The formula to find number of diagonals (D) given total number of vertices or sides (N) is
N * (N – 3)
D = ———–
2
Using the formula, we get
1325 * 2 = N * (N – 3)
N2 – 3N – 2650 = 0
Solving the quadratic equation, we get N = 53 or -50
It is obvious that answer is 53 as number of vertices can not be negative.
Alternatively, you can derive the formula as triange has 0 diagonals, quadrangel has 2, pentagon has 5, hexagon has 9 and so on……
Hence the series is 0, 0, 0, 2, 5, 9, 14, …….. (as diagram with 1,2 or 3 vertices will have 0 diagonals).
Using the series one can arrive to the formula given above.
55967
Ans: 60 kph
Suppose Person meets the train everyday at 3 PM at Station A.
His speed is 12kph.
So normally he reaches 5 km before the meeting point (pt B) at (5/12 hr = 25 min before) 2:35PM.
But if he is late by 30 min, then he will reach that point (pt B) by 3:05 PM.
Train is traveling at its normal speed so it covers the distance of 5 Km in 5 min starting from Station A and reaches the meeting point (pt B) at 3:05 PM.
So speed of the train is 5KM/5min = 60 kph.
3:7
1/10 + 1/12 -1/20 = 15/2 i.e 7.5 h means 7 h & 30 min
5436
Joe is fencing in a square area of 576 square feet.
Fence posts, which are needed every three feet, cost 32.00 each.
The fencing cost 4.50 per foot. What is the total cost of the fencing materials?
Solution:-
Area of Square is 576 sq ft.
so, the length of side = root(576) = 24 ft
Since the fencing would be done on the perimeter, we would need that
formula is 4*side = 96 ft.
Number of Fence post needed = 96/3 = 32
1 Fence post cost = 32
32 Fence Post cost = 32 * 32 = 1024
Fencing cost = Perimeter * fencing cost = 96 * 4.5 = 432
Total Cost = 432 + 1024 = 1456
Alice — 3844
Liu —30976
The first number is 36
Step-by-step explanation:
let their common factor be ‘x’
hence,
the ratio be 3x/5x
hence, by condition;
(3x-9)/(5x-9)=9/17 ch upu
9(5x-9)=17(3x-9)
45x-81=51x-153
153-81=51x-45x
72=6x
x=72/6
x=12
the first number is 3x=3×12=36
exactly
D = 180m
S = 42 – 6 = 36 * 5/18 = 10
T = D/S = 180/10
T = 18s
600
180*2/3 = 60degree
4
21
the answer is 3:10
explanation:
let the first number be x
and the second number be y
(7/8)((3/7)x)=(25/100)((45/100)y) given
ie.., 21x/56= 9y/80
on solving we get x:y= 3:10
is the answer