Answer:
Let the to consecutive odd integers be 2n-1 and 2n+1
their average is
=>
=
= 
The square of the average is 
= 
One less than the square of their average = 
-----------------------------(1)
Now the product of the two consecutive odd numbers
(2n-1)( 2n+1) =
= 
------------------------------------(2)
From (1) and (2) ,
We can say that the product of two consecutive odd integers is always one less than the square of their average is true
For consecutive even integers
The product of two consecutive integers
(2n)(2n+2) = 
----------------------------(3)
Whereas, the one less than the square of their average is
= 
= 
=
= 2n--------------------------------------------(4)
From (3) and (4) it is clear that product of two consecutive even integers is not one less than the square of their average.
(2,3). The vertex of a parabola is the highest or lowest point of the graph
Answer:
1. x >/= -1
2. x < 4
3. x </= -1
4. x >/= -2
5. x < -3
6. x </= 7
Step-by-step explanation:
Answer:
6x + 2y =5
y + 3x= 2
Step-by-step explanation:
*see attached picture for the diagram of the box
Answer:
130cm²
Step-by-step explanation
The amount of red appear needed by Marcus to cover his box = Surface Area of the cube - Area of the circle.
Surface area of cube = 6s² (where s is the side length of the cube. s² therefore is S.A of 1 face of the cube)
Given that s = 5cm,
S.A of cube = 6s² = 6*5² = 150cm²
Area of circle = πr²;
Given that π = 3.14, and r = ½ of diameter of circle (i.e. ½ of side length of cube)
Area of circle = 3.14*(½*5)² = 3.14*(2.5)² = 3.14*6.25 =19.625
Amount of red paper needed = S.A of the cube - Area of the circle = 150cm² - 19.625cm² = 130.375cm² = 130cm²
