If the diagonals of a quadrilateral bisect each other at right angles, it indicates that the quadrilateral is a rhombus.

A quadrilateral with diagonals that bisect each other is a parallelogram, but it can also be a rectangle or rhombus.

If the diagonals of a quadrilateral bisect each other, it is a property of parallelograms.

If the diagonals of a quadrilateral bisect each other, it is a property of parallelograms.

A quadrilateral with diagonals that bisect each other is a parallelogram.

To find the y-intercept, set x = 0. The equation becomes -3y + 6 = 0, leading to y = 2.

To find the y-intercept, set x = 0. The equation becomes -4y + 12 = 0, leading to y = 3.

To find the x-intercept, set y = 0. The equation becomes 0 = -1/2x + 3, leading to x = 6.

Substituting x = 4 into the equation gives y = -1/2(4) + 3 = -2 + 3 = 1.

'm' in the equation of a line represents the slope, which indicates the steepness and direction of the line.

The sum of the exterior angles of any polygon is 360 degrees. Therefore, the number of sides can be calculated as 360 / 30 = 12.

The exterior angle is equal to the sum of the two opposite interior angles. If the exterior angle is 120 degrees, the smallest interior angle can be calculated as 180 - 120 = 60 degrees.

Volume of a cylinder = πr²h. If height is doubled, volume becomes 2πr²h, which is double the original volume.

Let the original length be L and width be W. The new length is 1.2L and the new width is 0.9W. The original area is LW and the new area is (1.2L)(0.9W) = 1.08LW. The percentage change in area is ((1.08LW - LW) / LW) * 100 = 8% increase.

If the diagonals of a quadrilateral are equal, it can be concluded that the quadrilateral is a rectangle.

The area of a rhombus can be calculated using the formula (1/2) × d1 × d2 = (1/2) × 10 × 24 = 120 cm².

A triangle with sides in the ratio 3:4:5 satisfies the Pythagorean theorem, thus it is a right triangle.

Let the original angle be x. Then, x + 20 = 3x. Solving this gives x = 10 degrees, which is not an option. Hence, the correct answer is 30 degrees.

Let the other endpoint be (x, y). The midpoint formula gives (2 + x)/2 = 4 and (3 + y)/2 = 5. Solving these gives x = 6 and y = 7.

Let the other endpoint be (x, y). The midpoint formula gives (2 + x)/2 = 4 and (3 + y)/2 = 5. Solving these gives x = 6 and y = 7.

The midpoint M is given by M = ((x1 + x2)/2, (y1 + y2)/2). Setting up the equations: (1 + x)/2 = 3 gives x = 5.

The perimeter of a regular hexagon is the sum of the lengths of its 6 equal sides. Therefore, each side is 72 cm / 6 = 12 cm.

The perimeter of a regular octagon is 8 times the length of one side. Therefore, each side is 64 cm / 8 = 8 cm.

In an equilateral triangle, all sides are equal. Therefore, if the perimeter is 36 cm, each side is 36/3 = 12 cm.

Let the length of each equal side be x. The perimeter is given by 2x + 8 = 24. Solving for x gives 2x = 16, so x = 8 cm.

The perimeter is the sum of all sides. Therefore, base = 24 - (10 + 10) = 4 cm.

The area of a circle is given by A = πr². If the radius is increased by 50%, the new radius is 1.5r. The new area is A' = π(1.5r)² = 2.25πr². The increase in area is (2.25 - 1) = 1.25 times the original area, which is a 125% increase.

If the radius increases by 50%, the new radius is 1.5r, and the area becomes (1.5r)² = 2.25r², which is a 125% increase.

Volume of a sphere = (4/3)πr³. If radius is halved, volume becomes (4/3)π(1/2)³ = (4/3)π(1/8) = (1/6)π, which is one-eighth of the original volume.

A triangle with sides in the ratio 3:4:5 is a right-angled triangle, as it satisfies the Pythagorean theorem.