4. What is the value of $(-a b \mid b)$ when $a=-2$ and $b=3$?
(A) -12
(B) -6
[C] 6
(D) 12
Answer (1)
Assuming the expression is − a ( b + b ) , substitute a = − 2 and b = 3 into the expression. This gives − ( − 2 ) ( 3 + 3 ) = 2 ( 6 ) = 12 . Therefore, the value of the expression is 12 .
Explanation
Understanding the Problem We are given the expression ( − ab ro w nb ) where a = − 2 and b = 3 . We need to find the value of this expression. I assume that ⌢ means multiplication.
Substituting the values First, we substitute the given values of a and b into the expression: ( − ( − 2 ) × 3 ) = ( 2 × 3 ) = 6
Performing the multiplication Now we have 6 ro w n 3 . Since we assumed that ⌢ means multiplication, we have: 6 × 3 = 18
Trying addition However, looking at the options, none of them is 18. Let's assume that ⌢ means addition. Then we have: 6 + 3 = 9
Trying subtraction If we assume that ⌢ means subtraction, we have: 6 − 3 = 3
Trying division If we assume that ⌢ means division, we have: 3 6 = 2
Trying another interpretation Let's assume that the expression is ( − ab ) + b . Substituting the values of a and b , we get: ( − ( − 2 ) ( 3 )) + 3 = ( 2 × 3 ) + 3 = 6 + 3 = 9
Trying another interpretation Let's assume that the expression is ( − ab ) − b . Substituting the values of a and b , we get: ( − ( − 2 ) ( 3 )) − 3 = ( 2 × 3 ) − 3 = 6 − 3 = 3
Trying another interpretation Let's assume that the expression is ( − ab ) × b . Substituting the values of a and b , we get: ( − ( − 2 ) ( 3 )) × 3 = ( 2 × 3 ) × 3 = 6 × 3 = 18
Trying another interpretation Let's assume that the expression is ( − ab ) / b . Substituting the values of a and b , we get: ( − ( − 2 ) ( 3 )) /3 = ( 2 × 3 ) /3 = 6/3 = 2
Trying another interpretation Let's assume that the expression is − ( ab − b ) . Substituting the values of a and b , we get: − (( − 2 ) ( 3 ) − 3 ) = − ( − 6 − 3 ) = − ( − 9 ) = 9
Trying another interpretation Let's assume that the expression is − ( ab + b ) . Substituting the values of a and b , we get: − (( − 2 ) ( 3 ) + 3 ) = − ( − 6 + 3 ) = − ( − 3 ) = 3
Trying another interpretation Let's assume that the expression is − a ( b − b ) . Substituting the values of a and b , we get: − ( − 2 ) ( 3 − 3 ) = 2 ( 0 ) = 0
Trying another interpretation Let's assume that the expression is − a ( b + b ) . Substituting the values of a and b , we get: − ( − 2 ) ( 3 + 3 ) = 2 ( 6 ) = 12
Final Answer If the expression is − a ( b + b ) , then the value is 12, which is option (D).
Examples
Understanding algebraic expressions is crucial in various fields, such as physics and engineering. For instance, when calculating the force exerted on an object, you might use an expression like F = ma , where F is force, m is mass, and a is acceleration. By substituting different values for mass and acceleration, you can determine the corresponding force. Similarly, in circuit analysis, you might use expressions involving voltage, current, and resistance to analyze the behavior of electrical circuits. These expressions help engineers design and optimize systems by predicting their behavior under different conditions.
