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Option A. The water is draining at a constant rate of   gallon per minute and the tank contained exactly 14 gallons when the drain was opened

Step-by-step explanation:

Graph Analysis

We need to infer the situation presented in the graph. We first notice it's a line that relates the volume of water in a tank in gallons vs the time elapsed in minutes. The water is draining from the tank, it's evident since the line has a negative slope.

We can also notice the initial volume of water in the tank (at t=0) is 14 gallons. Two minutes later (at t=2 minutes) there are 13 gallons of water in the tank. Since the line will continue to decrease at the same rate, we can know the rate at which the water drains from the tank.

If there were 14 gallons of water and 2 minutes after, there were 13 gallons of water, then the gallon that left the tank took 2 minutes to do so, thus in one minute, the tank will lose half a gallon or gallon per minute.

The only possible answer to exactly describe the situation is the option A

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!