CPhill

I think we want to find x, not m

Angle CDG  =  Angle JDE    { vertical angles}

Angle JDE  =  Angle HCD    {corresponding angles }

Thus

Angle CDG  = Angle HCD   { substitution }

So

5x  -  5   =   3x  +   13       add 5 to both sides, subtract 3x from both sides

2x   =  18            divide both sides by 2

x  =  9

Ninth one :

Definition of Bisector

Alternate Interior Angles Theorem

Substitution Property

Tenth one  :

[ x + 8 ]  / 10  =  [2x + 5 ] / 14      cross-multiply

14 [ x + 8 ]  =  10  [ 2x - 5 ]

14x + 112  =  20x - 50         add 50 to both sides, subtract 14x from both sides

162  =  6x              divide both sides by 6

27  =  x   

Last one :

Base  =  √ [ 18^2   - 9^2 ]   =  9√ [ 2^2 - 1^2 ]  =  9√3   ≈ 15.6 in

Here's a few

First one :

AC / BC  = DF  = EF

12 / 18   =  10 / EF

2 / 3   =  10   /  EF      and we can write

3/2  =  EF / 10           multiply both sides by 10

10 (3/2)  = EF  =  15

Second one :

SSS  Similarity Theorem

Third one  :

x / 42  =  6  /36

x / 42   =  1 / 6

6x  =  42

x  =  7 cm

Fourth one :

Proportional

c²

Segment Addition Postulate

Fifth one....1st part

Corresponding Angles Postulate

2nd part

 ΔACE   similar to  Δ BCD

Segment Addition Postulate

Sixth one  :

Definition of Angle Bisector

Angle ADB  congruent to  Angle CDF

Substitution Property

Seventh One :

DB  / BA   =  CE  / AC

6  /  15  =  CE  /  25

2 / 5   =  CE  / 25     multiply through by 25

(2 / 5) (25)  =  CE   =  10

Eighth one :

CB  / CA    =  BD   / AD

7.5 / 4   =  BD   / 3        mutiply through by 3

(3/4) (7.5)   =  BD   =  x  =    5.625

No prob.....

4x +  3  -  9x        rearrange as

4x  -  9x   +  3 

-5x  +  3

These triangles are similar by the  AA congruency postulate

So

AC  / AB  =  PR  / PQ

 [  3x + 6  ]  /  24    =  28  / 32

[ 3x + 6 ] / 24  =    7 / 8      cross-multiply

8 [ 3x + 6 ]  =  24 * 7

24x +  48   =   168      subtract 48 from both sides

24x  =  120         divide both sides by  24

x  =  5

First one :

VY  / VT   =  KY  / KT

VY / 57  =  68 / 129.2         Multiply both sides by 57

VY  =   57 * 68  / 129.2  =   30

So.....

 x =  KY + VY  =  68  +  30  =   98 units

Second one :

Note that   MA  =  MN - AN  =  67.2  - 32   =    35.2

So

MA / MN   =  MB / MP

35.2  /  67.2   =   MB  / 81.9       mutiply both sides by 81.9

81.9 * 35.2 / 67.2  = MB  =  x   =  42.9

Third one :

62 / 99.2   = [ x + 2 ] / 112    cross-multiply

112 * 62   =   99.2  [ x + 2]      simplify

6944  =  99.2x  +  198.4          subtract 198.4 from both sides

6745.6  =    99.2x          divide both sides by 99.2

68  =  x

Last one :

[3x - 20 ]  / 56   =  9 / 72

[ 3x  - 20] / 56    =   1  / 8        cross-multiply

8 [ 3x - 20 ]     =   56

24x -  160   =  56       add 160 to both sides

24x  =  216           divide both sides by 24

x  = 9

(7, 3)     slope  =  4/7

The equation is

y  -  y coordinate of point   =  slope  (x  - x coordinate of point )

y  - 3   =  (4/7) ( x  - 7)

Look at the second one carefully, NSS

To  find the first  translation....we can solve this for x

8x  - 2  = 0

8x  = 2

x  = 2/8   =  1/4  ⇒  means 1/4 units to the right

To find the second translation....... -7   means  7 units down

So.....the vertex  is   (1/4, -7)    translated 1/4 units to the right and 7 units down

Here's the parent graph and the translated graph : 

https://www.desmos.com/calculator/jp0bpqh92i

4 +  7 (.50)  =

4  +  3.50  =

$7.50

First one  :

YP / PX  = YQ / QZ

16 / 5  =   8 / 2.5

Second  one :

For QS  to be parallel to MN....we must have that

QM * NR   =  SN * MR

2 * 5   =  3 * 4        Not parallel

2 * 15  =   6 * 5     Parallel

2 * 12  =  3 * 8      Parallel

Third one  :

The angle bisector sets up the following relationship

YZ   / MY   =  XZ  / MX

7 / 3.5   =  11  /   MX

2  =   11 / MX      rearrange as

MX  = XM  =   11/2   =    5.5

Last one :

Let  WZ    =  x

So.....WY  =  8  - x

And we have the following relationship

WY / XY  = WZ / XZ

[ 8 - x ]  /  6.5   =   x  / 6            cross-multiply

6 [ 8 - x ]   =  6.5x

48  -  6x   =  6.5 x        add 6x to both sides

48  =  12.5 x              divide both sides by 2.5

3.84    =  x   =     WZ