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I have to much practice.

First one....this is known as the Intersecting Chord Theorem

In this case

measure of angle BCF = (1/2)( sum of arcs ED + BF)   .....so we have

(11x - 9)  = (1/2) [ ( 9x - 3) + (15x - 39) ]      multiply both sides by 2

2(11x - 9)  =  (9x - 3) + (15x - 39 )        simplify

22x - 18 =  24x - 42         add 42 to both sides, subtract 22x from both sides

24 = 2x 

12 = x

So.......arc  ED  =  9(12) - 3   =  105°

ok im from the east coast and its currently 2:30 pm

Notice that when x = 3   and x = 7    then f(x) = g(x)

So....those are the solutions

10x+16 ≥  6x+20      subtract   6x, 16 from both sides

4x ≥ 4         divide both sides by 4

x ≥ 1

Second one......can be solved with a sum of differences

1         5          12            22           35

      4         7            10           13

            3           3           3

We have 2 non-ero rows....so.... will have a 2nd power polynomial     ax^2 + bx + c

a     +   b   +    c  = 1      (1)

4a   +  2b   +   c =   5      (2)

9a   +  3b    +  c   = 12    (3)

Subtract (1) from (2)       and  (1) from (3)

3a + b = 4   ⇒   -6a - 2b  = -8     (4)

8a  +2b = 11  (5)

Add (4) and (5)

2a = 3

a = 3/2

3(3/2) + b = 4

9/2 + b =4

b = 4 = 9/2

b = -1/2

3/2  - (1/2) + c = 1

1 + c = 1

c = 0

So....the generating function is

(3/2)x^2 - (1/2)x

So...the 100th term is

(3/2)(100)^2 - (1/2)(100) =

14,950

solve

10x+16>=6x+20

You should solve it algebraically as follows:

Let the cost of the pencil = P, then:

The cost of the pen          =P + 1. So, we have:

P + P + 1 =$1.10

2P + 1      =$1.10               Subtract 1 from both sides

2P            =$0.10                Divide both sides by 2

P              =$0.10 / 2

P  = $0.05 cents - the cost of the pencil

$1 + $0.05 =$1.05 - cost of the pen.