Two objects that are not initially in thermal equilibrium are placed in close contact. after a while, the temperature of the coder object will rise the same amount that the hotter one drops. the temperature of each object will be the same. the thermal conductivity of each object will be the same. the specific heats of both objects will be equal. the temperature of the coder object will rise twice as much as the temperature of the hotter one drops

If the temperature of  the colder object rises by the same amount as the temperature of the hotter object drops, then the specific heats of both objects will be equal.

Explanation:

If the temperature of  the colder object rises by the same amount as the temperature of the hotter object drops when the two objects of same mass are brought into contact, then their specific heat capacity is equal.

We can prove this by the equation of heat for the two bodies:

According to given condition,

when there is no heat loss from the system of two bodies then

The temperature of the colder object will rise twice as much as the temperature of the hotter object only in two cases:

OR

because it says use -2,0,and 2 for x, we can plug those numbers into the equation. y/4=3/4(-2)+2   y/4= -1 1/2 +2 now to get x by itself, we can multiply each side by 4. y=-6+8 which equals y=2 when x=-2. now you can do the same thing with 0 and 2 as x. you get y=8 when x=0 and y=14 when x=2.

x   |   y

-2 |   2

0   |   8

2   |   14

the answer for apex is the lowest