2D Geometry Questions and Answers

The two questions below ask for approximations of the derivative Make sure you show any calculations you use get a Pass give the best approximation for the derivative 1 Approximate f 2 f x 2 3 2 4 1 5 6 1 0 0 5 1 3 4 4 5 5 73 1 1 5 57 7 9 10

Find the equation for the plane through the points Po 4 2 5 Qo 1 1 4 and Ro 0 4 5 The equation of the plane is

Use an identity to write each expression as a single trigonometric function value or as a single number See Example 4 17 cos 15 sin 15 1 20 1 2 sin 22 22 12 2

44 Draw a diagram and find the remaining part of the right triangle If b 48 A 36 c A 35 OB 26 C 82 D 59

Given ZBAC LACD and ZADB ZDBC Prove ABCD is a parallelogram Step 2 Statement ZBAC LACD ZADB ZDBC LBEA ZDEC try Type of Statement A B Reason Given Vertical angles are congruent D

46 Draw a diagram and find the remaining part of the right triangle If a 2 52 c 4 75 A A 58 B 32 O C 28 D 62

Find the rectangular coordinates of the point 9 150 The rectangular coordinates of the point are Type an ordered pair Simplify your answer including any radicals Use integers or fractions for any numbers in the expression

operties of parallelograms Parallelogram 4 5 perpendicular congruent complementary 1 point bisect supplementary Consecutive same side angles are Answer bisect complementary congruent perpendicular 1 point supplementary Diagonal bisectors are Answer

9 Find EF C F 7x 39 Type your answer 1 point Find m BCE F 3x 5 A D 7x 5 E 11x 3 B D C E

The following shape is a rectangle Find the missing sides Rectangle 1 P 10 S 24 T R 18 1 point 19 20 21 What is QR Type your answer 1 point What is SR Type your answer 1 point What is SQ Type your answer 1 point What is PR Type your answer

Using the coordinate plane determine which of the following are parallelograms 16 Parallelogram No Answers Chosen Possible answers W 7 4 X 1 6 Y 5 13 Z 1 12 J P 4 2 Q 6 4 R 11 2 S 2 3 E 0 8 F 6 10 G 2 0 H 4 2 K 7x 2 7 12x 22 M Not a parallelogram 1 point What is the value of x in the following parallelogram No Answers Chosen J 9 2 K 5 1 L 1 4 M 3 7 A 7 4 B 1 2 C 9 8 D 1 6 L

The quadrilateral below is a parallelogram Find the missing measures Parallelogram 2 F 21 C 71 E m FED 134 D 11 12 1 point m DEC Type your answer 1 point m CDE Type your answer 13 1 point m ECD Type your answer

Parallelogram 4 Opposite angles are Answer perpendicular supplementary congruent complementary 1 point Consecutive same side angles are Answer bisect bisect congruent complementary DA

Parallelogram 2 Opposite side are parallel supplementary perpendicular complementary 1 point bisect bisect Answer Opposite side are Answer congruent perpendicular

X 17x 3 S 8 Given AMTW ABG T G 4x 3

stance is 8 3 Z 6 3t Type an exact answer using radicals as needed Try again The distance from a point S to a line that passes through a point P and is parallel to a vector v is given by the formula below where PS is the vector that has initial point P and terminal point S Distance PSXV v

Arrange the following step Prove cosa sin a tan a A cosa sin B COS sin a cos a

Find the distance from the point to the line 2 1 1 x 1 t y 1 2t z 6 3t The distance is Type an exact answer using radicals as neede

Find the equation for the plane through the points Po 1 2 3 Qo 2 1 2 and Ro 4 3 1

23 What is sin 550 equivalent to A sin 80 B sin 10 C sin 10 OD sin 80

19 Which of the following is the correct graph of the angle 128 in standard position A B C D 128 128 t 128 128

17 Which of the following is the correct graph of the angle 305 in standard position A OB O C D 305 305 305 305

25 What is sec 246 equivalent to O A OB sec 24 C sec 66 sec 66 OD sec 24

24 sin 550 OA 9848 OB 9848 OC 1736 OO D 1736

21 What is tan 212 equivalent to OA tan 32 B tan 58 C tan 32 D tan 58

20 What is the measure of the reference angle of 128 OA 52 B 232 O C 38 D 128

14 Find the following function value to four significant figures cot 8 13 A 6 885 OB 6 925 O C 6 910 D 6 869

18 What is the measure of the reference angle of 305 A 55 B 35 C 65 D 25

Which of the following transformations appears to be a trans O

5 In right triangle ABC AC 17 AB 7 Determir the length of BC in simplest radical form a 4 15 b 60 2 30

4 In the diagram below MR 8 Determine the length of NM and RN R 60

2 In right triangle ABC below AC 9 What is the length of AB a 4 5 b 3 3 c 6 3 d 18 A 60 B

1 Simplify the following expressions a 10 x 3 b 2 2 x 3 C 3

7 A B C In the figure above what is the value of x 2 6 6 6 2 2 3 45 X

write a sytem of linear equations that fits the desrciption the solution of the sytem is a point on the line y 9x 1

