Question

for problems 1–2, use the diagram of the thermometer if necessary.

1. the temperature decreases from 4°f to -9°f. by how many degrees does the temperature decrease?
2. during the day, the temperature increases from -2°f to 13°f. by how many degrees does the temperature increase?

for problems 3–5, use the number line.

1. what is the distance from point d to point b?
2. which is closer to 0, point d or point a? explain.
3. explain the meaning of |-3| > |1|.

Explanation:

Problem 1

Step1: Identify the formula

To find the temperature decrease, we calculate the difference between the initial temperature and the final temperature. The formula is \( \text{Decrease} = \text{Initial Temperature} - \text{Final Temperature} \) (since final temperature is lower, we'll get a positive value for the decrease).
Initial temperature \( = 4^\circ\text{F} \), Final temperature \( = -9^\circ\text{F} \)

Step2: Calculate the difference

\( 4 - (-9) = 4 + 9 = 13 \) (subtracting a negative is adding the positive)

Step1: Identify the formula

To find the temperature increase, we calculate the difference between the final temperature and the initial temperature. The formula is \( \text{Increase} = \text{Final Temperature} - \text{Initial Temperature} \)
Initial temperature \( = -2^\circ\text{F} \), Final temperature \( = 13^\circ\text{F} \)

Step2: Calculate the difference

\( 13 - (-2) = 13 + 2 = 15 \) (subtracting a negative is adding the positive)

Step1: Find the coordinates of points

From the number line, point \( D \) is at \( -3 \) and point \( B \) is at \( 8 \).

Step2: Calculate the distance

The distance between two points \( x_1 \) and \( x_2 \) on a number line is \( |x_2 - x_1| \). So, \( |8 - (-3)| = |8 + 3| = |11| = 11 \)

Answer:

The temperature decreases by \( \boldsymbol{13} \) degrees.

Problem 2