Geometry Questions

20 m tr 20 3 m 12 m 13

Assignment 5 17 points Given is the following optimization problem max 5x1 3x2 S t X1 12 10 01 2x2 36 3x1 x2 24 21 12 0 5 a Solve this problem graphically Draw the constraints and objective shade the region of feasible solutions and find an optimal solution by moving a ruler parallel to the objective function b Find an optimal solution using the two phase Simplex method When several variables could enter of leave the basis always select the one with the smallest index

16 A line segment has endpoints 2 7 and 5 4 The line segment is dilated by a factor of 3 around 4 3 What are the new endpoints and length of the line segment

1 Use the given values to evaluate if possible three trigonometric functions cos x csc x tan x 1 sin x cos x 0

4 Use the trigonometric substitution to rewrite the algebraic expression as a trigonometric function of 0 where 0 x 25x 36 5x 6tan

2 Use the given values to evaluate if possible two trigonometric functions tan and csc w cot 5 sin w 10

1 Hints All trapezoids have two pairs of consecutive supplementary angles Trapezoid Property All trapezoids have at least one pair of parallel sides Isosceles Trapezoid Property Sides All isosceles trapezoids have at least 1 pair of opposite congruent sides legs Isosceles Trapezoid Property Angles All isosceles trapezoids have 2 pair s of consecutive congruent angles Isosceles Trapezoid Property Diagonals The diagonals of all isosceles trapezoids are congruent P Triangle Angle Sum 180 Alternate Interior Angle Theorem T 76 34 R 73 410 A Vertical Angle Theorem Same Side Interior Angle Theorem 2 P 21 97 45 65 thir an Isosceles Trapezoid Yes or No agonal Is this an Isosceles Trapezoid Yes or No

Rectangle AE mLABD m2DAE A 20 EB 5m MLADE mzBAC B Woled Caugh audmona Square to cemuzeem D DE mLABD mLACD 7m AE C mLAED m DBC

Find the missing side lengths and angle measures indicated for the figures below Parallelogram D mLABD A EB 725 mLDAC 30 35 7 cm E 72 5 72 6 cm AE 35 m2ACD 80 MLADB Rhombus EB mLABD m2BAE D 30 9 cm 46 cm C AE B m AEB MLADE

Find all missing side lengths and angle measures of the figures below Parallelogram Rectangle 71 8 cm 10 ft 3 cm GOAsin HW 4 ft Rhombus Square Thurs 4 cm 5 m 101

State the most specific name for each figure or 1 3 5 7 30AM 3A8AM 2 4 6 8

5 P P T 24 6 cm TC 3 cm 310 AC 8 cm A s this an Isosceles Trapezoid Yes or No 6 RA 9 cm P 270 T 11 cm TC 18 6 cm R AC A Is this an Isosceles Trapezoid Yes or No

T P 50 R 34 26 A s this an Isosceles Trapezoid Yes or No 4 T P46 R 940 26 A Is this an Isosceles Trapezoid Yes or No

34 f x x 5x 6 4x 4 48 6 4 2 8 6f 4 2 2 61 8 6 X

D 13 Given the following parallelpiped state whether each of the following statements is true or false Explain a HC HG GC b AE EH HD CB E

that describes plotting points with polar coordinates Click here to watch the video Plot the point 3 150 Then find the rectangular coordinates of the given point Choose the graph of 3 150 below OA OB 180 O C 180 90 270 90 0 0 180 O D 180 90 270 90 0 0 Q A

14 In the following diagram x and y represent adjacent sides of a parallelogram Does x y x Explain A B y D

Does JM bisect J Explain cmpo 15 M

CD bisects C Solve for CA AE 21 8

Does JM bisect J Explain 15 L 5 M 6

symm Jennifer draws the rectangle ABCD Find all rotations and reflections that carry rectangle ABCD onto itself

What is the image of the point 6 2 after a rotation of 90 counterclockwise about the origin

For each figure determine how many lines of reflection and how many angles of rotation will carry the figure onto itself B

What is the image of the point 5 4 after a rotation of 270 counterclockwise about the origin

