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Sonja [21]
3 years ago
10

"What are the missing reasons in the proof?

Mathematics
2 answers:
givi [52]3 years ago
7 0
According to the theorem given in the question.The missing statements are in bold,given below.

Statements:
<span>Line segment AB is parallel to line segment CD (missing:It is the property of parallelogram) 
</span><span>Angle ABD is congruent to angle CDB (Missing : It is the reflexive property)

</span><span>Triangle ABD is congruent to triangle CDB (Missing: ASA Property)
</span>
ASA refers to Angle Side Angle.
I hope its is helpful
<span>

</span>
Flura [38]3 years ago
7 0

Answer:

AB is ║ to CD( property of parallelogram)

∠ABD is congruent to ∠CDB( Angles opposite of equal sides are congruent)

BD=BD( Reflexive property),

Step-by-step explanation:

Given: ABCD is a parallelogram with diagonal line segment BD.

Proof: In ΔABD and ΔCBD,we have:

AB is parallel to CD( Property of paralleogram),

∠ABD is congruent to ∠CDB( Angles opposite of equal sides are congruent)

BD=BD( Reflexive property),

Therefore, ΔABD≅ ΔCBD,

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1. A retirement account is opened with an initial deposit of $8,500 and earns 8.12% interest compounded monthly. What will the a
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Answer:

Part A) \$42,888.48  

Part B) A=\$22,304

Part C) The graph in the attached figure

Step-by-step explanation:

Part A) What will the account be worth in 20 years?

we know that    

The compound interest formula is equal to  

A=P(1+\frac{r}{n})^{nt}  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

t=20\ years\\ P=\$8,500\\ r=0.0812\\n=12  

substitute in the formula above  

A=8,500(1+\frac{0.0812}{12})^{12*20}  

A=8,500(1.0068)^{240}  

A=\$42,888.48  

Part B) What if the deposit were compounded monthly with simple interest?  

we know that

The simple interest formula is equal to

A=P(1+rt)

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

t=20\ years\\ P=\$8,500\\r=0.0812

substitute in the formula above

A=8,500(1+0.0812*20)

A=\$22,304

Part C) Could you see the situation in a graph? From what point one is better than the other?

Convert the equations in function notation

A(t)=8,500(1.0068)^{12t} ------> equation A

A(t)=8,500(1+0.0812t)  -----> equation B

using a graphing tool  

see the attached figure  

Observing the graph, from the second year approximately the monthly compound interest is better than the simple interest.

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