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:
9
Step-by-step explanation:
x=pens
.85x=8.15
.85x/.85= 8.15/.85
x=9.58
so 9 whole pens can be bought
Answer:
60
Step-by-step explanation:
to find w:
sin(44) = w/30
w = 30sin(44)
w = 20.8 to 1 decimal place
to find x;
cos(x) = 20.8/45
x =
(20.8/45)
x = 62.46940334
x = 60
Answer:
Step-by-step explanation:
A quadratic function is given to us . And we need to fill out the table by using the function . The given function is ,
Here we need to substitute the different values of x , to get the different values of y.
<u>Put</u><u> </u><u>x </u><u>=</u><u> </u><u>-</u><u>3</u><u> </u><u>:</u><u>-</u><u> </u>
<u>Put </u><u>x </u><u>=</u><u> </u><u>-</u><u>2</u><u> </u><u>:</u><u>-</u><u> </u>
<u>Put</u><u> </u><u>x </u><u>=</u><u> </u><u>-</u><u>1</u><u> </u><u>:</u><u>-</u><u> </u>

<u>Put </u><u>x </u><u>=</u><u> </u><u>1</u><u> </u><u>:</u><u>-</u><u> </u>
<u>Put </u><u>x </u><u>=</u><u> </u><u>2</u><u> </u><u>:</u><u>-</u><u> </u>
<u>Put </u><u>x </u><u>=</u><u> </u><u>3 </u><u>:</u><u>-</u><u> </u>
<u>Final </u><u>table</u><u> </u><u>:</u><u>-</u><u> </u>
