Answer:
53.3 rotations
Step-by-step explanation:
135/180=x/40
solve by cross multiply
Answer:
D. 29
Step-by-step explanation:
180 - 151 = 29
Answer:
FIRST NUMBER IS 20
AND
SECOND NUMBER IS 45
Step-by-step explanation:
LET THE RATIO BE X
FIRST NUMBER = 4X
SECOND NUMBER = 9X
A/Q,
=}4X - 5 / 9X - 5 = 3 / 8
CRISS CROSS,
=}8 ( 4X - 5 ) = 9X - 5 ( 3 )
=}32X - 40 = 27X - 15
=}32X - 27X = - 15 + 40
=}5X = 25
=}X = 25 / 5
=}X = 5
THEREFORE,
FIRST NUMBER
=} 4X
=} 5 × 4
=} 20
SECOND NUMBER
=} 9X
=} 5 × 9
=} 45
By induction:
It's true for

, since

clearly contains a factor of 3.
Suppose it's true for

, that

is divisible by 3. Then

where

is an integer. This reduces to

and both terms are clearly multiples of 3. We know that

is an integer since we had set

previously, which implies

is a multiple of

. So the statement is true.