Question

what is the value of the expression below when $a = 4$, $b = 12$, and $c = -1$?
\\(\frac{5a + b}{-2ac}\\)
a $-2$
b $4$
c $-4$
d $6$

Explanation:

Step1: Substitute the values of a, b, c into the numerator and denominator respectively.

For the numerator: \(5a + b = 5\times4 + 12\)
For the denominator: \(-2ac = -2\times4\times(-1)\)

Step2: Calculate the numerator.

\(5\times4 + 12 = 20 + 12 = 32\)

Step3: Calculate the denominator.

\(-2\times4\times(-1)= 8\)

Step4: Divide the numerator by the denominator.

\(\frac{32}{8}=4\)? Wait, no, wait. Wait, the original expression is \(\frac{5a + b}{-2ac}\), let's recalculate. Wait, a=4, b=12, c=-1. So numerator: 54 +12=20+12=32. Denominator: -24(-1)= -8(-1)=8? Wait, no, -24 is -8, times -1 is 8. Then 32/8=4? But wait, let's check again. Wait, maybe I made a mistake. Wait, the expression is \(\frac{5a + b}{-2ac}\). So a=4, b=12, c=-1. So numerator: 54 +12=20+12=32. Denominator: -24(-1)= 8. Then 32 divided by 8 is 4? But let's check the options. Option B is 4. Wait, but let me check again. Wait, maybe I messed up the signs. Wait, denominator: -2ac. a=4, c=-1. So -24(-1)= (-8)(-1)=8. Numerator: 54 +12=20+12=32. 32/8=4. So the answer is B? Wait, but let me check the original problem again. The expression is \(\frac{5a + b}{-2ac}\). Yes. So substituting a=4, b=12, c=-1. So numerator: 54 +12=32. Denominator: -24*(-1)=8. 32/8=4. So the answer is B.

Answer:

B. 4