![5x+y=-10\\ \\ 7x-3y=-36](https://tex.z-dn.net/?f=5x%2By%3D-10%5C%5C%20%5C%5C%207x-3y%3D-36)
Let's multiply the first equation by 3. (As you can see y's coefficient in the first one is 1 and in the second one is -3 , we will multiply the first equation by 3 so when we add the equations their sum will be 0)
![3\cdot (5x+y)=3\cdot -10\\ \\ 15x+3y=-30](https://tex.z-dn.net/?f=3%5Ccdot%20%285x%2By%29%3D3%5Ccdot%20-10%5C%5C%20%5C%5C%2015x%2B3y%3D-30)
Now let's add this new equation and our second equation.
![7x-3y=-36\\ \\ 15x+3y=-30\\ \\ (15x+3y)+(7x-3y)=(-30)+(-36)\\ \\ 15x+7x+3y-3y=-30-36\\ \\ 22x=-66\\ \\ x=\frac { -66 }{ 22 } \\ \\ x=-3](https://tex.z-dn.net/?f=7x-3y%3D-36%5C%5C%20%5C%5C%2015x%2B3y%3D-30%5C%5C%20%5C%5C%20%2815x%2B3y%29%2B%287x-3y%29%3D%28-30%29%2B%28-36%29%5C%5C%20%5C%5C%2015x%2B7x%2B3y-3y%3D-30-36%5C%5C%20%5C%5C%2022x%3D-66%5C%5C%20%5C%5C%20x%3D%5Cfrac%20%7B%20-66%20%7D%7B%2022%20%7D%20%5C%5C%20%5C%5C%20x%3D-3)
We found x=-3
Now let's plug x's value in one of the equations to find y's value.
![x=-3\\ \\ 5x+y=-10\\ \\ 5\cdot -3+y=-10\\ \\ -15+y=-10\\ \\ y=-10+15\\ \\ y=5](https://tex.z-dn.net/?f=x%3D-3%5C%5C%20%5C%5C%205x%2By%3D-10%5C%5C%20%5C%5C%205%5Ccdot%20-3%2By%3D-10%5C%5C%20%5C%5C%20-15%2By%3D-10%5C%5C%20%5C%5C%20y%3D-10%2B15%5C%5C%20%5C%5C%20y%3D5)
So we found y=5
Solution ;
(-3, 5)
Answer:
answer iss ( -2 , 0 )
Step-by-step explanation:
Answer:
2.2
Step-by-step explanation:
If you use the key on the calculator you should end up with this answer.
Answer:
The volume of each prism is 21 1/4
Answer:
<em>r=4.5% daily</em>
Step-by-step explanation:
<u>Exponential Growth</u>
The natural growth of some magnitudes can be modeled by the equation:
![P=P_o(1+r)^t](https://tex.z-dn.net/?f=P%3DP_o%281%2Br%29%5Et)
Where P is the actual amount of the magnitude, Po is its initial amount, r is the growth rate and t is the time.
We know after t=32 days, the population has increased by 309%. Being the original population P the 100%, then the population reached 309+100= 409%.
Substitute the given values into the model function:
![409\%P_o=100\%P_o(1+r)^{32}](https://tex.z-dn.net/?f=409%5C%25P_o%3D100%5C%25P_o%281%2Br%29%5E%7B32%7D)
Simplifying:
![4.09=(1+r)^{32}](https://tex.z-dn.net/?f=4.09%3D%281%2Br%29%5E%7B32%7D)
We need to solve for r. Taking the 32nd root:
![\sqrt[32]{4.09}=\sqrt[32]{(1+r)^{32}}](https://tex.z-dn.net/?f=%5Csqrt%5B32%5D%7B4.09%7D%3D%5Csqrt%5B32%5D%7B%281%2Br%29%5E%7B32%7D%7D)
Simplifying:
![1+r=\sqrt[32]{4.09}=1.045](https://tex.z-dn.net/?f=1%2Br%3D%5Csqrt%5B32%5D%7B4.09%7D%3D1.045)
Solving:
![r=1.045-1\Rightarrow r=0.045](https://tex.z-dn.net/?f=r%3D1.045-1%5CRightarrow%20r%3D0.045)
r=4.5% daily