when the product of 6 and the square of a number is increased by 5 times the number, the result is 4. which equation represents this situation?

$6x^2 + 5x - 4 = 0$
$6x^2 + 5x + 4 = 0$
$6^2x + 5 + x = 4$
$6 + x^2 + 5x = 4$

Question

when the product of 6 and the square of a number is increased by 5 times the number, the result is 4. which equation represents this situation?

$6x^2 + 5x - 4 = 0$
$6x^2 + 5x + 4 = 0$
$6^2x + 5 + x = 4$
$6 + x^2 + 5x = 4$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Algebraic Translation", "Algebraic Expressions", "Linear Equation Formulation" ], "new_concepts": [ "Quadratic Equation Formulation" ], "current_concepts": [ "Algebraic Translation", "Algebraic Expressions", "Quadratic Equation Formulation" ] } ## Translate the verbal statement into algebraic terms $$ \begin{aligned} &\text{Let the number be } x.\ &\text{"the square of a number": } x^2\ &\text{"the product of 6 and the square of a number": } 6x^2\ &\text{"5 times the number": } 5x\ &\text{"increased by": } +\ &\text{"the result is 4": } = 4 \end{aligned} $$ ## Formulate the initial equation $$ 6x^2 + 5x = 4 $$ ## Rearrange into standard quadratic form $$ \begin{aligned} &6x^2 + 5x - 4 = 0 \end{aligned} $$

(A) $6x^2 + 5x - 4 = 0$

(B) $6x^2 + 5x + 4 = 0$

(C) $6^2x + 5 + x = 4$

(D) $6 + x^2 + 5x = 4$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Equation Formulation" ] }

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Question

Explanation:

Translate the verbal statement into algebraic terms

Formulate the initial equation

Rearrange into standard quadratic form

Answer: