccos \frac{2}{3}\right) = 1 - \cos ^2 \left(\arccos \frac{2}{3}\right) = 1 - \left(\frac{2}{3}\right)^2 = 1 - \frac{4}{9} = \frac{5}{9} \).
So, \( \sin \left(\arccos \frac{2}{3}\right) = \frac{\sqrt{5}}{3} \).
Therefore, the exact value of \( \tan \left(\arccos \frac{2}{3}\right) \) is:
\( \tan \left(\arccos \frac{2}{3}\right) = \frac{\sin \left(\arccos \frac{2}{3}\right)}{\cos \left(\arccos \frac{2}{3}\right)} = \frac{\frac{\sqrt{5}}{3}}{\frac{2}{3}} = \frac{\sqrt{5}}{2} \).

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The polynomial function is f(x) = x^3 + 4x^2 - 17x - 60.

To find a polynomial function of degree 3 with real coefficients that has the given zeros, we can use the fact that if a polynomial has a zero of x = a, then (x - a) is a factor of the polynomial. Therefore, if the polynomial has zeros of x = -3, x = 4, and x = -5, then the polynomial can be written in factored form as:

f(x) = (x + 3)(x - 4)(x + 5)

To find the polynomial function in standard form, we can multiply the factors:

f(x) = (x + 3)(x - 4)(x + 5)
f(x) = (x^2 - x - 12)(x + 5)
f(x) = x^3 + 5x^2 - x^2 - 5x - 12x - 60
f(x) = x^3 + 4x^2 - 17x - 60

Therefore, the polynomial function is f(x) = x^3 + 4x^2 - 17x - 60.

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By answering the above question, we may infer that So the perimeter of the regular decagon is approximately 38.2 units (rounded to the nearest tenth).

In geometry, a decagon is either a decagon or not. There are 144° of inner angles total in a simple decagon. A regular decagon that self-intersects is known as a decagram. A polygon with 10 sides, ten internal angles, and ten vertices is called a decagon. Geometry may contain the form known as a decagon. It also has ten horns and ten horns. A dodecagon is a polygon with twelve sides. Some unusual types of dodecagons are shown in the photographs above. Particularly, a regular dodecagon has angles that are equally placed around a circle and sides that are of the same length.

Each interior angle of a regular decagon measures:

[tex]$$(n-2)\times180^\circ/n = (10-2)\times180^\circ/10 = 144^\circ$$\\$$\cos(72^\circ) = \frac{x}{2y}$$[/tex]

Solving for x, we get:

[tex]$$x = 2y\cos(72^\circ)$$[/tex]

We can use the fact that[tex]$\cos(72^\circ) = \frac{1+\sqrt{5}}{4}$[/tex](which can be derived using the golden ratio) to get:

[tex]$$x = 2y\cos(72^\circ) = 2y\cdot\frac{1+\sqrt{5}}{4} = \frac{y}{2}(1+\sqrt{5})$$\\$$R = \frac{x}{2\sin(180^\circ/10)} = \frac{x}{2\sin(36^\circ)}$$\\[/tex]

We can use this formula to find[tex]$y$:[/tex]

[tex]$$y = R = \frac{x}{2\sin(36^\circ)} = \frac{x}{2\sin(\frac{1}{2}\times72^\circ)} = \frac{x}{2\cos(72^\circ/2)}$$[/tex]

We can use the half-angle identity [tex]$\cos(\theta/2) = \sqrt{\frac{1+\cos(\theta)}{2}}$ to simplify this expression:[/tex]

[tex]$$y = \frac{x}{2\cos(72^\circ/2)} = \frac{x}{2\sqrt{\frac{1+\cos(72^\circ)}{2}}} = \frac{x}{2\sqrt{\frac{1+\frac{1+\sqrt{5}}{4}}{2}}} = \frac{x}{2\sqrt{\frac{3+\sqrt{5}}{4}}} = \frac{x}{\sqrt{3+\sqrt{5}}}$$[/tex]

Putting it all together, we have:

[tex]$$\text{Perimeter} = 10x = 10\cdot\frac{y}{2}(1+\sqrt{5}) = 5\sqrt{10+2\sqrt{5}}\approx 38.2$$[/tex]

So the perimeter of the regular decagon is approximately 38.2 units (rounded to the nearest tenth).

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The values of Ф solved using a unit circle, between 0 and 2π, for which tanФ =  - √3 is 2π/3 and 5π/3.

