Question

14 nso.1.3 find the absolute value of a rational number interpret the absolute value of a rational number as the distance from zero on a number line given a real - world context (l.4) the temperature in alaska was - 18.5°c during a winter storm. how far below freezing is the temperature? marias bank account shows a balance of $ - 42.75 after paying her bills. how much will maria need to deposit so that her account has no debt?

Explanation:

Step1: Understand the concept of absolute value

The absolute value of a number \( x \) is denoted as \( |x| \) and is defined as the distance of \( x \) from zero on the number line. For a negative number \( -a \) (where \( a>0 \)), the absolute value \( | - a|=a \) because distance is always non - negative.

Step2: Solve the temperature problem

The temperature in Alaska is \( - 18.5^{\circ}\text{C} \). We want to find how far below freezing (which is \( 0^{\circ}\text{C} \)) this temperature is. This is equivalent to finding the absolute value of \( - 18.5 \).
Using the definition of absolute value, \( |-18.5| = 18.5 \). So the temperature is \( 18.5^{\circ}\text{C} \) below freezing.

Step3: Solve the bank account problem

Maria's bank account balance is \( \$ - 42.75 \). We want to find how much she needs to deposit to have no debt (i.e., to get the balance to \( \$0 \)). This is equivalent to finding the absolute value of \( - 42.75 \).
Using the definition of absolute value, \( |-42.75|=42.75 \). So Maria needs to deposit \( \$42.75 \).

Answer:

For the temperature: The temperature is \( 18.5^{\circ}\text{C} \) below freezing. For the bank account: Maria needs to deposit \( \$42.75 \).