Given: ΔABC
Prove: The medians of ΔABC are concurrent.



Proof:
Statements Reasons
1. The vertices of ΔABC are unique points: A(x1,y1), B(x2,y2), and C(x3,y3). Given
2. Use rigid transformations to transform ΔABC into ΔA'B'C', so that vertex A' is at the origin and A'C' lies on the x-axis in the positive direction. In the coordinate plane, any point can be moved to any other point using rigid transformations and any line can be moved to any other line using rigid transformations.
3. Any property that is true for ΔA'B'C' will also be true for ΔABC. Definition of congruence
4. Let r, s, and t be real numbers such that the vertices of ΔA'B'C' are A'(0,0), B'(2r,2s), and C'(2t,0). Defining constants
5. Let D', E', and F' be the midpoints of A'B', B'C', and A'C' respectively. Defining points
6. D' = (r , s)
E' = (r + t, s)
F' = (t, 0) Definition of midpoints
7. Slopes of lines:
Definition of slope
8. Equations of lines:
Using point-slope formula
9. Lines A'E' and B'F' intersect at point P.


Algebra
10. ?
11. All three lines contain point P. Algebra
12. The three medians are concurrent. Definition of concurrent

2
What is step 10 in this proof?
A.
Statement: All three lines share point P.
Reason: Definition of midpoint
B.
Statement: Point P lies on line C'D'.
Reason: The coordinates of P satisfy the equation of line C'D'.
C.
Statement: Point P lies on line A'E' and line B'F'.
Reason: Algebra
D.
Statement: line A'E' and line B'F' are concurrent.
Reason: Definition of concurrence
E.
Statement: Two of the three medians share point P.
Reason: Using point-slope formula

Thus question lacks a picture or option, but nevertheless:

Answer:

There are 3 types of friction:1) Static friction - when you apply force and the object does not move.2) Sliding friction - when the surface if the object moves on other.3) Rolling friction - when any wheel or ball moves on any surface rolling friction is applied. it is very less than sliding friction.

If it's an open question, then 

Answer:

When it comes to areas that humanity does not affect in terms of vegetation, colder areas such the Tundra come to mind.

The Tundra is known for:

- Very cold climates

- Low number of animals and plants

- Limited sunlight

As a result of the cold weather and the limited number of plants and animals in the tundra, humans generally avoid this environment which ensures that there is little effect of humans on natural vegetation patterns.

In conclusion, tundra areas do not see a lot of human influence on vegetation.

Options:

A. They standardize prices for commodities in global markets 

B. They streamline the process of organizational decision making. 

C. They force organizations to reach a consensus before making decisions 

D. They provide a forum for individuals to voice discontent with organizations.​

Answer:

B. They streamline the process of organizational decision making. 

Explanation:

A geographic information system (GIS) is a type of database containing geographic data (that is, descriptions of phenomena for which location is relevant), combined with software tools for managing, analyzing, and visualizing those data. In a broader sense, one may consider such a system to also include human users and support staff, procedures and workflows, body of knowledge of relevant concepts and methods, and institutional organizations.

Answer:

The article states that the Incas developed knowledge of farming in the Andes region over the course of 11,000 years. This information shows that they refined their farming practices over time. The use of gravel, terraces, and canals allowed the Incas to adapt farming to the difficult terrain.

Answer:

More refugees fled Southeast Asia when Vietnam invaded Cambodia in 1979 to overthrow the murderous regime of Pol Pot. Thousands of refugees from that unhappy land began to escape over the border into neighboring Thailand.

Also the majority of Vietnamese came to Victoria after the Communist government took over their homeland at the end of the Vietnam War. Those already in Australia were offered permanent residence, and refugees began to be admitted through resettlement camps based in South East Asia.
 

Answer:

When birds are hungry, they will peck unripened fruit. Also, if there is no other fruit around, the birds might go after unripened fruit. Heavy bird pecking can be used as an indicator that it's ready to start harvesting.

Birds need food to eat, and plants need to disperse their seeds. Fruit-eating animals are called frugivores, and birds are the most important frugivores of all. More than 300 trees, shrubs, and vines in North America have small fruits that depend on birds for seed dispersal.

b

Explanation:

Quito (B)

Explanation:

The valley of Guayllabamba River where Quito lies is flanked by volcanoes, some of them snow-capped, and visible from the city on a clear day. Quito is the closest capital city to the equator.