choose the function that represents the triangular numbers.

$y = 0.5x + 0.5$
$y = 0.5^x + 0.5x$
$y = \frac{x}{0.5} + 0.5x$
$y = 0.5x^2 + 0.5x$

Question

choose the function that represents the triangular numbers.

$y = 0.5x + 0.5$
$y = 0.5^x + 0.5x$
$y = \frac{x}{0.5} + 0.5x$
$y = 0.5x^2 + 0.5x$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Triangular Numbers", "Quadratic Modeling" ], "current_concepts": [ "Triangular Numbers", "Quadratic Modeling" ] } ## Count the dots for each given value of $x$ $$ \begin{aligned} x = 2 &\implies y = 3 \ x = 3 &\implies y = 6 \ x = 4 &\implies y = 10 \ x = 5 &\implies y = 15 \ x = 6 &\implies y = 21 \end{aligned} $$ ## Test the given options with $x = 2$ $$ \begin{aligned} \text{Option 1: } y &= 0.5(2) + 0.5 = 1.5 eq 3 \ \text{Option 2: } y &= 0.5^2 + 0.5(2) = 0.25 + 1 = 1.25 eq 3 \ \text{Option 3: } y &= \frac{2}{0.5} + 0.5(2) = 4 + 1 = 5 eq 3 \ \text{Option 4: } y &= 0.5(2)^2 + 0.5(2) = 2 + 1 = 3 \end{aligned} $$ ## Verify the correct option with $x = 3$ $$ y = 0.5(3)^2 + 0.5(3) = 4.5 + 1.5 = 6 $$

y = 0.5x + 0.5

y = 0.5^{x} + 0.5x

y = \frac{x}{0.5} + 0.5x

y = 0.5x^2 + 0.5x

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

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QUESTION IMAGE

Question

Explanation:

Count the dots for each given value of \(x\)

Test the given options with \(x = 2\)

Verify the correct option with \(x = 3\)

Answer: