# PLEASE HELP!!! DUE TOMORROWwhat is the relationship between thermal energy, kinetic energy, and the physical state of a substance?

###### Question:

## Answers

Thermal energy measures the total kinetic energy of the particles in a substance. The greater the motion of particles, the higher a substance's temperature and thermal energy. A substance's total thermal energy depends on its temperature, number of atoms, and physical state.

[tex]\frac{2y^2-5y-7}{6y^2+10y+4}-\frac{7}{9y^2+6y}=\frac{6y^2-21y-14}{6y\left(3y+2\right)}[/tex]

step-by-step explanation:

we are given

[tex]\frac{2y^2-5y-7}{6y^2+10y+4}-\frac{7}{9y^2+6y}[/tex]

we have to simplify it

firstly, we will factor it

[tex]2y^2-5y-7=\left(y+1\right)\left(2y-7\right)[/tex]

[tex]6y^2+10y+4=2\left(y+1\right)\left(3y+2\right)[/tex]

[tex]9y^2+6y=3y(3y+2)[/tex]

[tex]=\frac{\left(y+1\right)\left(2y-7\right)}{2\left(y+1\right)\left(3y+2\right)}-\frac{7}{3y(3y+2)}[/tex]

now, we can cancel like terms

[tex]=\frac{\left(2y-7\right)}{2\left(3y+2\right)}-\frac{7}{3y(3y+2)}[/tex]

now, we can combine it

[tex]=\frac{3y(2y-7\right)}{6y\left(3y+2\right)}-\frac{7\times 2}{6y(3y+2)}[/tex]

[tex]=\frac{3y(2y-7\right)-14}{6y\left(3y+2\right)}[/tex]

[tex]=\frac{6y^2-21y-14}{6y\left(3y+2\right)}[/tex]

so, we get

[tex]=\frac{6y^2-21y-14}{6y\left(3y+2\right)}[/tex]

if they have a finite resultant