x is 
<u>Explanation:</u>
Given:
EP = FP
GQ = FQ
Since the sides are equal, the ΔFPQ and ΔFEG are similar.
According to the property of similarity:
On substituting the value:
Perimeter will be sum of all the sides. If y is known then substitute the value and then find the perimeter.
<span>This question is a simple one. To answer this question, you need to understand the description in the question and determine to multiply or divide the number.
The first problem would be:
50.75 x 0.18= 9.135
</span>If you need to estimate, 50.75 is near 50; 0.18 is near 0.2 or 1/5 so it would be: 50/0.2= 10<span>
The second problem would be:
196 / 0.499: 392.785
If you need to estimate, 0.499 is near 0.5 then 196/0.5 would be 392</span>
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
<em>alternate interior angles theorem</em>
EXPLANATION
According to the alternate interior angles theorem, when two parallel lines are are intercepted by a straight line (transversal) the angles in the interior corners of a Z-shape pattern are congruent.
From the above diagram line r is parallel to line s, therefore
and
because they are alternate interior angles.
See attachment for how to spot alternate interior angles.
The answer can't be C or D because the unit of volume is always cubed. The formula for volume of cylinder is (pi)(r^2)(h) . The pi(r^2) part is the formula for area of a circle which is what the base of the cylinder is. Fortunately the area is already given as 28.2. Plug that into the volume formula and plug in 3.1 for the height and multiply. I get 87.42 and the answer choice B seems to be the closest option
