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incorrect

1 / [x^2 + x]

x = 1,  4

x = 4 is the 2nd smallest x

Using the Law of Sines

sin A / 19  =sin B  / 9

(4/5) / 19  = sin B  / 9

sin B =  9(4/5) / 19

sin B =  36 / 95

cos B    = sqrt [   1 - sin^2 B ] 

cos  B = sqrt [  1 - (36/95)^2 ]  =  sqrt [ 95^2 - 36^2 ] / 95  = sqrt [ 7729 ] / 95

Using arithmetico-geometric series, S = -1004.  In mod 2010, this is 2010 - 1004 = 1006.

incorrect

1 is correct

3 is correct

The pattern repeats every 8 counts. Therefore:

99 mod 8 =3 - the 99th count should land on 3.

The stone that is counted as 99 is stone 1.

incorrect

x - 1 = - 1/3

x = - 1/3 +1

x = 2/3

x - 1 =1/3

x =1/3 + 1

x = 4/3

t = 5, so n = 35.

5^30 =931,322,574,615,478,515,625 mod 7 =1

37,000 / [50,000 + 37,000] =37,000 / 87,000 =42.53% spent on cable TV.

(1+12+123+1234+12345+123456+1234567+12345678) mod 9==3

n = 3

1^2009 + 2^2009 + 3^2009 +...........+ 2009^2009 mod 10^10 =.........3945778985 - These are the last 10 digits.

629_10 =1556_7

629_10 =1165_8

3 digits =1,  5,  6

Solve the following system:
{x + y - z = -8 | (equation 1)
x - y + z = 18 | (equation 2)
-x + y + z = 30 | (equation 3)

Subtract equation 1 from equation 2:
{x + y - z = -8 | (equation 1)
0 x - 2 y + 2 z = 26 | (equation 2)
-x + y + z = 30 | (equation 3)

Divide equation 2 by 2:
{x + y - z = -8 | (equation 1)
0 x - y + z = 13 | (equation 2)
-x + y + z = 30 | (equation 3)

Add equation 1 to equation 3:
{x + y - z = -8 | (equation 1)
0 x - y + z = 13 | (equation 2)
0 x+2 y+0 z = 22 | (equation 3)

Divide equation 3 by 2:
{x + y - z = -8 | (equation 1)
0 x - y + z = 13 | (equation 2)
0 x+y+0 z = 11 | (equation 3)

Add equation 2 to equation 3:
{x + y - z = -8 | (equation 1)
0 x - y + z = 13 | (equation 2)
0 x+0 y+z = 24 | (equation 3)

Subtract equation 3 from equation 2:
{x + y - z = -8 | (equation 1)
0 x - y+0 z = -11 | (equation 2)
0 x+0 y+z = 24 | (equation 3)

Multiply equation 2 by -1:
{x + y - z = -8 | (equation 1)
0 x+y+0 z = 11 | (equation 2)
0 x+0 y+z = 24 | (equation 3)

Subtract equation 2 from equation 1:
{x + 0 y - z = -19 | (equation 1)
0 x+y+0 z = 11 | (equation 2)
0 x+0 y+z = 24 | (equation 3)

Add equation 3 to equation 1:
{x+0 y+0 z = 5 | (equation 1)
0 x+y+0 z = 11 | (equation 2)
0 x+0 y+z = 24 | (equation 3)

x = 5,     y = 11,      z = 24          xyz =5  x  11  x  24 =1,320

q(-1) = -15.

Sorry but no

If \(\log_9{(x-1)^2}=-1\) then \((x-1)^2=9^{-1}=\frac{1}{9}\)  so  \(x-1=\pm\frac{1}{3}\)

Can you take it from here?