Answer: After 7 years the number of birds of species A and B are same. and the number of birds during that year will be 140.
Step-by-step explanation:
Given: Sharon is conducting research on two species of birds at a bird sanctuary.
The number of birds of species A is represented by the equation below,where S represents the number of birds, x years after beginning her research.
![S=2^x+12](https://tex.z-dn.net/?f=S%3D2%5Ex%2B12)
The number of birds of species B is represented by the equation below,where S represents the number of birds, x years after beginning her research.
![S=15x+35](https://tex.z-dn.net/?f=S%3D15x%2B35)
To plot the above function, first find points by which they are passing.
For species A, At x=0 , ![S=1+12=13](https://tex.z-dn.net/?f=S%3D1%2B12%3D13)
At x=2 , ![S=2+12=14](https://tex.z-dn.net/?f=S%3D2%2B12%3D14)
Similarly find more points and plot curve on graph.
For species A, At x=0 , ![S=0+35=35](https://tex.z-dn.net/?f=S%3D0%2B35%3D35)
At x=2 , ![S=15+35=50](https://tex.z-dn.net/?f=S%3D15%2B35%3D50)
Plot a line with the help of these two points.
Now, from the graph the intersection of curve (for A) and line (for B) is at (7,140) which tells that After 7 years the number of birds of species A and B are same. and the number of birds during that year will be 140.
Answer:
the answer is (A)
Step-by-step explanation:
A line segment can be divided into ratios.
<em>The coordinate of P on line segment AB is (5,1)</em>
Given
![A = (-3,-5)](https://tex.z-dn.net/?f=A%20%3D%20%28-3%2C-5%29)
![B = (9,4)](https://tex.z-dn.net/?f=B%20%3D%20%289%2C4%29)
The position of P from A to B is:
![P_A = \frac 23](https://tex.z-dn.net/?f=P_A%20%3D%20%5Cfrac%2023)
So, from P to B would be:
![P_B =1 - \frac 23](https://tex.z-dn.net/?f=P_B%20%3D1%20-%20%20%5Cfrac%2023)
![P_B = \frac 13](https://tex.z-dn.net/?f=P_B%20%3D%20%5Cfrac%2013)
So, the ratio is:
![m : n = \frac 23 : \frac 13](https://tex.z-dn.net/?f=m%20%3A%20n%20%3D%20%5Cfrac%2023%20%3A%20%5Cfrac%2013)
Simplify
![m : n = 2 :1](https://tex.z-dn.net/?f=m%20%3A%20n%20%3D%202%20%3A1)
<u>The coordinate of point P is:</u>
![P = (\frac{mx_2 + nx_1}{m + n},\frac{my_2 + ny_1}{m + n})](https://tex.z-dn.net/?f=P%20%3D%20%28%5Cfrac%7Bmx_2%20%2B%20nx_1%7D%7Bm%20%2B%20n%7D%2C%5Cfrac%7Bmy_2%20%2B%20ny_1%7D%7Bm%20%2B%20n%7D%29)
So, we have:
![P = (\frac{2 \times 9 + 1 \times -3}{2 + 1},\frac{2 \times 4 + 1 \times -5}{2 + 1})](https://tex.z-dn.net/?f=P%20%3D%20%28%5Cfrac%7B2%20%5Ctimes%209%20%2B%201%20%5Ctimes%20-3%7D%7B2%20%2B%201%7D%2C%5Cfrac%7B2%20%5Ctimes%204%20%2B%201%20%5Ctimes%20-5%7D%7B2%20%2B%201%7D%29)
![P = (\frac{15}{3},\frac{3}{3})](https://tex.z-dn.net/?f=P%20%3D%20%28%5Cfrac%7B15%7D%7B3%7D%2C%5Cfrac%7B3%7D%7B3%7D%29)
![P = (5,1)](https://tex.z-dn.net/?f=P%20%3D%20%285%2C1%29)
<em>Hence, the coordinate of P is (5,1)</em>
Read more about line ratios at:
brainly.com/question/8847082
Multiplication. If you need help just remember PEMDAS.
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