Answer:
|AC| =√18 and |BD| =√68. They are not equal in length.
Step-by-step explanation:
To find |AC| and |BD| of the parallelogram, we will simply use the distance formula.
Using the line distance formula;
D = √(-
)² + (
-
)²
A(2,1) C(5,-2)
=2
=1
= 5
=-2
|AC| = √(-
)² + (
-
)²
=√(-2-1)² + (5-2)²
=√(-3)² + (3)²
=√9+9
=√18
Distance |AC| =√18
B(3,6) D (1,-2)
=3
=6
= 1
=-2
|BD| = √(-
)² + (
-
)²
=√(-2-6)² + (1-3)²
=√(-8)² + (-2)²
=√64+4
=√68
Distance |BD| =√68
|AC| and |BD| are not equal in length
Answer:
$7,544.58
Step-by-step explanation:
We will use the compound interest formula provided to solve this:
<em>P = initial balance</em>
<em>r = interest rate (decimal)</em>
<em>n = number of times compounded annually</em>
<em>t = time</em>
<em />
First, change 3.3% into its decimal form:
3.3% -> -> 0.033
Since the interest is compounded monthly, we will use 12 for n. Lets plug in the values now:
The balance after 1 year will be $7,544.58
Given that total number of books in the book store = 75972
Given that total number of books in science section = rd of total books =
= 25324
Then remaining number of books = 75972 - 25324 = 50648
Given that 75% of the remaining books are in business section = 75% of 50648 = 0.75*50648 = 37986
Then number of books in the math section = 50648 - 37986 = 12662
Hence final answer is 12662 books in the math section.