1 Eleonore works 63 hours one week and earns a 164322 payche

1. Eleonore works 63 hours one week and earns a $1643.22 paycheck. She earns time and a half for the hours she works between 40 and 50 hours and double time for anything over 50 hours. What is Eleonore\'s regular hourly wage?

Solution

working 63 hours Eleonore earns $ 1643.22

let $x is hourly wage

so upto 40 hours wage is 40x

between 40 to 50 = 10*(1.5x)

and over 50 = 13*2x

therefore, the equations becomes

so 40*x + 10* 1.5*x + 13*2*x = 1643.22

81x = 1643.22

x = 1643.22 / 81 = $20.286

therefore, Eleonore hourly wage is $20.286

2) (x+1) / (-3x+12)

domain is all values of x that a function can take in

in rational function denominator cannot be zero

setting denominator to zero

-3x+12 = 0

x = 4

hence , the rational function denominator becomes 0 at x = 4

so domain is all values of x , except x = 4

interval notation (-infinity , 4) U ( 4, infinity )