In your own words, explain to me what is absolute value? Make sure to talk about the definition of it, how you find it, and how it's different from just plotting an integer on a number line. You must provide 3 sentences or more.

It's a function that associates a real number x with a positive real number using the flowing definition: If the number is not negative (so either positive or 0) the absolute value is x. If x is negative, the absolute value is -x.

This means that to find the absolute value of x you must first determine if x is negative or not, and if it is, multiply it by -1. If it isn't, leave it as it is.

Since the absolute value is a function (of a given number), you can't just plot that number in the number line but the function (so in this case absolute value must be taken first.

The absolute value of x is never negative, so given the absolute value of x we can't determinate if x was positive or negative (if x =/ 0) before the absolute value was taken.

4sqrt5

step-by-step explanation:

the base has dimensions of 8 x 4, so the diagonal is 64 + 16 square rooted or 4sqrt5.

hope this !

step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)