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question:If the measure of angle AOC is 180 degrees and the measure of angle BOC is 134 degrees, what is the measure of angle AOB, in degrees?
answer:Since angles AOC and BOC form a straight line, they are supplementary angles. Therefore, the sum of their measures is 180 degrees. We can use this to find the measure of angle AOB: m∠AOC + m∠BOC = 180° 180° + 134° = m∠AOB 314° = m∠AOB However, angles cannot have a measure greater than 180 degrees. Therefore, we must subtract 180 degrees from 314 degrees to find the measure of angle AOB: m∠AOB = 314° - 180° m∠AOB = 134° Therefore, the measure of angle AOB is 134 degrees.
question:If angle LON is a right angle and m angle MON = 66^circ, what is m angle LOM, in degrees?
answer:Since angle LON is a right angle, we know that m angle LON = 90^circ. Additionally, since angle MON and angle LOM are adjacent angles that form a straight line, we know that m angle MON + m angle LOM = 180^circ. Substituting the given value of m angle MON, we have 66^circ + m angle LOM = 180^circ. Solving for m angle LOM, we get m angle LOM = 180^circ - 66^circ = 114^circ. Therefore, the measure of angle LOM is boxed{114^circ}.
question:Find the magnitude and argument (phase angle in radians) of the complex number frac{11-27 i}{e}.
answer:The magnitude (or norm) of a complex number a+bi is given by sqrt{a^2+b^2}. In this case, we have: |z| = left|frac{11-27 i}{e}right| = frac{sqrt{11^2+(-27)^2}}{e} = frac{5 sqrt{34}}{e} The argument (or phase angle) of a complex number a+bi is given by tan^{-1}left(frac{b}{a}right). In this case, we have: arg(z) = argleft(frac{11-27 i}{e}right) = tan^{-1}left(frac{-27}{11}right) = -tan^{-1}left(frac{27}{11}right) Note that the argument is negative because the complex number is in the fourth quadrant. Magnitude: frac{5 sqrt{34}}{e} Argument: -tan ^{-1}left(frac{27}{11}right)
question:Regular exercise often leads to an improved body image. Which of the following statements best reflects this concept? A) Exercise has no impact on body image. B) Exercise can negatively affect body image. C) Exercise typically contributes to a more positive body image. D) The relationship between exercise and body image is inconclusive.
answer:C) Exercise typically contributes to a more positive body image, as it can help reduce body fat, build or enhance muscles, and create a more toned appearance.