CPhill

One  rectangle  with  dimensions of  4  x 8   =  32 ft^2

One  trapezoid  with bases of   8  and 14  and a  height  of  4

Area  =   (1/2) height  ( sum of bases)  =  (1/2) ( 4) ( 8 + 14)  = 44 ft^2

Total area=  (  32 + 44)   =   76 ft^2 

Notice  the first few  terms in the expansion of  both terms (where C1, C2, C3....   are  the terms on  the 51st row of Pascal's triangle)

(x +a)^51  =  C1 x^51  + C2x^50 a  + C3x^49a^2 + C4x^48 a^3 + C5x^47a^4  + C6 x^46a^5 +.......+.x^0*a^51

-(x - a)^51 = -C1x^51 + C2x^50a  -  C3x^49a^2   + C4x^48a^3  - C5x^47a^4  +  C6x^46a^5 +  ....+ x^0 * a^51

Adding  these  we  get

2C2x^50a  +  2C4x^48a^3  + C6x^46a^5 +  ....+ 2x^0a^51

The  number of  terms  is   [ 51 + 1]  / 2  =   26

Correct  !!!

1/ ( x + 2)

The degree of the polynomial in the  numerator  is less than  the  degree of the polynomial in the denominator....thus...we will have a horizontal asymptote  at  y = 0 .....the behavior at  both ends  will  approach  this asymptote y  = 0

See the graph here :  https://www.desmos.com/calculator/s6j0qch9li

(98.6 - 32)  /  1.8  =   37° C

This is a quadriateral inscribed in a circle......the  opposite  angles sum to 180°

Therefore....

x + 77  + x + 103 =  180

2x  + 180   = 180

2x   =180  - 180

2x   = 0

x   = 0

So  RST =  77°

B. Infinitely many

x +  8y =  - 8

8y  =  -x  - 8          divide  through  by 8

y  = (-1/8)x    -  1

Since  they are parallel ....slope of s = slope of t =  -1/8

So  the equation for  t  is

y =(-1/8) (x -5) -  1             multiply yhrough by 8

8y = - (x - 5) - 8

8y = -x + 5  - 8

x  + 8y  =  -3

Since  the apex angle is  bisected....we  have  the  following relationship

(x + 1) / 16  =  (x - 2)  / (x + 1)         cross-multiply

(x + 1) ( x + 1)    16 ( x - 2)

x^2 + 2x  + 1  =  16x  - 32        rearrange as

x^2 - 14x + 33  = 0             factor

(x - 11)  ( x -  3)  =  0

Set each factor  to 0  and solve for  x  and we  have  that

x  = 11       and    x   =  3

The  secant-chord theorem

6 ( 6 + 4)   =  5 ( 5 + 2x)               

36  + 24  =  25  + 10x

60  =  25 + 10x

60 - 25  =  10x

35  = 10x

35 / 10  = x   =   3.5

NL  = 2x + 5   =   2 (3.5) + 5  =  7 + 5  =  12

HL = 6 + 4  =10