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:
Step-by-step explanation:
we know that
A quadratic function in factored form is equal to
where
a is the leading coefficient
x_1 and x_2 are the zeroes of the function
substitute the given values
Find the value of a
Remember that
For x=0 ----> f(0)=4
substitute
so
Given the simple interest formula:
I = P•R•T
where:
I = interest
P = principal
R = interest rate
T = time (in years)
We can isolate R algebraically to find out the interest rate:
I = P•R•T
Divide both sides by P•T:
I / (P•T) = (P•R•T)/(P•T)
The formula for the interest rate is:
R = I / (P•T)
Substitute the given values into this formula to solve for the interest rate (R):
R = I / (P•T)
R = $490/ ($1,400 • 5 years)
R = $490 / $7,000
R = 0.07 or 7%
Therefore, the interest rate is 7%.
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Answer:
x=6, x=0
Step-by-step explanation:
+ 
= 25
+ 
= 25
x=6, x=0
Answer:
Step-by-step explanation:
a) sub in 600 for 6
600-25/40 =14.375
b) switch x and y
x=y-25/40
Solve for y
40x=y-25
y=40x+25
c)Plug in 2.5 for z(x)
2.5= x-25/40
100=x-25
x=125
