Segment addition pleas help in struggling

Exact value:  [tex]c = \frac{-11+\sqrt{165}}{22}[/tex]

Approximate value:    c = 0.08387

Round the approximate value however you need to

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Work Shown:

Let x = 1+c

[tex]\displaystyle S = \sum_{n=2}^{\infty}(1+c)^{-n}\\\\\\\displaystyle S = \sum_{n=2}^{\infty}x^{-n}\\\\\\\displaystyle S = \sum_{n=2}^{\infty}\frac{1}{x^n}\\\\\\\displaystyle S = \frac{1}{x^2}+\frac{1}{x^3}+\frac{1}{x^4}\ldots\\\\\\[/tex]

We have an infinite geometric series here. The first term is a = 1/(x^2). The common ratio is r = 1/x.

Each new term is found by multiplying the previous term by 1/x.

Assuming -1 < r < 1 is true, the infinite geometric sum is

[tex]S = \frac{a}{1-r}\\\\\\S = \frac{1/x^2}{1-1/x}\\\\\\S = \frac{1/x^2}{x/x-1/x}\\\\\\S = \frac{1/x^2}{(x-1)/x}\\\\\\S = \frac{1}{x^2}\div\frac{x-1}{x}\\\\\\S = \frac{1}{x^2}*\frac{x}{x-1}\\\\\\S = \frac{1}{x^2-x}\\\\\\[/tex]

Plug in S = 11 and solve for x

[tex]S = \frac{1}{x^2-x}\\\\11 = \frac{1}{x^2-x}\\\\11(x^2-x) = 1\\\\11x^2-11x = 1\\\\11x^2-11x-1 = 0\\\\[/tex]

Use the quadratic formula to find the two solutions

[tex]x = \frac{11+\sqrt{165}}{22} \approx 1.08387\\\\x = \frac{11-\sqrt{165}}{22} \approx -0.08387\\\\[/tex]

Using these x values, we find that the corresponding r values are

r = 1/x = 1/(1.08387) = 0.92262

r = 1/x = 1/(-0.08387) = -11.92321

The first r value makes -1 < r < 1 true, but the second r value does not. So we will be ignoring the solution x = -0.08387

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Using the solution that corresponds to x = 1.08387, we find the value of c is

[tex]x = c+1\\\\c = x-1\\\\c = \frac{11+\sqrt{165}}{22}-1\\\\c = \frac{11+\sqrt{165}}{22}-\frac{22}{22}\\\\c = \frac{11+\sqrt{165}-22}{22}\\\\c = \frac{-11+\sqrt{165}}{22}\\\\c \approx 0.08387\\\\[/tex]

Answer:

x= 8

z= 116 degrees

Step-by-step explanation:

the two given angle measures are vertical angles so they are equal to each other, the equation is: 12x-32 = 11x-24

simplify this to get: x= 8

plug the value of x into either of the given equations, I will use the first one: 12(8) - 32

this means that the angle of one of them is 64

and since z and 12x-32 make a straight angle (180 degrees)

you can subtract 64 from 180 to find z

this gives you 180-64 = 116

Answer: (0,-1/2)

Step-by-step explanation:

Edge :-)

Answer: (0,-1/2)

Step-by-step explanation:

Answer:

(2x-2)/x

Step-by-step explanation:

x/x-2/x+1

LCM is x

(x-2+x)/x

(2x-2)/x

Answer:

A is the answear. so jst pick A

Answer:

Step-by-step explanation:

g(2)= 5-9(2)

= -13

f(g(2))= 5+3(-13)

= -34

Answer:

g(2) = -13

f(g(2)) = -34

Explanation:

For g(2), just substitute 2 in for the x, multiply, and simplify.

g(x) = 5-9(x)

g(2) = 5-9(2) = 5-18 = -13

For f(g(2)), substitute this output in for x, multiply, and simplify.

f(x) = 5 + 3(x)

f(g(2)) = 5 + 3(g(2)) = 5 + 3(-13) = 5-39 = -34

Answer:

detailed one

Please mark as the BRAINLIEST

(ㆁωㆁ)

Answer:3/9

Step-by-step explanation: 2/6=1/3. And 1/3x3=3/9

Answer:

28 or it is 42

Step-by-step explanation:

Answer:

35

Step-by-step explanation:

First, you need to know 7 dozen, which is 7*12, which equals 84. Altogether, Pedro had 84 candy bars. He had 14 candy bars left over. 84-14=70  He used 70 candy bars. He gave 2 to each trick-or-treater, so do 70/2=35. He had 35 trick-or-treaters.

Answer:

B:3/4

Step-by-step explanation:

4/5÷16/15= 4/5×15/16= 60/80.

And take 60/80 ÷ 2= 3/4

Answer:

100 grams

Step-by-step explanation:

Formala: multiply the mass value by 100

Answer:

1,000g

Step-by-step explanation:

1kg is equal to 1,000 grams, so just convert it.

1 times 1,000 = 1,000

Answer:

6h

Step-by-step explanation:

If he drove 72 mph and you know how long he drove, just need to divide:

[tex]Distance / Speed = Time[/tex]

Therefore:

[tex]432 / 72mph = 6h[/tex]

Answer:

hi its just like the dood above me said *dude sorry if i was late

Step-by-step explanation:

Answer:

The equation for the question above is y = -1/3x.

Answer:

(4,5)

Step-by-step explanation:

A reflection is a mirror image of the shape.

A reflection across the x-axis maps point (4,-5) to point (4. 5).

A reflection is a mirror image of the shape.

