Let G = {a + b/2|a, b € Z}. Show that G is a group under ordinary addition.

. A preschool field trip required 7 buses. Thirteen children rode in cars with their parents and the rest rode on a bus. If there were 258 children on the trip altogether, how many were on each bus? Equation Solution 8-49-8 + 4

Solve the system. X1 6x3 = 23 4x₁ + 4x₂ 9x3 = 63 2x2 + 5x3 = -7 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The unique solution of the system is (ID). (Type integers or simplified fractions.) B. The system has infinitely many solutions. C. The system has no solution.

A bank teller has a total of 73 bills in five-, ten-, and twenty-dollar denominations. The total value of the money is $810. (a) Find the total number of solutions. (b) Find the solution with the smallest number of five-dollar bills. (c) Find the solution with the largest number of five-dollar bills. (a) Let x be the number of five-dollar bills, y be the number of ten-dollar bills, and z be the number of twenty-dollar bills. Translate the given information into two equations, using x, y, and z as the variables. x+y+z = 73 5x + 10y + 20z = 810 (Do not factor. Use integers or decimals for any numbers in the expressions.) There are a total of solutions.