How many and what type of solutions does the equation have?

2c2=16c−32

two rational solutions

two irrational solutions

one rational solution

two nonreal solutions

One rational solution.

Just took the test.

The answer is (C).

Step-by-step explanation: The given quadratic equation is

We know that the type of the solution of a quadratic equation depends upon the discriminant.

Here, the discriminant is given by

Since the discriminant is zero, so the two roots are real and equal.

Thus, we can say that the equation has one rational solution.

Hence, (C) is the correct option.

(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