Geometry Questions

Linear Equations When a new charter school opened in 1993 there were 440 students enrolled Write a formula for the equation N representing the number of students attending this charter school t years after 1993 assuming that the student population Increased by 36 students per year Decreased by 24 students per year Increased by 20 students every 2 years Decreased by 40 students every 4 years Remained constant did not change Increased by 5 students every semester twice each year N N N N N N II

Watch help video Find the volume of the right cone below Round your answer to the nearest tenth if necessary 25 18

A jewelry store buys small boxes in which to wrap items that they sell The diagram below shows one of the boxes Find the lateral area and the surface area of the box to the nearest whole number 1 66 cm O 14 cm 70 cm 266 cm O 35 cm Not drawn to scale 2 2 35 cm 364 cm O 35 cm 35 cm 266 cm 2 2 O 70 cm 364 cm 2 2 7 cm

Type the correct answer in the box 5 cm 5 cm 12 cm A rectangular prism has a height of 12 centimeters and a square base with sides measuring 5 centimeters A pyramid with the same base and half the height of the prism is placed inside the prism as shown in the figure The volume of the space outside the pyramid but inside the prism is cubic centimeters

Complete the table below Equation y 5x 4 y 8 7t y 2a y 6 Rate of Change Initial Value Behavior Select an answer Select an answer Select an answer Select an answer

Match each statement with its symbolic notation G A q P B pq C pv q D p q E q p F p q G 4 Conjunction 5 Disjunction 6 Conditional 7 Inverse 8 Converse 9 Contrapositive 10 Riconditional n a

Draw the image of this rotation using the interactive graph The direction of a rotation by a positive angle is counter clockwise 9 8 7 6 5 4 3 2 T 9 8 7 6 art 5 Y 4 43 3 2 1 2 3 4 5 6 7 8 x 1 2 3 4 5 6 7 8 9 V

someone explain Look at the diagram below J K N question JK and MN will be dilated by a scale factor of 1 25 centered at point J to create J K and M N respectively Select all of the true statements M N will be the same line as MN M N will be parallel to MN but they will not be the same line J K will be parallel to JK but they will not be the same line

Find the area The figure is not drawn to scale 40 in O 138 in 2 2 O 69 in O 1440 in 2 O 1188 in 2 36 in 33 in

2 In the accompanying diagram tangent PA and secant PBC are drawn to circle O If mADC is twice mAB and m P is 50 what is mAB C 0 A 50 P

Find the lateral area of the cone to the nearest whole number 40 m 60 m Not drawn to scale O 3770 m 2 O 7540 m O 4712 m

When a new charter school opened in 2002 there were 290 students enrolled Write a formula for the equation N representing the number of students attending this charter school t years after 2002 assuming that the student population Increased by 40 students per year Decreased by 28 students per year Increased by 48 students every 2 years Decreased by 44 students every 4 years Remained constant did not change Increased by 5 students every semester twice each year N N N N N N

What are the minor arcs of 00 H L OJK and LH J HJ and KL K HJ HK JK JL KL and LH HJ JK KL and LH

Find the surface area of the cone in terms of 60 cm Not drawn to scale 2 111 cm 55 5 cm 2 3 2 O 57 cm R 17 cm 2 3 cm

Find the area of the rhombus 9 m 6561 m O 162 m O 13 5 m 40 5 m 9 m 9 m 9 m

The trapezoids are similar The area of the smaller trapezoid is 709 m Find the area of the larger trapezoid to the nearest whole number 27 m Not drawn to scale O 1521 m 11 m O 729 m 39 m C

b B M D C a In the above diagram OA a and OB b C lies on 04 where OC the midpoint of AB BC and OD intersect at M i Express the following vectors in terms of a and b A AD B OM Hence evaluate BM MC OA D is 3 marks 3 marks 4 marks

The volume of the rectangular pyramid below is 120 units Find the value of x X 9 4

Identify a semicircle that contains C A O ABC CB 0 B

C Directions Complete the two column proof 10 15 Given A LMN where IM IN MN Prove MN IN IM MN LM IN ZM IN MN 1 2 3 Statements 1 2 3 N Reasons

y y Use linear regression to find the equation for the linear function that best fits this data Round to two decimal places Hint 876 1407 2237 3454 5545 8731

Are the triangles similar How do you know 30 4 84 6 O no O yes by SSS O yes by AA O yes by SAS 84 6

The polygons are similar but not necessarily drawn to scale Find the value of x A 5x B 4 C 04 O 20 5 01 D

iven the three statements below identify which represent exponential equations 1 The cost of living allowance for state employees increases salaries by 3 1 each year 2 The value of an investment is increasing by 300 each year 3 Tuition costs have increased by 2 8 each year for the last 3 years ooking at the following two equations that represent the balance in two different avings accounts which account is growing faster and which account will have a higher balance after 3 years A 1 000 1 05 t B 900 1 075 t Complete the table The first one has been done for you Equation Initial Value y 615 0 79 y 500 1 03 y 3 200 1 2 y 19 611 0 98 615 50 Growth or Decay Decay Growth Rate as a 21 12

