Answer:
9;10
Step-by-step explanation:
What we can first do is make them into one double sided inequality and then interpret it from there.
After combining them we get: 7<x<12
This means that any number between 7 and 12 can be picked.
Keep in mind, this means that 7 and 12 cannot be picked, they have to be in between.
Therefore, we get our aswers of 9 and 10!
<h2>Solution :</h2>
= 2x = 9
= x = 9 ÷ 2 ( transposing ×2 from LHS to RHS changes ×2 to ÷2 )
= x = 4.5
Therefore , x = 4.5 .
Step-by-step explanation:
First, we want to find profit given revenue and cost. Because profit = revenue - cost, we can write the profit function, P(x), as R(x) - C(x) and go from there.
P(x) = R(x) - C(x)
P(x) = (-x²+24x) - ( 10x + 30)
P(x) = -x²+24x - 10x-30
P(x) = -x²+14x-30
In a quadratic function such as this, the graph opens downward (meaning that it goes from up to down) if the leading coefficient is negative and vice versa. Here, since -1 is attached to x², we can say that the graph opens downward. The point where the direction of the slope changes (when it goes from up to down), or the peak of the quadratic, is called the vertex.
The x value of the vertex is given by -b/(2a) in a quadratic of form ax²+bx+c. As a=-1 and b=14 here, we can say that -b/(2a) =
-14/(2*-1) = -14/-2
= 7
Therefore, the x value of the vertex, or the number of containers sold that maximizes profit, is 7.
Answer:
There are two possible options: 
or 
.
Step-by-step explanation:
There are two possible options depending on what the point of origin is. Vectorially speaking, we can determine the coordinates of the point that partitions the segment is described below:
![P(x,y) = A(x,y) + r\cdot [B(x,y) - A(x,y)]](https://tex.z-dn.net/?f=P%28x%2Cy%29%20%3D%20A%28x%2Cy%29%20%2B%20r%5Ccdot%20%5BB%28x%2Cy%29%20-%20A%28x%2Cy%29%5D)
(1)
Where:
- Point of origin.
- Point of destination.
- Partition factor.
Option 1: 
, 
, 
![P(x,y) = (-1, - 8) + \frac{1}{3}\cdot [(5,-2)-(-1,-8)]](https://tex.z-dn.net/?f=P%28x%2Cy%29%20%3D%20%28-1%2C%20-%208%29%20%2B%20%5Cfrac%7B1%7D%7B3%7D%5Ccdot%20%5B%285%2C-2%29-%28-1%2C-8%29%5D)
Option 2: 
, 
,
![P(x,y) = (5,-2) + \frac{1}{3}\cdot [(-1,-8)-(5,-2)]](https://tex.z-dn.net/?f=P%28x%2Cy%29%20%3D%20%285%2C-2%29%20%2B%20%5Cfrac%7B1%7D%7B3%7D%5Ccdot%20%5B%28-1%2C-8%29-%285%2C-2%29%5D)
There are two possible options: or .
