Question

Julie chooses two nonzero numbers, m and n, where m+n=0.Select whether each statement is always true, sometimes true, or never true.Always true Sometimes trueNever truem and n are odd.m and n are positive.m and n are negative.Im is equal to Inl.Im| is not equal to In.m is positive and n is negative.

Answer 1

two non zero numbers : m & n

m + n =0

1) m & n are odd - Never true

$m+n>0$

2) m & n are positive - never true

$_{(+m)\text{ + (+n)>}0}$

3) m and are negative- never true

$(-m)\text{ + (-n)=-m-n<}0$

4) Im is equal to Inl.- Always true

$\begin{gathered} |m|=\pm m,\text{ |n|=}\pm n \\ so,\text{ +m-n=0 or -m+n=0} \end{gathered}$

5) |m| is not equal to |n|- Never true

$\begin{gathered} |m|\text{ and |n| are not equal.} \\ So\text{ during summation they will show a poistive number} \end{gathered}$

6) m is positive and n is negative. - Sometimes true

If m is equal to n then:

+m + (-n) = m-n =0