Least common multiples 3,5,10
1 answer:
You might be interested in
Answer:
Approximately 62 gallons of water will be used by Lee County by the year 2025.
Step-by-step explanation:
The amount, in millions gallons of water, spent by Lee County, in t years after 2019, is given by the following equation:
In which P(0) is the amount spent on 2019 and r is the increse rate, as a decimal.
In the year 2019, Lee County used approximately 55 million gallons of water.
This means that
Historical trends show that each year the water demand is increasing by a rate of approximately 2.1%.
This means that
So
Approximately how many million gallons of water will be used by Lee County by the year 2025?
2025 is 2025 - 2019 = 6 years after 2019. So this is P(6).
Rounded to the nearest millions
Approximately 62 gallons of water will be used by Lee County by the year 2025.
All the theorems are proved as follows.
<h3>What is a Triangle ?</h3>A triangle is a polygon with three sides , three vertices and three angles.
1. The Triangle sum Theorem
According to the Triangle Sum Theorem, the sum of a triangle's angles equals 180 degrees.
To create a triangle ABC, starting at point A, move 180 degrees away from A to arrive at point B.
We turn 180 degrees from B to C and 180 degrees from C to return to A, giving a total turn of 360 degrees to arrive to A.
180° - ∠A + 180° - ∠B + 180° - ∠C = 360°
- ∠A - ∠B - ∠C = 360° - (180°+ 180°+ 180°) = -180°
∠A + ∠B + ∠C = 180°
(Hence Proved)
2. Isosceles Triangle Theorem
Considering an isosceles triangle ΔABC
with AB = AC, we have by sine rule;
as AB = AC
sin B = sin C
angle B = angle C
3.Converse of the Isosceles theorem
Consider an isosceles triangle ΔABC with ∠B= ∠C, we have by sine rule;
as ∠B= ∠C ,
AB = AC
4. Midsegment of a triangle theorem
It states that the midsegment of two sides of a triangle is equal to (1/2)of the third side parallel to it.
Given triangle ABC with midsegment at D and F of AB and AC respectively, DF is parallel to BC
In ΔABC and ΔADF
∠A ≅ ∠A
BA = 2 × DA, BC = 2 × FA
Hence;
ΔABC ~ ΔADF (SAS similarity)
BA/DA = BC/FA = DF/AC = 2
Hence AC = 2×DF
5.Concurrency of Medians Theorem
A median of a triangle is a segment whose end points are on vertex of the triangle and the middle point of the side ,the medians of a triangle are concurrent and the point of intersection is inside the triangle known as Centroid .
Consider a triangle ABC , X,Y and Z are the midpoints of the sides
Since the medians bisect the segment AB into AZ + ZB
BC into BX + XB
AC into AY + YC
Where:
AZ = ZB
BX = XB
AY = YC
AZ/ZB = BX/XB = AY/YC = 1
AZ/ZB × BX/XB × AY/YC = 1 and
the median segments AX, BY, and CZ are concurrent (meet at point within the triangle).
To know more about Triangle
#SPJ1