Adjacent angles ABD and DBC. The measure of angle ABD is 20 degrees. If m∠ABC = 80°, what is m∠DBC? Justify your reasoning. Using the Angle Addition Postulate, 20 + m∠DBC = 80. So, m∠DBC = 60° using the subtraction property of equality. Using the Angle Addition Postulate, 20 + 80 = m∠DBC. So, m∠DBC = 100° using the addition property of equality. Using the addition property of equality, 20 + 80 = 100, so m∠DBC = 100°. Using the subtraction property of equality, 80 − 20 = 60, so m∠DBC = 60

What are the solutions to the following equation? |m| = 8.5 the value of m is equal to 8.5 and because each distance from zero is 8.5.

Acaterer knows he will need 60, 50, 80, 40 and 50 dinner napkins on five successive evenings. he can purchase new napkins initially at 25 cents each, after which he can have dirty napkins laundered by a fast one-day laundry service (i.e., dirty napkins given at the end of the day will be ready for use the following day) at 15 cents each, or by a slow two-day service at 8 cents each or both. the caterer wants to know how many napkins he should purchase initially and how many dirty napkins should be laundered by fast and slow service on each of the days in order to minimize his total costs. formulate the caterer’s problem as a linear program as follows (you must state any assumptions you make): a. define all variables clearly. how many are there? b. write out the constraints that must be satisfied, briefly explaining each. (do not simplify.) write out the objective function to be minimized. (do not simplify.)

Find the power set of each of these sets, where a and b are distinct elements. a) {a} b) {a, b} c) {1, 2, 3, 4} show steps