An air-conditioning company counted 56 invoices at the end of the month. They charge $450 for a new installation and $75 for a service call. The total dollar amount of the invoices was $9,450.
How many installations and service calls did the company perform?

14 installatons

42 service calls

Step-by-step explanation:

Let x = no. of new installations

      y = no. of service calls

(1)    x + y = 56           (2)    450x + 75y = 9450

            y = 56 - x               450x + 75(56 - x) = 9450

                                           450x + 4200 - 75x = 9450

                                            375x = 5250

                                                   x = 14 installatons

             y = 56 - 14 = 42 service calls

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."