answer:1. Let ( M ) be the midpoint of the arc ( AC ) of the circle, and let ( N ) be the midpoint of the segment ( AC ). 2. Draw a line through point ( N ) that is parallel to ( B M ). Case Analysis: - **Case 1:** If ( AB = BC ) - In this case, we note that the line ( M B ) will divide the area of the figure into two equal parts. - **Case 2:** If ( AB < BC ) 1. Consider the broken line segment ( B N M ). We want to show that this line divides the area of the figure into two equal parts. 2. Construct a point ( P ) on the segment ( BC ) such that the line ( P N ) is parallel to ( B M ). Here are the detailed steps for this construction: - By construction, the triangles ( triangle BNM ) and ( triangle BPM ) will have equal areas because the triangles share the same base ( |BM| = |BM| ), and since ( P N parallel B M ), the height from ( G ) to ( BM ) (say if it is retraced or reflected horizontally) is equal. - Therefore, the area of triangle ( BNP ) and triangle ( BPM ) follows: [ S_{BNM} = S_{BPM} ] Thus, the segment ( MP ) will also divide the area of our convex figure into two equal parts. # Conclusion: Hence, through the use of these constructions, we have successfully identified and constructed a line segment that divides the area of the convex figure described in the problem into two equal areas, conditional on the defined cases. [ boxed{} ]

answer:To find out how many pencils Kathryn gave to Anthony, we need to subtract the number of pencils Anthony originally had from the total number of pencils he has now. Anthony originally had 9 pencils, and now he has 65 pencils in total. So, the calculation would be: 65 (total pencils) - 9 (original pencils) = 56 pencils Kathryn gave Anthony boxed{56} pencils.

answer:Express 2.36 as a mixed number, which is 2 frac{36}{100}. Next, simplify the fraction part. The greatest common divisor of 36 and 100 is 4. Dividing the numerator and the denominator by 4, we get: [ frac{36}{100} = frac{36 div 4}{100 div 4} = frac{9}{25} ] Therefore, combining the integer part with the fractional part: [ 2 + frac{9}{25} = 2 times frac{25}{25} + frac{9}{25} = frac{50}{25} + frac{9}{25} = frac{59}{25} ] Thus, 2.36 can be expressed as a fraction boxed{frac{59}{25}}.

answer:Elena's Eastern Hemisphere postcards issued before the 1970s include those from Asia and Africa. - For Asia: From the 1950s and 1960s, 5 + 8 = 13 postcards at 7 cents each cost 13 times 0.07 = 0.91. - For Africa: From the 1950s and 1960s, 3 + 6 = 9 postcards at 7 cents each cost 9 times 0.07 = 0.63. Their total cost is 0.91 + 0.63 = boxed{1.54}.