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.
Answer:
x would equal x
Step-by-step explanation:
Answer:
4 and 13
Step-by-step explanation:
You want integer solutions to ...
15 ≤ n(n+1) ≤ 200
If we let the limits be represented by "a", then the equality is represented by ...
n² +n -a = 0
(n² +n +1/4) -a -1/4 = 0
(n +1/2)^2 = (a +1/4)
n = -1/2 + √(a +1/4)
For a=15, we have
n ≥ -1/2 + √15.25 ≈ 3.4 . . . . . minimum n is 4
For a=200, we have
n ≤ -1/2 + √200.25 ≈ 13.7 . . . maximum n is 13
The least and greatest integers on the cards are 4 and 13.
Answer:
24, 91
Step-by-step Explanation:
Answer: 9 1/3
Step-by-step explanation: There are four of them and, assuming there is no space in between them, they all take up the same amount of space. So that means, if they were added up, it’d be 2 1/3 +2 1/3 + 2 1/3 +2 1/3. That can be simplified to 4 x (2 + 1/3). When multiplied, it equals 8 + 4/3=8 + 1 +1/3=9 + 1/3=9 1/3.
