Hello!
To find the maximum value of the function f(x) = -3(x - 10)(x - 4), the easiest way is to find the vertex using the formula: x = -b/2a.
Firstly, we need to simplify f(x).
f(x) = -3(x - 10)(x - 4)
f(x) = -3(x² - 14x + 40)
f(x) = -3x² + 42x + -120
Since the equation f(x) is now simplified to standard form, we can find the vertex.
a = -3, b = 42, and c = -120
x = -(42)/2(-3) = -42/-6 = 7
Then, we substitute 7 into the the function f(x) = -3(x - 10)(x - 4), or
f(x) = -3x² + 42x + -120, to find the y-value of the vertex.
f(x) = -3(7 - 10)(7 - 4)
f(x) = -3(-3)(4)
f(x) = 27
The vertex of f(x) is (7, 27).
Therefore, the maximum x-value for the function f(x) is 7.
Easy,
the Pythagorean theorem is:
The a and b, being a value that you HAVE
and
c, being the value you are trying to find.
Example: have 1,2 for a triangle what is the third side?
1+4=
5=
Then, just square root to find c.
=c
2.2≈c
Given parameters:
Number of sides of the regular body = 10
A decagon has 10 sides.
Unknown:
Sum of the measures of the interior angles = ?
Solution;
To find the sum of the interior angles of a decagon; use the expression below:
Sum of interior angles = (n - 2) x 180
where;
n = number of sides;
So,
Sum of interior angles = (10 - 2) x 180 = 1440°
The sum of interior angle of a decagon is 1440°
-5(x-4)=-30
-5x - -20=-30
-5x+20=-30
-20 -20
-5x=-50
divide both sides by -5
x=10
