Answer:
As Given, x+y=w+z
To Prove: AOB is a line or x+y=180
∘
(linear pair.)
According to the question,
x+y+w+z=360
∘
∣ Angles around a point.
(x+y)+(w+z)=360
∘
(x+y)+(x+y)=360
∘
∣ Given x+y=w+z
2(x+y)=360
∘
(x+y)=180
∘
Hence, x+y makes a linear pair.
Therefore, AOB is a straight line
Answer:
Step-by-step explanation:
We would apply the formula for determining compound interest which is expressed as
A = P(1 + r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited
From the information given,
P = $300
r = 10% = 10/100 = 0.1
n = 2 because it was compounded 2 times in a year(6 months).
t = 3 years
Therefore,
A = 300(1 + 0.1/2)^2 × 3
A = 300(1 + 0.05)^6
A = 300(1.05)^6
A = $402.03
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Answer: See explanation
Step-by-step explanation:
Total number of text messages = 800
Amount used by Tommy and Mary = 1/2 × 800 = 400
Number of messages uses by Jack and Stefanie = 240
The expression to find the number of messages Cathy uses will be:
= 800 - (1/2 × 800) - 240
Since the expression is 800 - (1/2 × 800) - 240, the number of messages that Cathy will use will be:
= 800 - (1/2 × 800) - 240
= 800 - 400 - 240
= 160 messages
