Question 1107689
you have 2 equations.


c = 2x + b is the first equation.


y = x * (x + b) is the second equation.


you are given that c = 10 which makes the first equation 10 = 2x + b.


if you solve this first equation for b, you get b = 10 - 2x.


replace b in the second equation with this to get y = x * (x + 10 - 2x).


simplify that to get y = x * (10 - x).


simplify further to get y = 10x - x^2.


reorder the terms in descending order of degree to get y = -x^2 + 10x.


that's a quadratic equation in the form of y = ax^2 + bx + c.


in that equation, a = -1 and b= 10.


the maximum value of y in that equation is when x = -b/2a.


this results in x = -10/-2 which results in x = 5.


when x = 5, the value of y is equal to -5^2 + 10*5= -25 + 50 = 25.


your maximum value of y should be 25.


if you graph the equation of y = -x^2 + 10x, it will look like this.


<img src = "http://theo.x10hosting.com/2018/012802.jpg" alt="###">


you can see that the maximum value of the equation is y = 25 when x = 5.