K, so an even numer is 2, 4 of them?, 2^4=16
the number is 16
We have that
<span>f(x) =2/x
</span>and
<span>g(x)=1/(-3-x)
we know that
</span>the solutions to f(x) = g(x) is the intersection of both graphs
the <span>intersection of both graphs is the point (-2,-1)
</span>
the answer is the option
<span>
A) (-2, -1)
</span>
see the attached figure
Given the points H(6,7) and I(-7,-6).
If point G lies
of the way along line segment HI.
Therefore, we can say that the point G divides the line segment HI in the ratio 1:1.
So, by using the cross section formula we can determine the coordinates of point G.
For the given points say
and
divided is in the ratio
, the coordinates are ![(\frac{m_1x_2+m_2x_1}{m_1+m_2} , \frac{m_1y_2+m_2y_1}{m_1+m_2} )](https://tex.z-dn.net/?f=%28%5Cfrac%7Bm_1x_2%2Bm_2x_1%7D%7Bm_1%2Bm_2%7D%20%2C%20%5Cfrac%7Bm_1y_2%2Bm_2y_1%7D%7Bm_1%2Bm_2%7D%20%29)
Coordinates G = ![(\frac{(1 \times -7)+(1 \times 6)}{2} , \frac{(1 \times -6)+(1 \times 7)}{2})](https://tex.z-dn.net/?f=%28%5Cfrac%7B%281%20%5Ctimes%20-7%29%2B%281%20%5Ctimes%206%29%7D%7B2%7D%20%2C%20%5Cfrac%7B%281%20%5Ctimes%20-6%29%2B%281%20%5Ctimes%207%29%7D%7B2%7D%29)
= (-0.5 , 0.5)
Hence, the coordinates of G are (-0.5 , 0.5).
So, Santiago argues that point G is located at the origin. The point G is located at (-0.5, 0.5). Therefore, he is not correct.
Answer:
$732
Step-by-step explanation:
Given
![y \to profit](https://tex.z-dn.net/?f=y%20%5Cto%20profit)
![x \to widgets](https://tex.z-dn.net/?f=x%20%5Cto%20widgets)
![y = -x^2 + 64x - 292](https://tex.z-dn.net/?f=y%20%3D%20-x%5E2%20%2B%2064x%20-%20292)
Required
The maximum profit
First, we calculate the maximum amount of widgets that can be sold using:
![x = -\frac{b}{2a}](https://tex.z-dn.net/?f=x%20%3D%20-%5Cfrac%7Bb%7D%7B2a%7D)
Where:
![a = -1; b = 64; x = -292](https://tex.z-dn.net/?f=a%20%3D%20-1%3B%20b%20%3D%2064%3B%20x%20%3D%20-292)
So, we have:
![x = -\frac{64}{2 * -1}](https://tex.z-dn.net/?f=x%20%3D%20-%5Cfrac%7B64%7D%7B2%20%2A%20-1%7D)
![x = -\frac{64}{-2}](https://tex.z-dn.net/?f=x%20%3D%20-%5Cfrac%7B64%7D%7B-2%7D)
![x = -(-32)](https://tex.z-dn.net/?f=x%20%3D%20-%28-32%29)
![x = 32](https://tex.z-dn.net/?f=x%20%3D%2032)
The maximum profit is:
![y = -x^2 + 64x - 292](https://tex.z-dn.net/?f=y%20%3D%20-x%5E2%20%2B%2064x%20-%20292)
![y = -(32)^2 + 64 * 32 - 292](https://tex.z-dn.net/?f=y%20%3D%20-%2832%29%5E2%20%2B%2064%20%2A%2032%20-%20292)
Using a calculator, we have:
![y = 732](https://tex.z-dn.net/?f=y%20%3D%20732)