The average rate of change of g(x) between x = 4 and x = 7 is 5/6. which statement must be true?
a. g(7)-g(4)=5/6
b. g(7-4)/7-4=5/6
c. g(7)-g(4)/7-4=5/6 d. g(7)/g(4)=5/6

So it looks like C.

Step-by-step explanation:

Average rate of a function g(x) on the interval from x=a to x=b is given by the formula:

.

You can even say:

.

So we have from x=4 to x=7, so the formula becomes:

We are given this is equal to 5/6.

(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