Select the correct answer.
What is the value of the expression when $a=-2, b=3$, and $c=-6$ ?
$\frac{a b+2 c}{-b c}$
A. 1
B. $-\frac{1}{3}$
C. -1
D. $\frac{1}{3}$
Answer (1)
Substitute the given values a = − 2 , b = 3 , and c = − 6 into the expression − b c ab + 2 c .
Calculate the numerator: ( − 2 ) ( 3 ) + 2 ( − 6 ) = − 6 − 12 = − 18 .
Calculate the denominator: − ( 3 ) ( − 6 ) = − ( − 18 ) = 18 .
Divide the numerator by the denominator: 18 − 18 = − 1 .
Explanation
Understanding the Problem We are given the expression − b c ab + 2 c and the values a = − 2 , b = 3 , and c = − 6 . Our goal is to find the value of the expression when we substitute these values.
Substituting the Values First, we substitute the given values into the expression: − b c ab + 2 c = − ( 3 ) ( − 6 ) ( − 2 ) ( 3 ) + 2 ( − 6 )
Simplifying the Numerator Next, we simplify the numerator: ( − 2 ) ( 3 ) + 2 ( − 6 ) = − 6 + ( − 12 ) = − 18
Simplifying the Denominator Then, we simplify the denominator: − ( 3 ) ( − 6 ) = − ( − 18 ) = 18
Dividing Numerator by Denominator Now, we divide the numerator by the denominator: 18 − 18 = − 1
Final Answer Therefore, the value of the expression is − 1 .
Examples
Imagine you are calculating the efficiency of a simple machine where 'a' represents energy loss, 'b' represents energy input, and 'c' represents energy output. The expression could model a ratio that helps determine overall performance. By substituting the given values, you can quickly assess the machine's efficiency under specific conditions, providing a practical application of algebraic substitution in engineering or physics.
