Here are six cards arrange the card into three pairs with the same total -4 -2 -1 5 6 8

(-4,8),(-2,6),(-1,5)

Step-by-step explanation:

There are six cards numbered -4,-2,-1,5,6,8

The cards need to be arranged into 3 pairs such that the sum of each pair is the same.

Note that the numbers are arranged in ascending order and include equal number of positive and negative integers. For the required property to be satisfied, largest positive card needs to be paired with largest negative card ; smallest positive card needs to be paired with smallest negative card and the middle positive card needs to be paired with middle negative card.

So the pairing will be as follows:

(-4,8),(-2,6),(-1,5)

Note that the sum of each of these pairs is 4.

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.

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.