reyna runs a textile company that manufactures t-shirts. the profit, \$p\$, made by the company is modeled by the function \$p = s^2 + 9s - 142\$, where \$s\$ is the number of t-shirts sold. how many t-shirts should be sold to earn a profit of more than \\$2,000?

\$s < 42\$
\$s > 42\$
\$s > 51\$
\$s < 51\$

Question

reyna runs a textile company that manufactures t-shirts. the profit, \$p\$, made by the company is modeled by the function \$p = s^2 + 9s - 142\$, where \$s\$ is the number of t-shirts sold. how many t-shirts should be sold to earn a profit of more than \\$2,000?

\$s < 42\$
\$s > 42\$
\$s > 51\$
\$s < 51\$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Quadratic Inequalities" ], "new_concepts": [], "current_concepts": [ "Quadratic Inequalities", "Quadratic Functions" ] } ## Set up the quadratic inequality $$ s^2 + 9s - 142 > 2000 $$ ## Solve the quadratic equation for boundary values $$ \begin{aligned} s^2 + 9s - 2142 &= 0 \ (s - 42)(s + 51) &= 0 \ s = 42 \quad &\text{or} \quad s = -51 \end{aligned} $$ ## Determine the solution set for the inequality $$ \begin{aligned} s > 42 \quad &\text{or} \quad s < -51 \ \text{Since } s \ge 0: \quad &s > 42 \end{aligned} $$

$s < 42$

$s > 42$

$s > 51$

$s < 51$

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

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QUESTION IMAGE

Question

Explanation:

Set up the quadratic inequality

Solve the quadratic equation for boundary values

Determine the solution set for the inequality

Answer: