CPhill

Gotta' be careful here, EP.....dividing out sin x is like throwing away a polynomial root....

sin x  - 2sin x cos x  = 0

sin x ( 1 - 2cosx)  = 0

So

sin x  = 0    at    0° + n*180°   where n is an integer    .....or

1 - 2cosx  = 0

1 = 2cos x

1/2  = cos x        at    60° + n360°    and at  300° + n360°

3. Definition of Bisector

5. Alt.Interior Angles Theorem

9. Substitution Property

3 is based on Euclid's Elements...a bisected apex angle proportions the sides of the triangle thusly :

[2x - 1] / 9 =  3x / 15     cross-multiply

15 [2x - 1 ] = 9 * 3x

30x - 15  = 27x

3x  = 15

x = 5

Thanks, EP....!!!!

Footballgirl...I can't get the pic to upload....but it's a rhombus.....

I'll see if the image thingy works later....!!!!!

W(0 , 1) , X(4 , 2) ,Y( 3 , 2) , Z(-1 , -3)

Are you sure that you have the correct points???

This is not a parallelogram......

This forms a rectangle

AB  =  √ [  (4 - 0 )^2 + ( - 1 - 3)^2]  = √[4^2 + (-4)^2 ] = √[16 + 16] = √ 32 = 4√2

BD  =  √ [  (4 - 2 )^2 + ( - 3 - - 1)^2]  = √[2^2 + (-2)^2 ] = √[4 + 4] = √ 8 = 2√2

So...the area  =   4√2  * 2√2 =   8 * 2  = 16  sq units

2x-3y = 8 

4x+3y = -2       add these  giving

6x = 6      divide by 6

x = 1

And use either equation to find  y

4(1) + 3y = - 2

4 + 3y  = - 2      subtract 4 from each side

3y  = -6        divide by 3

y = - 6/3  = - 2

a)   sqrt(50) / 5 = sqrt(2)

√50/ 5  = √ [2 * 25] / 5  =  [ √2 *√25] / 5  = [√2 * 5] / 5  = √2 * [5/5]  = √2 * 1  = √2

b)   (sqrt(24) - sqrt(6))^2 = 6

[√24 - √6] [√24 -√6]  =

24 -  2*√24*√6  +  6  =

30 - 2√144  =

30 - 2 (12)  =

30 - 24  =   6

c)   sqrt(27) - sqrt(12) + sqrt(75) - sqrt(18) x sqrt(6) = 0

[The key here is to wrtie  each using a similar sqrt]

√ 27 - √12 +√75 - [√18 * √6]

√[9 * 3] - √[4 *3] + √[25 * 3] - √108

√9* √3 - √4 *√3 + √25 *√3  - √36*√3

3√3 - 2√3 + 5√3 - 6√3      ......   factor out √3  ......

√3  [ 3 - 2 + 5 - 6]

√3 [ 1 + 5 - 6]

√3 [6 - 6 ]

√3 [0]  =   

0

d)   (sqrt(2) - sqrt(3)) x (sqrt(2) + sqrt(3)) = -1

[ √2 -√3 ] [√2 + √3 ]

√2*√2 -√3*√2 +√2*√3 -√3*√3

2 - √6   + √6  - 3

2 - 3  =  

- 1

a) Solve:   logx^3 + 2logx^2 - 14 = 0

3log x + 4 log x  = 14

7 log x  = 14      divide by 7

log x  = 2    means  that      10^2  = x   →  x  = 100

b) Solve:   (log x)^2 - log x - 6 = 0      Factor

[ log x - 3 ] [ log x + 2]  = 0         set each factor to 0

log x - 3  = 0   →   log x  = 3     →  10^3  = x  = 1000   .... and........

log x + 2  = 0  →   log x = - 2  →   10^-2 = x  =  1 / 100