CPhill

 -30 + 6p = 7(p-5)       simplify the right side

-30 + 6p  = 7p  -  35      subtract 6p from both sides, add 35 to both sides

5  =  p

Remember.....dividing two numbers with the same sign produces a positive result. Dividing two numbers with opposite signs produces a negative result.......so.....

-54   =  54   =   6

 -9         9

V_sphere  =   (4/3) * pi * radius^3    ....   so  ....

250  =  (4/3) * pi * radius^3            divide both sides by (4/3) pi

250 / [ (4/3) pi ]   =   radius^3        take the cube root of each side

∛ [ 250 /  (4/3 pi) ]   =  r   ≈  3.9   inches

Just a slight error on Melody's part ....

(2x+6)^1/3 - (6x-1)^1/3 =0

Following the same procedure as Melody, we arrive at

2x + 6  =  6x - 1 

4x    =   7

x  =  7/4  =  1.75

Look  at the graph, here :  https://www.desmos.com/calculator/a7lljbl5oz

The break-even point  is  (40, 800).......since both functions are linear, there are no "intervals"

I already answered it by private message.......!!!

Let  one side  =  x

The......the  other side  =   (16 - 2x) / 2  =  8 - x

And the  area, A(x),  can be represented  as

A ( x)  =  x ( 8 - x)   =     -x^2 + 8x

To  find  out  the dimensions that would make the area > 12 m^2   we have

-x^2 + 8x  > 12       

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

It  shows  that  the area will be greater than 12m^2  when   2 m < x < 6 m

Call the portion of the house that Bailey can paint in one day =   1 / x

Call the portion of the house that Andrew can paint in one day  =   5* (1 / x)  =

 5 / x 

And  we know that

Rate per day * number of days  =  1 whole job  .....so, working together, we have

(1/x) *4  + (5/x) * 4  = 1

4/x  +  20/x   = 1

(24) / x  = 1   →   x  =  24

So.....Bailey  can paint (1/24) of the house in one day = 24 days to paint the whole house by himself

And  Andrew can paint  (5/24)  of the house in one day =  24/5  =  4.8  days to paint the house by himself 

25x^4 - 20x^2 + 3 = 0        factor

(5x^2 - 3) (5x^2 - 1)   = 0

Set  each factor to 0  and solve

5x^2  - 3  =  0

add 3 to both sides

5x^2  = 3      divide both sides by 5

x^2  =  3/5    take both square roots

x  =  ± √(3/5)

Similarly.....setting the second factor to 0 and solving for x produces

x   =  ± √(1/5)

And those are the 4 solutions

These  are easy  to solve when we know the rates

Sally can paint 1/7  of a room in 1 hour

Steven can paint 1/3 of a room in 1 hour

So.......

(1/7)  + (1/3)  =  [ 7 + 3 ] / 21  =   10/21

Invert this fraction    =  21 /10   =   2.1  hrs.  working together