answer:To factor the quadratic, we can first find two numbers that add up to -frac{388}{5} and multiply to -frac{1232}{5}. These numbers are -frac{77}{5} and -4. Then, we can write the quadratic as: -4x^2 - frac{388}{5}x - frac{1232}{5} = -4(x^2 + frac{388}{5}x + frac{1232}{5}) = -4(x^2 + frac{77}{5}x + 4x + frac{1232}{5}) = -4[(x^2 + frac{77}{5}x) + (4x + frac{1232}{5})] = -4[x(x + frac{77}{5}) + 4(x + frac{77}{5})] = -4(x + frac{77}{5})(x + 4) Therefore, the factors of -4x^2 - frac{388}{5}x - frac{1232}{5} are -4, (x + frac{77}{5}), and (x + 4). The answer is -4(x + frac{77}{5})(x + 4)

answer:45 inches is equal to 1.5 yards. To convert inches to yards, remember that 1 yard is equivalent to 36 inches. Therefore, you can divide the number of inches by 36 to find the equivalent in yards: ( frac{45}{36} = 1.25 ) yards. However, it is more common to express the result in terms of whole yards and the remaining fraction, which gives 1 yard and ( frac{3}{4} ) yard, or simply 1.5 yards.

answer:While there is no explicit analytic formula for sinleft(frac{theta}{3}right) and cosleft(frac{theta}{3}right) in terms of sintheta and costheta, they can be derived using the triple angle formulas: sin 3theta = 3sintheta - 4sin^3theta cos 3theta = 4cos^3theta - 3costheta Substituting theta with frac{theta}{3} in these formulas, we obtain: sintheta = 3sinleft(frac{theta}{3}right) - 4sin^3left(frac{theta}{3}right) costheta = 4cos^3left(frac{theta}{3}right) - 3cosleft(frac{theta}{3}right) These equations can be used to express sinleft(frac{theta}{3}right) and cosleft(frac{theta}{3}right) in terms of sintheta and costheta, although the resulting expressions may be complex and involve higher powers of trigonometric functions.

answer:(2/5) / 1 = (1/2) / x.....2/5 oatmeal to 1 batch = 1/2 oatmeal to x batches cross multiply (2/5)(x) = (1/2)(1) 2/5x = 1/2 x = (1/2) / (2/5) x = 1/2 * 5/2 x = 5/4 x = 1 1/4 <==== 1 1/4 batches were made