Algebra, arithmetic, reasoning.
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Distance is √[(3 - 0)² + (4 - 0)²].
This equals √25 = 5.
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The equally likely outcomes are HH, HT, TH, and TT.
Exactly one head occurs in HT and TH, giving 2/4 = 1/2.
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Matrix addition is performed entry by entry.
Each corresponding pair sums to 5.
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The exterior angles of any polygon sum to 360°.
For a regular octagon, each is 360° ÷ 8 = 45°.
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Triangle area is one-half × base × height.
Thus, 1/2 × 10 × 6 = 30 cm².
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Average the x-coordinates and the y-coordinates separately.
The midpoint is ((2 + 8)/2, (3 + 7)/2) = (5, 5).
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There are 36 equally likely ordered outcomes.
Six outcomes have sum 7, so the probability is 6/36 = 1/6.
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For [[a, b], [c, d]], determinant = ad - bc.
Thus, 2 × 4 - 3 × 1 = 5.
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The common ratio is 3, so a₆ = 2 × 3⁵.
This equals 2 × 243 = 486.
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The number of diagonals is n(n - 3)/2.
For n = 6, this gives 6 × 3 ÷ 2 = 9.
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Parallelogram area is base times perpendicular height.
Thus, 15 × 8 = 120 cm².
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Slope is change in y divided by change in x.
Thus, (10 - 2)/(5 - 1) = 8/4 = 2.
