Geometry Questions

1 Find the area of the quadrilateral 24 LA 10 4 M 5 4 3 2 1 2 H 1 2 4 S 1 2 3 4 5

7 If ZA 48 ZB 72 ZC 60 and the measures of the arcs are as indicated in the following figure find the measures of EF GH and DI A 100 D I B ENF 110 60 G H C

The figure shows a 700 foot tower on the side of a hill that forms a 7 angle with the horizontal Find the length of each of the two guy wires that are anchored 80 feet uphill and downhill from the tower s base and extend to the top of the tower how Transcribed Text 700 feet 80 feet J AIKAIPANNE TAKELT C 80 feet

A tank contains 9 000 L of brine with 19 kg of dissolved salt Pure water enters the tank at a rate of 90 L min The solution is kept thoroughly mixed and drair From the tank at the same rate a How much salt is in the tank after t minutes kg y b How much salt is in the tank after 30 minutes Round your answer to one decimal place y kg

1 2 3 4 5 in 15 81 11 7 14 m 13 42 11 15 16 16 11 10 in 14 m 15 12 1 m 8 in 15 56 14 m 12 13

y 2 tan 3x 2 1 Drag the movable black point to shift the function the red points to set the vertical asymptotes and the blue point at the correct set of coordinates You may click on a point to verify its coordinates Note that only one period of the function is shown Shift the given graph using the general form in order to ensure you are graphing the correct period Provide your answer below TE 211 3 5 11 3 4 3 2 2 1 4 1 2 0 0 71 3 T 2 1 21 3 IT

6 7 8 9 7 7 m 1 5 yd 5 8 m 6 m 5 9 in 14 9 ft ft 5 m 7 ft 6m 4 yd 15 1 ft 5 8 m 4 in

Sure arc 1 are 2 4 Find the measure of arc 1 round to one decimal place degrees wing two questions arc 2 5 Find the measure of arc 2 round to one decimal place degrees

Use the diagram for the following two questions 4x 3 6 Find the measure the arc degrees arc 7 Find the measure of the angle angle degrees

2 Find arc x degrees 409

8 Find angle x round to one decimal place degrees

A gardener designed a circular surrounded by bushes that approximate and equilateral triangle He planted bushes at each vertex of the triangle and at 6ft intervals along its boundary Each side of the triangle is tangent to the circle which has a radius of 6 3 ft how many bushes did he use by A 6 36 60640 869 sn B 18 D 54

In Exercises 17 to 22 use proportions to solve each problem 17 A recipe calls for 4 eggs and 3 cups of milk To prepare for a larger number of guests a cook uses 14 eggs How many cups of milk are needed

x 1 12 a N 2 7 x 1 b x 1 3 5 x 2

3 a 15 24 b 2 ft 2 yd 1 yd 3 ft c 2 m 150 cm 1 m 100 cm d 2 m 1 lb

5 Sarah ran the 300 m hurdles in 47 7 seconds In meters per second find the rate at which Sarah ran Give the answer to the nearest tenth of a meter per second

36 If the ratio of the measure of the complement of an angle the measure of its supplement is 1 4 find the measure of t angle

14 a x 1 X X x 1 b x 2 X 2x x 2

In Exercises 5 to 14 find the value of x in each proportion 7 21 24 5 a X 4 9 12 b X

1 State if the following statement is true or false If the statement is false then correct it If we perform the row operation R 2R R and then R3 2R R and then R3 2R R3 on the matrix we obtain 0 1 0 20 1 1 2 3 423 4 5 2 3 2 1 2 Use matrices and elementary row operations to solve the following system of equations 2x 3z 8 3x 3y 6z 9 x y z 5 2

Write a two column proof to show that the two triangles are congruent Given AB DE D B E C is the midpoint of AE and DB Prove AACB AECD

Identify the type and number of local extrema 8 6 80 60 40 20 20 40 60 80 y 2 4 6 8 X

32 A point of symmetry of the function f where f x a 3 4 b 3 5 c 3 4 d 3 4 x 3 4 is

Solve ABC subject to the given conditions if possible Round the lengths of the sides and measures of the angles in degrees to 1 decimal place if necessary Round Intermediate steps to at least four decimal places b 833 c 21 4 109 45 O The triangle with these conditions does not exist The triangle with these conditions does exist af B 0 C 0

es 153846 assignments 12018853 Write an equation for the line containing the point 1 3 and parallel to the line y x 6 9 10 perpendicular to the line y x 6 Write an equation for the line containing the point 5 3 and 11 parallel to the line y 4

8 perpendicular to the line y 2x 3

Write an equation for the line containing the point 2 3 and parallel to the line y 2x 3

