geno3141

We know that given any whole number n, 2n + 1 represents an odd number.

We also know that multiplying any number by 2 results in an even number                                                                             and an even number added to an odd number results in an odd number.

Proof:

Is it true when n = 1?

   1 x 3 = 3

   Yes, it is true for n = 1

Assume true for n = k; that is:  (k)(k+2) is an odd number.

Under this assumption, will it be true for k+1?

   [k+1][(k+1) + 2]  =  [k + 1][k + 3]  =  k² + 4k + 4  

                               =  k² + 2k + 2k + 4  =  (k)(k + 2) + 2(k + 2)

   Since, by assumption, (k)(k+2) is an odd number,                                                                                              and 2(k + 2) is an even number (because it is a number multiplied by 2),                                          then (k)(k + 2) + 2(k + 2) is an odd number (because it is an odd number added to an even number).

   Yes, it is true under the assumption.

Q.E.D.

If you would like to do this by using proportions:

wins / all games  =  40% / 100%

10 / x  =  .4 / 1.00

Cross multiply:  .40x  =  10 x 1.00

                        .40x  = 10

Divide by .40          x  = 10 / .40  =  25 games

What are we supposed to do with this expression?

First, let's find out where the racer was when s/he was 60 miles closer to the finish that the start.

The midpoint of the race is the 150 mile mark; half of 60 miles is 30 miles; if we add 150 + 30, we get the 180 mile mark; this will be 60 miles closer to the finish than the start because it's 180 miles from the start but only 120 miles to the finish.

The time is not important for this problem.

According to the problem:

when n = 1, the answer is 1

when  n = 2, the answer is 4

when  n = 3, the answer is 9

when  n = 4, the anser is 16, etc.

Try each of the possibilities:

n = 1   --->   2n = 2   --->   n + 3  =  4   --->   n² + 1  =  2   --->   n² = 1

n = 2   --->   2n = 4   --->   n + 3  =  5   --->   n² + 1  =  5   --->   n² = 4

Which one works?

For this, you will first need some statistics of iron deficiency in the general population. If you can find this information, we can help you calculate the probability.

For F(x) = x² + 2

F(x + h)  =  (x + h)² + 2                                   (replace x with x+h throughout the problem)

              = x² + 2xh + h² + 2                            (multiply out)

This problem can be solved several ways, including factoring and using the quadratic formula. 

By factoring:         -12x² - 4x  = 0               Factor out -4:

                            -4(3x² + 1) = 0              Divide both sides by -4:

                                3x² + 1  =  0

                                      3x²  =  -1

                                        x²  =  -1/3

                                        x  =  ±√(-1/3)        

F(x+h) means to replace 'x' with 'x+h' everywhere there is an 'x'.

If you have entered this correctly, then you have just: F(x+h) + x² = 2 which can't be solved.

Did you mean:  find F(x+h) when F(x) = x² - 2 ?  If so, write back.

Factor each number:  625  =  5 x 5 x 5 x 5

                                  16  =  2 x 2 x 2 x 2

Since they have no common factors, the number that divides evenly into both is 1.