Answer:
![x=4](https://tex.z-dn.net/?f=x%3D4)
![y=-3](https://tex.z-dn.net/?f=y%3D-3)
Step-by-step explanation:
we are given system of equations as
![4x+2y=10](https://tex.z-dn.net/?f=4x%2B2y%3D10)
![3x+2y=6](https://tex.z-dn.net/?f=3x%2B2y%3D6)
we can subtract both equations
and we get
![4x+2y-(3x+2y)=10-6](https://tex.z-dn.net/?f=4x%2B2y-%283x%2B2y%29%3D10-6)
![4x+2y-3x-2y=10-6](https://tex.z-dn.net/?f=4x%2B2y-3x-2y%3D10-6)
![x=4](https://tex.z-dn.net/?f=x%3D4)
now, we can find y
we can plug x=4 into anyone equation
![4\times 4+2y=10](https://tex.z-dn.net/?f=4%5Ctimes%204%2B2y%3D10)
![16+2y=10](https://tex.z-dn.net/?f=16%2B2y%3D10)
![16+2y-16=10-16](https://tex.z-dn.net/?f=16%2B2y-16%3D10-16)
![2y=-6](https://tex.z-dn.net/?f=2y%3D-6)
![y=-3](https://tex.z-dn.net/?f=y%3D-3)
so, we get solution as
![x=4](https://tex.z-dn.net/?f=x%3D4)
![y=-3](https://tex.z-dn.net/?f=y%3D-3)
D.)
Explanation: subtract orange from red orange=35 red=25 35-25=10 hope this helps have a great day!
Answer:
The rewritten equation is: ![x = \ln{4}](https://tex.z-dn.net/?f=x%20%3D%20%5Cln%7B4%7D)
Step-by-step explanation:
The inverse operation of the exponential is the natural logarithm,
, and the following property is used to solve this question:
![\ln{e^x} = x](https://tex.z-dn.net/?f=%5Cln%7Be%5Ex%7D%20%3D%20x)
In this question, we have that:
![4e^x = 16](https://tex.z-dn.net/?f=4e%5Ex%20%3D%2016)
![e^x = \frac{16}{4}](https://tex.z-dn.net/?f=e%5Ex%20%3D%20%5Cfrac%7B16%7D%7B4%7D)
![e^x = 4](https://tex.z-dn.net/?f=e%5Ex%20%3D%204)
Applying the natural logarithm to both sides:
![\ln{e^x} = \ln{4}](https://tex.z-dn.net/?f=%5Cln%7Be%5Ex%7D%20%3D%20%5Cln%7B4%7D)
![x = \ln{4}](https://tex.z-dn.net/?f=x%20%3D%20%5Cln%7B4%7D)
The rewritten equation is: ![x = \ln{4}](https://tex.z-dn.net/?f=x%20%3D%20%5Cln%7B4%7D)
For this case we have the following data:
The recipe for cookies requires:
If the flour becomes the main ingredient, it will be represented by 100%.
Now, you want to know the percentage of butter, taking into account that the flour represents 100%. For this, we use a rule of three:
2 pounds of flour ------> 100%
0.75 pounds of butter ------> x
Where x represents % butter, since flour represents 100%.
So, we have:
![x =\frac{0.75*100}{2}](https://tex.z-dn.net/?f=x%20%3D%5Cfrac%7B0.75%2A100%7D%7B2%7D)
![x = \frac{75}{2}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B75%7D%7B2%7D)
![x = 37.5%](https://tex.z-dn.net/?f=x%20%3D%2037.5%25)
Thus, butter represents 37.5% of the recipe.
Answer:
37.5%