A bowl is shaped like a hemisphere with diameter 60 cm A heavy ball with diameter 32 cm is placed in the bowl and water is poured into the bowl to a depth of h centimeters Find the volume V of water in the bowl Consider two cases one in which the ball is not completely submerged and the other in which it is V V 3 cm the ball is not completely submerged cm the ball is completely submerged

Use the formula for the present value of an ordinary annuity or the amortization formula to solve the following problem PV 15 000 i 0 01 PMT 550 n n Round up to the nearest integer

ind the unknown angles in triangle ABC for the following triangle if it exists C 45 20 b 25 4 m c 361 m Select the correct choice below and if necessary fill in the answer boxes to complete your choice OA There is only one possible set of remaining angles The measurements for the remaining angles are A Do not round until the final answers Then round to the nearest whole number as needed OB There are two possible sets of remaining angles The measurements for when B is larger are A and B O not round until the final answers Then round to the nearest whole number as needed OC No such trange exists and B and B The measurements for when B is smaller are

Suppose functions f x and g x are defined as follows x 1 2 3 f x g x 3 2 1 4 2 1 4 3 4 5 5 That is f 1 3 g 1 2 f 2 1 g 2 1 and so on Evaluate each of the following expressions ff 1 fog 2 gof 3 gog 4 5

An engineer designs a satelite dish with a parabolic cross section The dish is 18 ft wide at the opening and the focus is placed 9 ft from the verlex a Position a coordinate system with the origin at the vertex and the x axis on the parabola s axis of symmetry and find an equation of the parabola b Find the depth of the satellite dish at the vertex a The equation for the parabola is Type an equation Simplify your answer 180 G The figure may not be drawn to sca

10 If G is the midpoint of FH FG 14x 25 and GH 73 2x find

Find the measure of 0 in the triangle Do not use a calculator 0 3 2 3 3

Find the following b if A 27 3 and c 5 kht Srove to C B a

3 The triangle is inscribed in the circle below Find x 5 units

7 Find x units 24 8 Explain the logic process you when through to arrive at your answer A What properties did you use B What formulas did you use

1 Find x units 2 Explain the logic process you when through to arrive at your A What properties did you use B Wat formulas did you use

22 In trapezoid RSTV RV ST m SRV 90 and M and N are R midpoints of the nonparallel sides a What type of triangle is ARMN b If ST 13 RV 17 and RS 16 how long is RN c What type of triangle is ARVN HINT Use lengths of sides found in part b M S T N

19 In isosceles trapezoid WXYZ with bases ZY and WX 10 and ZY 8 YX WX 20 Find height h the length of ZD or YE 20 In trapezoid WXYZ with bases ZY and WX ZY 12 YX 10 WZ 17 and W N D Exercises 19 20 Y E X

5 Given isosceles trapezoid ABCD find a AC if BD 12 3 cm b x if AC 3 x 7 and BD A B D C 9 x 6

A D 18 Given E Exercises 17 18 Prove C B Isosceles AABE with AE BE also D and are midpoints of AE and BE respectively ABCD is an isosceles trapezoid

17 Given Prove A D E ABCD is an isosceles trapezoid AABE is isosceles C B

25 In the figure a b c and B is the midpoint of AC If AB 2x 3 BC x 7 and DE 3x 2 find the length of EF 26 In the figure a b c and B is the midpoint of AC If AB 2x 3y a b A B C E FL

In Exercises 11 to 16 the drawing shows trapezoid ABCD with AB DC also M and N are midpoints of AD and BC respectively M A Exercises 11 16 11 Given Find 12 Given Find B N AB 7 3 and DC 12 1 MN MN 6 3 and DC AB 7 5

K Exercises 7 8 8 If LH and LJ are supplementary in HJKL are a ZK and LL necessarily supplementary also b LH and ZK necessarily supplementary

5 If the diagonals of a parallelogram are perpendicular and congruent what can you conclude regarding the parallelogram

1 Being as specific as possible name the type of quadrilatera that a has four congruent sides

In Exercises 11 to 14 considerMNPQ with diagonals MP and NQ When the answer is not a whole number leave a square root answer 11 If MQ 6 and MN 8 find NQ and MP 12 If QP 9 and NP find NQ and MP 6 13 If NP 7 and MP 11 find QP and MN M Exercises 11 14 N P

In Exercises 8 to 10 use the properties of rectangles to solve each problem Rectangle ABCD is shown in the figure A B Exercises 8 10 8 Given Find 9 Given Find D C AB 12 5 and BC CD AD and AC not shown AB 2x 7 BC CD 3x 2 x and DA 3x 4 and