Question

Which of the following correctly uses absolute value to show the distance between -80 and 15? A. abs(-80 - 15) = abs(-95) = -95 units B. abs(-80 + 15) = abs(-65) = 65 units C. abs(-80 - 15) = abs(-95) = 95 units D. abs(-80 + 15) = abs(-65) = -65 units

Piecewise-Defined Functions
ANSWERED
asked 2021-02-12
Which of the following correctly uses absolute value to show the distance between -80 and 15?
A.
\(\displaystyle{\left|{-{80}-{15}}\right|}={\left|{-{95}}\right|}=-{95}\) units
B.
\(\displaystyle{\left|{-{80}+{15}}\right|}={\left|{-{65}}\right|}={65}\) units
C.
\(\displaystyle{\left|{-{80}-{15}}\right|}={\left|{-{95}}\right|}={95}\) units
D.
\(\displaystyle{\left|{-{80}+{15}}\right|}={\left|{-{65}}\right|}=-{65}\) units

Answers (1)

2021-02-13
Step 1
Our aim is to calculate the distance between −80 and 15 using absolute value.
Step 2
The distance between any two points 'a' and 'b' on th enumber line is \(\displaystyle{\left|{{a}−{b}}\right|}{\quad\text{or}\quad}{\left|{{b}−{a}}\right|}\)
\(\displaystyle\Rightarrow\) The distance between - 80 and 15 is \(\displaystyle{\left|{-{80}-{15}}\right|}={\left|{-{95}}\right|}\), but absolute value changes a negative number into its positive additive inverse.
\(\displaystyle\Rightarrow{\left|{-{80}-{15}}\right|}={\left|{-{95}}\right|}={95}\) units.
Hence, option (c) is correct.
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