Question

what is the solution to the inequality \\(x^2 < 16 - 6x\\)?

a) \\(-8 < x < 2\\)
b) \\(x < -8\\) and \\(x > 2\\)
c) \\(x < -8\\) or \\(x > 2\\)
d) \\(-8 \le x \le 2\\)

question 10 (5 points)
find the solution(s) of the system of equations.
\\(y = x^2 + 4x\\)
\\(y + x^2 = -4x\\)

a) \\((-4, 0)\\) and \\((0, 0)\\)
b) \\((0, 0)\\) and \\((4, 0)\\)
c) \\((0, 0)\\)
d) \\((-4, 0)\\) and \\((4, 0)\\)

question 11 (5 points)
solve \\(x^2 + 8x + 22 = 0\\) by completing the square.

a) \\(x = -4 + i\sqrt{6}, x = -4 - i\sqrt{6}\\)
b) \\(x = -4 + i\sqrt{14}, x = -4 - i\sqrt{14}\\)
c) \\(x = -4 + \sqrt{6}, x = -4 - \sqrt{6}\\)
d) \\(x = -4 + \sqrt{14}, x = -4 - \sqrt{14}\\)

Explanation:

Solve the quadratic inequality

Using the Quadratic Inequalities knowledge point

$$
LATEXBLOCK0
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Solve the system of equations

Using the Systems of Quadratic and Linear Equations knowledge point

$$
LATEXBLOCK1
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Solve by completing the square

Using the Completing the Square knowledge point

$$
LATEXBLOCK2
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Answer:

Question 1

• A) \(-8 < x < 2\) (Correct answer)
• B) \(x < -8\) and \(x > 2\)
• C) \(x < -8\) or \(x > 2\)
• D) \(-8 \le x \le 2\)

Question 2

• A) \((-4, 0)\) and \((0, 0)\) (Correct answer)
• B) \((0, 0)\) and \((4, 0)\)
• C) \((0, 0)\)
• D) \((-4, 0)\) and \((4, 0)\)

Question 3

• A) \(x = -4 + i\sqrt{6}, x = -4 - i\sqrt{6}\) (Correct answer)
• B) \(x = -4 + i\sqrt{14}, x = -4 - i\sqrt{14}\)
• C) \(x = -4 + \sqrt{6}, x = -4 - \sqrt{6}\)
• D) \(x = -4 + \sqrt{14}, x = -4 - \sqrt{14}\)