Question

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Answer 1

Answer:

$\text{C. }1$

Step-by-step explanation:

In the question, we're given that the notation $\#\#(a,b,c)$ produces a number $a$ less than the product of $b$ and $c$ raised to the $a$ power. Let the number produced be $n$. As a mathematical equation, we can write this production as $n=(bc)^a-a$

For $\#\#(2, 5, x)$, we can assign:

• $a\implies 2$
• $b\implies 5$
• $c\implies x$

Substituting these values into $n=(bc)^a-a$, we get:

$23=(5x)^2-2$

Add 2 to both sides:

$25=(5x)^2$

Take the square root of both sides:

$5=|5x|$

For $y=|z|$, there are two cases:

$\begin{cases}y=z,\\y=-z\end{cases}$

Therefore, we have:

$\begin{cases}5=5x, x=\boxed{1}\\5=-(5x), 5=-5x, x=\boxed{-1}}\end{cases}$

The only answer choice applicable is $\boxed{\text{C. }1}$.