Robert Bosch Coordinate Geometry Quiz 3

Ans: (-3/2, -1/4)
Explanation: The vertex of a parabola in the form y = ax^2 + bx + c is given by the coordinates (-b/2a, f(-b/2a)),
where f(x) is the function defined by the parabola.
In this case, the vertex coordinates are
(-b/2a, f(-b/2a)) = (-(3)/(21), f(-(3)/(21))) = (-3/2, (9/4) - (9/2) + 2) = (-3/2, -1/4).

Solution: 12 cm
Explanation :
Let the length of the other leg be x cm.
According to the Pythagorean theorem,
In a right-angled triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.
So, using the Pythagorean theorem:
x^2 + 5^2 = 13^2
=> x^2 + 25 = 169
=> x^2 = 144
=> x = √144
=> x = 12 cm

Solution: 48 cm
Explanation :
A regular hexagon has six equal sides. The perimeter of a regular hexagon is given by:
Perimeter = 6 × Side Length
So, Perimeter = 6 × 8 cm = 48 cm
In a regular hexagon, all sides are equal in length, so the perimeter is the sum of all six sides.

Solution: 100π cm²
Explanation :
The area of a circle is given by the formula:
Area = π × Radius^2
Substitute the value: Area = π × 10^2 = 100π cm²

Solution: 80°
Explanation :
The sum of the angles in any triangle is 180°.
So, to find the measure of angle Z, we subtract the measures of angles X and Y from 180°.
Angle (Z) = 180° - 40° - 60° = 80°

Solution: 40 metres
Explanation :
The perimeter of a rectangle is given by:
Perimeter = 2 × (Length + Width)
Substitute the values:
Perimeter = 2 × (12 + 8) meters
= 2 × 20 meters
= 40 meters

Solution: 10 cm
Explanation :
In a parallelogram, opposite angles are equal.
So, angle B = 120°.
In a parallelogram, opposite sides are equal in length.
Hence, side BC = side AB = 10 cm.

Solution: 336 cm²
Explanation :
The total surface area of a triangular prism is given by the formula:
Total Surface Area = 2(Area of the Base) + (Perimeter of the Base × Height)
First, find the area of the base using Heron's formula for the area of a triangle: Semi-perimeter (s) = (6 + 8 + 10) / 2 = 12 cm
Now, Area of the base = √(s(s-6)(s-8)(s-10))
= √(12 × 6 × 4 × 2)
= √(576)
= 24 cm²

Now, find the perimeter of the base:
Perimeter = 6 + 8 + 10
= 24 cm
Substitute the values into the total surface area formula:
Total Surface Area = 2 × 24 cm² + (24 cm × 12 cm)
= 48 cm² + 288 cm²
= 336 cm²

Solution: 60 cm²
Explanation :
The area of a trapezoid is given by the formula:
Area = ((Sum of the lengths of the bases) × Height) / 2
Substitute the values:
Area = ((12 cm + 8 cm) × 6 cm) / 2
= (20 cm × 6 cm) / 2
= 120 cm² / 2
= 60 cm²

Solution: 565.2 cm³
Explanation :
The volume of a cone is given by the formula:
Volume = (1/3) × π × (Radius^2) × Height
Substitute the values:
Volume = (1/3) × 3.14 × (6 cm)^2 × 15 cm
= (1/3) × 3.14 × 36 cm² × 15 cm
= 565.2 cm³