the graph represents the ways janelle can win the beanbag toss game. which describes a way janelle can win the game?

- land on round 7 times; land on square 1 time
- land on round 6 times; land on square 2 times
- land on round 5 times; land on square 3 times
- land on round 4 times; land on square 4 times

Question

the graph represents the ways janelle can win the beanbag toss game. which describes a way janelle can win the game?

- land on round 7 times; land on square 1 time
- land on round 6 times; land on square 2 times
- land on round 5 times; land on square 3 times
- land on round 4 times; land on square 4 times

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Linear Inequalities" ], "new_concepts": [ "Graphing Inequalities", "Feasible Region" ], "current_concepts": [ "Linear Inequalities", "Boundary Line Intercepts", "Real-world Constraints", "Graphing Inequalities", "Feasible Region" ] } ## Identify the shaded region Using the *Linear Inequalities* knowledge point $$ \begin{aligned} &\text{Shaded region: } y > -\frac{3}{5}x + 6 \quad (\text{or above the dashed boundary line})\ &\text{Boundary line passes through: } (0, 6) \text{ and } (10, 0) \end{aligned} $$ ## Test the given coordinate options Using the *Linear Inequalities* knowledge point $$ \begin{aligned} &\text{Option 1: } (7, 1) \implies 1 > -\frac{3}{5}(7) + 6 \implies 1 > 1.8 \quad (\text{False})\ &\text{Option 2: } (6, 2) \implies 2 > -\frac{3}{5}(6) + 6 \implies 2 > 2.4 \quad (\text{False})\ &\text{Option 3: } (5, 3) \implies 3 > -\frac{3}{5}(5) + 6 \implies 3 > 3 \quad (\text{False, dashed line})\ &\text{Option 4: } (4, 4) \implies 4 > -\frac{3}{5}(4) + 6 \implies 4 > 3.6 \quad (\text{True}) \end{aligned} $$

land on round 7 times; land on square 1 time

land on round 6 times; land on square 2 times

land on round 5 times; land on square 3 times

land on round 4 times; land on square 4 times

{ "elements": [ { "type": "inequality", "params": [ { "js": "-0.6*x + 6", "latex": "y > -0.6x + 6" }, [5, 5] ], "properties": { "inverse": true, "strict": true, "strokeColor": "#8C55F2", "fillColor": "rgba(140, 85, 242, 0.3)" } }, { "type": "point", "params": [[7, 1]], "properties": { "name": "(7, 1)", "color": "#F2557F", "withLabel": true } }, { "type": "point", "params": [[6, 2]], "properties": { "name": "(6, 2)", "color": "#F2557F", "withLabel": true } }, { "type": "point", "params": [[5, 3]], "properties": { "name": "(5, 3)", "color": "#F2557F", "withLabel": true } }, { "type": "point", "params": [[4, 4]], "properties": { "name": "(4, 4)", "color": "#5583F2", "withLabel": true } } ], "timestamps": [0.5, 1.0, 1.5] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Linear Inequalities" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the shaded region

Test the given coordinate options

Answer: