This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Step 1: Answer Question 1. The function f(x) = x^2 + 5x + 6 is a polynomial function of degree 2. Quadratic function Step 2: Answer Question 2. The Remainder Theorem states that if a polynomial P(x) is divided by a linear divisor (x-a), then the remainder is P(a). Step 3: Answer Question 3. A function f(x) is continuous at the point x=a if and only if: • f(a) is defined. • _x a f(x) exists. • _x a f(x) = f(a). Step 4: Answer Question 4. A singular matrix is a square matrix whose determinant is zero. The determinant value of a singular matrix is 0. Step 5: Answer Question 5. Two lines with slopes m_1 and m_2 are parallel if and only if their slopes are equal. m_1 = m_2 Step 6: Answer Question 6. A circle is formed when a plane intersects a cone perpendicular to the cone's axis. Step 7: Answer Question 7. The formula for 2 in terms of is: 2 = (1 - ^2 )/(1 + ^2 ) Step 8: Answer Question 8. Given A = 1. For an acute angle A: A = ^-1(1) A = 0^ 0^ Step 9: Answer Question 9. If is the angle between two vectors p and q, the formula for is: = p · q|p| |q| Step 10: Answer Question 10. For inversion, the relation between OP, OP', and the radius r is: OP · OP' = r^2