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love history [14]
3 years ago
12

HELLO? Can anyone answer my question PLS!!! HELP!!!

Mathematics
2 answers:
il63 [147K]3 years ago
8 0

Answer:

a_{n} = 13 - 4n

Step-by-step explanation:

Note the common difference d between consecutive terms, that is

d = 5 - 9 = 1 - 5 = - 3 - 1 = - 7 - (- 3) = - 4

This indicates the sequence is arithmetic with n th term

a_{n} = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 9 and d = - 4, thus

a_{n} = 9 - 4(n - 1) = 9 - 4n + 4 = 13 - 4n ← explicit equation

mario62 [17]3 years ago
6 0

Answer:

13-4n

Step-by-step explanation:

The generic formula to calculate this is. a+(n-1) d

“a” is the first term and “d” is the difference in our case “a” is 9 and “d” is -4

9+(n-1)(-4)

9-4n+4

13-4n

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<u>Solving Q1: Given BE = ED and AE = EC.</u>

Considering triangles ΔAED and ΔCEB;

1. AE = EC (given)

2. ∠AED = ∠CEB (vertical angles)

3. ED = EB (given)

ΔAED ≡ ΔCEB (Side-Angle-Side congruency of triangles)

∠DAE = ∠BCE and AD = BC (using CPCTC)

⇒ AD║BC (Converse of Alternate Interior angles theorem)


Similarly consider triangles ΔABE and ΔCDE;

1. AE = CE (given)

2. ∠BEA = ∠DEC (vertical angles)

3. BE = DE (given)

ΔABE ≡ ΔCDE (Side-Angle-Side congruency of triangles)

∠ABE = ∠CDE and AB = CD (using CPCTC)

⇒ AB║CD (Converse of Alternate Interior angles theorem)


Since we have AB║CD, AB = CD and AD║BC, AD = BC.

Therefore, quadrilateral ABCD is a parallelogram.

****************************************************************************************************

<u>Solving Q2: The parallelogram has the angle measures shown in the diagram.</u>

It is clearly visible that both the triangles are Isosceles triangles, so opposite sides in each triangle are equal.

Consider two triangles given in the problem, we have two sets of congruent angles and one included side is common in both triangles.

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Using CPCTC, we can say opposite sides of quadrilateral would be congruent.

Therefore, all sides in given quadrilateral are equal.

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3 years ago
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