State whether the system is consistent and independent, consistent and dependent or inconsistent. y = 0.5x 2y = x + 4 a. consistent and independent c. inconsistent

The correct option is c. The given system is inconsistent.

Step-by-step explanation:

Inconsistent system: If the given system has no solutions, then it is an inconsistent system.

Consistent and independent system: If the given system has only one solutions, then it is an consistent and independent system.

Consistent and dependent system: If the given system has many solutions, then it is an consistent and dependent system.

The given equations are

      ... (1)

Divide the second equation by 2, to rewrite the given equation in slope intercept form.

      ..... (2)

The slope intercept form of a line is

y = mx + b       ....(3)

Where, m is slope and b is y-intercept.

On comparing the (1), (2) and (3), we get the slope of first line is 0.5 and slope of second line is 0.5.

Since the slope of two parallel lines are same, therefore both the given equations are parallel and parallel equations have no solutions.

Therefore option c is correct.

3201

step-by-step explanation:

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204