Vectors Questions and Answers

10 Which theorem compares two sides and the included angle of two triangles F Hinge Theorem G Converse of the Hinge Theorem H Exterior Angle Inequality Theorem I Triangle Inequality Theorem

he blade of a creu r saw rotales at a rate of 4000 revolubons per minute What is the inear velocity in miles per hour of a point on on the 5p of the outer edpe of a 7 t 4 inch diameter blade The linear velocily as approximately triles per hour Round to the at tanth ded 7

Right triangle ABC is shown A 3 m G 50 C a B Which equation can be used to solve for c sin 50 3 sin 50 O cos 50 O cos 50

Copy vectors u v and w head to tail as needed to sketch the indicated vectors a u v b u v w C U V d u w Choose the correct sketch for u v OA OB 4 Q O C Q W Q OD

Find an equation of the hyperbola having foci at 6 1 and 10 1 and vertices at 7 1 and 9 1 0

The number of cars waiting at a bank for 60 minutes is as follows Cars Frequency 0 2 1 9 2 3 4 16 12 8 P 5 5 6 Find the probability of 5 cars waiting in line Probability 6 7 8 4 2 1

Find a vector equation and parametric equations for the line Use the parameter t the line through the point 4 6 1 and perpendicular to the plane 2x 4y 4z r t x t y t z t

What is the value of x in Clue 11 Enter the numeric value for x only rounded to the nearest tenth 6x 15 4x

Warm Up 3 Area of Regular Polygons Words to Know polygon radius of a regular polygon in a plane a closed figure formed from three or more line segments such that each segment exactly two other segments one at each and no segments with a common endpoint are collinear a segment that extends from the regular polygon to a of the polygon a polygon that is both equiangular and

4 Solve for the values of x y and z yx N 76

Find the area of a circle with a diameter of 14 meters Round your answer to the nearest hundredth of a square meter The area of the circle is about square meters

7 Convert to fractions 23 0 330 700

Question 16 Points 1 Quadrilateral ABCD is reflected over y axis Which of the following is true about the quadrilaterals 2 B 1 1 A DE 4 0 D AO 1 Quadrilaterals are similar B D Quadrilaterals are congruent None of the choices To C Quadrilaterals are not congruent

The number on the red die is 3 Select one a 1 4 b 1 6 O c 1 2 Od 1 3 8 7 6 91 5 Select one What is the probability of spinning an odd number or a number greater than 7 C 63 79 2 3 a 13 b 1 2 333 d 8 3

Given the vector with magnitude 15 and directional angle 120 Write the vector in unit vector form

Choose the correct vector Select one O a O b O C 2 5 2 8

Let 2 1 1 B 1 2 3 A 0 02 2 13 2 points Part c 6 points Part d Evaluate each of the following if possible If it is not possible justify your answer Show all your work 4 points Part a Evaluate CD 3AT 3 points Part b Evaluate Evaluate DB Evaluate 8E tr CD I C 2 D 2 1 1 E 3 E 2 6 BC 4 2

gths 4 Will be used later as a theorem In triangle ABC let D be a point on BC and let E be a point on AD Prove that Let ABE ACE BD CD ABD U ACD V PBD u PCD v BD CD ABP x ACP y a Which theorem states that U V t t V t t b Conclude that Uv uV i e u x v u v y Then conclude the desired poult

6 Jan wants to move to one of the towns below He wants to live in the one that has less people around him Which town should he move to Why 18 000 6 miles 24 000 8 miles

1 SAT Question The density d of an object is found by dividing the mass m of the object by its volume V Which of the following equations give the mass m in terms of d and V a m dv b C d m DID m V d m V d

B 57 A C BL is tangent to the circle centered at A Find the measure of angle BCA Explain or show your reasoning

34 1 point A student wants to write an expression for all of the elements which are in set A AND all of the elements in set B Which expression below matches the statement AUB ANB P ANB AUB

3 1 point WJC JFK WHT HH BHO RMN DDE WGH C HCH GWB JEC LBJ FDR RWR GHB GRF HST If a student represented by initials was chosen at random find P HHIC P HH C 1 2 P HHIC 2 5 P HHIC 3 5 P HHIC 9 16

y 2 x find the value of y elect one a 1 4x b 4x C 22x d 24x

A regular heptagon has a radius of approximately 27 87 cm and the length of each side is 24 18 cm What is the approximate area of the heptagon rounded to the nearest whole number Recall that a heptagon is a polygon with 7 sides O 1 173 cm O2 125 cm O2 359 cm D

1 Draw an SVAJ diagram 2 Find the coordinates of Q at q p 2 p and 3p 2 However Rb 1m W S 0 0 1 2 YA Rb base circle sin 20 S 0 2 2 0 1 2 sin 20 Efl m

