Shelia is dividing x4 – 4x3 + 4x2 – 6x + 5 by x – 1 using a division table. Quotient Divisor x3 – 3x2 + x – 5 x x4 –3x3 x2 A – 1
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A) Plan A requires for a percentage increase of a number of students. This means that year after year the number of new students will increase. Plan B requires for a constant number of new students each year. This means that year after year the percentage increase would get smaller.
B) To solve this problem we will use formula for a growth of population:
Where:
final = final number of students
initial = initial number of students
percentage = requested percentage increase
t = number of years
We can insert numbers and solve for t:
For Plan B we can use simple formula
increase = 120
increase per year = 20
number of years = increase / (increase per year) = 120 / 20 = 6 years
Plan B is better to double the <span>enrollment.
C)We use same steps as in B) to solve this.
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For Plan B we can use simple formula
increase = 240
increase per year = 20
number of years = increase / (increase per year) = 240 / 20 = 12 years
Plan A is better to triple the enrollment.
B) To solve this problem we will use formula for a growth of population:
Where:
final = final number of students
initial = initial number of students
percentage = requested percentage increase
t = number of years
We can insert numbers and solve for t:
For Plan B we can use simple formula
increase = 120
increase per year = 20
number of years = increase / (increase per year) = 120 / 20 = 6 years
Plan B is better to double the <span>enrollment.
C)We use same steps as in B) to solve this.
</span>
For Plan B we can use simple formula
increase = 240
increase per year = 20
number of years = increase / (increase per year) = 240 / 20 = 12 years
Plan A is better to triple the enrollment.
m□ebd=4 x-8 and m□ebc=5 x+20
This is solvable only if e b is the initial side and b d and b c lies on opposite side of each other and lies on a line i.e c,b,d are Collinear.
∠ebd and ∠ebc will form a linear pair.The meaning of linear pair is that angles forming on one side of a straight line through a common vertex which are adjacent is 180°.
i.e
∠ ebd + ∠ebc = 180°
4 x- 8 + 5x + 20= 180°
adding like terms
⇒ 9 x +12 =180°
⇒ 9 x = 180° - 12
⇒ 9 x = 168°
⇒ x =( 168/9)°=(56/3)°
now m□ebc =5 x +20
= 5 × 56/3 + 20
= 280/3 + 20
=340/3
m□ebc=( 340/3)°
So, solution set is x =(56/3)° and m□ebc =(340/3)°
