Question

1. point c is 5 units from 0 on a number line. write two numbers that could each be the location of point c.
2. point d is 8 units from its opposite on a number line. write the numbers that point d and its opposite represent.
3. use the number line to complete parts (a) and (b).

a. plot point f at -5.
b. plot point g at -(-5).
c. describe the relationship between point f and point g.

1. write the number and describe its relationship to 0 on a number line.

a. ten
b. the opposite of ten
c. the opposite of the opposite of ten

1. sasha says that -(-25) is equal to -25. julie disagrees and says that -(-25) is equal to 25. who is correct? explain.

Explanation:

Question 5

Step1: Understand number line positions

A point 5 units from 0 on a number line can be in two directions: positive and negative.

Step2: Determine the numbers

The positive direction gives \( 5 \), and the negative direction gives \( -5 \).

Step1: Let the number be \( x \), its opposite is \( -x \)

The distance between \( x \) and \( -x \) is \( |x - (-x)| = |2x| \).

Step2: Set up the equation

We know \( |2x| = 8 \), so \( 2x = 8 \) or \( 2x = -8 \).

Step3: Solve for \( x \)

For \( 2x = 8 \), \( x = 4 \); for \( 2x = -8 \), \( x = -4 \). So the opposite of \( 4 \) is \( -4 \), and vice versa.

Step1: Analyze point \( F \)

Point \( F \) is at \( -5 \), so it is 5 units to the left of 0 on the number line.

Step2: Analyze point \( G \)

Simplify \( -(-5) = 5 \), so point \( G \) is at \( 5 \), 5 units to the right of 0 on the number line.

Step3: Describe the relationship

Point \( F \) (\( -5 \)) and point \( G \) (\( 5 \)) are opposites of each other. They are equidistant from 0 (both 5 units away) and lie on opposite sides of 0 on the number line.

Answer:

The two numbers could be \( 5 \) and \( -5 \).

Question 6