United Express, a national package delivery service, charges a base price for overnight delivery of packages weighing 1 pound or less and a surcharge for each additional pound (or fraction thereof). A customer is billed $21.85 for shipping a 44-pound package and $58.60 for a 1919-pound package. Find the base price and the surcharge for each additional pound. The base price is $ .

The correct answer is the base price is $14.50 and surcharge is $2.45 per pound.

Step-by-step explanation:

United Express charges a base price on packages weighing less than or equal to 1 pound and a surcharge for additional pounds.

Let the base price be $b and surcharge be $s.

For a 4 pound package, the customer is billed $21.85. Therefore the equation of his billing looks like b + 3s = 21.85.

For a 19 pound package, the customer is billed $58.60. Therefore the equation of his billing looks like b + 18s = 58.60.

Subtracting both the equation from each other we get 15s = 36.75

⇒ s = $2.45 and b = $14.50.

Thus the base price is $14.50.

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.