Determine whether each equation below is linear or nonlinear.
equation
y = ½ x + 3
y = 4x + 2
xy = 12
linear or non-linear

A) - Linear

B) - Linear      

C) - Nonlinear

Step-by-step explanation:

To determine whether a function is linear or nonlinear.

The function of a straight line is given as :

where represents slope of line and represents the y-intercept.

Any function that can be represented as a function of straight line is called a linear function otherwise it is nonlinear.

We will check the equations given for linear or nonlinear.

A)

The function is in the form and hence it is a linear function with slope and y-intercept .

B)

The function is in the form and hence it is a linear function with slope and y-intercept .

C)

On solving for

Dividing both sides by  

This function cannot be represented in the form , hence it is a nonlinear function.

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