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Free_Kalibri [48]
3 years ago
7

Question 11 of 11 -

Mathematics
1 answer:
alex41 [277]3 years ago
6 0

Answer:

AA similarity

Step-by-step explanation:

Your question is not well presented.

See attachment

Given

Triangles ABC and DBE

Required

Which postulate supports the similarities of ABC and DBE

At the first transformation (180 degrees rotation) both triangles maintain SSS and AAA relationships. i.e <em>Side-Side-Side</em> and <em>Angle-Angle-Angle</em>

This is so because rotations do not alter the side lengths; neither does it alter the angles.

When the second transformation (dilation) takes place, the lengths of both triangles ABC and DBE become different because dilation alters side lengths.

However, angle measurements remain unaltered.

<em>Hence, AAA similarity answers the question</em>

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3 years ago
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mart [117]

Answer: \sum_{n=1}^{5}4^n=1364

Step-by-step explanation:

Since we have given that

\sum_{n=1}^{5}4^n

Now, we know the rule for summation , we'll apply this ,

\sum_{n=1}^{5}4^n\\=4^1+4^2+4^3+4^4+4^5\\

Now, it becomes geometric progression, so we us the formula for sum of terms in g.p. which is given by

S_n=\frac{a(r^n-1)}{r-1}\\\\\text{where 'a' is the first term and 'r' is the common ratio}

So, our equation becomes ,

a=4 \\\\r=\frac{a_2}{a_1}=\frac{4^2}{4}=4\\\\S_5=\frac{4(4^5-1)}{4-1}\\\\S_5=1364

Hence ,

\sum_{n=1}^{5}4^n=1364

7 0
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3 years ago
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