Find the area of the circle Leave your answer in terms of 4 1 m 2 4 2025 m 8 405 m O 11 2 m 16 81 m

4 y you 44 y 0 1 y 0 0 y 0 2 e

Gumball A gumball has a radius that is 25 mm The radius of the gumball s spherical hollow core is 21 mm What is the volume of the gumball if you do not include its hollow core Answer stion Help Read Viden mm Use 3 14 or the key on your calculator Round your answer to the nearest tenth if necessary

Find the volume of the cone 12 cm r 8 cm V cm

Use the Law of Cosines to determine the indicated side x Assume b 14 and c 18 Round your answer to one decimal place C b c a Step 1 The Law of Cosines states that for the triangle ABC with sides a b and c b 108 a 18 x 14 B 324 196 In the given triangle you know sides b and c and angle A and need to find a So you can rewrite this formula a c b 6 cos A Step 2 Substitute known values into the alternate form of the Law of Cosines Round your answer to three decimal places a 2 b 2ab cos A 2 2 2ab 28 14 2bc cos C 1 18 cos 108 1x cos 108

What is the solution of each proportion D 5 A 120 10 10 C bo B 5 Not drawn to scale N 3 12 M 120 1 2 O ABCD KIMN 10 1 2 1 2 The polygons are not similar O ABCD NKLM 5 3 12 O ABCD KIMN 5 1 2 K 3 12 L

Which theorem or postulate proves the two triangles are similar 20 19 7615 Not drawn to scale O SA Postulate O SSS Theorem OAA Postulate 16

What is the value of x x 5 O 10 O 7 5 O 2 5 X 2 x 1

What similarity statement can you write relating the three triangles in the diagram T U V ATWV AVUW AUWT O AWUT AVUW AWVT O AUVW AUWT AWVT O AUVW AWUT AWVT

Segment BD bisects segment AC Solve for x Round to the nearest tenth if necessary Image not necessarily to scale A 20 Answer p 8 B D 17 X

Qu GivensABC A B C midpoint of the sives respectively let O the perpendicular from it onto L M B a let feet of the onto bisects 6 Compute the angle between OmJ 13 c P be the BC CA ond var be the foot of BC be the respective perpendiculars from D C A A B prove that ADJ 28 12 3 U LM

5 In the accompanying diagram of quadrilateral QRST LRST SRLQR and ST 1QT Prove QR QR QT QT is the angle bisector of R T S

Which trigonometric statement is NOT an identity Select one a cse 0 1 cot 0 b 1 cos sin 0 c 1 sin 0 cos 0 Od 1 tan 0 sec 0

Solve each equation to the nearest tenth Use the given restriction tan 1 4 for 180 270

7 10 points Given ui 5j and v 3i 4j find i the dot product u ii 2u 3v

rom what you learned about radians which circle best represents how radians are meas elect one a O b OC 66 42 44 41 41 a 44 SA a 41 44

Choose the statement that is NOT true Select one Oa As B gets larger the period gets smaller and frequency becomes greater O b The period and the frequency vary indirectly OC The red graph is y sin x The phase shift for the blue graph is 1 2 1 Od The vertical phase shift of y 3sin 5x T 6 is 5

Use an addition or subtraction formula to find the ex sin 67T 44 COS 3T 11 COS 67T 44 sin 3 T 11

ividing sin 0 cos20 1 by yields 1 cot csc

Find all the values of arcsin 3 Select one or more 0 0 a 3 b 5 C KM 0 e f d 7 g 3 5n 6 6 2x 3 4 3 11x 6

The angle 810 rotate clockwise counter clockwise full time s around the origin and is radians

Simplify the following Hint Use the unit circle sin 5m 3 Select one O a 1 2 Ob undefined OC 3 2 d 3 2

Which trig functions are equal to Select one or more 3A a tan 32 b sin st C cos d cos e sin 11 it 16

2 1 9 8 7 6 5 4 3 2 10 1 2 3 U 5 6 1 2 3 4 5 6 7 8 9 R S What are the coordinates of Point S after a dilation with the center at the origin and a scale factor of 2 1 8 4 O 2 1 O 16 8 4 2

Consider the following figure b mz1 P c m 2 N Given Q Find the following in degrees a m MRP M O T V In OQ PR contains Q MR is a tangent mMP 116 mMN 60 and mMT 46 R

Use the graph of the function f x to answer the questions below 6 4 2 6 4 2 2 4 12 4 6 a On what interval s is f x increasing If necessary you should use the union symbol U to indicate that f x is increasing on multiple intervals b What is the local minimum of f x Enter your answer as an ordered pair c What is the local maximum of f x Enter your answer as an ordered pair