After the reflection, every point in a figure is equidistant from each corresponding point in the reflected figure.

We have,

A point = (4, -5)

The point is reflected across the x-axis.

The reflection formula is given as:

Reflection across the x-axis:

(x, y) → (x, -y)

Reflection across the y-axis:

(x, y) → (-x, y)

The point (4, -5) reflected across the x-axis is:

(4, -5) → (4, - (-5)) = (4, 5)

Thus,

A reflection across the x-axis maps point (4,-5) to point (4. 5).

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Answer: x2-4xy+4y=2xy-5y+2y

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

The correct option that should come next at the end of this row of letters is OOXX.

A sequence can be defined as an arrangement of letters or numbers in a particular manner.

If you look at the given sequence it can be seen as the set of 5 letters where X is starting the set while O is ending the series. Also, the number of X will tend to increase in the next set as well while the number of O will be reduced. Therefore, the series can be seen as,

XOOOO  XXOOO  XXXOO  XXXXO

Thus, the correct option that should come next at the end of this row of letters is OOXX.

Learn more about Sequence:

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Answer:

The number of attendance is 5 times greater than in 1902.

Step-by-step explanation:

Since we have given that

Number of attendance at a major league baseball park in 1902 =

Number of attendance at a major league baseball park in 2002 =

We need to find the number of times that the attendance in 2002 is greater than in 1902.

So, number of times becomes,

Hence, the number of attendance is 5 times greater than in 1902.

Step-by-step explanation:

2B=

10 8 6

0 -6 6

4 12 14

6C=

24 30 36

42 0 18

6 -12 0

so 2B+6C=. 34 38 42

42 -6 24

10 0 14

Answer:

A. commutative property of multiplication

Step-by-step explanation:

The commutative property of multiplication ,

States that when two numbers are being multiplied, their order can be changed without affecting the product.

Answer:

9

Step-by-step explanation:

you would need to find the square root of the total amount of tiles. luckily 81 is a square number meaning the answer is each side is 9 tiles long.

9514 1404 393

Answer:

  L = (x, y) = (1/5, -7)

Step-by-step explanation:

The given relation tells you ...

  (L -J)/(K -L) = 4/1

Cross-multiplying, we have ...

  L -J = 4(K -L)

  5L = 4K +J . . . . add 4L+J

  L = (4K +J)/5

  L = (4(1, -10) +(-3, 5))/5 = (4-3, -40+5)/5

  L = (x, y) = (1/5, -7)

Answer:

28

Step-by-step explanation:

7*4

Answer:

x=7,1

Step-by-step explanation:

Use Math  Way

Answer:

6

Step-by-step explanation:

The given ratio specifies the number of apples to be found in the basket

for a given number of oranges.

Correct response:

The given ratio of apples to oranges in the basket of fruits = 2:7

The number of oranges = 21 oranges

Required:

The number of apples in the basket.

Solution:

The given ratio can be expressed as follows;

Which gives;

[tex]\dfrac{Number \ of \ apples}{21} = \dfrac{2}{7} [/tex]

7 × (Number of apples) = 2 × 21

[tex]Number \ of \ apples = \dfrac{2 \times 21}{7} = 6[/tex]

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[tex]y = 1.38x + 12.60[/tex]

Step-by-step explanation:

Answer:

D.  y = arccosx and y = arcsecx

Step-by-step explanation:

got it right on edge :)

Answer:

The trigonometric function which have the same maximum value is:

y = arcsinx and y = cos x

Concept:

What are Inverse trigonometric functions?

Inverse trigonometric functions are represented as arcsinx, arccosx, arcsecx, and so on.

The trigonometric functions that are used to calculate an angle from any of the angle's trigonometric ratios are called inverse functions.

The formula which is used to in inverse  trigonometric equations are:

arcsinx = -arcsinx

arccosx = pi-arccosx

arctanx = -arctanx

arcsecx = pi - arcsecx

Solution:

The maximum values we obtain from the following equations are:

arcsinx = -1 to 1

arccosx = -1 to 1

arctanx = -pi/2 to pi/2

arcsecx = ∞

So the trigonometric functions which have the same maximum value is arcsinx and arccosx.

Learn more about "inverse trigonometric functions" here-

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Answer:

The monthly payments ≅ $258.335

The total interest of the loan ≅ $1400.095

Step-by-step explanation:

The rule of the monthly payments is

[tex]M.P=\frac{P(\frac{r}{n})}{1-(1+\frac{r}{n})^{-nt}}[/tex] , where

∵ You borrow ​$11000

∴ P = 11000

∵ It will be for 4 years

∴ t = 4

∵ The rate is 6%

∴ r = 6% = [tex]\frac{6}{100}[/tex] = 0.06

∵ It is a monthly payment

∴ n = 12

→ Substitute these values in the rule above

∴ [tex]M.P=\frac{11000(\frac{0.06}{12})}{1-(1+\frac{0.06}{12})^{-12(4)}}[/tex]

→ Use your calculator to find the answer

∴ M.P = 258.3353195

∴ The monthly payments ≅ $258.335

→ The total interest of the loan is the difference between the total

   of the monthly payments and the initial amount

∴ The total interest of the loan = T.M.P - P

∵ The total of the monthly payments = M.P × t × n

∴ The total of the monthly payments = 258.3353195 × 4 × 12

∴ The total of the monthly payments = $12400.09534

∵ The initial amount P = $11000

∴ The total interest of the loan = 12400.09534 - 11000

∴ The total interest of the loan = 1400.095

∴ The total interest of the loan ≅ $1400.095