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Fed [463]
3 years ago
8

Find the value of x and explain how you found it. Make sure to cite the problem and share what you see before you explain your s

olution. In your explanation, include how you know that these triangles are similar. You may use a postulate such as AA, SSS, SAS, Triangle Proportionality Theorem, or a creative alternative. Justify why you were able to use the postulate/theorem and give the equation you used to find x.

Mathematics
1 answer:
klemol [59]3 years ago
6 0

Answer:

THE VALUE OF X = 3 .

Step-by-step explanation:

From the Δ RQP and Δ TSP ;

⇒ ∠  TPS = ∠ RPQ       ( since both are common angle )

⇒ RQ ≈ TS                    ( parallel lines )

⇒ ∠ PRQ = ∠ PST            ( Corresponding angle )

∴ Δ RQP ≅  Δ TSP          ( BY ASA RULE )

Now ,

 \frac{RP}{TP}  = \frac{QP}{PS}

\frac{9 + X}{9}  = \frac{6 + 2}{6}

⇒ X = 3

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The values of x for which the given vectors are basis for R³ is:

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We know that for a set of vectors are linearly independent if the matrix formed by these set of vectors is non-singular i.e. the determinant of the matrix formed by these vectors is non-zero.

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\left[\begin{array}{ccc}-1&2&1\\0&1&1\\-1&2&x\end{array}\right]

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