CPhill

(ƒ+g)(x), ƒ(x) = x+3, g(x) = x - 3

(ƒ+g)(x)  = f(x) + g(x)   =  (x + 3) + (x - 3)  =   2x

2x^2 -3x - 20  =  0   

This factors as

(2x + 5) (x - 4)  = 0

Setting both factors to 0 and solving for x gives the zeroes x = 5/2  and x  = 4

Since ABC  is a right angle, then DBC is supplemental.....so it's = 90°as well

Snd EA is parallel to DC......and since transversal EC  cuts these, then angle DCE and angle CEA form equal alternate interior angles

Thus by angle - angle congruency......triangle CBD  is similar to triangle EBA

Thus BC / BD  =  BE / BA

So  BC * BA  =  BE * BD    or, put another way

AB * BC  =  EB * BD

Here's a pic :

6y - 3(8x + 5)  =

6y - 24x - 15 

2(7 - 3m) + 4m  =

14 - 6m + 4m =

14 -  2m

6.75  *  3600 seconds in  one hour  = 24300 cm^3   per hour

cm^3  in one gallon  = 3785.41

So

24000 / 3785.41  ≈  6.34 gallons in one hour

We can use a proportion to solve this

Height of Stick                              =               Height of Tree

___________________                                ___________________

Length of Tree Shadow                                  Length of Tree Shadow

33                             =                        Height of Tree

__                                                       ___________

1.2                                                        14.16 

Multiply both sides by 14.16

33 (14.16) / 1.2  =   Height of Tree  = 389.4 ft   

22−22​(a+22) = 7+a       simplify the left side

22 - 22a - 484 = 7 + a

-22a - 462 = 7 + a        add 22a to both sides, subtract 7 from both sides

-469  = 23a                divide both sides by 23

-469 / 23  = a

Here]s the steps to create this [ I probably can't explain it  better !!] 

http://www.purplemath.com/modules/boxwhisk.htm

Here's the plot :

csc x / [ cot x + tanx ]  =   write in terms of sine and cosine

[ 1 / sin x] / [( cos x / sinx) + (sin x / cos x) ]      get a common denominator on the bottom 

[ 1 / sinx] / ( [ cos^2 x +  sin^2 x ]  / [sin x cosx ] )  =

 1                               [ cos^2 x +  sin^2 x ]

___         ÷               ___________________       =

sin x                              sin x cosx 

  1                                    sin x cos x

___          X               ___________________   =        swap numerators

sin x                             [ cos^2 x +  sin^2 x ]

 sin x cos x        X           1

_________                  ____     =

  sin x                              1 

cos x

Total distance traveled  =  6 trips * 500 miles each  =  3000 miles

3000 miles  / 11 miles per minute = total time  ≈ 272.7 minutes 

272.7 / 60 ≈  4.54 hrs