Answer: 
Step-by-step explanation:
If we draw RP and PS, then in the quadrilateral formed, we know that 
, and since angles in a quadrilateral add to 360 degrees, this means 
.
Thus, arc RS also measures 126 degrees
Answer:
3
Step-by-step explanation:
The factors of 12a are ...
2×2×3×a
The factors of 27 are ...
3×3×3
The only common factor is 3.
_____
12a -27 = 3(4a -9)
Answer:
Only table C shows proportional relationship
Step by Step Explanation:
Given
Tables A, B an C
Required
Which table shows proportional relationship?
In table A .
x = 2 and y = 20
k = 20/2
k = 10
Also, x = 12, y = 132
k =. 132/12.
k = 11
Both values of k are not equal.
Hence, the table is not proportional
In table B
x = 5 and y = 20
k = 20/5
k = 4
Also, x = 7, y = 30
k =. 30/7
k = 4.29
Both values of k are not equal.
Hence, the table is not proportional
In table C
x = 9 and y = 90
k = 90/9
k = 10
Also, x = 14, y = 140
k =. 140/14
k = 10
Also, x = 24, y = 240
k =. 240/24
k = 10
All values of k are equal.
Hence, the table is proportional
Answer:
Step-by-step explanation:
Total number of antenna is 15
Defective antenna is 3
The functional antenna is 15-3=12.
Now, if no two defectives are to be consecutive, then the spaces between the functional antennas must each contain at most one defective antenna.
So,
We line up the 13 good ones, and see where the bad one will fits in
__G __ G __ G __ G __ G __G __ G __ G __ G __ G __ G __ G __G __
Each of the places where there's a line is an available spot for one (and no more than one!) bad antenna.
Then,
There are 14 spot available for the defective and there are 3 defective, so the arrange will be combinational arrangement
ⁿCr= n!/(n-r)!r!
The number of arrangement is
14C3=14!/(14-3)!3!
14C3=14×13×12×11!/11!×3×2
14C3=14×13×12/6
14C3=364ways
Let x = width
x+1 is then the length
2x+2(x+1)=66
2x+2x+2=66
4x=64
x=16
deck will be 16x17, nice for a BBQ. :)