Follow the guided instructions below to rotate the figure 270 clockwise about th origin Draw a circle centered at the center of rotation such that one of the vertices of the figure is on the circle 10 9 8 7 6 5 4 3 2 1 10 y 9 8 7 6 5 2 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 10 X

Does JM bisect J Explain Nound 15 L 5 M 6

Solve for x 15 2r 4 18 8

Complete the following problems after the mini lesson CD bisects C Solve for CA D 11 22 B

Tyler says that since triangle ACD is similar to triangle ABC the length of CB is 11 96 Noah says that since ABC is a right triangle we can use the Pythagorean Theorem So the length of CB is 12 exactly Do you agree with either of them Explain or show your reasoning AD 5 4 6 13 B

Next draw CD perpendicular to AB as shown in the next figure Label the red triangle as triangle 2 The blue triangle as triangle 3 How many triangles do you see in the figure Why are the three triangles similar to each other

a Determine if each transformation represents a translation rotation reflection or none CC D How I know b A B 7 A How I know B C C A A B B 02 How I know C

Next draw CD perpendicular to AB as shown in the next figure Label the red triangle as triangle 2 The blue triangle as triangle 3

Symmetry For each figure determine how many lines of reflection and how many angles of rotation will carry the figure onto itself B

Triangle 1 green is the original right triangle we started with Triangle 2 red is the other triangle formed by constructing CD Its right angle is angle D By comparing these two triangles we see that Therefore a cp Now let s complete the proof By adding the two equations we will get What do we notice about the side length p q So we can substitute p q for a b cp cq a b c p q By substitution we get a b c

1 3 2 4 8 60 10 7 9 11 5 59 6 m21 m 2 m23 m24 m25 m26 m27 m28 m 9 m 10 m 11

As shown in the figure AABC satisfies ZABC 30 AB 4 take the circumcenter of AABC as the center to make a circle I AABC is within I extend AB to intersect I at D extend BC to intersect I at E if BD 6 CE 5 find the area of T E A B D

as a zero 1 In Geogebra create the following function f x y 2sin x cos y which will plot the surface defined by the function and plot point A for the value in the function s domain The point should be a 3D point on the surface

44 Interpret a government spending multiplier of 7 5 points

Find the exact value of the expression if possible If not possible enter IMPOSSIBLE a cos arc sin b sin arc tan

The likelihood of falling into an alcohol induced coma is highest when consuming Group of answer choices 5 alcoholic drinks in 2 hours a whole 750 mL bottle of whisky in 2 hours a whole 750 mL bottle of beer in 2 hours enough alcohol to raise blood alcohol levels above 0 55

8 Find the area of the region inside r 4 sin but outside r 2

9 Find the slope of the tangent line to the polar curve r when 0

5 A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at 0 degrees from the horizonta Find 0 if F 5 100 pounds and W 14 000 lb Approximate the answer to one decimal place 21 4 22 4 23 4 20 4 19 4

6 Select a value for b such that a triangle with A 59 and a Ob 15 O b 24 O b 16 O b 11 Ob 17 14 has only one solution

28 In the figure a and are positive angles CL a 9 b 18 e 20 e C

19 Find the magnitude and direction angle of v 2i 6j Round the direction angle to the nearest degree O 67 0 279 O v 2 10 0 252 O lv 30 0 239 O v 2 13 0 260 ly l 3 7 A 269

21 Given C 119 B 42 and c 15 use the Law of Sines to solve the triangle for the value of a Round your answer to two decimal places a 7 3 O a 6 81 O a 4 36 O a 19 61 a 5 58

6 To approximate the length of a marsh a surveyor walks 275 meters from point A to point B then turns 76 and walks 245 meters to point C se figure Approximate the length AC of the marsh where a CO a 245 m b 275 m B b A

4 Given A 50 B 74 and c 8 use the Law of Sines to solve the triangle for the value of a Round your answer to two decimal places O O A a 7 39 a 6 38 a 8 66 a 6 9 a B

12 Determine the area of a triangle having the following measurements Round your answer to two decimal place B 84 38 a 7 and c 8 22 30 sq units 27 88 sq units 25 09 sq units 33 45 sq units