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.
The function is even with a negative leading coefficient. Even means the tails both go the same way, negative means they both go down.
Answer:
24
Step-by-step explanation:
Given the solution
2 < x ≤ 24
The ≤ symbol means less than or equal to
Thus x can equal 24
At the other end 2 < x which means x cannot equal 2
Thus x = 24 will make the inequality true
If 3z=2z+5 and z=5, then you’d just plug the 5 in.
3(5)=2(5)+5 —> 15=10+5 —> 15=15
This statement is TRUE because 15 does equal 15.
I hope this helps. :)
