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If  f( f(x) ) = 0  then  f( f(x) )  and   f(x)  must be inverses; indeed, f(x) must be its own inverse.

Since  f(0)  =  2003,  f(2003)  =  0.

 OOppps....sorry...didn't type that correctly....

Still have a problem with the tetrahedron......when it is rolled it lands on one face...the other three faces are equally showing....

wouldn't the probability of NOT showing a '1' be just 1/4

Still have a problem with the tetrahedron......when it is rolled it lands on one face...the other three faces are equally showing....wouldn't the probability of NOT showing a '1' then be 3/4 ?

The probability of not getting a 1 on a cube is  5/6.

The probability of not getting a  1  on a tetrahedron is  3/4.

The probability of not getting a  1  on either of them is:  (5/6) · (1/4)

(3a) / ( a² - b² )  -  4 / (b - a)

Find a common denominator by first factoring  a² - b²   --->   (a + b)(a - b)

The problem now is:  (3a) / [ (a + b)(a - b) ]  -  4 / (b - a)

Since the first term has  a - b  in the denominator while the second term has  b - a  in the denominator, change

b - a  into  -(a - b), so the problem now is:   (3a) / [ (a + b)(a - b) ]  -  4 / [ -(a - b) ]

Change   -  4 / [ -(a - b) ]   into   + 4 / (a - b)

The problem has become:  (3a) / [ (a + b)(a - b) ]  +  4 / (a - b)

To get a common denominator for both terms, multiply the second term by  (a + b) / (a + b):

--->     (3a) / [ (a + b)(a - b) ]  +  4(a + b)  / [ (a - b)(a + b) ]

Combining both fractions using the common denominator, it now is:   [ 3a + 4(a + b) ] / [ (a - b)(a + b) ]

--->     [ 3a + 4a + 4b ] / [ (a - b)(a + b) ]     --->     [ 7a + 4b ] / [ (a - b)(a + b) ]

₁₀C₁ · (1/6)¹ · (5/6)⁹

The ₁₀C₁ is the number of ways that one of the dice can show a 1.

(1/6)¹ is the probability that one of the dice will show a 1.

(5/6)⁹ is the probability thtat the other 9 dice will not show a 1.

Find these values and multiply the three answers together.

1.619884429116927

(400.58-332.48)/400.58 x 100% = 17 %

6+x+x+x+x/6=1.5. What is x

= 6 + (3x +1/6 x) = 1.5

3 1/6 x = -4.5

x = -4.5 / (3 1/6) =  -4.5 / (19/6)  = -4.5 * (6/19) = -27/19

There is a WHOLE LINE of answers for this as it is the quation for a line......if you gaph it, any point on the line graph will be a solution.

idk.

4/5 x 2/2

= 4/5 x 1 = 4/5        or   =  (4x2) / (5 x 2)  = 8/10 = 4/5

It means basically find 'x' values that satisfy the quadratic equation of the form  ax^2 + bx + c = 0    

If you graph the equation you will see where it crosses the 'x' axis in two places ......these would be the 'zeroes'  which are sometimes also called 'roots'  .

Hmmmmm..... I'm a little confused as to how a 'four sided' die shows ANYthing.   Isn't it basically of a triangular pyramid shape?

x2+6y=-17  .....................             (1)

y2+4z=1     .....................             (2)

z2+2x=2     ......................            (3)

now add 1,2&3

we get x2+6y+y2+4z+z2+2x=-17+1+2

                                          =-14

adding 1,4,9 on LHS and RHS

i.e.

x^2 +6y+y^2+4z+z^2+2x++9+4+1= -14+1+9+4

therefore

(x^2+2x+1)+(y^2+6y+9)+(z^2+4z+4)=0

(x+1)^2+(y+3)^2+(z+2)^2=0

we did the above step by adding (1^2=1)+(2^2=4)+(3^2=9) on both side of the equation and factorizing the LHS.

so the equation becomes (x+1)^2+(y+3)^2+(z+2)^2=0

therefore to get 0 each of the three squares should be equal to 0

(x+1)^2=0              x=-1

(y+3)^2=0              y=-3

(z+2)^2=0              z=-2

so the value of x2+y2+z2=(-1)^2+(-3)^2+(-2)^2

                                      =1+4+9=14

ans-14

#guest4

yes i have checked the solution by using substituition method.       and if still you are not satisfied by my solution then plz be clear with your question so that even i can be more clear in my explaination..!!!

27 cubic CENTIMETERS

Surface area of Cube = 6a^2

Volume of CUbe = a^3

54=6a^2

sqrt54/6=a

a=3

Volume=(3)^3

Volume=27cu.mtrs

Guest # 3

Did you check your "solutions" by substituting to see if they balance? Well, they don't!!.

if xsquare-3x= 13 what does x equal?

x^2 - 3x =13

Solve for x:
x^2-3 x = 13

Add 9/4 to both sides:
x^2-3 x+9/4 = 61/4

Write the left hand side as a square:
(x-3/2)^2 = 61/4

Take the square root of both sides:
x-3/2 = sqrt(61)/2 or x-3/2 = -sqrt(61)/2

Add 3/2 to both sides:
x = 3/2+sqrt(61)/2 or x-3/2 = -sqrt(61)/2

Add 3/2 to both sides:
Answer: |  x = 3/2+sqrt(61)/2      or      x = 3/2-sqrt(61)/2

x2+6y=-17  .....................             (1)

y2+4z=1     .....................             (2)

z2+2x=2     ......................            (3)

now add 1,2&3

we get x2+6y+y2+4z+z2+2x=-17+1+2

                                          =-14

we can rewrite the equation as (x+1)^2+(y+3)^2+(z+2)^2=-14+1+4+9

                                                                                       =0

we did the above step by adding (1^2=1)+(2^2=4)+(3^2=9) on both side of the equation and factorizing the LHS.

so the equation becomes (x+1)^2+(y+3)^2+(z+2)^2=0

therefore to get 0 each of the three squares should be equal to 0

(x+1)^2=0              x=-1

(y+3)^2=0              y=-3

(z+2)^2=0              z=-2

so the value of x2+y2+z2=(-1)^2+(-3)^2+(-2)^2

                                      =1+4+9=14

ans-14

what are the factors of 56= 2 x 2 x 2 x 7

A debt payment of $5500 is due in 27 months. If money is worth 8.4% p.a. compounded quarterly, what is the equivalent payment.

FV=PV[1 + R]^N

FV=5,500[1 + .084/4]^27/3

FV=5,500[1 + .021]^9

FV=5,500 x 1.021^9

FV=5,500 x  1.20567895

FV=$6,631.23