question 19 (5 points) simplify $-\sqrt{-48}$. a) $-4\sqrt{3}$ b) $4\sqrt{3}i$ c) $4\sqrt{3}$ d) $-4\sqrt{3}i$ question 20 (5 points) which of the following ordered pairs is not a solution of the system of inequalities? $y x^2 - 4x - 5$ $y

Question

question 19 (5 points)
simplify $-\sqrt{-48}$.
a) $-4\sqrt{3}$
b) $4\sqrt{3}i$
c) $4\sqrt{3}$
d) $-4\sqrt{3}i$

question 20 (5 points)
which of the following ordered pairs is not a solution of the system of inequalities?
$y > x^2 - 4x - 5$
$y < -x^2 - 5x + 6$
a) $(-1, 6)$
b) $(1, -7)$
c) $(1, -5)$
d) $(1, 7)$

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Complex Number Simplification", "Quadratic Inequalities" ], "new_concepts": [], "current_concepts": [ "Complex Number Simplification", "Quadratic Inequalities", "Systems of Inequalities" ] } ## Simplify the radical expression $$ -\sqrt{-48} = -\sqrt{48 \cdot (-1)} = -\sqrt{16 \cdot 3} \cdot i = -4\sqrt{3}i $$ ## Test ordered pairs in the first inequality $$ \begin{aligned} &y > x^2 - 4x - 5 \ &\text{For } (-1, 6): 6 > (-1)^2 - 4(-1) - 5 \implies 6 > 0 \quad (\text{True}) \ &\text{For } (1, -7): -7 > (1)^2 - 4(1) - 5 \implies -7 > -8 \quad (\text{True}) \ &\text{For } (1, -5): -5 > (1)^2 - 4(1) - 5 \implies -5 > -8 \quad (\text{True}) \ &\text{For } (1, 7): 7 > (1)^2 - 4(1) - 5 \implies 7 > -8 \quad (\text{True}) \end{aligned} $$ ## Test ordered pairs in the second inequality $$ \begin{aligned} &y < -x^2 - 5x + 6 \ &\text{For } (-1, 6): 6 < -(-1)^2 - 5(-1) + 6 \implies 6 < 10 \quad (\text{True}) \ &\text{For } (1, -7): -7 < -(1)^2 - 5(1) + 6 \implies -7 < 0 \quad (\text{True}) \ &\text{For } (1, -5): -5 < -(1)^2 - 5(1) + 6 \implies -5 < 0 \quad (\text{True}) \ &\text{For } (1, 7): 7 < -(1)^2 - 5(1) + 6 \implies 7 < 0 \quad (\text{False}) \end{aligned} $$ ## Question 19 A) $-4\sqrt{3}$

B) $4\sqrt{3}i$

C) $4\sqrt{3}$

D) $-4\sqrt{3}i$ ## Question 20 A) $(-1, 6)$

B) $(1, -7)$

C) $(1, -5)$

D) $(1, 7)$

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

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QUESTION IMAGE

Question

Explanation:

Simplify the radical expression

Test ordered pairs in the first inequality

Test ordered pairs in the second inequality

Answer:

Question 19

Question 20