2D Geometry Questions and Answers

If 21% of males and 15% of females in a given state play the guitar, what is the probability that a randomly selected subject in the state plays the guitar, given that the subject is male? A. 0.15 B. 0.21 C. 0.79 D. 0.85

Here is a right pyramid with a rectangular base: What are the two shapes of cross- sections we could create by slicing the pyramid perpendicular to its base? Choose 2 answers: A Triangle B Rectangle C Trapezoid D Pentagon

Plane X contains point C. Plane Y contains points A and B How many planes exist that pass through points A, B, and C?

Prove that the involute of a circle is a constant and explain its form is it a spiral? a closed curve?

What is the surface area of a square pyramid with a height of 12 mm and a base that measures 10 mm on each side? Round to the nearest square millimeter if necessary. A. 120 mm² B. 360 mm² C. 240 mm² D. 620 mm²

Dixon and his little sister Ariadne stand next to each other on the playground on a sunny afternoon. Their mother measures their shadows. Dixon's shadow is 9 feet long and Ariadne's shadow is 6 feet long. If Dixon is 6 feet tall, how tall is Ariadne?

A semi-circle sits on top of a rectangle to form the figure below. Find its area and perimeter. Use 3.14 for π. A≈ 14.28 square inches, P≈ 20.56 inches A ≈33.12 square inches, P≈ 14.28 inches A≈14.28 square inches, P≈ 14.28 inches A≈ 33.12 square inches, P≈ 20.56 inches

Solve each equation with the quadratic formula. 1) 3k² - 7k-20 = 6

In the figure above, the radius of the inscribed circle is 4 inches (in.). What is the perimeter of square CABD? 8π in. 16π in. 16 in. 32 in.

Angle A and angle B are a linear pair. If m∠A =4∠B, find, m∠A and m∠B 72, 18 36, 144 18,72 144, 36

The figures are similar. Give the ratio of the perimeters and the ratio of the areas of the first the second. The figures are not drawn to scale. A. 8/3 and 10/5 B. 9/4 and 64/9 C. 9/4 and 10/5 D. 8/3 and 64/9

The complement of an angle is 53°. What is the measure of the angle? 37° 47° 127° 137°

Name the line and plane shown in the diagram. QP and plane SR line P and plane PQS PQ and plane PQS PQ and plane SP

Supplementary angles are two angles whose measures have a sum of _____. Complementary angles are two angles whose measures have a sum of_____. 180; 360 90; 180 180; 90 90; 45

Noam walks home from school by walking 8 blocks north and then 6 blocks east. How much shorter would his walk be if there were a direct path from the school to his house? Assume that the blocks are square. 10 blocks 14 blocks 4 blocks The distance would be the same.

Find the area of a rectangle with base of 2 yd and a height of 5 ft. 10 yd2 30 ft2 30 yd2 10 ft2

Are points C, G, and H collinear or noncollinear? collinear impossible to tell noncollinear

Jose wants to put a fence around his rectangular garden. His garden measures 33 feet by 39 feet. The garden has a path around it that is 3 feet wide. How much fencing material does Jose need to enclose the garden and path? 168 ft 120 ft 84 ft 156 ft

Are M, N, and O collinear? If so, name the line on which they lie. No, the three points are not collinear. Yes, they lie on the line NP. Yes, they lie on the line MO. Yes, they lie on the line MP

Given the triangle find the length of side x using the Law of Sines. Round your final answer to 4 decimal places.

Find a parametrization for the following paths (a) ellipse {z € C: |z-1| + |z+1| = 4}, oriented counter-clockwise. (b) the rectangle with vertices +1+2i, oriented counter-clockwise

Given a circle of radius 13 m, find the length of the arc subtended by a central angle of 210°. Round decimals to the nearest hundredth.

What are the coordinates of point Bon AC such that AB is 3 times as long as BC?

Find the area of a parallelogram with corner points at (1,4) (4,6) (8,6) and (5.4)

3. In ΔABC, AO intersects BC at P. If |AP| = 5, |BP| = 2, and |CP| = 3, then what is b? (As usual, O is the circumcenter of ΔABC and b = |AC|.)

