Express the following as a single fraction in its simplest form

4x-18y-18/12

Step-by-step explanation:

x/3 - 2(y+1)/4

1. Find the Least Common Multiple for the denominators (in this case it is 12)

4x/12 - 6(3y+3)/12

2. Use PEMDAS

4x/12 - 18y+18/12

3. Distribute the arithmetic sign

4x/12 + -18y-18/12

4. Combine the fractions

4x-18y-18/12

option 1 is correct.

step-by-step explanation:

y varies inversely with x and constant of variation is 4

the equation will be:

y = k/x

where k =4 so,

y = 4/x

if we put values of x of option 1 in the above equation and find values of y

y = 4/-2 => y =-2

y = 4/-1 => y = -4

y = 4/1 => y = 4

y = 4/2 => y =2

so, all the values of x and y are correct.

if we put values of x given in other options and find value of y we cannot find whole table satisfying the equation.

hence option 1 is correct.

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.