Questions: If t=-3, then 3t^2+5t+6 equals (a) -36 (b) -6 (c) 6 (d) 18

Transcript text: Homework 1 If $t=-3$, then $3 t^{2}+5 t+6$ equals (a) -36 (b) -6 (c) 6 (d) 18

Solution

To solve the given expression $3t^2 + 5t + 6$ for $t = -3$, we need to substitute $-3$ for $t$ in the expression and then evaluate it.

Step 1: Substitute $ t = -3 $ into the expression

We start with the expression $ 3t^2 + 5t + 6 $. To find its value when $ t = -3 $, we substitute $-3$ for $ t $:

\[ 3(-3)^2 + 5(-3) + 6 \]

Step 2: Evaluate the expression

First, calculate $ (-3)^2 $:

\[ (-3)^2 = 9 \]

Next, multiply by 3:

\[ 3 \times 9 = 27 \]

Then, calculate $ 5(-3) $:

\[ 5 \times (-3) = -15 \]

Finally, add all the terms together:

\[ 27 + (-15) + 6 = 27 - 15 + 6 = 18 \]

The value of the expression $ 3t^2 + 5t + 6 $ when $ t = -3 $ is $\boxed{18}$.

The answer is (d) 18.

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