Answer:
The distance betweem the two points is about 14
Step-by-step explanation:
The distance formula is ![d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28x_%7B2%7D-x_%7B1%7D%29%5E%7B2%7D%2B%28y_%7B2%7D-y_%7B1%7D%29%5E%7B2%7D%7D)
According to the problem:
,
,
, and ![y_{1} =7](https://tex.z-dn.net/?f=y_%7B1%7D%20%3D7)
Substitute these numbers into the problem to get ![d=\sqrt{(8-1)^{2}+(-5-7)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%288-1%29%5E%7B2%7D%2B%28-5-7%29%5E%7B2%7D%7D)
![(8-1)^2=(7)^2=49](https://tex.z-dn.net/?f=%288-1%29%5E2%3D%287%29%5E2%3D49)
![(-5-7)^2=(-12)^2=144](https://tex.z-dn.net/?f=%28-5-7%29%5E2%3D%28-12%29%5E2%3D144)
![\sqrt{49+144}=\sqrt{193} =13.8923349894](https://tex.z-dn.net/?f=%5Csqrt%7B49%2B144%7D%3D%5Csqrt%7B193%7D%20%20%3D13.8923349894)
You can round this number to approximately 14.
Answer:
Step-by-step explanation:
Let (x,y) be midpoint of P(3,4) & Q(5,−2)
Midpoint formula for two points (a,b) and (c,d) is
(x,y) =(
2
a+c
,
2
b+d
).
x=
2
3+5
=4
y=
2
4−2
=1
∴ (x,y)=(4,1)
Answer:
All the populations in an ecosystem form the community.
Step-by-step explanation:
Answer:
![m\angle ECB+m\angle EFB=180](https://tex.z-dn.net/?f=m%5Cangle%20ECB%2Bm%5Cangle%20EFB%3D180)
![m\angle CDB\cong m\angle EDF](https://tex.z-dn.net/?f=m%5Cangle%20CDB%5Ccong%20m%5Cangle%20EDF)
![m\angle CDB+m\angle DCB+m\angle CBD=180 \degree](https://tex.z-dn.net/?f=m%5Cangle%20CDB%2Bm%5Cangle%20DCB%2Bm%5Cangle%20CBD%3D180%20%5Cdegree)
Step-by-step explanation:
From the diagram, quadrilateral BCEF is a cyclic quadrilateral.
Opposite angles if a cyclic quadrilateral sum up to 180°
![m\angle ECB+m\angle EFB=180](https://tex.z-dn.net/?f=m%5Cangle%20ECB%2Bm%5Cangle%20EFB%3D180)
The diagonals intersect at D to form two pairs of vertical angles, and vertical angles are congruent.
![m\angle CDB\cong m\angle EDF](https://tex.z-dn.net/?f=m%5Cangle%20CDB%5Ccong%20m%5Cangle%20EDF)
Also sum of angles in triangle CBD is 180°.
![m\angle CDB+m\angle DCB+m\angle CBD=180 \degree](https://tex.z-dn.net/?f=m%5Cangle%20CDB%2Bm%5Cangle%20DCB%2Bm%5Cangle%20CBD%3D180%20%5Cdegree)