(1) Select the expressions that are equivalent to $$ -3(t-4) $$ $$ \begin{array}{l}-4(-3+t) \ (-4+t) \cdot-3 \ -7 t \ -3(-4+t)\end{array} $$

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UpStudy AI · Accepted Answer

To determine which expressions are equivalent to $$ -3(t - 4) $$, let's simplify each option:

1. **$$-4(-3 + t)$$**
   $$
   -4(-3 + t) = -4(t - 3) = -4t + 12
   $$
   This simplifies to $$-4t + 12$$, which is **not** the same as $$-3t + 12$$.

2. **$$(-4 + t) \cdot -3$$**
   $$
   (-4 + t) \cdot -3 = (t - 4) \cdot -3 = -3t + 12
   $$
   This simplifies to $$-3t + 12$$, which **matches** $$-3(t - 4)$$.

3. **$$-7t$$**
   $$
   -7t
   $$
   This is simply $$-7t$$, which does **not** match $$-3t + 12$$.

4. **$$-3(-4 + t)$$**
   $$
   -3(-4 + t) = -3(t - 4) = -3t + 12
   $$
   This simplifies to $$-3t + 12$$, which **matches** $$-3(t - 4)$$.

**Therefore, the expressions that are equivalent to $$ -3(t - 4) $$ are:**

- $$(-4 + t) \cdot -3$$
- $$-3(-4 + t)$$

**Final Answer:**
Both $$(-4 + t) \cdot -3$$ and $$-3(-4 + t)$$ are equivalent to $$-3(t-4)$$.
The expressions equivalent to $$ -3(t - 4) $$ are $$(-4 + t) \cdot -3$$ and $$-3(-4 + t)$$.

(1) Select the expressions that are equivalent to

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