Answer:
The given statement is correct for all positive integers.
Step-by-step explanation:
The given inequality is
for all positive integers
Area of a rectangle = length x height
Area = 135
Height = X
Lenght = x +6
135 = x * x+6
Simplify:
135 = x^2 +6x
Subtract 135 from both sides:
x^2 + 6x - 135 = 0
Solve:
2 numbers when added need to equal 6 and when multiplied equal -135
x = 9 and x = -15
The height can't be a negative number so the height is 9
Length = 9 +6 = 15
Height = 9cm, Length = 15 cm
Pablo : 3(2x) = 6x
Sofia : 2x
Mia : x
Assuming x = 10
Mia : x = 10
Sofia : 2x = 2(10) = 20
Pablo : 3(2x) = 3(20) = 60
10 + 20 + 60 = 90
90/3 = 30 candy eggs per person
Pablo: 60 x 1/2 = 30
Sophia: 30-20 = 10 : 10
Mia : 30 - 10 = 20 : 20
Ratio of eggs given to sophia from pablo's set = 10/60 = 1/6
Ratio of eggs given to mia from pablo's set = 20/60 = 2/6 = 1/3
The rate of change is the slope of this line
m = (y2 - y1)/(x2 - x1) = (13 - 5)/(4 - 0) = 8/4 = 2
