Answer:
Step-by-step explanation:
Use midpoint formula to find the coordinates of each midpoint.
(x, y) = (½ (x₁ + x₂), ½(y₁ + y₂))
The coordinates of B and C are given.
Coordinates of D:
(x, y) = (½ (4 + 2), ½(6 + -2))
(x, y) = (3, 2)
Coordinates of E:
(x, y) = (½ (4 + -2), ½(6 + -4))
(x, y) = (1, 1)
Slope of DE:
m = Δy / Δx
m = (2 − 1) / (3 − 1)
m = 1/2
Slope of BC:
m = Δy / Δx
m = (-2 − -4) / (2 − -2)
m = 1/2
Therefore, DE is parallel to BC.
Tuesday=
![x](https://tex.z-dn.net/?f=x)
Wednesday=
![2x](https://tex.z-dn.net/?f=2x)
Thursday=<u />
![\frac{1}{2} x](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%20x)
![x+2x+ \frac{1}{2} x=9 \\ \frac{7}{2}x=9 \\ \frac{7}{2}x*2=9 *2\\ 7x=18\\ \frac{7}{7} x=\frac{18}{7}\\ x=\frac{18}{7}](https://tex.z-dn.net/?f=x%2B2x%2B%20%5Cfrac%7B1%7D%7B2%7D%20x%3D9%20%5C%5C%20%5Cfrac%7B7%7D%7B2%7Dx%3D9%20%5C%5C%20%5Cfrac%7B7%7D%7B2%7Dx%2A2%3D9%20%2A2%5C%5C%207x%3D18%5C%5C%20%5Cfrac%7B7%7D%7B7%7D%20x%3D%5Cfrac%7B18%7D%7B7%7D%5C%5C%20x%3D%5Cfrac%7B18%7D%7B7%7D)
Remember that the x value is only for Tuesday's distance; therefore:
Tuesday=
![\frac{18}{7}](https://tex.z-dn.net/?f=%20%5Cfrac%7B18%7D%7B7%7D%20)
miles
Wednesday=
![\frac{36}{7}](https://tex.z-dn.net/?f=%20%5Cfrac%7B36%7D%7B7%7D%20)
miles
Thursday=
![\frac{9}{7}](https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B7%7D)
miles
Answer:
x = 2 yd
Step-by-step explanation:
Angles of 45 degreees = two congruent legs
for the Pythagorean theorem
2x^2 = 8
x^2 = 4
x = 2
The ODE is separable:
![3y\,\mathrm dx+(xy+5x)\,\mathrm dy=0\implies x(y+5)\,\mathrm dy=-3y\,\mathrm dx\implies\dfrac{y+5}y\mathrm dy=-\dfrac3x\,\mathrm dx](https://tex.z-dn.net/?f=3y%5C%2C%5Cmathrm%20dx%2B%28xy%2B5x%29%5C%2C%5Cmathrm%20dy%3D0%5Cimplies%20x%28y%2B5%29%5C%2C%5Cmathrm%20dy%3D-3y%5C%2C%5Cmathrm%20dx%5Cimplies%5Cdfrac%7By%2B5%7Dy%5Cmathrm%20dy%3D-%5Cdfrac3x%5C%2C%5Cmathrm%20dx)
Integrating both sides gives
![\displaystyle\int\left(1+\frac5y\right)\,\mathrm dy=-3\int\frac{\mathrm dx}x\implies y+5\ln|y|=-3\ln|x|+C](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint%5Cleft%281%2B%5Cfrac5y%5Cright%29%5C%2C%5Cmathrm%20dy%3D-3%5Cint%5Cfrac%7B%5Cmathrm%20dx%7Dx%5Cimplies%20y%2B5%5Cln%7Cy%7C%3D-3%5Cln%7Cx%7C%2BC)
The IQR is q1-q3! Put the numbers in order, least to greatest. then find the quartiles.