Triangle XYZ has points X = (–4,4), Y = (0,1), and Z = (4,4). Triangle X'Y'Z' has points X ’= (–5,–4), Y’ = (–1,–1), Z’ = (3,–4)
Rama09 [41]
So they moved down one and reflected over the y axis
Answer:
-6.5
Step-by-step explanation:
n/-0.5=13
multipy by -0.5 so
n=
-6.5
Hello from MrBillDoesMath!
Answer:
x = 80/3 ( 26 2/3)
y = 11
Discussion:
Step 1:
-2 + y = 9 => add 2 to both sides
2 + -2 + y = 9 +2 =>
y = 11
Step 2:
Substitute y = 11 (from Step 1) into
3x - 7y = 3 =>
3x - 7(11) = 3 => y = 11 from Step 1
3x - 77 = 3 => add 77 to both sides
3x - 77 + 77 = 3 + 77 =>
3x = 80 =>
x = 80/3
Thank you,
MrB
![\Bbb E[Y^2] = \Bbb E[(4X - 2)^2]](https://tex.z-dn.net/?f=%5CBbb%20E%5BY%5E2%5D%20%3D%20%5CBbb%20E%5B%284X%20-%202%29%5E2%5D)
so by definition of expectation,
![\Bbb E[Y^2] = \displaystyle \int_{-\infty}^\infty (4x-2)^2 f_X(x) \, dx = \int_0^\infty 3(4x-2)^2 e^{-3x} \, dx](https://tex.z-dn.net/?f=%5CBbb%20E%5BY%5E2%5D%20%3D%20%5Cdisplaystyle%20%5Cint_%7B-%5Cinfty%7D%5E%5Cinfty%20%284x-2%29%5E2%20f_X%28x%29%20%5C%2C%20dx%20%3D%20%5Cint_0%5E%5Cinfty%203%284x-2%29%5E2%20e%5E%7B-3x%7D%20%5C%2C%20dx)
Integrate by parts (twice).
First, let
so that
![\displaystyle \Bbb E[Y^2] = -(4x-2)^2 e^{-3x} \bigg|_{x=0}^{x\to\infty} + 8 \int_0^\infty (4x-2) e^{-3x} \, dx \\\\ ~~~~ = 4 + 8 \int_0^\infty (4x-2) e^{-3x} \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5CBbb%20E%5BY%5E2%5D%20%3D%20-%284x-2%29%5E2%20e%5E%7B-3x%7D%20%5Cbigg%7C_%7Bx%3D0%7D%5E%7Bx%5Cto%5Cinfty%7D%20%2B%208%20%5Cint_0%5E%5Cinfty%20%284x-2%29%20e%5E%7B-3x%7D%20%5C%2C%20dx%20%5C%5C%5C%5C%20~~~~%20%3D%204%20%2B%208%20%5Cint_0%5E%5Cinfty%20%284x-2%29%20e%5E%7B-3x%7D%20%5C%2C%20dx)
Next,
so that
![\displaystyle \Bbb E[Y^2] = 4 + 8 \left(-\frac13 (4x-2) e^{-3x} \bigg|_{x=0}^{x\to\infty} + \frac43 \int_0^\infty e^{-3x} \, dx\right) \\\\ ~~~~ = 4 + 8 \left(-\frac23 - \frac49 e^{-3x}\bigg|_{x=0}^{x\to\infty}\right) \\\\ ~~~~ = 4 - \frac{16}3 + \frac{32}9 = \boxed{\frac{20}9}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5CBbb%20E%5BY%5E2%5D%20%3D%204%20%2B%208%20%5Cleft%28-%5Cfrac13%20%284x-2%29%20e%5E%7B-3x%7D%20%5Cbigg%7C_%7Bx%3D0%7D%5E%7Bx%5Cto%5Cinfty%7D%20%2B%20%5Cfrac43%20%5Cint_0%5E%5Cinfty%20e%5E%7B-3x%7D%20%5C%2C%20dx%5Cright%29%20%5C%5C%5C%5C%20~~~~%20%3D%204%20%2B%208%20%5Cleft%28-%5Cfrac23%20-%20%5Cfrac49%20e%5E%7B-3x%7D%5Cbigg%7C_%7Bx%3D0%7D%5E%7Bx%5Cto%5Cinfty%7D%5Cright%29%20%5C%5C%5C%5C%20~~~~%20%3D%204%20-%20%5Cfrac%7B16%7D3%20%2B%20%5Cfrac%7B32%7D9%20%3D%20%5Cboxed%7B%5Cfrac%7B20%7D9%7D)
Answer:
440 ft
Step-by-step explanation:
Perimeter(p) of a rectangle is 2l + 2w
Where 'l' is the length and 'w' is the width.
p = 2(96ft) + 2(124ft) = 192 ft + 248 ft = 440 ft
