CPhill

 8x+3y=40     16x+6y=41       if we multiply the first equation by 2  we get

16x + 6y  = 80                but the second equation says that 16x + 6y = 41

Then   16x + 6y    has two different values and this is impossible.......so......the answer is "e"

y=9x-21   3x-y=3

Note that we can substitute the first equation into the second for y......and we have....

3x - [ 9x - 21]  = 3      simplify

3x - 9x + 21  = 3

-6x + 21  = 3      subtract 21 from each side

-6x  = -18            divide both sides by -6

x = 3     and to find y....we can use   y = 9(3) - 21  = 27 - 21   = 6

So    {x, y}  = {3 , 6}

Here's the explanation:

-3x^3+5x+2        write the middle term as 3x + 2x.......so we have

-3x^3 + 3x + 2x + 2       factor by grouping

3x(1 -x^2) + 2(x + 1)

3x (1 + x) (1 -x) + 2 (x + 1)

3x (x + 1) (1 - x) + 2 (x + 1)   factor out the (x + 1)

(x + 1) [ 3x (1 -x) +  2 )

(x + 1) (-3x^2 + 3x + 2)  factor out a " -1 " from the second term

(x + 1) (-1)(3x^2 - 3x - 2 )

-(x + 1)(3x^2 - 3x - 2)

Guest...I see how your answer of  [0; 1, 2, 3, 1, 2, 1, 6]  will produce the necessary fraction.......could you explain how this works????......I don't think I have seen this method before.....!!!

106 + ? = 180  subtract 106 from both sides

?  =  180 - 106  

? =   74

(6.9 X 10^-14)(3.4 X 10^11) (7.7 X 10^-16)(1.1 X 10^14) =

Reorder as

(6.9 * 3.4 * 7.7 * 1.1)  * (10^14 * 10*11 * 10^-16*10^14)   =

(6.9 * 3.4 * 7.7 * 1.1) * [ 10^(14 + 14 + 11 - 16) ]  =

(6.9 * 3.4 * 7.7 * 1.1) * [ 10^23] = 

(198.7062) * [10^23]  = 

1.987062 * 10^25  =

19,870,620,000,000,000,000,000,000

Turn 82.693 with the 9 and 3 repeating, into a mixed number.

Forget about the 82 for a second

.693  with the 9 and 3 repeating can be turned into a fraction thusly:

Writh the 693 without the decimal......from this, subtract the non-repeating part, 6.....[693 - 6] = 687 ...   this will be the numerator of our fraction.........for the denominator......writte the same number of 9's as the number of repeating digits  =  99 and append  the same munber of 0's as the non-repating part [ i.e, one "0" ]....this gives us 990

So we have :

[693 - 6] / 990   = 687/990    and we can reduce this by dividing the numerator and denominator by 3 →  229/330

And our mixed number is     82 + 229/330........check this for yourself .....https://www.wolframalpha.com/input/?i=82+%2B687%2F990

-3(2y+v)-5(-v+5y)   use  the distributive property

-6y - 3v + 5v - 25y     combine like terms

-31y + 2v

See my responses here : http://web2.0calc.com/questions/counting-and-probability-problem-urgent-please-help

(b) We have 10 standard 6-sided dice, all different colors. In how many ways can we roll them to get a sum of 20?

Like the last question , this just boils down to the number of ways to roll a "20"  with 10 dice.....

The probability =    21307 /   15116544   =   85228 / 6^10  =     85228 /  60466176

https://www.wolframalpha.com/input/?i=probability+of+rolling+a+20+with+10+dice

So.....the number  of ways of rolling a "20"  with 10  dice = 85228