In which table does y vary inversely with x? A. x y 1 3 2 9 3 27 B. x y 1 -5 2 5 3 15 C. x y 1 18 2 9 3 6 D. x y 1 4 2 8 3 12

In Table C, y vary inversely with x.

1×18 = 18

2×9 = 18

3×6 = 18

18 = 18 = 18

Step-by-step explanation:

We are given four tables and asked to find out in which table y vary inversely with x.

We know that an inverse relation has a form given by

y = k/x

xy = k

where k must be a constant

Table A:

x     |      y

1     |      3

2     |     9

3     |    27

1×3 = 3

2×9 = 18

3×27 = 81

3 ≠ 18 ≠ 81

Hence y does not vary inversely with x.

Table B:

x     |      y

1     |     -5

2     |     5

3     |    15

1×-5 = -5

2×5 = 10

3×15 = 45

-5 ≠ 10 ≠ 45

Hence y does not vary inversely with x.

Table C:

x     |      y

1     |      18

2     |     9

3     |     6

1×18 = 18

2×9 = 18

3×6 = 18

18 = 18 = 18

Hence y vary inversely with x.

Table D:

x     |      y

1     |      4

2     |     8

3     |    12

1×4 = 4

2×8 = 16

3×12 = 36

4 ≠ 16 ≠ 36

Hence y does not vary inversely with x.

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.

a=24; b=12

step-by-step explanation:

a/b=2: 1

a=2b

36/(1+2)=12

b=12

a=24