answer:(1) When m+1=0, i.e., m=-1, we have x-2=0. Therefore, x=2, and in this case, the equation has real roots. When m+1 neq 0, i.e., m neq -1, from Delta = m^2 - 4(m+1)(m-1) geq 0, we get 3m^2 - 4 leq 0. Solving this, we find - frac {2}{3} sqrt {3} leq m leq frac {2}{3} sqrt {3}. In this case, - frac {2}{3} sqrt {3} leq m leq frac {2}{3} sqrt {3} and m neq -1. In summary: A = {m | - frac {2}{3} sqrt {3} leq m leq frac {2}{3} sqrt {3}}. (2) Since A cup B = B, we have A subseteq B. Also, B = {x | x^2 - (a+2)x + 2a > 0}. Therefore, when a > 2, B = {x | x < 2 text{ or } x > a}, in this case, A subseteq B. When a leq 2, B = {x | x < a text{ or } x > 2}. Because A subseteq B, it implies a > frac {2}{3} sqrt {3}. In this case, 2 geq a > frac {2}{3} sqrt {3}. In summary, the range of a is boxed{(frac {2}{3} sqrt {3}, +infty)}.

answer:For an odd function, we have the property that f(-x) = -f(x). Given that f(x) is an odd function and f(x) = x(1 - x) when x > 0, we want to find f(x) when x < 0. Since x < 0 implies -x > 0, we can apply the odd function property to find f(x) for negative x values. Step-by-step: 1. We know that for x > 0, f(x) = x(1 - x). 2. For x < 0, since the function is odd, we must have f(x) = -f(-x). 3. Since -x > 0, we can substitute -x into the given equation: f(-x) = (-x)(1 - (-x)) = (-x)(1 + x). 4. Hence, by applying the odd function property: f(x) = -f(-x) = -[-x(1 + x)] = x(1 + x). So when x < 0, f(x) = x(1 + x). Therefore, for x leq 0, we have f(x) = boxed{x(1 + x)}.

answer:Let's denote the oil bill for February as F and the oil bill for January as J. According to the information given, we have: J = 119.99999999999994 (rounded to 120 for simplicity) The original ratio of the oil bill for February to January is 3:2, which means: F / J = 3 / 2 We can solve for F using the value of J: F = (3 / 2) * J F = (3 / 2) * 120 F = 3 * 60 F = 180 Now, if the oil bill for February had been 20 more, the new February bill would be: F_new = F + 20 F_new = 180 + 20 F_new = 200 The new ratio of the oil bill for February to January after adding 20 to the February bill would be: F_new / J = 200 / 120 To simplify this ratio, we can divide both the numerator and the denominator by their greatest common divisor, which is 40: F_new / J = (200 / 40) / (120 / 40) F_new / J = 5 / 3 So, the new ratio of the oil bill for February to January after adding 20 to the February bill is boxed{5:3} .

answer:1. Since point M(a,b) is outside the circle O: x^{2}+y^{2}=4, we have: a^{2}+b^{2} > 4 2. The distance d between the center of the circle O(0,0) and the line ax+by=4 is given by the formula: d= frac{|Ax_0+By_0+C|}{sqrt{A^2+B^2}} = frac{4}{sqrt{a^{2}+b^{2}}} < 2 = r where r is the radius of the circle. 3. Since d < r, the line ax+by=4 intersects the circle O. Therefore, the answer is: boxed{C}.