--- Introduction ---

- If we pour cl of water from bottle A to bottle B, B would have times of water as in A.
- If we pour cl of water from bottle B to bottle C, C would have times of water as in B.
- If we pour cl of water from bottle C to bottle A, A would have the same amount of water as C.

- The distance between p and q
_{1}=(,) equals that between p and q_{2}=(,). > - The distance between p and r
_{1}=(,) equals that between p and r_{2}=(,).

x y = , x y = .

Determine the point p=(x,y) where the two lines meet.
- The average of and is .
- The average of and is .
- The average of and is .

- The average of and is .
- The average of and is .
- The average of and is .
- The average of and is .

- The average of
*a*,*b*and*c*is . - The average of
*b*,*c*and*d*is . - The average of
*c*,*d*and*a*is . - The average of
*d*,*a*and*b*is .

- The middle of the side AB is (,).
- The middle of the side BC is (,).
- The middle of the side AC is (,).

In order to give your reply, we suppose A=(x_{1},y_{1}), B=(x_{2},y_{2}), C=(x_{3},y_{3}).

- The average of
*a*and*b*is . - The average of
*b*and*c*is . - The average of
*c*and*a*is .

type | iron | nickel | copper |
---|---|---|---|

metal A | % | % | % |

metal B | % | % | % |

metal C | % | % | % |

_{1} _{2} | = |

_{2} _{3} | = |

. . . | |

_{-1} _{} | = |

_{} | = |

1=(,) , _{2}=(,) , _{3}=(,) .

2+^{2} = ++,

where ,, are real numbers. Find the equation of the circle *C* passing through the 3 points

= 0 | (1) | |||

= 0 | (2) |

= 0 | (1) | ||||

= 0 | (2) | ||||

= 0 | (3) |

- The middle of the side is ( , ).
- The middle of the side is ( , ).
- The middle of the side is ( , ).

- The average of and is .
- The average of and is .
- The average of and is .
- The average of and is .
- The average of and is .

= | ||

= |

= | |||

= | |||

= |

_{1}+_{2}+_{3}+...+_{} | = |

_{2}+_{3}+...+_{} | = |

. . . | |

_{-1}+_{} | = |

_{} | = |

- A. The system may have no solution.
- B. The system may have a unique solution.
- C. The system may have infinitely many solutions.

Other exercises on: linear systems linear algebra

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