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Sophie [7]
3 years ago
8

A conjecture and the two-column proof used to prove the conjecture are shown. Given: segment A B is congruent to segment B D, se

gment B D is congruent to segment C E, and segment C E is congruent to segment A C. Prove: triangle A B C is an isosceles triangle. Segment A D with endpoints D and A moving from left to right. Segment A D is diagonally down to the left from point A. B is the midpoint of segment A D. Segment A E shares endpoint at point A with segment A D. Segment A E is diagonally down to the right from point A. C is the midpoint of segment A E. Segment B C is horizontal between segment A D and segment A E. Drag an expression or phrase to each box to complete the proof. Statement Reason 1. AB¯¯¯¯¯≅BD¯¯¯¯¯ Given 2. BD¯¯¯¯¯≅CE¯¯¯¯¯ Given 3. Transitive Property of Congruence 4. Given 5. AB¯¯¯¯¯≅AC¯¯¯¯¯ 6. △ABC is an isosceles triangle.

Mathematics
2 answers:
rusak2 [61]3 years ago
5 0

Answer:

3.Transitive Property Of Congruence

daser333 [38]3 years ago
4 0

Answer:

Step-by-step explanation:

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Ana has won a lottery. She was offered two options to receive the award: She can either take it in five installments of $60,000
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Results are below.

Step-by-step explanation:

Giving the following information:

She can either take it in five installments of $60,000 annually, starting from now; or she can take a lump-sum of $255,000 now.

<u>First, we determine the value of the 5 installments using a 5% annual compounded rate.</u>

We calculate the future value, and then the present value:

FV= {A*[(1+i)^n-1]}/i

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FV= {60,000*[(1.05^5) - 1]} / 0.05

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<u>Now, if the annual rate is 6% continuously compounded.</u>

<u>First, we need to calculate the effective interest rate:</u>

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r= e^0.06 - 1

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PV= 339,443.23/1.0618^5

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