CPhill

Quick solution.....add 7 to both sides....then, divide both sides by 7....ask us if you get "lost"

This is a partial fraction problem.....getting a common denominator on the right will give us equal denominators on both sides....then, we can set the numerators equal on each side and solve....so we have

x + 7 = A(x+1) + B(x-2)   simplify

x + 7  = (A+B)x + (A - 2B)    equating co-efficients, we have

A + B  = 1 

A - 2B = 7     subtract the first equation form the second, and we have

-3B = 6         so B = -2     and using the first equation....A - 2  = 1  ...so A = 3

So, (A, B)  = (3, -2)

Here's the answer to this one, shania....

9x+3y=0

-36x-12y=0

This set of equations wiill have infinite answers because they are actually the same........multiply the top equation by -4 and we have -36x - 12y  = 0 ......which is just the second equation in disguise.....

[ BTW,,,if you take Linear Algebra, you will discover that the determinant of this system = 0  ....which means that we would quickly be able to see that it has either infinite solutions, or no solutions, dependening upon the right hand side ]

-4(2x-1)=36    divide both sides by -4

2x - 1  = -9     add 1 to both sides

2x = -8           divide both sides by 2 and you will have your answer....

17 IS a prime number...!!!....thus, it has no other prime factors......

The convention is that we assume the positive root, unless we are solving an equation...

So.... √49 = 7

But

x² = 49

x = ±√49 = ± 7

floor [ (2-3x) / (x + 5) ]

This isn't as daunting as it seems

Notice the first few terms....

f(1) = floor( -1 /6) = -1   ..   f(2) = floor (-4/7) = -1... f(3) = floor (-7/8) = -1  ...f(4) = floor (-10/9)= -2

And f(11)  = floor (-31/16) = -2   ....and f(12) = floor (-34 / 17) = -2 and f(13) =floor (-37/18) = -3

And every successive term has has a floor of -3....for example f(1000) = floor(-2998/ 1005) = -3

So.... 3 terms have a floor = -1

And 9 terms have a floor of -2

And (1000 - 12) = (988) terms have a floor of -3

So the sum is   3(-1) + 9(-2) + 988(-3)  = -2985

According to  a formula that I found online, we have

t = [ ln (N / N₀) / (-0.693) ]  * 5730      where t is the age of the fossil, N / N₀ is the percent of  C-14 that remains and 5730 is the half-life of C-14....so we have

t = ( ln (.63) / (-0.693)) * 5730 = about 3820 yrs old

Just put this into the onsite calculator.....