Answer:
Here is the question attached with.
is a straight line.
is a right angled triangle.
Options 
are correct answers.
Step-by-step explanation:
⇒As 
is ⊥
so it will forms right angled triangle then 
.
⇒Measure of 
as 
as 
is the bisector of 
,meaning that is half of so 
.
⇒ is a straight line as the angles measure over it is 
.
⇒Measure of 
from linear pair concept.
As 
,plugging the values of we have .
The other two options are false as:
it is exceeding whereas is a
straight line.
- And
is not true.
As 
and 
So we have total 
answers.
The correct options are .
Answer:
A + B + C = π ...... (1)
...........................................................................................................
L.H.S.
= ( cos A + cos B ) + cos C
= { 2 · cos[ ( A+B) / 2 ] · cos [ ( A-B) / 2 ] } + cos C
= { 2 · cos [ (π/2) - (C/2) ] · cos [ (A-B) / 2 ] } + cos C
= { 2 · sin( C/2 ) · cos [ (A-B) / 2 ] } + { 1 - 2 · sin² ( C/2 ) }
= 1 + 2 sin ( C/2 )· { cos [ (A -B) / 2 ] - sin ( C/2 ) }
= 1 + 2 sin ( C/2 )· { cos [ (A-B) / 2 ] - sin [ (π/2) - ( (A+B)/2 ) ] }
= 1 + 2 sin ( C/2 )· { cos [ (A-B) / 2 ] - cos [ (A+B)/ 2 ] }
= 1 + 2 sin ( C/2 )· 2 sin ( A/2 )· sin( B/2 ) ... ... ... (2)
= 1 + 4 sin(A/2) sin(B/2) sin(C/2)
= R.H.S. ............................. Q.E.D.
...........................................................................................................
In step (2), we used the Factorization formula
cos x - cos y = 2 sin [ (x+y)/2 ] · sin [ (y-x)/2 ]
Step-by-step explanation:
Answer:
The goat population reaches 1000 in 12.4 years
Step-by-step explanation:
After <em>t </em>years, the number of goats is given by
where 
is the initial number of goats and <em>b</em> is the per capita growth rate.
From the question,
- <em>b</em> = 0.5
- <em>N</em> = 1000
Answer:
I believe "The height of each pyramid is one-half h units"
Answer:
21 minutes
Step-by-step explanation:
Given the following :
Taking CITY STREET:
Time taken to drive to nearest bowling alley = 45 minutes = 45/60 = 0.75 hours
Speed of travel = 30 miles per hour
Taking FREEWAY:
speed of travel = 65miles per hour
If the distance to bowling alley is the same along both routes, The time taken along FREEWAY will be :
.
Distance to bowling alley taking city center :
Speed = distance / time
30 mph = distance / 0.75 hour
Distance = 30 × 0. 75 = 22.5 miles
Since distance is the same :
Time taken along FREEWAY :
Time taken = distance / speed
Time taken = 22.5 / 65 = 0.3461538 hour
Converting to minutes :
0.3461538 × 60 = 20.769 minutes
= 21 minutes ( to the nearest minute)
