Final Answer:
Sure, the equation (1*3)M = 18 translates to (1² + 3²)M = 18, simplifying to 10M = 18, resulting in M = 6 (B).
Step-by-step explanation:
The given equation (1*3)M = 18 simplifies to 3M = 18 after resolving the multiplication of 1 and 3. To solve for M, divide both sides of the equation by 3, which yields M = 18 ÷ 3, resulting in M = 6.
To explain further, the equation (13)M = 18 can be rewritten using the property ab = a² + b², which states that the product of two numbers equals the sum of their squares. Here, a = 1, b = 3, and the result is 18. Translating this, (13)M = 18 becomes (1² + 3²)M = 18. Simplifying 1² + 3² = 1 + 9 = 10, we then get 10M = 18. Finally, solving for M by dividing both sides by 10 yields M = 18 ÷ 10 = 6.
In summary, the solution is M = 6 (Option B). By applying the property of the sum of squares to the equation (1*3)M = 18, breaking it down to (1² + 3²)M = 18, and further simplifying, we arrive at 10M = 18, leading to the final solution of M = 6 after division. Therefore the correct option is B.