Answer:
16+12i
Step-by-step explanation:
<u>Given</u>:
Given that ABCD is a rectangle.
The diagonals of the rectangle are AC and DB.
The length of AE is (6x -55)
The length of EC is (3x - 16)
We need to determine the length of the diagonal DB.
<u>Value of x:</u>
The value of x can be determined by equating AE and EC
Thus, we have;
![AE=EC](https://tex.z-dn.net/?f=AE%3DEC)
Substituting the values, we get;
![6x-55=3x-16](https://tex.z-dn.net/?f=6x-55%3D3x-16)
![3x-55=-16](https://tex.z-dn.net/?f=3x-55%3D-16)
![3x=39](https://tex.z-dn.net/?f=3x%3D39)
![x=13](https://tex.z-dn.net/?f=x%3D13)
Thus, the value of x is 13.
<u>Length of AC:</u>
Length of AE = ![6(13)-55=78-55=23](https://tex.z-dn.net/?f=6%2813%29-55%3D78-55%3D23)
Length of EC = ![3(13)-16=39-16=23](https://tex.z-dn.net/?f=3%2813%29-16%3D39-16%3D23)
Thus, the length of AC can be determined by adding the lengths of AE and EC.
Thus, we have;
![AC=AE+EC](https://tex.z-dn.net/?f=AC%3DAE%2BEC)
![AC=23+23](https://tex.z-dn.net/?f=AC%3D23%2B23)
![AC=46](https://tex.z-dn.net/?f=AC%3D46)
Thus, the length of AC is 46.
<u>Length of DB:</u>
Since, the diagonals AC and DB are perpendicular to each other, then their lengths are congruent.
Hence, we have;
![AC=DB](https://tex.z-dn.net/?f=AC%3DDB)
![46=DB](https://tex.z-dn.net/?f=46%3DDB)
Thus, the length of DB is 46.
A = $ 861.69
Equation:
A = P(1 + rt)
Calculation:
First, converting R percent to r a decimal
r = R/100 = 5.5%/100 = 0.055 per year,
putting time into years for simplicity,
1 quarters ÷ 4 quarters/year = 0.25 years,
then, solving our equation
A = 850(1 + (0.055 × 0.25)) = 861.6875
A = $ 861.69
The total amount accrued, principal plus interest,
from simple interest on a principal of $ 850.00
at a rate of 5.5% per year
for 0.25 years (1 quarters) is $ 861.69.
Answer:
11 + x
Step-by-step explanation:
addition uses the communtitve property meaning the numbers can be swaped and still result in the same answer