Mathematical Evaluation: Absolute Values

Quiz Content Overview

Background

  • This quiz appears to assess mathematical concepts related to absolute values and basic arithmetic operations.

Question Breakdown

  • The quiz consists of multiple-choice questions focusing on the evaluation of expressions based on given values of variables.

Variables

  • x = -5
  • y = 3

Key Mathematical Concepts

Absolute Values

  • Absolute Value Definition: The absolute value of a number is its distance from zero on the number line, always expressed as a non-negative value.
    • Notated as: ( |a| ) where ( a ) is a real number.
    • For example, ( |-5| = 5 ) and ( |3| = 3 ).

Evaluations to Perform

  1. Calculate |x + y|:

    • Expression: ( x + y = -5 + 3 )
    • Calculation: ( x + y = -2 )
    • Absolute Value: ( |x + y| = |-2| = 2 )

  2. Calculate |x| + |y|:

    • Calculation: ( |x| = |-5| = 5 )
    • Calculation: ( |y| = |3| = 3 )
    • Combined: ( |x| + |y| = 5 + 3 = 8 )

Possible Answer Choices

  1. ( |x+y| = 0, |x| + |y| = 0 )
  2. ( |x+y| = 8, |x| + |y| = 2 )
  3. ( |x+y| = 2, |x| + |y| = 8 )
  4. ( |x+y| = -2, |x| + |y| = 2 )

Correct Answers

  • Based on the calculations above:
    • Correct Calculation of |x + y|: ( |x + y| = 2 )
    • Correct Calculation of |x| + |y|: ( |x| + |y| = 8 )
  • Therefore, the correct answer is:
    • Choice 3: ( |x+y| = 2, |x| + |y| = 8 )

Notes on Incorrect Options

  • The first option states both values as 0, which is incorrect given the calculations.
  • The second option incorrectly reverses the values for the absolute results.
  • The last option is logically flawed as it suggests a negative absolute value, which is not possible.

Summary

  • In mathematical terms, correctly calculating absolute values and understanding their definitions is crucial for solving problems involving variables. Evaluations show the importance of knowing how to manipulate and interpret numerical expressions accordingly.