Answer: 1 minute and 43 seconds faster
Step-by-step explanation:
Answer: 6 students
What we know:
Students: 24
Students who play checkers: 
Students who also play sudoku:
of the 
24 ÷ 3 = 8, so 8 × 2 = 16 (students who play checkers)
× 2 = 
So the answer is,
6 students play both checkers and sudoku
Answer:
Minimum value of function
is 63 occurs at point (3,6).
Step-by-step explanation:
To minimize :

Subject to constraints:

Eq (1) is in blue in figure attached and region satisfying (1) is on left of blue line
Eq (2) is in green in figure attached and region satisfying (2) is below the green line
Considering
, corresponding coordinates point to draw line are (0,9) and (9,0).
Eq (3) makes line in orange in figure attached and region satisfying (3) is above the orange line
Feasible region is in triangle ABC with common points A(0,9), B(3,9) and C(3,6)
Now calculate the value of function to be minimized at each of these points.

at A(0,9)

at B(3,9)

at C(3,6)

Minimum value of function
is 63 occurs at point C (3,6).
Answer:





Step-by-step explanation:
The figure has been attached, to complement the question.



Given that J is the centroid, it means that J divides sides CD, DE and CE into two equal parts respectively and as such the following relationship exist:



Solving (a): DG
If
, then



Make DG the subject

Substitute 52 for DE


Solving (b): GE
If
, then


Solving (c): DF

So:

Solving (d): CH


Solving (e): CE
If
, then