Can you explain by detail how to find modulo inverse by using euclidean algorithm Find the value of 3 mod 43

point Suppose nd an invertible matrix P and a diagonal matrix D so that A 16 9 30 17 PDP Use your answer to find an expression for A7 in terms of P a power of D and P 1 in that order A

Let ABCD be the trapezoid below You are given that D a AB 6 and DC 26 as demonstrated in the diagram The point E is the midpoint of AC and the point F is the midpoint of BC The midpoint of a line segment is as the name suggests the middle point between the two ends of the line segment B 6 A D E 26 F C a Write each of the vectors DB A and BC as a linear combination of a and 6 b Show that EF is parallel to DC

1 Students from River City High School were randomly selected and asked How many siblings do you have The results are recorded below 0 2 0 2 0 2 0 3 1 3 a Make dot plot of the data set 1 4 1 5 1 5 1 6 1 6 1 7 1 8 1 9 1 10 2 12 b Describe the distribution shape center spread outliers of the number of siblings of students at River City HS

Suppose you form 5 letter strings from the letters C O M P U T I N and G What are the number of permutations as a ratio of factorials

5 An 18 inch tall cone has a volume of 2167 in What is the radius of this cone C 16 in A 18 in B 12 in D 6 in

Make a table to determine the sample space for the sum of rolling 2 dice Die 2 SUM 1 2 3 4 5 6 1 2 1 What is the size of the sample space 2 How many ways can you roll a 5 3 What is the probability of rolling a 5 3 Die 1 4 5 6

Name Line Line Segment Ray May 18 8 44 19 PM Name the figure below in two different ways Symbol and

the diagram below a right circular cone has a diameter of 8 inches and a height of 12 inches 8 inches H 1 201 2 481 12 inches What is the volume of the cone to the nearest cubic inch 3 603 4 804

Lines I and m are parallel lines cut by the transversal line t Which THREE angles are congruent to 5 x A 41 x B x 28 C 22 4x D 1 2 3 4 5 6 7 8 24 m

0 420 28 0 2 0 48 3 Monica has 12 different flavors of coffee and is selecting which one she will drink each morning before work How many different ways can Monica choose a group of 5 flavors so that has a different flavor each day

Using the z score table the z score of corresponds to 32

12 Determine whether the triangles can be proved similar If they are similar write a similarity statement and explain how you know they are similar If they are not similar explain why 4 points each 1 3 4 Find the missing values Leave answers in simplified radical form 2 points each 3 8 45 t 2 45 4 9 3 f O 60

3 Q1 Review In the diagram below n l m and mz4 x 45 and m27 x 45 De possible values of the m27 m 7 8 4

A balloon has a circumference of 11 cm Use the circumference to approximate the surface area of the balloon to the nearest square centimeter Select one O a 39 cm O b 121 cm O c 380 cm d 154 cm

Find a plane containing the point 7 7 1 and the line x t 7 3 y t 8 3t and orthogonal to the plane 7x 7y z 1 z t 6 3t

1 What is the value of x if sin 60 cos x 10

Which is true regarding secants and chords O Chords intersect the perimeter of a circle at two points Secants intersect the perimeter of a circle once O Chords intersect the perimeter of a circle at one point Secants intersect the perimeter of a circle twice O Chords and secants intersect the perimeter of a circle twice Chords are segments entirely within a circle while secants are lines or rays that extend through a circle O Chords and secants intersect the perimeter of a circle twice Chords are lines or rays that extend through a circle while secants are segments entirely within a circle

How can the following theorem be useful If is the angle between aandb then a b lal 1b1 cos Select one or more O a This formula could be used to find the angle between two vectors by solving for Cos then using the inverse cos function to find the angle Ob This formula could be used to find the angle between two vectors by solving for Cos then using the law of cosines to find the angle OC This formula could be useful to find the magnitude of one of the vectors when the angle and dot product are known values Od This formula could be used to find one of the vectors when given the angle dot product and magnitude of each vector

4 1 8 Triangle ABC has vertices A 1 3 B 0 1 and C 4 0 Under a translation A the image point of A is located at 4 4 Under this same translation point C is located at

A n double napped hyperbola O circle parabola ellipse is a conic section formed when a plane intersects both nappes of a cone

Events M and N have probabilities such that P M 0 4 P N 0 28 P M U N 0 56 and P Mn N 0 12 Are event M and event N independent A Yes because P M P N P M U N B No because P M P N P Mn N C Yes because P M P N P M U N D No because P M P N P Mn N

Given set P 5 1 3 and set Q 4 2 1 2 3 What is Pn Q A 1 2 3 B 5 4 2 1 2 3 C 1 3 D do not have an intersection

Which point is on the circle centered at the origin with a radius of 5 units Distance formula x x V V O 2 21 O 2 23 O 2 1 O 2 3