Simplify the following expression:(4t − 10t2) + 15(6t + 2)After simplifying, what number is multiplied by the t?

1. Break Down the Problem

We need to simplify the expression $(4t - 10t^2) + 15(6t + 2)$ and find the coefficient of $t$.

2. Relevant Concepts

We'll use the distributive property and combine like terms in algebra to simplify the expression.

3. Analysis and Detail

1. Distribute $15$ in $15(6t + 2)$: $15(6t + 2) = 15 \cdot 6t + 15 \cdot 2 = 90t + 30$

2. Now substitute this back into the expression: $(4t - 10t^2) + (90t + 30)$

3. Combine like terms:

   • Combine $t$ terms: $4t + 90t = 94t$
   • The constant $30$ remains as is.
   • The term $-10t^2$ also stays.

   Therefore, the expression simplifies to: $-10t^2 + 94t + 30$

4. Verify and Summarize

We have simplified the expression and combined all the like terms correctly:

Final Simplified Expression: $-10t^2 + 94t + 30$

Final Answer

The number multiplied by $t$ is 94.