Area = (√3/4) * side² = (√3/4) * 6² = 9√3 cm².

The area of an equilateral triangle is given by the formula: Area = (√3/4) * side² = (√3/4) * 12² = 36√3 cm².

Using the Pythagorean theorem, the height can be found by splitting the triangle in half: height = √(10^2 - 6^2) = √(100 - 36) = √64 = 8 cm.

Circumference of a circle is given by C = 2πr. Therefore, C = 2π(5) = 10π cm.

Distance = √((4-1)² + (6-2)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Using the distance formula, d = √((x2 - x1)² + (y2 - y1)²) = √((7 - 3)² + (1 - 4)²) = √(16 + 9) = √25 = 5.

The midpoint M of a segment with endpoints (x1, y1) and (x2, y2) is given by M = ((x1 + x2)/2, (y1 + y2)/2) = ((2 + 4)/2, (3 + 7)/2) = (3, 5).

Parallel lines have the same slope. The slope of the given line is 3.

The slope of a line perpendicular to another is the negative reciprocal. The negative reciprocal of -3 is 1/3.

The slope is calculated as (y2 - y1) / (x2 - x1) = (7 - 3) / (4 - 2) = 2.

The slope of a line is calculated using the formula (y2 - y1) / (x2 - x1). For the points (2, 3) and (4, 7), the slope is (7 - 3) / (4 - 2) = 4 / 2 = 2.

The slope m = (y2 - y1) / (x2 - x1) = (6 - 2) / (3 - 1) = 4 / 2 = 2.

The number of arrangements is 5! / (3!2!) = 10.

The number of combinations of 2 fruits from 5 is C(5, 2) = 5! / (2!(5-2)!) = 10.

The number of combinations of 10 fruits taken 3 at a time is C(10, 3) = 10! / (3!(10-3)!) = 120.

The number of combinations of 4 toppings from 10 is C(10, 4) = 10! / (4!(10-4)!) = 210.

The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides. Therefore, (2/3)^2 = 4/9.

The ratio of the perimeters of similar triangles is the same as the ratio of their corresponding sides, which is 1:5.

The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides. Therefore, (2:3)² = 4:9.

Mode is the number that appears most frequently. Here, 10 appears twice.

The mode is the number that appears most frequently. Here, 20 appears twice, so the mode is 20.

The mode is the number that appears most frequently, which is 7.

The mode is the number that appears most frequently. Here, 5 appears twice, so the mode is 5.

The mode is 4, as it appears most frequently (three times).

The mode is the number that appears most frequently. Here, 7 appears twice.

The mode is 10, as it appears most frequently (three times).

Angle 2 is corresponding to angle 1, so angle 2 = 70 degrees.

Corresponding angles are equal when two parallel lines are cut by a transversal.

Angle 2 is supplementary to angle 1, so 180 - 70 = 110 degrees.

Using the Law of Cosines: BC² = AB² + AC² - 2(AB)(AC)cos(A) = 12² + 16² - 2(12)(16)(0.5) = 144 + 256 - 192 = 208. Therefore, BC = √208 = 14.42 cm.