evaluate the following expression for (a) $x = 4$ and $y = 1$ and (b) $x = 1$ and $y = 5$.
\6x^2 + y^2\
(a) for $x = 4$ and $y = 1$, $6x^2 + y^2 = \square$.
(type an integer or a simplified fraction.)

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Evaluating Expressions" ], "new_concepts": [], "current_concepts": [ "Evaluating Expressions", "Order of Operations", "Exponents" ] } ## Substitute the given values into the expression $$ \begin{aligned} &\text{Expression: } 6x^2 + y^2 \ &\text{Given: } x = 4, \quad y = 1 \ &6(4)^2 + (1)^2 \end{aligned} $$ ## Evaluate exponents according to order of operations $$ \begin{aligned} &4^2 = 16 \ &1^2 = 1 \ &6(16) + 1 \end{aligned} $$ ## Perform multiplication and addition $$ \begin{aligned} &6 \times 16 = 96 \ &96 + 1 = 97 \end{aligned} $$ For $x = 4$ and $y = 1$, $6x^2 + y^2 =$ 97. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Evaluating Expressions" ] }

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Substitute the given values into the expression

Evaluate exponents according to order of operations

Perform multiplication and addition

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