Answer: x = 1 and y = 2
Step-by-step explanation:
Solve for y in the first equation by adding 2x to both sides
![y=2x](https://tex.z-dn.net/?f=y%3D2x)
Then plug this in for the y value in the second equation
![3x+4(2x)=11](https://tex.z-dn.net/?f=3x%2B4%282x%29%3D11)
Combine like terms and simplify
![3x+8x=11\\11x=11\\x=1](https://tex.z-dn.net/?f=3x%2B8x%3D11%5C%5C11x%3D11%5C%5Cx%3D1)
Plug x into either equation to find the y value
![y=2x\\y=2(1)\\y=2](https://tex.z-dn.net/?f=y%3D2x%5C%5Cy%3D2%281%29%5C%5Cy%3D2)
Lets write this as a ratio 1st.
For every 5 coins Carmen gives Frankie 2
5:2
9:?
5 - 2 = 3
So 3:2
9 ÷ 3 = 3
3 × 2 = 6
So, Caamen has 9 coins and Frankie has 6 coins.
Hope I helped ya!!!!!!
Answer:
k=17
Step-by-step explanation:
k+10=27
k=27-10
k=17
Answer:
5.09 units
Step-by-step explanation:
Given equation
in the interval ![1\le x\le 4](https://tex.z-dn.net/?f=1%5Cle%20x%5Cle%204)
So we integrate
in the given interaval
![\int f(x)=2\int\limits^4_1 {\ln x}dx](https://tex.z-dn.net/?f=%5Cint%20f%28x%29%3D2%5Cint%5Climits%5E4_1%20%7B%5Cln%20x%7Ddx)
Let us integrate
first.
let
![u=\ln x, dv=dx](https://tex.z-dn.net/?f=u%3D%5Cln%20x%2C%20dv%3Ddx)
![du=\dfrac{1}{x}, v=x](https://tex.z-dn.net/?f=du%3D%5Cdfrac%7B1%7D%7Bx%7D%2C%20v%3Dx)
![\int\ln x dx=udv](https://tex.z-dn.net/?f=%5Cint%5Cln%20x%20dx%3Dudv)
Using integration by parts we get
![uv-\int vdu](https://tex.z-dn.net/?f=uv-%5Cint%20vdu)
![=x\ln x-\int x\dfrac{1}{x}dx](https://tex.z-dn.net/?f=%3Dx%5Cln%20x-%5Cint%20x%5Cdfrac%7B1%7D%7Bx%7Ddx)
![=x\ln x-dx](https://tex.z-dn.net/?f=%3Dx%5Cln%20x-dx)
![=x\ln x-x+C](https://tex.z-dn.net/?f=%3Dx%5Cln%20x-x%2BC)
So here
![\int f(x)=2\int\limits^4_1 {\ln x}dx\\ =2(x\ln x-x)_1^4\\ =2[(4\ln 4-4)-(1\ln 1-1)]\\ =2[4\ln 4-4+1]\\ =5.09\ units](https://tex.z-dn.net/?f=%5Cint%20f%28x%29%3D2%5Cint%5Climits%5E4_1%20%7B%5Cln%20x%7Ddx%5C%5C%20%3D2%28x%5Cln%20x-x%29_1%5E4%5C%5C%20%3D2%5B%284%5Cln%204-4%29-%281%5Cln%201-1%29%5D%5C%5C%20%3D2%5B4%5Cln%204-4%2B1%5D%5C%5C%20%3D5.09%5C%20units)
The area of the the region between the curve and horizontal axis is 5.09 units.
I think the answer would be d.
Hope it's right.