Find z. Write your answer in simplest radical form.

Let's solve ~

The given triangle is a right angled Triangle, so we can apply Trigonometric relations to find the required result ;

That is :

So, the value of z is

x=-1 is a maximum vaue.

Step-by-step explanation:

To find the minimum and maximum values of the function f(x), we're going to derivate it:

f(x) = –5x^2 – 10x + 6 ⇒ f'(x) = -10x - 10

The points where f'(x) is zero, could be a maximum or a minimum. Then:

f'(x) = -10x - 10 = 0 ⇒ x=-1

Now, to know if x=-1 is a maximum or a minimum, we need to evaluate the original function for x when it tends to -1 from the right and from the left.

Therefore:

For x=-2:

f(x) = 6 (Positive)

For x=0:

f(x) = 6 (Positive)

For x=-1

f(x) = 11 (Positive)

Given that at x=-1, f(x) = 11, and then it goes down to 6 when x=0, we can say that it's a maximum.