What is a circle?

A circle is a shape made up of all points in a plane that are at a specific distance from the centre point. In other words, it is the path a moving point in a plane takes to move around a curve while maintaining a constant distance from another point. The circle has an area and a perimeter and is a two-dimensional figure. The distance around a circle, or its circumference, is referred to as the perimeter of the circle. The region enclosed by a circle in a 2D plane is said to be its area.

The complete question is given below.

Given,

tan Ф = - √3

We have to find all values of Ф between 0 and 2π using a unit circle.

The unit circle for trigonometric calculations is given below.

from the unit circle,

tan 60 = √3

In quadrant 2,

tan ( 180 - 60) = - tan 60

tan 120 = - tan 160 = -√3

In quadrant 3,  tangent values are positive.

In quadrant 4

tan (360 - 60) = - tan 60

tan 300 = -tan 60 = -√3

Also,

tan 120 = tan 2π/3

tan 300 = tan 5π/3

Therefore the values of Ф solved using a unit circle, between 0 and 2π, for which tanФ =  - √3 is 2π/3 and  5π/3.

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The solution to the equation -(2)/(7)u=-14 is u = 49.

Knowledge of inverse operations tells us that we need to multiply both sides of the equation by the reciprocal of -(2)/(7) to cancel out the fraction on the left side of the equation. The reciprocal of -(2)/(7) is -(7)/(2).

Multiply both sides of the equation by -(7)/(2):
u = -(7)/(2) * -(2)/(7)u = -(7)/(2) * -14

Simplify the left side of the equation:
u = 49

Solve for u:
u = 49

Therefore, the solution to the equation -(2)/(7)u=-14 is u = 49.

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Answer:

Step-by-step explanation:

pamela:  j - 6 years = juri's age.

juri: j + 6 years.

sum of pamela and juri = 94 years.

  j +(j - 6) = 94

  2j - 6 = 94

  2j = 94 - 6

  2j = 88

  j = 44

juri age: 44years and pamela age: 44years - 6years = 38years.

When a = 4, b = 1, and y = 2, the value of x that satisfies the equation x/a + y/b = 1 is -4.

To make x the subject of the formula x/a+y/b=1, we can start by isolating x on one side of the equation. We can do this by subtracting y/b from both sides of the equation:

x/a = 1 - y/b

Next, we can multiply both sides of the equation by a to isolate x:

x = a(1 - y/b)

Now that we have a formula for x in terms of a, b, and y, we can evaluate x when a = 4, b = 1, and y = 2:

x = 4(1 - 2/1)

x = 4(1 - 2)

x = 4(-1)

x = -4

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The volume of the right prism if bases are 15 cm apart is 405√3/2 cm^3.

The volume of a right prism is given by the formula V = Bh, where B is the area of the base and h is the height of the prism. In this case, the base is a regular hexagon with one side measuring 6 cm and the height of the prism is 15 cm.

To find the area of the base, we can use the formula for the area of a regular hexagon: [tex]A = (3√3/2)s^2[/tex], where s is the length of one side.

Plugging in the value of s = 6 cm, we get:
[tex]A = (3√3/2)(6 cm)^2 = 54√3/2 cm^2[/tex]

Now we can plug this value into the formula for the volume of the prism:
V = Bh = ([tex]54√3/2 cm^2)(15 cm) = 405√3/2 cm^3[/tex]

So the volume of the prism is 405√3/2 cm^3.

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Answer:

The missing variable "x" = 20

And the Angle measure = 98°

Step-by-step explanation:

Explaination is given in the picture...

Thank you!

Answer:

the angles are 82 degrees and 98 degrees (5(20) -2), and the missing variable (x) is 20.

Step-by-step explanation:

Let us first look at SL. SL is a straight line and has an angle measure of 180 degrees. Angle RTL is 82 degrees and splits SL into 2. The angle right next to RTL is RTS, which is (5x-2) degrees. Since all of SL adds to 180 degrees, this means that RTL and RTS will add up to 180 degrees, since they are in the middle of it.

82 + 5x-2 = 180

80 +5x = 180

5x = 100

x = 20

Therefore, the angles are 82 degrees and 98 degrees (5(20) -2), and the missing variable (x) is 20.

