Answer:8 cups
Step-by-step explanation:2/3 × 12 = 8 or 2 × 12 = 24
24 ÷ 3 = 8
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.
Answer:
x+7
Step-by-step explanation:
Answer: 3/10 * 100 = 30
Step-by-step explanation:
3/10 * x = 30
Solve for x
Cos(pi) = -1
You should have this memorized along with other values such as
sin(0) = 0
cos(0) = 1
sin(pi/2) = 1
cos(pi/2) = 0
sin(pi) = 0
cos(pi) = -1
sin(3pi/2) = -1
cos(3pi/2) = 0
and remember that tan = sin/cos
