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Thank : )

thx guest

this might help: https://web2.0calc.com/questions/midpoint-of-a-segment

OK....good deal   !!!!

Thank you! I kind of understand it now!

Yep....this makes it easier when we can reduce the size of the coefficients.....

20 )

x  - 2y   =  18      rearrange as    x  = 18  + 2y    (1)

-6x - 4y  = 4        (2)

Put  (1)  into (2)  for  x

-6(18 + 2y) - 4y   = 4       simplify

-108 - 12y  - 4y  = 4

-108 - 16y   = 4      add 108 to  both sides

-16y  = 112    divide both sides by  -16

y  = -7

And using (1)....   x  = 18  + 2(-7)   =  18  - 14    =  4

ok so I divide by 3 because there is a factor of 3 in each one?

19)

21x  - 3y   = -42     divide through by  3  ⇒    7x  - y  = -14   (1)

y  = 7x + 14     (2)

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

7x -  [ 7x + 14]  = -14    simplify

-14   = -14       this is always true...whenever this happens....we have infinite solutions...!!!!

5 0 0     =  3 ways   -  any of the 5 candies can  be given to one person

4 1 0  =   6 ways  = one candy can be given to any one person (3 ways) and the other 4 can be given to one of the other two (2 ways)  ...so...3 x 2  =  6

3 2 0  =   6 ways -  any of the three candies can br given to one person (3 ways)  and the other two can be given to one of the other two (2 ways)...so....3 x  2  = 6

3 1 1  =   3 ways    -  any of the 3 candies can be given to any one person (3 ways) ...since the other two candies are indistinguishable...we can distribute them to the other two people in any manner

2 2 1   =   3 ways  -  any 1 of the candies can be given to any of the three people....the other 4 can be split equally between the remaining two people

So...  3 + 6 + 6 + 3 + 3  = 21 ways

Good....!!!!

2)   294n^3  + 343n^2  + 126n  + 147

This one isn't as obvious....

Take out the GCF between 294n^3  and 343n^2   =  49n^2

Take out the GCF between  126  and 147  = 21

So we have

49n^2 [ 6n + 7 ]  + 21 [ 6n + 7 ]      

[6n + 7 ] [ 49n^2 + 21]      note....in the second factor...we can take out a  "7"  and we have

[6n + 7]  [ 7n^2 + 3] *7  

7 [ 6n + 7 ] [7n^2 + 3 ] 

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)

thanks CPhill

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

I'm not going to answer this one as you need to start doing your own work but I will tell you how to look at it to solve it.

Put the 5 candies down on a table.

Use 2 straws to divide them up into 3 groups.

Now figure out how many different ways you can place the straws.

There i another alternative to this question using the factors theorem let me know if you want that

It is really simple 

consider a polynomial 

4x^2-12x

now we can see that we have 4x as a common term hence takin out 4x common

4x^2-12x = 4x(x-3)

so its factors are 4x and x-3

                                                                                     Regards ~ Darkside

Very funny, joker always do these to becomes a top of the joker list..Btw this is quite funny  

Hi I'm Houzy and I'm from california, great community with very informative stuff..Thumbs up with all community members..

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