Math problems HELP!!!!!?

Question

complete the conjecture based on the pattern you observe in the specific cases.

1. The sum of any two odd numbers is ___ ?

2. The product of a number (n-1) and the number (n+1) is always equal to ____?

Show the conjecture is false by finding a counterexample.

1. The sum of two numbers is always greater than the larger number.

2.If the product of two numbers is positive, then the two numbers must both be positive.

3. If M is a nonzero integer, then M+1 / M is always greater than 1.

please help im so confused!

Answer 1

1. even

2. (n-1)(n+1)=n^2-1

1.-2+5=3

2. (-2)(-2)=4

3. m=-1

(-1+1)/-1

0/-1

0

make it a good day

Answer 2

1.  Even (1+3=4, 11+23=34, etc.)

2.  (n^2)-1



1.  -5 + -3 = -8 (-8 < -3)

2.  5 x 8 = 40 (5 is odd)

3.  If M=-1, then 0/-1 = 0 (0 <1)

Answer 3

Your directions say to observe specific cases.  So try some numbers....

1)  Specific cases  1 + 1 = 2,  3 + 5 = 8, 7 + 1 = 8

The sum of any two odd numbers is odd.

2) Specific cases  

n = 1, 0*1 = 0

n = 2, 1*3 = 3

n = 3, 2*4 = 8

n = 4, 3*5 = 15

n = 5, 4*6 = 24

This may be a little hard to see, but in each case, the value is n*n - 1

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A counter example is a specific case that shows the conjecture is false

1) 10 + -10 = 0.  0 is not greater than 10

2)  -2 * -3 = 6.  6 is positive, but -2 and -3 are not.

3) M = -1,  M+1/M = 0/-1 = 0.  0 is not greater than 1

Answer 4

1. The sum of any two odd numbers is ___ ?  EVEN (ex: 1+3.... 1+7.... 3+7.... etc..)

2. The product of a number (n-1) and the number (n+1) is always equal to ____? n^2-1 (When you FOIL n-1 and n+1.. you get n^2-1)

Answer 5

even

an even number

4 + -3 = 1   1 is not greater than four

not sure bout this one, it's a tuffy

M = -3

-3 +1 = -2 which is not greater than zero

Answer 6

1.even

2. n^2+n-n-1

so

n^2-1

1.false

7+-1=6

2.false

-5x-5=25

3. false

-1+1=0