Amixture of 30 pounds of candy sells for $1.10 a pound. the mixture consists of chocolates worth $1.50 a pound and
chocolates worth 90¢ a pound. how many pounds of the $1.50 chocolate were used to make the mixture?
if x represents the pounds of $1.50 chocolates used, then which of the following represents the pounds of 90¢
chocolates used?
30-x
30
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Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .

The figure shows the front side of a metal desk in the shape of a trapezoid. what is the area of this trapezoid? 10 ft²16 ft²32 ft²61 ft²

Which of the following would be a correct step in proving that triangle abc is congruent to triangle cda? a. use a protractor to measure the angles and show that all the corresponding angles are equal in measure. this will allow you to prove congruence by aaa. b. show that segment ab is parallel to segment cd and segment ad is parallel to segment cb. this will allow you to prove congruency by asa. c. show that is segment ab is perpendicular to segment ad. this will allow you to prove congruence by sas. d. none of the above.