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lord [1]
2 years ago
6

Short Proofs - No Triangle Congruence

Mathematics
1 answer:
Marat540 [252]2 years ago
3 0

Step-by-step explanation:

Given,

∠CBE ≅ ∠DBE ----> 1

∠CBE ≅ ∠BCA ----> 2

From 1 & 2,

∠BCA≅ ∠DBE ----> 3

∠DBE ≅ ∠BAC ----> 4

Reason,

Since BE II AC, corresponding angles are equal.

From 3 & 4,

∠BCA ≅ ∠BAC

BC is opposite to ∠BCA

AB is opposite to ∠ABC

Side opposite to congruent angles are always congruent.

Therefore,

AB ≅ BC

Hence proved.

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What is the value of log625^5? A: -4 B:-1/4 C:1/4 D:4
shtirl [24]

Answer:

The value of log_{625}(5) is \frac{1}{4}

Step-by-step explanation:

We want to evaluate log_{625}(5).


The base of this logarithm is 625 and the number is 5.


We need to express the number 5 as the base 625 raised to a certain index.


This implies that, log_{625}(5)=log_{625}(625^{\frac{1}{4}})


Recall now that,

log_a(m^n)=nlog_a(m).


We apply this property to obtain,

log_{625}(5)=\frac{1}{4}log_{625}(625)


Recall again that,


log_a(a)=1,a\ne0\:or\:1.This implies that,


log_{625}(5)=\frac{1}{4}(1)


log_{625}(5)=\frac{1}{4}


The correct answer is C.



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