Geometry question to verify it

Mathematics

1 answer:

Oksana_A [137]3 years ago

4 0

Step-by-step explanation:

here's the solution,

in the given figure , sum of all angles formed with O measures 360°

because, it forms a complete angle

so,

=》mPOQ + mQOR + mROS + mSOT + mTOP = 360°

=》mPOQ + mQOR + mROS + mSOT + mTOP = (90° × 4)

=》mPOQ + mQOR + mROS + mSOT + mTOP = 4 × right angle

(cuz.. right angle = 90°)

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PLEASE HELP!!!!!!!

gayaneshka [121]

Answer: The first set's mad is 2

The 2nd set's mad is 2 as well

The mean of the 1st set is 2

The mean of the 2nd set is 2

Based on even a calculator this is the information. I made sure it is correct with the calculator.

6 0

3 years ago

Prove or give a counterexample:

ozzi

Answer:

See proof below.

Step-by-step explanation:

True

For this case we need to use the following theorem "If $v_1, v_2,....v_k$ are eigenvectors of an nxn matrix A and the associated eigenvalues $\lambda_1, \lambda_2,...,\lambda_k$ are distinct, then $v_i's$ are linearly independent". Now we can proof the statement like this:

Proof

Let A a nxn matrix and we can assume that A has n distinct real eingenvalues let's say $\lambda_1, \lambda_2, ....,\lambda_n$

From definition of eigenvector for each one $\lambda_i$ needs to have associated an eigenvector $v_i$ for $1 \leq i \leq n$

And using the theorem from before , the n eigenvectors $v_1,....,v_n$ are linearly independent since the $\lambda_i$ $1\leq i \leq n$ are distinct so then we ensure that A is diagonalizable.