CPhill

Go ahead and post your method....I might have just gotten "lucky"

I used this application.....

http://www.softschools.com/math/venn_diagram/venn_diagram_maker/

You can capture and drag the circles and the text box......after you have a completed diagram, you can use Tiny-Pic to create an "up-loadable" file

BTW...I'm not totally sure about my answer...I may get heureka to look at it....he's pretty good with this stuff...

Look at the graph, here : https://www.desmos.com/calculator/ekrnfonsjr

We have two areas to consider

One is a triangle with a base of 4 and a height of 1.....so...its area is 2 units^2

The other area is 3/4  of a semi-circle  with  a radius of 4

And the area of this is    (1/2)(3/4)  pi (4)^2  =  6 pi units^2

And the feasible region will be the sim of these =  [ 6pi + 2] units^2

The area of a rhombus =

(1/2) product of the diagonal lengths

One diagonal length is 8.....so the other must be 20

And the mid-point of this diagonal is at the origin

So.....(0,10)  and (0, -10)   are the other two vertices

So....K  must be 10

.001p^3 + 6  =  -.02p^2 + 80

p^3 + 6000  = -20p^2 +  80000

p^3 + 20p^2 - 74000  = 0

Note, AT.......there IS a "formula" for finding  cubic root(s)...but...it's EXTREMELY messy....!!!!!

The  "actual"  real-number answer is :

p = 10/3 (-2 + (991 - 3 sqrt(109113))^(1/3) + (991 + 3 sqrt(109113))^(1/3))

Let's just go with hectictar's solution...!!!!!

1.   7y = 8x – 14              Given

2.    y = 6                         Given

3.    7(6) = 8x – 14           Substitution of 2  into 1

4.    42  =  8x - 14            Simplification of 3 

5.    56  =  8x                   Addition Property of Equality

6.     7  = x                       Division Property of Equality

I'll give it a  " shot "  

CAUTION :     MATH HUMOR DETECTED

[ sin x  * tan x ]  + cos x  =   sec x

[sin x *  sin x / cos x ]  +  cos x  = sec x

[ sin^2 x  /  cos x]  + cos x =  sec x            ...  get a common denominator on the left

[sin^2 x  /  cos x]  +  [cos^2 x / cos x ] =  sec x        .... sin^2 x  + cos^2 x = 1

[ sin^2 x  + cos^2 x] / cos x    =   sec x

1 / cos x   =  sec x

a is correct

To see this.....

Jessie must take at least 30 minutes

So

x/2  >=  15      multiply both sides by 2

x >= 30

Look at the graph :

https://www.desmos.com/calculator/xjyluwiltf

Intervals of decrease    (-1.81, 0.168)  U  ( 1.642, infinity )