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slega [8]
3 years ago
12

What is m∠ABC? Justify your reasoning. Using the addition property of equality, 40 + 15 = 55, so m∠ABC = 55°. Using the subtract

ion property of equality, 40 − 15 = 25, so m∠ABC = 25°. Using the Angle Addition Postulate, 15 + m∠ABC = 40. So, m∠ABC = 25° using the subtraction property of equality. Using the Angle Addition Postulate, 15 + 40 = m∠ABC. So, m∠ABC = 55° after simplifying.
Mathematics
1 answer:
N76 [4]3 years ago
8 0

Answer:

Using the Angle Addition Postulate, 15 + 40 = m∠ABC. So, m∠ABC = 55° after simplifying.

Step-by-step explanation:

The  Angle Addition Postulate is gotten from angles placed side by side to form a resulting angle that is the sum of all the individual angles.

If D is the interior of ABC then, ABC is split into two parts i.e ABD and DBC, then the measure of ABC is the sum of the individual two parts

m∠ABC = m∠ABD + m∠DBC.

Using the Angle Addition Postulate:

m∠ABC = m∠ABD + m∠DBC

m∠ABC = 15 + 40 = 55°

m∠ABC = 55°

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Part C) The graph in the attached figure

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we know that    

The compound interest formula is equal to  

A=P(1+\frac{r}{n})^{nt}  

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A is the Final Investment Value  

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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}  

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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

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substitute in the formula above

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using a graphing tool  

see the attached figure  

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