CPhill

We need to use the midpoint theorem here

[ 1 + p ] / 2  =  8

Multiply both sides by 2

1 + p  = 16     subtract  1 from both sides

p  = 15

And to find q, we have that

[ 7 + q ] / 2  = 2

Multiply both sides by 2

7 + q   =  4      subtract 7 from both sides

q  = -3

None of these

We know that    m - 2  = n  ⇒    m = n + 2

So....using the Pythagorean Theorem....we have that the remaining side =

√ [ m^2 - n^2 ]

√ [ ( n + 2)^2  - n^2 ]      simplify

√ ( n^2 + 4n + 4  - n^2 )

√  [4n + 4]

So....the square of this side  =    4n + 4     [ in terms of n ]

All we need to do  to find the scale factor is to take the ratio of the x coordinate of A' to he x coordinate of A

So we have

-0.6 / - 3  =  .6 / 3  =    (6 /10)  / (3 /1)  =  (6 / 10) * (1/3)  =  6 / 30  = 1/5

2. A transversal cutting parallel lines forms congruent corresponding angles 

3. Definition of congruent

4. A line standing on a line forms a linear pair

5. Linear Pair Theorem

6. Definition of Supplementary

7. Substitution of (3)  into (6)

8. Definition of Suppllementary

2. A line standing on a line forms a linear pair

3. Linear Pair Theorem

4. Definition of Supplementary

5 ,6 look good

7 Subtraction Property  of Equality

These angles will be vertical, and thus, equal...so...

[ 3x + 34 ]  =  [ 7x + 10]    subtract 3x, 10 from both sides

24  =  4x      divide both sides by 

6  = x

So.....using   7x + 10.....the angles will measure   7(6) + 10  =  52°

I finally figured this one out without relying on "technology"

(4x^2 + 6x + 4) ( 4y^2  - 12y + 25)  =  14    factor out a 2

2 (2x^2 + 6x + 4) (4y^2 - 12 + 25)  =  28     divide by 2 on each side

(2x^2 + 3x + 2) ( 4y^2  - 12y + 25)  =  14   

Factor 2, 4  out of each of the first two terms, respectively

(x^2 + (3/2)x + 1) (y^2 - 3y + 25/4)  = 7/4

Complete the square on  x and y  

( x^2 + (3/2)x + 9/16 +  7/16) ( y^2 - 3y + 9/4 + 4)  = 7/4

[ ( x + 3/4)^2  + 7/16 ] [ ( y - 3/2)^2 + 4 ]  = 7/4    expand

 ( x + 3/4)^2  * ( y - 3/2)^2 + 4  ( x + 3/4)^2 + (7/16)  ( y - 3/2)^2 + 7/4  =  7/4

Subtract 7/4 from each side

 ( x + 3/4)^2  * ( y - 3/2)^2 + 4  ( x + 3/4)^2 + (7/16)  ( y - 3/2)^2  =  0

Note that each term will equal 0  when x = -3/4  and y = 3/2.....!!!!

OK....so we have that

[8x + 2 ] + [8x + 8]  =  90       simplify

16x + 10  = 90       subtract 10 from both sides

16x  = 80    divide both sides by 16

x = 5

So...one angle is   8(5) + 2  = 42°  and the other is 90 - 42 = 48°

Are these angles supposed to lie next to each other on a line ??

Base area  = area of a square =   9^2  = 81 units^2     (1)

Area of the sides  =  area of 4 trianges each with a base of 9 and height of 5 =   

4*  (1/2)(9)(5)  = 90 units^2   (2)

Surface area  = (1)  + (2)  =  [ 81 + 90 ] =  171 units^2