In the xy plane the point 2 6 lies on the graph of the function g x 2x kx 18 What is the value of k

A rectangular container with a base that measures 10 feet by 10 feet is filled with jelly beans The container is divided into regions each with the same height as the container and a square base with sides that measure 1 foot each Sherman randomly selects ten of these regions and counts the number of blue jelly beans in each region The results are shown in the table below Region Blue Jelly Beans I 20 II 21 III 27 IV 31 V 19 Region VI VII VIII IX X A 25 000 B 2 500 C 250 D 25 Blue Jelly Beans 22 25 24 28 23 Which of the following is a reasonable approximation of the number of blue jelly beans in the entire container

26 F X O bea G In the circle above the length of arc FXG is 14 If FG is a chord that passes through the circle s center O what is the length of the segment XO A 7 B 14 C 28 D 56

20 Mass kg 60 000 55 000 50 000 45 000 40 000 Volume versus Mass 10 10 5 11 11 5 12 11 11 5 12 Volume m 12 5 13 13 5 14 Selin weighs 14 different objects of similar density The scatterplot shown above shows the volume of ea object and the corresponding weight of each object The line of best fit for the data is shown above For object that had a volume of 11 5 m the actual mas was about how many kilograms more than the ma predicted by the line of best fit A 1 000 B 2 000 C 3 000 D 4 000

21 Jessica owns a store that sells only laptops and Last week her store sold 90 laptops and 210 tal This week the sales in number of units of lap increased by 50 percent and the sales in numb of units of tablets increased by 30 percent By percentage did total sales in units in Jessica s increase A 20 percent B 25 percent C 36 percent D 80 percent

In order to determine the effect that caffeinated beverage C would have on sleep researchers conducted a study From a large population of people without sleep disorders 500 subjects were randomly selected Half the subjects were randomly selected to consume beverage C and the rest did not consume beverage C The results of the study showed that the subjects who consumed beverage C slept less than those who did not consume beverage C Based on the design and results of the study which of the following statements is the best conclusion A Beverage C will cause more loss in sleep than all other caffeinated beverages B Beverage C will cause a substantial loss in sleep C Beverage C is likely to reduce the amount of sleep of people without sleep disorders D Beverage C will reduce sleep of anyone who consumes it The sum of four numbers is 1 764 One of the numbers n is 40 more than the sum of the other hree numbers What is the value of n 287 0735 1 029

8 What is the slope of the line in the xy plane that 8 passes through the points 5 and 1 3 A B C N AIW WIA N D 2

When function h is graphed in the xy plane it has x intercepts at 4 2 and 4 Which of the following could define h A h x x 4 x 2 x 4 B h x x 4 x 2 x 4 C h x x 4 x 2 D h x x 2 x 4

David has a mobile data plan for which the monthly fee is 20 00 and the data usage fee is 2 50 per gigabyte Which of the following functions expresses David s cost in dollars for a month in which he uses g gigabytes of data A fig 22 50g B f g 20g 2 50 C f g 20 250g D f g 20 2 50g BER 3 In order to must be a Jim can c believes t ups each number complete A 7y B 7y C 14y D 14

Question 5 1 point Which transformation would take Figure A to Figure B a b d 40 9 A b 5 4 1 3 4 Rotation of 90 degrees clockwise Reflection over y x Rotation of 180 degrees Rotation of 270 degrees clockwise B

1 In the diagram below MN 5 Determine the length of LM and LN N 30 60 JM

In the diagram ATEC AZRH Find the value of x 30 T 25 Answer A 34 B 33 C 28 X AR 24 C Z 28 20 H

Consider the 2 implicitly defined curves and 5x 2y x xy 0 3 2x 5y y xy 0 Plot these 2 functions on the same graph Notice that it appears as though they intersect at a right angle at the origin For this discussion post you will figure out using Calculus whether or not these 2 functions actually intersect at a right angle You do not need to include a graph in your post but you must explain your answer fully

Graph the equation using the x and y interce x y 7

A newspaper offers delivery for up to a 40 mile radius of their location If this is represented on a graph with the newspaper located at the coordinates 0 0 what is the equation that represents the delivery area Select one a x y 6400 b x y 1600 c x y 1600 O d x2 y 6400