Geometry Questions

xtra Practice 1 A quadrilateral has vertices at A 3 1 B 5 9 C 7 1 and D 3 3 Prove that the midsegments form a parallelogram 10 14 lie on a circle with

What is the rate of return when 25 shares of Stock A purchased for 30 share are sold for 825 The commission on the sale is 6 Rate of Return Give your answer as a percent rounded to the nearest tenth Enter

Tax Table Standard Deduction Taxable income Income Tax Rate 0 9 700 9 701 39 475 39 476 84 200 84 201 160 275 Above 160 275 12 200 00 10 12 22 24 32 37 A 48 200 B 38 500 C 26 300 D 36 000 After applying the standard deduction how much of a 48 200 salary is taxable income

This table shows the amount of commission earned for a broker receiving 2 5 commission on sales How much would this agent earn in commission for 1 000 000 in sales Commission Earned Sales in thousands of Commission in thousands of A 40 000 B 400 000 C 25 000 D 250 000 200 5 400 10 600 15 800 20 1000

67 A lake is in the shape of an isosceles triangle as shown in the picture You want to go from point A to point E 4 miles away on the opposite side of the lake in the shortest time possible You can walk at a rate of 4 miles per hour and row a boat at 2 miles per hour How should you proceed You may row a boat from A directly to E but that may not be the shortest time possible or is it Instead you may walk along the shore to a point B and then row a boat from B to E Determine the point B that will minimize the time of your travel A 0 0 B r C 4 2 E 4 0 D 1 2

Graph the hyperbola x 4y 6x 24y 63 0 12 4 124 0 a 9 S 4 NO 10 2 2 12 23 41 4 14 OX X V

V Find an equation of the line L The equation is Tyne an equation Simplify your answer

deo The angle below is the image formed when a figure containing RS is dilated by a scale factor of 5 What is the measure of ZRST R 94 S T

What is the volume of a hemisphere with a diameter of 8 9 cm rounded to the nearest tenth of a cubic centimeter

Match each of the coordinate points on the unit circle with the given angle V 3 1 22 0 1 1 0 2 4 22 3 1 4 2 2 1 2 3 5 2 81 3 4 5 6 7 6 5 25 6 4

Step Prove ABEC ADFA H 5 arallelogram BE 1 AC and DF LAC pa Statement Type of Statement ABCD is a parallelogram BEL AC DF LAC B E Reason Given F C

Give one pair of supplementary angles and one pair of vertical angles shown in the figure below 1 2 3 4 5 6 m 8 a Supplementary angles b Vertical angles X 40 and and 40 40 and 40

Give one pair of vertical angles and one pair of supplementary angles shown in the figure below 7 8 5 6 3 4 12 a Vertical angles b Supplementary angles X 40 and 40 40 and 40 G

For problems 1 and 2 find the value of each variable If your answer is not an integer express it in simplest radical form 1 2 12 7 45 b

points A supplier is late with a delivery which has caused a delay in completion of Derek and Addison s project In which part of their project status report would Derek and Addison discuss this Problems encountered Project overview Impact on budget The delay should not be mentioned

Multiple Concept Example 9 deals with the concepts that are important in this problem A grasshopper makes four jumps The displacement vectors are 1 33 0 cm due west 2 28 0 cm 44 0 south of west 3 20 0 cm 63 0 south of east and 4 23 0 cm 60 0 north of east Find a the magnitude and b direction of the resultant displacement Express the direction as a positive angle with respect to due west a Number i b Number i 72 73 8 Units Units TA 0 7 W Start N S E

You are driving into St Louis Missouri and in the distance you see the famous Gateway to the West arch This monument rises to a height of 192 m You estimate your line of sight with the top of the arch to be 7 71 above the horizontal Approximately how far in kilometers are you from the base of the arch Number Units

In a right triangle the side adjacent to angle has length 3 79 meters and the hypotenuse has length 6 19 meters What is the cosine of the angle cose i e Textbook and Media

Some questions make use of the Interactive Graphing Tool in order to draw a parabola using two points Click the icon to view instructions for the Interactive Graphing Tool Draw a solid vertical parabola overlaying the dashed parabola on the graph Use the vertical parabola tool button on the graphing palette to draw a solid vertical parabola Place the first point at the vertex of the parabola shown as the solid dot on the graph and place the second point at another location on the parabola shown as the dashed curve on the graph Click to enlarge graph Careful Be sure to use a second point that is exactly on the parabola causing the dashed curve to be completely covered 8 6 A 4 P 8 Ay 6 9 1 2 14 6 48 40

2 Find the values of the six trig functions whose terminal ray passes through point Q 2 21 10 points Sin B Cos B Tan B Csc B Sec B Cot B

Show that the equation sin x X x 0 has a solution Provide all the necessary ju

For the function find the points on the graph at which the tangent line is horizontal If none exist state that fact y 2x 8 List all the points where the tangent line is horizontal Select the correct choice below and if necessary fill in the am A The point s at which the tangent line is horizontal is are Type an ordered pair Use a comma to separate answers as needed B The tangent line is horizontal at all points of the graph C There are no points where the tangent line is horizontal

