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Thank ya 

Excellent, RP  !!!

An insribed angle  measures  1/2  of its intercepted arc  ...

So

(1/2) *DG  =   55      multiply both sides by 2

DG  =  110°

Good job Cphill!

9.  Yes,  2/3

10.  

10th term   =  81(1/3)^{n -1}   =  81(1/3)^10-1  =  81(1/3)⁹  = 1/243

They are the answers  .....I just used "?"  to stand for a variable

6. Not arithmetic because the difference between terms is not constant

7.  12th term  =

15  - 4 (12 - 1)  =

15 - 4(11)  =

15  -  44 =

-29

8.  To find the missing term

[ First term + Third term ]  /  2   =

[ 20 + 32 ]  / 2

52  / 2  =

26

I'm guessing I have to solve those two or are those the answers..

thanks electric pavlov

Hello

8.

16 / 8  =   ? / 20

2  = ? / 20           multiply both sides by 20

40  = ?

9.

25/ 20  = ? / 8

5/4  = ? / 8     multiply both sides by 8

8 * 5/4  =  40/4  =  10  =  ?

10.  Note that the missing side of A  =  1/6 * 48    =  8

4.  After Third Bounce 

6 (.80)^3  = 3.072 ft  =  3.1 ft  

5.   The number of bacterium increases by 22 every hour....so we have

a_n  =  22n 

My understanding of this is as follows:

There are 8 people, 2 of which must sit together. So, we have 6 + 1(as one unit) =7

The 2 people can sit together in 2! ways. The remaining 6 can be seated in 6! ways without any restrictions. 

So we have a total of: 2! x 6! =1,440 ways without any restrictions. But, we have a restriction that Rosa cannot sit on either side of Pierre and Thomas. Of the 6! ways that the 6 people can sit, Rosa sits to the left of Pierre and Thomas in 6!/6 = 120 ways. And, similarly, she can sit to the right of Pierre and Thomas in 6!/6 = 120 ways. So, 120 x 2 = 240 positions that must be excluded from 1,440. Or:

1,440 - 240 =1,200 ways that the 8 people can be seated on a round table with the restrictions given.

Tan 30 = sin 30 / cos 30

 = 1/2 / sqrt3/2

= 1 /sqrt 3  

tan (30°)  =  1 / √3  =  √3 / 3

3.)

x^2 - 6x + 8 = x-2

x^2 - 7x -6 = 0

(x-7)(x+1) = 0

x = 7 or -1 

Scale factor  =  40 / 24  =  10/6  =  5/3

Using Google translate we have:

.

Last one

We have 8 congruent triangles each with a base  of 5.8 cm

We can use the Pythagorean Theorem to find the slant height of each  =

√[ 7^2 + 7^2]  =  √ [2 * 7^2]   =  7√2

So.....the lateral area  is

8 (1/2) (base) (slant height)  =

4 (5.8) (7√2 )  =  229. 7 cm^2

Area of a circle = pi * r^2

Area =  3.14  * 18.4^2  = 1063.08 m^2

Now we are looking for a fraction of this total area    2 pi radians is the entire circle angle....

    we need  10 pi / 7 ths of this:

10pi/7  / 2pi  *  1063.08 = 759 . 34 m^2

3.   We have 8 congruent 30-60-90 triangles

The base of each  =  4.6/ 2   =  2.3

The height of each is opposite the 60° angle  = √3 * base  = √3 * 2.3

So.....the lateral surface area  is

8 (1/2) (base) (height) =

4 (2.3)(√3 * 2.3)  ≈  36.65 yd^2 

The base area  =  side^2  =  4.6^2  = 21.16 yd^2

So....the total area  is     36.65 + 21.16  =  57.8 yd^2

We have a 30-60-90 triangle

The side opposite the 30°  angle  =  1/2  of the hypotenuse  = 6

The side opposite the 60°  angle  is √3  times this  =  6√3  =  x

Area  =   1/2 (diameter/2)^2* (theta in rads)  =

1/2 ( 21.2 / 2)^2 (3 *3.14 / 5 )  =

1/2 ( 10.6)^2  * (3 *3.14 / 5)  ≈   105.84 cm^2