Answer
Find out the Area of a triangle .
To proof
Formula
Area of Triangle
Now vertices are D(3, 3) , E(3, −1) , and F(−2, −5) .
Solving the above
= -10 units²
(Neglected the negative sign as area cannot be negative.)
= 10 units ²
Area of a triangle is 10 units ²
Hence proved
Given:
First term of an arithmetic sequence = 5
Second term = 3
To find:
The explicit formula for the given arithmetic sequence.
Solution:
We have,
First term:
Second term:
Common difference is
Now, the explicit formula for an arithmetic sequence is
where, a is first term and d is common difference.
Putting a=5 and d=-2, we get
It can also be written as
Here, n is an integer greater than or equal to 1.
Domain is the set of input values.
Therefore, the explicit equation is or
and domain is all interest greater than or equal to 1.
The length of the rectangle is 14 feet and the width of the rectangle is 9 feet.
The length of a rectangle is 5 more than the width. The area is 126 square feet.
We need to find the length and width of the rectangle.
<h3>What is the area of a rectangle?</h3>The area of a rectangle is calculated by multiplying the rectangle's length by its width.
Let the width of the rectangle be x, then the length of the rectangle be x+5.
We know that the area of the rectangle = Length×Width
Now, the area of the rectangle = (x+5)×x=126 square feet.
⇒
⇒
⇒
⇒.
Since length cannot be a negative integer.
So, Width=9 feet and Length=9+5=14 feet.
Hence, the length of the rectangle is 14 feet and the width of the rectangle is 9 feet.
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