A moving sidewalk in an airport moves people between gates. It takes Jason's 9-year-old daughter Josie 33 sec to travel 165 ft walking with the sidewalk. It takes her 7 sec to walk 21 ft against the moving sidewalk (in the opposite direction). Find the speed of the sidewalk and find Josie's speed walking on non-moving ground. The sidewalk moves at ft/sec.

Use trigonometry and other methods to calculate and estimate the area of a region. 1) Charlie the goat is tied with a 10 meter rope to the corner of a non-rectangular building. The sides closest to him have lengths 7 meters and 12 meters. Choose a building shape and determine the area of grass that Charlie can eat. (triangle? Parallelogram? Which one is better) 2) Choose another building shape to investigate - be creative! It is unlikely that you will be able to find an exact solution - you are being asked to estimate reasonably and find a solution that makes sense.

Find the value of x in each of the following exercises:

A regular pentagon (a polygon with 5 equal sides) is inscribed in a circle of radius 12.2 cm. Find the perimeter of the pentagon.

What is the most precise name for quadrilateral ABCD with vertices A(-5,2), B(-3, 4), C(5, 4), and D(3, 2)? A. kite B. parallelogram C. rhombus D. rectangle

Two sides of a triangle for the third side measure 4 and 9. What are the possible values

Find the radius of a circle with a circumference of 287 m.

A car traveling on a 1.6° uphill grade has a grade resistance of 124 lb. Determine the weight of the car to the nearest hundred pounds. The weight of the car is approximately lb.

Solve the right triangle using the given information. a=77.9 yd, b=42.1 yd c= (Simplify your answer. Type an integer or a decimal. Round to the nearest tenth if needed.) A=' (Simplify your answers. Type integers. Round to the nearest ten minutes if needed.) B=' (Simplify your answers. Type integers. Round to the nearest ten minutes if needed.)

The shadow of a vertical tower is 78.0 ft long when the angle of elevation of the sun is 33.0°. Find the height of the tower. The tower is___ft tall. (Simplify your answer. Type an integer or decimal rounded to the nearest tenth as needed.)

The area of a circle is 25mcm². What is the circumference of the circle? Write you answer as exact.

The sum of the interior angles of a convex polygon is 2520°. Determine how many sides the polygon has.

The equation D=1/2 n(n-3)gives the number of diagonals D for a polygon with no sides. Find the number of sides for polygon that has 152 diagonals.

Suppose that the measure of an interior angle of a regular polygon is 157.5". How many sides does that polygon have? # of Sides =

What is the measure of EACH exterior angle of the following polygons? a) Square > Exterior Angle = b) Regular Hexagon -> Exterior Angle = c) Regular Octagon --> Exterior Angle = d) Regular 12-gon- --> Exterior Angle =

What is the sum of the measures of the exterior angles of a polygon with 12 sides?

Find the lateral surface area and total surface area of the cube with side length s = 4.2 mm. Round to the nearest whole number, if necessary. LSA = TSA =

If W(-10, 4), X(-3, -1), and Y(-5, 11) classify AWXY by its sides. Show all work to justify your answer. Classify: WX = XY = WY=

Sketch the graph of: y=5cot (3x+ π/2) y = 3sec (1/4x - π/6)

A parallelogram is a four-sided figure whose opposite sides are parallel and equal in length. Alex is drawing parallelogram ABCD on a coordinate plane. The parallelogram has the coordinates A(4,2), B(0,-2), and D(8,-1). Which of the following coordinates should Alex use for point C? A (6,-3) B (4,-5) C (10,-3) D (4,3)

Sketch the graph of the function y = 2csc(2x-π/2) over one period. Please label at least 2 key points and show and label any vertical asymptotes on your graph.

Select the graph of the transformation of f(x)=3x Give the horizontal asymptote, the domain, and the range. f(x) = 3x - 2

Can two points on a line be on a parabola? Proceed by contradiction

Given the equation of f(x)=1/4 (x-3)² - 6 list the EXACT VALUES of any invariant points for y = √f(x)

Convert, 2x+7y=-3, from rectangular to polar form