# mathcounts problems 81 through 85

Jan 3rd, 2015
Anonymous
Category:
Mathematics
Price: \$5 USD

Question description

81. If (x+y)^2=x^2+y^2, what is the value of xy?

83. Enoch has a photo that is 8 inches high and 6 inches wide. He wants to enlarge it so that it can fit into a frame that is 10 inches by 7 inches. How much will he need to crop from the width to exactly fill the entire frame? Express your answer as a decimal to the nearest tenth.

84. At 1:00 p.m. an airplane left the local airport and flew due east at 300 mi/h. At 3:00 p.m. a second plane left the same airport and flew due north at 400 mi/h. Assuming the curvature of the earth is negligible, how many miles apart are the planes at 8:00 p.m.?

85. If the mean of the integers 7, 3, 11, 13, 5 and x is 4 more than the mode of the six integers, what is the value of x?

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