The pressure exerted on the walls of a container by a gas enclosed within it is directly proportional to the temperature of the gas. if the pressure is 6 pounds per inch when the temperature is 440 f, find the pressure exerted when the temperature of the gas is 380 f?

Step-by-step explanation:

If y is directly proportional to x, then the formula for that is a linear one:

y = kx, where k is the constant of proportionality.  In our situation, if the pressure is directly proportional to the temp, then our formula is

P = kT.  We need to find that value of k.  Plug in what we have:

6 = k(440) so

k = .01363636 or as an equivalent fraction,

Now that have that value of k, we can use it in the formula again, this time with a different value for T to solve for P.

so

P = 5.181818 or as an equivalent fraction,

table 1

step-by-step explanation:

1-16

2-32

4-64

8-128

all multiples of 16

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3