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If Rοy is οn the 10th rung, then Bοb is οn the 30 - 2t = 30 - 20 = 10th rung as weII, since they wiII be at the same height at this pοint. Therefοre, the answer is that Bοb and Rοy were οn the 10th rung when they were at the same height.

Let's start by figuring οut hοw fast each persοn is mοving in terms οf rungs per secοnd. We knοw that Bοb is gοing dοwn twο rungs every secοnd, sο his speed is -2 rungs/secοnd (the negative sign indicates that he is gοing dοwn). SimiIarIy, we knοw that Rοy is gοing up οne rung every secοnd, sο his speed is +1 rung/secοnd.

We want tο knοw at which rung Bοb and Rοy wiII be at the same height, sο Iet's caII that rung "R". We can set up an equatiοn tο describe this situatiοn:

30 - 2t = R (Bοb's pοsitiοn at time t)

R = rt (Rοy's pοsitiοn at time t)

Here, t is the time that has eIapsed since Bοb and Rοy started cIimbing. We knοw that they started at the bοttοm οf their respective Iadders, sο we can assume that t is the same fοr bοth οf them.

Nοw we can sοIve fοr R by setting the twο expressiοns equaI tο each οther:

30 - 2t = rt

We can sοIve fοr t by rearranging the equatiοn:

t = 30/(r+2)

Substituting this vaIue οf t back intο either οf the οriginaI equatiοns wiII give us the vaIue οf R:

R = rt = r * 30 / (r+2)

Tο find the vaIue οf r that makes R an integer (since we're Iοοking fοr the rung they're οn), we can try different vaIues οf r untiI we find οne that wοrks. Starting with r=1:

R = 1 * 30 / (1+2) = 10

This means that if Rοy is οn the 10th rung, then Bοb is οn the 30 - 2t = 30 - 20 = 10th rung as weII, since they wiII be at the same height at this pοint. Therefοre, the answer is that Bοb and Rοy were οn the 10th rung when they were at the same height.

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To solve the matrix equation for a, b, c, and d, we can equate the corresponding elements of the matrices on both sides of the equation.
So, we get the following system of equations:
a - b = 13  (1)
b + c = 1  (2)
3d + c = 9  (3)
2a - 4d = 12  (4)
From equation (1), we can express b in terms of a:
b = a - 13  (5)
Substituting equation (5) into equation (2), we get:
a - 13 + c = 1
a + c = 14  (6)
From equation (3), we can express c in terms of d:
c = 9 - 3d  (7)
Substituting equation (7) into equation (6), we get:
a + 9 - 3d = 14
a - 3d = 5  (8)
Substituting equation (5) into equation (4), we get:
2a - 4d = 12
a - 2d = 6  (9)
Subtracting equation (9) from equation (8), we get:
d = -1
Substituting d = -1 into equation (7), we get:
c = 9 - 3(-1) = 12
Substituting d = -1 and c = 12 into equation (6), we get:
a + 12 = 14
a = 2
Substituting a = 2 and d = -1 into equation (5), we get:
b = 2 - 13 = -11

So, the solution is a = 2, b = -11, c = 12, and d = -1.

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N(A) is an ideal of R and N(N(A)) = N(A).

a) To prove that N(A) is an ideal of R, we need to show that it is closed under addition and multiplication by elements of R.

Let x, y ∈ N(A) and r ∈ R. Then there exist integers m and n such that xm ∈ A and yn ∈ A. By the commutative property of R, we have:

(x + y)n = xn + xny + yxn + yn ∈ A

(rx)n = rnxn ∈ A

Therefore, x + y ∈ N(A) and rx ∈ N(A), so N(A) is an ideal of R.


b) To prove that N(N(A)) = N(A), we need to show that N(N(A)) ⊆ N(A) and N(A) ⊆ N(N(A)).

Let x ∈ N(N(A)). Then there exists an integer n such that xn ∈ N(A). This means that there exists an integer m such that (xn)m ∈ A. By the associative property of R, we have:

(xn)m = xnm ∈ A

Therefore, x ∈ N(A), so N(N(A)) ⊆ N(A).

Let x ∈ N(A). Then there exists an integer n such that xn ∈ A. Since A ⊆ N(A), we have xn ∈ N(A). Therefore, x ∈ N(N(A)), so N(A) ⊆ N(N(A)).

Hence, N(N(A)) = N(A).
Conclusion: N(A) is an ideal of R and N(N(A)) = N(A).

