answer:The slope of the given line is -3. Therefore, the slope of the parallel line is also -3. Using the point-slope form, the equation of the parallel line is: y-(-2)=-3(x-1), which simplifies to y+2=-3x+3 or 3x+y=1.

answer:To complete the square for the quadratic expression -frac{99 x^2}{7} + frac{100 x}{7} - 13, we follow these steps: 1. Move the constant term to the left side: -frac{99 x^2}{7} + frac{100 x}{7} = 13 2. Take the coefficient of x (which is frac{100}{7}), divide it by 2, then square it. This will give us the value to complete the square: left(frac{frac{100}{7}}{2}right)^2 = left(frac{50}{7 cdot 99}right)^2 = frac{2500}{5929} 3. Add and subtract this value inside the expression, keeping the equation balanced: -frac{99}{7} left(x^2 - frac{100}{99} x + frac{2500}{5929}right) - frac{2500}{5929} = 13 4. Factor the perfect square trinomial: -frac{99}{7} left(left(x - frac{50}{99}right)^2right) - frac{2500}{5929} = 13 5. Move the constant to the other side and simplify: -frac{99}{7} left(x - frac{50}{99}right)^2 = 13 + frac{2500}{5929} -frac{99}{7} left(x - frac{50}{99}right)^2 = frac{7 cdot 13 cdot 5929 + 2500}{5929} -frac{99}{7} left(x - frac{50}{99}right)^2 = frac{10073}{5929} 6. Finally, multiply through by -frac{7}{99} to isolate the squared term: left(x - frac{50}{99}right)^2 = frac{10073}{5929} cdot frac{-7}{99} left(x - frac{50}{99}right)^2 = -frac{10073}{53379} So the expression in completed square form is: -frac{99}{7} left(x - frac{50}{99}right)^2 - frac{10073}{53379} However, note that the resulting expression will be negative inside the square, which is not possible for a square of a real number. This indicates an error in the original expression or the steps taken. The expression should have a positive constant under the square, so let's verify the original quadratic. The quadratic is of the form ax^2 + bx + c, with a = -frac{99}{7}, b = frac{100}{7}, and c = -13. The constants used to complete the square should give us the correct expression, so let's double-check: left(frac{b}{2a}right)^2 = left(frac{frac{100}{7}}{2 cdot -frac{99}{7}}right)^2 = left(frac{50}{-198}right)^2 = frac{2500}{39201} Now, completing the square: -frac{99}{7} left(x^2 + frac{100}{99}x + frac{2500}{39201}right) - frac{2500}{39201} = -13 -frac{99}{7} left(x - frac{-50}{99}right)^2 - frac{2500}{39201} = -13 Moving the constant to the other side and simplifying, we get: -frac{99}{7} left(x - frac{-50}{99}right)^2 = -13 + frac{2500}{39201} -frac{99}{7} left(x - frac{-50}{99}right)^2 = -frac{9703}{39201} So the corrected expression in completed square form is: -frac{99}{7} left(x - frac{-50}{99}right)^2 - frac{9703}{39201} However, the original answer seems to be the result of a mistake in completing the square. Let's correct the original answer based on the revised calculations:

answer:Angles: {frac{pi }{15}, angle B = cos ^{-1}left(-frac{1}{2} csc left(frac{pi }{15}right) left(cos left(frac{11 pi }{45}right)-sin left(frac{11 pi }{90}right)right)right), angle C = cos ^{-1}left(-frac{csc ^2left(frac{pi }{15}right) left(sin left(frac{pi }{18}right) csc left(frac{17 pi }{90}right)-1right)}{8 sqrt{frac{cos left(frac{2 pi }{15}right)-1}{-6+4 sin left(frac{pi }{90}right)+6 sin left(frac{11 pi }{90}right)-sin left(frac{13 pi }{90}right)-2 sin left(frac{7 pi }{30}right)+cos left(frac{pi }{9}right)+8 cos left(frac{2 pi }{15}right)-4 cos left(frac{11 pi }{45}right)}}}right)} Vertices: {A = {0,0}, B = left{frac{13}{2} sin left(frac{11 pi }{90}right) csc left(frac{pi }{15}right),0right}, C = left{frac{13}{2} sin left(frac{17 pi }{90}right) cot left(frac{pi }{15}right),frac{13}{2} sin left(frac{17 pi }{90}right)right}} Note: The angles angle A, angle B, and angle C are labeled according to the standard notation where angle A corresponds to the angle of frac{pi }{15}, angle B to the angle of frac{73 pi }{90}, and angle C to the remaining angle.

answer:The Medici family was the most powerful family in Florence during the Renaissance period. They acquired their wealth primarily through banking. The Medici Bank, founded by Giovanni di Bicci de' Medici in 1397, became one of the most prominent banks in Europe. The Medici family also engaged in other business ventures, such as trade and manufacturing, but banking remained their primary source of wealth.