CPhill

Last one

The denominator is the only problem

1 / 6   +   1 / [ x + 1 ]    =

[ 1] [x + 1]                       [1] [ 6]

__________  +        __________ =

    6 *[x + 1]                [ x + 1 ] *6

  [ x + 1 ] + 6

 __________   =

   6 [ x + 1]

x + 7

_______

6x + 6

So

[ 5 /1 ]  /   (   [  x + 7]  / [ 6x + 6 ] )  =       { invert the second fraction and multiply }

5         *       [ 6x + 6]                  30x + 30

__              ________   =          ________

1                 [ x + 7]                      x + 7

Second one

x^2 + 3x - 28    factors as    (x + 7) (x - 4)

x^2  -7x + 12  factors as   (x - 3) (x - 4)

So

(x + 7) ( x - 4)               ( x + 7)

_____________  =     _______

(x - 3) ( x - 4)                ( x - 3)

First one

Let x be the number of additional FT's......so we have that

[ 12 + x]

_______  =     .85           multiply both sides by  15 + x

[15 + x ]

12 + x  =  85 [ 15 + x]     simplify

12 + x = 12.75 + .85x        subtract 12, .85x   from both sides

.15x  =  .75     divide both sides by  .15

x =  5

So....she needs 5 more consecutive FT's     [ 12 + 5 =  17   total]

Answered here :   https://web2.0calc.com/questions/hard-math-easy-to-those-who-know-it

Lee has 5/7 of a gallon of water. He gives 1/2 of a gallon of water to his dog, Gilligan. What fraction of the amount of water that Lee had originally did he give to Gilligan?

Frational amount =

Amt he gave to Gilligan                     (1/2)

_____________________     =       _______   =    (1/2) * (7/5)  =  7 / 10

Amt he started with                           (5/7)

Well done, heureka!!!!

I always learn a lot from your geometric proofs   !!!

Thanks for that reference, PM....I'm not familiar with this......!!!!!

Factors of 120  :

1 | 2 | 3 | 4 | 5 | 6 | 8 | 10 | 12 | 15 | 20 | 24 | 30 | 40 | 60 | 120

7 is the smallest

Second one

To find out what the original expression was under the radical, we can evaluate this :

( 2^3)*12  * (a^3)^3  *  (b^2)^3 * b   =

8*12  * a^9  * b^6*b =

96a^9b^7

So   "A" is correct

First one

Notice that the last term  has to be  "+25"

So....we can eliminate  A and D  because their final terms  will yield  " -25"

Since all therr terms of the polynomial are positive, the factors will only have a "+" involved

Look  at C

(2x + 5) (x + 5)   = 2x^2 + 5x + 10x + 25  = 2x^2 + 15x + 25

So....this is the correct choice......