Which statements about opposites are true?
select each correct answer.
the opposite of a negative number is always a positive number.
a number and its opposite are located the same distance from zero on a number line.
the product of a number and its opposite is always 1.
the opposite of zero is zero.

The statements about opposites that are true include:

It should be noted that the opposite of a negative number is always a positive number. This is referred to as an additive inverse.

Also, the opposite of zero is zero. In such a case, 0-0 = 0. The opposite of a negative number is always a positive number. For example 4 - (-4) = +8.

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(a) TRUE

(b) TRUE

(c)  FALSE

(d) TRUE

Step-by-step explanation:

" The "opposite" of any number is also known as it's " additive inverse" i.e. for any number 'a' the additive inverse is 'a' ".

(a) TRUE

Since let us consider any negative number '-5' then it's opposite is '5' since (-5)+5=0

(b) TRUE

this could be seen clearly from the number line.

(c) FALSE

this statement is false since we can take example of zero.

the opposite of zero is 0 but 0×0≠1.

(d) TRUE

since 0-0=0.

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.