Question

Find ||, ||, |2|, 1 2 , | |, | − |, and || − ||. = −9, 9 , = −1, −3.

A) 9,3,18,−1.5,27,6,8
B) 9,3,−18,−1.5,−27,−6,−8
C) 9,3,−18,−1.5,27,6,−8
D) 9,3,18,1.5,−27,6,−8

Answer 1

The computed values are: absolute values of Λ and Μ are 9 and 1, respectively; the absolute value of twice Λ is 18; the division of Λ by Μ is 9; |ΛΛ| is 81; the absolute value of the difference between Λ and Μ is 8; and the absolute value of Λ minus itself is 0.

Step-by-step explanation:

The question involves computing absolute values, subtraction and multiplication of numbers with same and opposite signs, and division of numbers following multiplication rules for signs. Given that Λ = -9, and Μ = -1, we will need to substitute these values into the expressions provided and use rules for operations with signed numbers to find the correct answers.

• Absolute value: The absolute value of a number is its distance from zero, without considering its sign. For example, |-9| = 9.
• Subtraction: When subtracting, change the sign of the number being subtracted and then add. Subtracting a negative is the same as adding the absolute value of that number.
• Multiplication and Division: The sign of the product or quotient depends on the signs of the values involved. Multiplying or dividing two numbers with the same sign results in a positive, whereas with opposite signs, the result is negative.

Let's compute the given expressions:

• ||Λ|| = |-9| = 9
• ||Μ|| = |-1| = 1
• |2Λ| = |2(-9)| = |-18| = 18
• Λ/Μ = -9/(-1) = 9
• |ΛΛ| = |-9 x -9| = |81| = 81
• |Λ - Μ| = |-9 - (-1)| = |-8| = 8
• |Λ - Λ| = |-9 - (-9)| = |0| = 0

So, the correct answers are:

• ||Λ|| = 9
• ||Μ|| = 1
• |2Λ| = 18
• Λ/Μ = 9
• |ΛΛ| = 81
• |Λ - Μ| = 8
• |Λ - Λ| = 0