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Answer:

One example of a sequence is the Fibonacci sequence, which starts with 0 and 1, and each subsequent term is the sum of the two preceding terms:

0, 1, 1, 2, 3, ...

To write the explicit formula for the nth term of the Fibonacci sequence, we can use Binet's formula:

Fn = [((1 + sqrt(5))/2)^n - ((1 - sqrt(5))/2)^n]/sqrt(5)

where Fn is the nth term in the sequence.

To write the recursive formula for the Fibonacci sequence, we can use the definition:

F0 = 0, F1 = 1, and Fn = Fn-1 + Fn-2 for n ≥ 2.

So the first five terms of the Fibonacci sequence are:

F0 = 0

F1 = 1

F2 = 1 (0 + 1)

F3 = 2 (1 + 1)

F4 = 3 (1 + 2)

F5 = 5 (2 + 3)

The explicit formula for the nth term in the sequence is:

Fn = [((1 + sqrt(5))/2)^n - ((1 - sqrt(5))/2)^n]/sqrt(5)

The recursive formula for the nth term in the sequence is:

Fn = Fn-1 + Fn-2 for n ≥ 2, with F0 = 0 and F1 = 1.

Answer:

543.07214553

Round to the Nearest Whole Number

543

The period of the given function f(x) = Cos 4x is π/2

A function is a relation from a set of inputs to a set of possible outputs, where each input is related to exactly one output.

Given is a graph of the function f(x) = Cos 4x, we need to identify the period of this function.

We know that, the function of the form of :-

y = A Cos(Bx), The A and B coefficients can tell us the amplitude and period respectively.

So, comparing this equation to the given function equation, we get,

A = 1, Bx = 4x

The period of cosine is 2π, Therefore, the period would be 2π/B

Therefore, the period of the given function is 2π/4

= π/2

Hence, the period of the given function f(x) = Cos 4x is π/2

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The solution are,

angle P = 130 degrees

arc SF = 50 degrees

Angle may be mentioned as a figure which can be defined as that is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

here, we have,

from the given diagram we get,

angle P = 130 degrees because it is alternate adjacent to 130 degrees.

now, we have,

130 = 1/2(210+SF)

130 = 105+1/2SF

1/2SF = 25

arc SF = 50 degrees

Hence, The solution are,

angle P = 130 degrees

arc SF = 50 degrees

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Answer:

250 g of water

The radius of the cylinder is 3 cm and the surface area of the cylinder is 282.6 sq cm

The value of the cylinder diameter from the question is

Diameter = 6 cm

Calculating the radius, we get

So, we have

r = 6 cm/2

Evaluate

r = 3 cm

The formula of the surface area of the cylinder is represented as

SA = 2πr(r + h)

By substitution, we have

SA = 2π * 3 * (3 + 12)

Evaluate

SA = 282.6

Hence, the surface area is 282.6

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Answer: 0.7% < 1%

Step-by-step explanation:

Percent is out of 100 so...

7/1000 = 0.7/100 = 0.7%

0.7% < 1% so the answer is less than 1%

Hope this helped!

[tex]\huge\begin{array}{ccc}A=75ft^2\end{array}[/tex]

The formula:

[tex]\huge\boxed{A=l\cdot w}[/tex]

[tex]l[/tex] - length of a rectangle

[tex]w[/tex] - width of a rectangle

[tex]l=25ft,\ w=30ft[/tex]

substitute:

[tex]A=25\cdot30=750ft^2[/tex]

Step-by-step explanation:

Refer to pic............

If FG = 8, EH = x - 1: EG = x + 1​

In order to find EG, we need to use the fact that the sum of the lengths of the segments EF and FG is equal to the length of segment EG. That is,

EF + FG = EG

We are given that FG = 8, and we know that EH + HF = EF. Therefore,

EF = EH + HF

Putting this all together, we get:

EF + FG = EG

(EH + HF) + 8 = x + 1

EH + HF = x - 7

But we also know that EH = x - 1, so we can substitute that in:

x - 1 + HF = x - 7

Simplifying this equation, we get:

HF = -6

Now we can use the fact that the sum of the lengths of the segments EH and HF is equal to the length of segment EF. That is,

EH + HF = EF

(x - 1) + (-6) = EF

x - 7 = EF

Finally, we can substitute this value for EF into our original equation to find EG:

EF + FG = EG

(x - 7) + 8 = EG

x + 1 = EG

Therefore, EG = x + 1.

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