Final answer:
The expressions equivalent to 9(4t+4)+2 are 36t + 38 and 3(12t + 12) + 2. Other options provided are not equivalent as they either have different coefficients for 't' or constants.
Step-by-step explanation:
Let's begin by distributing 9 in the provided algebraic expression 9(4t+4)+2. Distributing 9 gives 36t + 36 + 2, which simplifies to 36t + 38. Therefore, the expressions equivalent to 9(4t+4)+2 are those which simplify to 36t + 38. Checking the options provided:
- 4t + 38, this does not equal 36t + 38 as the coefficient of 't' is different
- 36t + 38, this is indeed equivalent as it matches ours.
- 38t + 36, isn't equivalent as coefficients and constant are exchanged.
- 3(12t + 12) + 2, on simplifying this, we get 36t + 36 + 2 = 36t + 38. Hence, it is also equivalent.
In conclusion, the expressions equivalent to 9(4t+4)+2 are 36t + 38 and 3(12t + 12) + 2.
Learn more about Equivalent Linear Expressions