The principal of a high school needs to plan seating for commencement. The following two-way table displays data for the student
1 answer:
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Answer:
The required result is proved with the help of angle bisector theorem.
Step-by-step explanation:
Given △ABD and △CBD, AE and CE are the angle bisectors. we have to prove that
Angle bisector theorem states that an angle bisector of an angle of a Δ divides the opposite side in two segments that are proportional to the other two sides of triangle.
In ΔADB, AE is the angle bisector
∴ the ratio of the length of side DE to length BE is equal to the ratio of the line segment AD to the line segment AB.
→ (1)
In ΔDCB, CE is the angle bisector
∴ the ratio of the length of side DE to length BE is equal to the ratio of the line segment CD to the line segment CB.
→ (2)
From equation (1) and (2), we get
Hence Proved.
Answer:
The account balance six months from today is $5,187.5.
Step-by-step explanation:
This is a compound interest problem
The compound interest formula is given by:
In which A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.
In this problem, we have that
The total amount formula changes after 6 years, at which point each of the principal(initial money), interest rate, and n changes.
This item asks only the balance six months from today, so we use the information given for the first 6 years.
A is the account balance, the value we hope to find.
The loan is of $5,000. So
The account earns 7.5% per annum compounded half yearly, so .
We want to find the account balance in 6 months. However, t is measured in years. So
Solving the equation:
The account balance six months from today is $5,187.5.