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,\textn\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|\textn \\ 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