Answer:
6
Step-by-step explanation:
Factorize of the above numbers :
30 = 2 • 3 • 5
66 = 2 • 3 • 11
84 = 22 • 3 • 7
Build a prime factors table
Number of times each prime factor
appears in the factorization of :
Prime
Factor Number
30 Number
66 Number
84 G.C.F
(min)
2 1 1 2 1
3 1 1 1 1
5 1 0 0 0
7 0 0 1 0
11 0 1 0 0
GCF = 2 • 3
Greatest Common Factor is :
6
You'll find it easier to understand if you illustrate the problem as what is shown in the attached picture. From the illustration and the problem description, two equations can be formulated:
HJ = 2JK
HJ + JK = HK
2JK + JK = 78
3JK = 78
JK = 78/3
JK = 26
Answer:
A dashed straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the right of the line is shaded.
Step-by-step explanation:
To graph the solution set of the inequality 2x - 3y < 12, first plot the dashed line 2x - 3y = 12 (dashed because the inequality has sign < without notion "or equal to"). This line passes through the points (0,-4) and (3,-2) (their coordinates satisfy the equation of the line). this line has positive slope because

and the slope of the line is 2/3.
Now, identify where the origin is (in the region or outside the region). Substitute (0,0) into the inequality:

This means coordinates of the origin satisfy the inequality, so origin belongs to the shaded region. Thus, shade that part which contains origin.
From the diagram you can see that plane cuts each lateral face of hexagonal pyramid and do not cut the base. A hexagonal pyramid has six lateral faces. The intersection of each of these lateral faces with given cutting plane is segment. The figure which consists of these segments is hexagon. This hexagon is not the same as base and even is not similar to the base because the cutting plane is not parallel to the base.
Answer: resulting cross section is a hexagon, correct choice is option 4.