8 A girl 160 cm tall stands 360 cm from a lamp post at night Her shadow from the light is 90 cm long How high is the lamp post 6104

5 Your new job requires you to calculate the material costs for manufactured goods One of goods you manufacture is a fabric sample in the shape of a circle Given the formula A Tr find the 2 area A of the fabric sample whose radius r is 6 2 x 105 m Write your answer in scientific notation Use 3 14 for T A m

If you already know lal and lvl then the formula a xv2 gives a convenient way to ind the curvature Use it to find the curvature and radius of curvature of the curve r t cost t sin t i sin t t cos t j t 0

O GRAPHS FUNCTIONS AND SYSTEMS Finding the slope and y intercept of a line given its equation in Find the slope and the y intercept of the line 7x 2y 10 Write your answers in simplest form slope 0 y intercept 8 08 X Undefined

A car has wheels with a 8 inch radius If each wheel s rate of turn is 3 revolutions per second find the angular speed in units of radians second 3 n 8 24 3 n 6 3r

Find a solution to the equation sec B 12 csc 29B 10

A Bolat leaves a port traveling due east at 12 mi hr At the same time another boat leaves the same port traveling northeast at 15 mi hr The angle of the line between the boals is measured relative to due north see the figure to the right What is the rate of change of this angle 30 min after the boats leave the port 3 hr after the boats leave the port Purt Let x be the distance from the port to the eastbound boat and let z be the distance from the port to the northeast bound boat Write an equation relating x z and 2 2 x Z 2 tan 2 Type an exact answer Type any angle measures in radians The rate of change of this angle 30 min after the boats leave the port is Round to the nearest thousandth as needed 15 mih 12 mih

In the diagram below of circle O GO 8 and m GOJ 60 8 G 60 What is the area in terms of 7 of the shaded region

A circle with a diameter of 10 cm and a central angle of 30 is drawn below 10 cm 30 What is the area to the nearest tenth of a square centimeter of the sector formed by the 30 angle 1 5 2 2 6 5 3 13 1 4 26 2

Find the angle of the sector below if the area of the sector is 36T P 18 Q

Find the area of the sector created below Round to the nearest tenth 120 4 cm B

1 Find the length of arc s in the diagram below To the nearest tenth 8 in 60 S

3 A ball is rolling in a circular path that has a radius of 10 inches as shown in the accompanying diagram What distance has the ball rolled when the subtended arc is 54 F Express your answer to the nearest hundredth of an inch 10 in 54

2 Find the length of minor arc AB to the nearest tenth The diagram below shows circle O with radii OA and OB The measure of angle AOB is 120 and the length of a radius is 6 inches O 120 6 B

1 If DE is the perpendicular bisector of AC which of the following statements is not true A BD BE OZABD CBD OAB BC AD CD D B E C

4 Find the height in centimeters of a square pyramid with a volume of 455cm and a base edge length equal to the height Give the approximate answer rounded to 2 decimal places

ect the correct answer from each drop down menu BC has vertices at A 11 6 B 5 6 and C 5 17 YZ has vertices at X 10 5 Y 12 2 and Z 4 15 NO has vertices at M 9 4 N 3 4 and O 3 15 KL has vertices at J 17 2 K 12 2 and L 12 7 PQR has vertices at P 12 3 Q 12 2 and R 3 2 can be shown to be congruent by a sequence of reflections and transl can be shown to be congruent by a single rotation

2 A tent is in the shape of a right pyramid with a square floor The square floor has side lengths of 8 feet If the height of the tent at its center is 6 feet what is the volume of the tent in cubic feet

Complete the wage table for an employee who receives time and a half overtime pay after 40 hours of work Hours Worked Money Earned Hourly Pay Table 10 140 00 280 00 420 00 560 00 A 770 00 B 650 00 C 840 00 D 1020 00 20 30 40 50

3 The volume of a triangular prism is 70 in The base of the prism is a right triangle with one leg whose measure is 5 inches If the height of the prism is 4 inches determine and state the length in inches of the other leg of the triangle

1 The Pyramid of Memphis in Tennessee stands 107 yards tall and has a square base whose side is 197 yards long What is the volume of the Pyramid of Memphis to the nearest cubic yard

Find the distance from the point to the plane 2 4 1 x 4y 4z 18 The distance is

Determine the graph of the equation 2 2 4 Choose the correct graph of the equation OA O C B O D G 0 y

Determine the graph of the ellipsoid 36x y 2 36 Choose the correct graph of the equation OA OB O C

5x 2z 133 hes Identify the surface by type paraboloid ellipsoid etc Choose the correct graph of the equation below OA O B HID O C

graph of the hyperbolic paraboloid 2 x 9z Choose the correct graph of the hyperbolic paraboloid OA O C OB O D y

Determine the graph of the paraboloid z x 9y Choose the correct graph of the equation OA B O C Y

Find the equation for the plane through the point Po 0 5 5 and normal to the vector n 7i 2j k Choose the correct answer below OA 7x 2 y 5 z 5 0 OB 7x 2y z 5 OC 7x 2y z 0 O D x 7 5 y 2 5 z 1 5