CPhill

AB  =   AC   .....so  .....angles  ABD  = ACD

So....we have that

47 + 47 + 2y  =  180

94 + 2y  = 180       subtract 94 from both sides

2y  =  86      divide both sides by 2

y  = 43°

And

47 + x + y  = 180

47 + x +  43  = 180

90 + x  = 180      subtract 90 from both sides

x  = 90°

Since two sides of this triangle are equal.......the angles opposite these sides are also equal

So......we can solve this

x + x +  38  = 180

2x + 38  = 180     subtract 38 from both sides

2x  = 142      divide both sides by 2

x = 71°

8. All angles in an equilateral triangle are equal

9. The hypotenuse is always the longest side in a right triangle

10. Congruent parts of congruent triangles are themselves congruent

Example

 If ABC   congruent to  DEF   ...then......

Angle A  = angle D

Angle B  = angle E

Angle C  = angle F

AB = DE

AC = DF

BC = EF

3.  by ASA    [ Angle - Side - Angle ]

4.  CPCTC   [ Congruent Parts of Congruent Triangles are Congruent ]

Both  angles across the equal sides are themselves equal  = x

And using the exterior angle theorem,,,we have that

116  =  x  + x

116   = 2x       divide both sides by 2

58° =  x

OK..... I thought that might be the other form that you wanted....let me show you how to get this

We have two points  on the line  (0, -5)  and  ( 1,1)

The slope between these points is  [ 1 - -5 ] / [ 1 - 0 ]  =   6/1  = 6

Now ....using (0, -5)  we have that

y -  (-5)  =  6 (x - 0)

y  + 5  = 6x

y  = 6x  - 5

√ [28x] * √[ 15x ] *   √[21x ]   =

√[ 4 * 7 * x ] * √ [3 * 5 * x ]  * √ [3 * 7 * x ]  =

√4 * √7 * √x *√ 3 *√5 *√x *√3 * √7 *√x  =

2 * √x^3 * √3^2 * √7^2 *√5  =

2 * x √x *  3 * 7 *√5  =

42x √ [ 5x ]

Since  l a l   = √ a^2....we can write

y  = 5x  - l x - 5 l  =

y =  5x - √ (x - 5)^2

P.S.  -  I don't know if this is exactly what you want, or not.....!!!!

4, 4/5, 4/25, 4/125 ..... =   4(1/5)^(n - 1)   where n is the nth term

1/2, -2, 8 , - 32...... 

a₁  =  (1/2) ,   a_n  =  (-4) *a_n-1

a₁=2/3;a_n=9⋅a_n−1

The terms are  2/3, 6, 54, 486......so the explicit formula is

(2/3)*9^(n - 1)      where n is the nth term

8000*(1/2)^6.......in the 6th month, the business pays  $125

Q  = 175000 ( 1 + .07)^t     ...... where t is the number of years after 2007