Part A: Determine the vertex. What does this calculation mean in the context of the problem? (5 points)
Part B: Determine the x-intercepts. What do these values mean in the context of the problem? (5 points)
(10 points)
Answer:
Vertex = (12,64)
The meaning of this pair of values is that the y-coordinate is the maximum profit obtainable, and the x-coordinate is how many cups sold will make the maximum profit.
X-intercepts: 4 and 20
The meaning of theses values is that these amounts of cups sold (4 and 20) will make zero profit.
Step-by-step explanation:
To find the vertex we can use the formula for the x-coordinate of the vertex:
x_v = -b/2a
Where a and b are coefficients of the quadratic equation (in this case, a = -1 and b = 24)
So we have that:
x_v = -24 / (-2) = 12
The vertex is 12 cups of coffee. Now we apply this value to find the y-coordinate of the vertex:
f(x) = -12^2 + 24*12 - 80 = 64
So the vertex is (12,64). The meaning of this pair of values is that the y-coordinate is the maximum profit obtainable, and the x-coordinate is how many cups sold will make the maximum profit.
To find the x-intercepts, we need to make f(x) = 0 and find the values of x:
-x2 + 24x - 80 = 0
Delta = 24^2 - 80*4 = 256
sqrt(Delta) = 16
x1 = (-24 + 16)/(-2) = 4
x2 = (-24 - 16)/(-2) = 20
The x-intercepts are 4 and 20. The meaning of theses values is that these amounts of cups sold (4 and 20) will make zero profit.
Lets write this into an expression.
-2x = -24
Now, lets solve for x.
~Divide -2 to both sides
-2x/-2 = -24/-2
~Simplify
x = 12
Best of Luck!
Answer:
The answer is 12
Step-by-step explanation:
Step 1: Convert words into an equation
What do you is you multiply -2 by something to get -24
-2 * something = -24
We can represent something with a variable called x.
-2 * x = -24
-2x = -24
Step 2: Solve for x by dividing both sides by -2
-2x / -2 = -24 / -2
x = 12
Answer: The number we can multiply -2 by to get -24 is 12
B4/5x+3
C.8x+20
D.4/5x+30
The required simplified equivalent expression is given as 8x + 3.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Given expression,
= 8x+30/10
Simplify the above expression, as 30/10 = 3
= 8x + 3
Thus, the required simplified equivalent expression is given as 8x + 3.
Learn more about simplification here:
#SPJ2