CPhill

We need to  solve this

150  + 40N  ≤ 1060        where  N  is the max number of boxes that can be brought at one time

Subtract  150   from  both sides

40N ≤  910       divide both sides  by 40

N ≤ 22.75

So...22  boxes at one time  [ if we can't bring "partial" boxes  ]

Simple...

"Magic"   !!!!

[ As my Algebra 2 teacher used to say..... ] 

Correct....good job  !!!!

OK....good deal  !!!!

21.

The perimeter of a triangle =  the sum of the sides

So.....we need to solve this

x + ( x + 3)  + (x + 5)   = 26

Can you take it from there, critical ???   [ P.S......if so....post your answer and  I'll check it  ]

22.

Mmmm...this is a more interesting problem  !!!

The radiator holds 480  oz of fluid and leaks at 4 oz / min

So...the number of minutes it takes to  drain is  just  480  / 4   = 120  minutes  = 2  hrs

Since the truck travels at 35 mph...the distance it travels before the radiator is empty  is

35 mph x 2 hours  =   70  miles

Just plug  210 [ for  x ]  into  y = 50x +200 

And 195  [for x ]  into y  = 150 + 55x

And 185 [ for x ]  into y =  60x

Evaluate all three

Whichever gives the minimum value is the contractor that should be chosen.....

Thanks, Fiora and Sincerelyrose....

Here is the proof :

Since  BD   = AB...then angles ADB  and DAB  are equal

And angle AEB  = 90

And since the diagonals bisect each other...then AE  = BE

So...angles DBA  and CAB  are equal  = 45

Then...in triangle DAB....angle DBA  =  45

Andl angles DAB  and ADB  are equal....so

DAB  =  [180 - mDBA] / 2  =   [ 180 - 45 ] /  2 =   135 / 2  = 67.5

And...using the same sort of argument, we can show that angle  CBA  also  =  67.5

And.....these are the  two acute angles of the trapezoid....so their sum  = 135

HAHAHA!!!!!....not too hard,  MJ  !!!!!

Thanks, Alan !!!!

x^3 + x^2 - 8x  - 8  = 0

Factor  as

x^2  ( x + 1)  - 8 (x  + 1)   = 0

(x + 1)  ( x^2 - 8)  = 0

So either                                            or

x + 1  = 0                                       x^2 -  8  =  0 

And x  =  -1                                    ( x - √8) ( x + √8)  = 0

                                                        x - √8  = 0          or   x + √8  = 0      

                                                       And  x = √8                x  = - √8

So

C) The function has three real zeros. The graph of the function intersects the x-axis at exactly three locations.