CPhill

I assume we want to factor, RP.....so

1)  56b^3  + 7b^2  + 168b  + 21

We need to do something called "factor by  grouping"....there isn't a standard proceedure, necessarily, but here's one way we can proceed

Take the GCF  out of 56b^3  + 7b^2  =    7b^2

Take the GCF out of 168b + 21   =  21

Write the expression back like this :

7b^2 (8b + 1)   + 21 (8b + 1)   ......note that  (8b + 1)  is common...so write it...and then follow it with the other two terms as a second factor....so we have

(8b + 1) ( 7b^2 + 21)   .....note....in the second factor, we can take out a "7"...so we have...

(8b + 1) (b^2 + 3) *7  =

7(8b + 1) (b^2 + 3)

Let x be the number of people in each van and y  be the number of people in each bus....and we have that

6x  + 1y  = 146    rearrange as   1y  = 146  - 6x  ⇒   y  =  146  - 6x    (1)

12x + 8y  = 592     (2)

Put  (1)  into (2)  for  "y"  and we have

12x  + 8(146  - 6x)  = 592    simplify

12x + 1168  - 48x   = 592

-36x  + 1168  = 592   subtract  1168 from both sides

-36x  = -576    divide both sides by -36

x  = 16  ⇒   number of students in  each van

Amd using  (1)...the number of students in each bus is  146  - 6(16)  =  146  - 96  =  50

You are correct, RP!!!

Distance  Iowa City to Ames  = √ [ (120^2 + 30^2  ] = √15300 minutes  =  30√17 minutes

Distance  Iowa City to Cedar Rapides  =√ [(120 - 120)^2  + 30^2 ]  = √900  =  30 minutes

So...the difference in distance is  :   30√17 - 30  minutes  =   -30 + 30√17 minutes

(a) a rectangular prism that is 4 feet wide, as tall as it is wide, and twice as long as it is tall 

  _____ ft2 

The surface area  is   2 (W*L  + H*L  + W*H )  = 2 (4*8  + 4*8  + 4*4)   = 160 ft^2

(b) a regular hexagonal pyramid with a base area of 166.3 square centimeters, a base side length of 8 centimeters, and a slant height of 8 centimeters 

The surface area is given by    :  Area of the base  + Area of  6  conguent triangles forming the sides  =

166.3   +  6(1/2)(8)(8)   =    166.3  + 3*64   =   166.3 + 192  = 358.3  cm^2

Let x be the number of hockey cards he sells and y be the number of baseball  cards he sells ....so we have these inequalities

x ≥ 6y

x + y ≤ 525

And we wish to  maximize this objective  revenue function, R

R = .03x  + .05y

Here's the graph of the inequalities  :   https://www.desmos.com/calculator/h7qwjcc9g2

It can be shown that the max  revenue  occurs at the  corner point  (x, y)  = (450, 75)

So...the max revenue is  

.03(450) + .05(75)  =  $17.25

(1/8)x−5<−8  or  7x−4 ≥38

In the first inequality, add 5 to both sides

(1/8)x < -3  multiply both sides by 8

  x < -24

In the second inequality  add 4 to both sides

7x  ≥ 38     divide both sides by 7

x  ≥ 38/7

So..the answer is

(-infinity, -24) U [ 38/7, infinity ) 

4m +  t     just substitute  m = 7 and  t  = 2  and we have

4(7) + 2  =

28  +  2   =

30

The first is the improper subset {1,2,3, 4, 5}

Next...we can choose any 3 of the 4 remaining elements to  include in a set with 5  = 4C3  = 4 more subsets

Then, we can choose any 2 of the remaining elements to include in a set with 5  = 4C2  = 6  additional subsets

Then, we can choose any 1 of the remaining elements to include in a set with 5  = 4 C1   = 4 additional subsets

Lastly...we can  just have a set only including 5   =  1  additional subset

Note....these  are just  the sum of the entries in Row 4 of Pascal's Triangle  = 1 4 6 4 1  =  2^4  =  16  subsets  [if we include the improper subset ] 

9400  - [ 3200 + 445 + 225 + 385 + 214 + 156 + 96   ] =  $4679  left 

Their take-home pay is  2(2300) + 4800  = 9400

Now....add all  the amounts in the table  and subtract this total from  9400....that will be your answer...