If
, then
. So, in the first gap you can write 5 and in the second you can write -4.
Since
, the minimum value of y is when
. The solution of the last equation is x=-5 and then y=-4 -- these are numbers, which you can write in the third and fourth gaps.
Given : tan 235 = 2 tan 20 + tan 215
To Find : prove that
Solution:
tan 235 = 2 tan 20 + tan 215
Tan x = Tan (180 + x)
tan 235 = tan ( 180 + 55) = tan55
tan 215 = tan (180 + 35) = tan 35
=> tan 55 = 2tan 20 + tan 35
55 = 20 + 35
=> 20 = 55 - 35
taking Tan both sides
=> Tan 20 = Tan ( 55 - 35)
=> Tan 20 = (Tan55 - Tan35) /(1 + Tan55 . Tan35)
Tan35 = Cot55 = 1/tan55 => Tan55 . Tan35 =1
=> Tan 20 = (Tan 55 - Tan 35) /(1 + 1)
=> Tan 20 = (Tan 55 - Tan 35) /2
=> 2 Tan 20 = Tan 55 - Tan 35
=> 2 Tan 20 + Tan 35 = Tan 55
=> tan 55 = 2tan 20 + tan 35
=> tan 235 = 2tan 20 + tan 215
QED
Hence Proved
C.) Old Price: $148.80; New Prices: $142.60
Using The Formula Given
M = O x P = O + M
Markup Value After 20% Is $148.80
Markup Value After 15% is $142.60
Answer:
81
Step-by-step explanation:
6 over 12 equals 3 over 6 6 over 3 equals 6 over 12 6 over 6 equals 3 over 12 12 over 6 equals 3 over 6
