5. Point D lies between Points E and F. If ED= 4x-2, DF= 5x-7, and EF= 6x+18, find x, then find the length of ED, DF, and EF.

Step-by-step explanation:

D lies between E and F.

Length of ED + Length DF = Length of EF

       4x -2 + 5x - 7 = 6x + 18         {combine like terms}

       4x + 5x - 2 - 7 = 6x +18

                 9x - 9    = 6x + 18         {Subtract 6x form both sides}

               9x - 9 - 6x = 18

                        3x -9 = 18          {Add 9 to both sides}

                              3x = 18 + 9

                              3x = 27          {divide both sides by 3}

                                x = 27/3

x = 9

ED = 4x - 2 = 4*9 - 2 =36 - 2 = 34

DF = 5x - 7 = 5*9 - 7 = 45 - 7 = 38

EF = 6x + 18 = 6*9 + 18 = 54 + 18 = 72        

total amount of money that he should pay if he has not used his duty free exemption is $98

step-by-step explanation:

given a united states citizen returning to the states declares the following items at the customs office: 3 shirts at $8.50 each 2 dresses at $27.50 each 1 pair of gold cuff links at $17.50 per pair. we have to find how much he pay

cost of 3 shirts if one cost at $8.50 is

cost of 2 dresses if one cost at $27.50 is  

cost of 1 pair of gold cuff at $17.50

so, total amount of money that he should pay if he has not used his duty free exemption is   $25.5+$55+$17.50=$98

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.