Coordinate system Questions and Answers

An experiment starts with four cards which are numbered 1 4 6 and 9 respectively One card is chosen at random State the probability that it is the card numbered 9 Select one a 1 3 b 1 2 c 1 4 d 1 8

A bag contains 6 red marbles 3 blue marbles and 7 green marbles If a marble is randomly selected from the bag what is the probability that it is blue or red Select one a 18 16 b 1 2 c 9 16 d 1 3

A sample space consists of 80 separate events that are equally likely What is the probability of each Select one O a 1 b 0 c 1 80 d 80

A car assembly line has a 70 yield meaning that 70 of the cars are good and 30 are defective If three cars are randomly selected find the probability that all of them are acceptable Select one a 0 49 Ob 0 343 OC 0 7 Od 0 349

In how many ways can Jake Claire and Ryan arrange themselves in a line Select one a 3x2x1 Ob 2x1 c 2x2x2 d 3x1

Janie has to take a test which consists of 4 true or false questions In how many possible ways can she answer all the questions if she is totally guessing Select one O a 2x2x2x2 Ob 4x2 Oc 2x2 d 2x2x2x2x2

In how many ways can 9 different books be arranged on a shelf Select one O a 3 628 800 b 36 288 Oc 362 880 d 362 800

For the points P and Q find the coordinates of the P 7 9 Q 3 2 OA 5 17 OB 4 7 OC C 2 7 OD 10 11

1 Write the equation of the circle in standard form Then identify the center radius and graph a x y 6x 2y 6 0 b x y 22x 6y 129 0 c x y 22x 4 0 d x y214x 49 0 2 a Given that 3 5 and t is in the quadrant IV find the other function value 1 cost sin b Given that 3 and c Given that cot 2 and is in the quadrant III find the other function value is in the quadrant IV find the other function value d Given that tant 5 and tis in the quadrant I find the other function value

8 4 Round to the nearest hundredth

Rewrite the vector components in using the unit vector form 12 4 12 4

Solve for a Q 12 sin30 sin115 Select one a 24 6 Ob 24 c 6 6 d 21 8

Find the measure of the each angle to the nearest degree cos 112

When graphing the polar equation r 3 cos 20 as 0 moves from to r the radius changes from quadrant to and the graph is

Gien polynomial is below h x x 19x 30 a 5 is a zero Find all zeros of the polynomial Enter your answers as a comma separated list If an answer does not exist enter DNE XM b Write the polynomial as the product of linear factors

Select the region you wish to be shaded O the union of the individual solution sets O the intersection of the individual solution sets PO 5 1 HOL 10

Consider the following equation 2y2 3 2 2x Step 2 of 2 Find the equation of the line which passes through the point 10 5 and is parallel to the given line Express your answer in slope intercept form Simplify your answer Answer 4 Points Keypad Keyboard Shortcu

The point Com in the graph below represents 1 O

Which polar equation below is the graph of TT 5 5TT 6 7 TT 6 Select one 2TT 3 4T 3 a r sin 40 cos Ob r sin 50 cos 60 c none of these Od r sin 30 cos 30 5 5 TT 2 3TT 2 TT 3 5TT 3 TT 6 11TT 6 0 5

0 S 3 Select one O a x2 3 y2 5 1 O b x2 9 y2 5 1 O c x2 3 y2 5 1 O d x2 9 y2 5 1 88 ap

Choose the equation that matches the graph 5 Select one 10 x a x 1 y 4 4 b x 1 y 4 16 Oc x 1 y 4 16 Od x 1 y 4 16

When the inverse function exists we can sketch a graph by switching the roles of x and y For every point on the graph swap the x and y values Another way of describing this transformation is to reflect the graph over the line Example In the graph below is shown in black is shown in red and is shown in blue Line graph with f x black line its inverse red line and y x blue line all intersecting at 4 4 Question Choose the graph of the inverse function Hint The line is drawn in blue in the answer choices Half a parabola with the points starting 6 0 intersecting 2 2 ending 6 3point5

Write the tangent ratios for ZY and ZZ 7 Z XO a Select one b C 4 d 65 Y tan Y tan Y tan Y 7 4 65 7 tan Z tan Z 4 tan Y tan Z 7 65 4 7 4 tan Z 65 4 4 65

Determine the leading coefficient for the rational y 10 8 3 6 8 10

3 3 43 3 3 a 10 pts Find the matrices A6 and A8 A 2 b 10 pts Use the matrices found in part 1 to find A 4 Question 3 20 points Let A be a 2 x 2 matrix

Question 9 0 1 pt100 99 Details 31 A pilot is flying over a straight highway He determines the angles of depression to two mileposts 5 3 mi apart to be 31 and 45 as shown in the figure 5 3 mi 450 A B NOTE The picture is NOT drawn to scale Find the distance of the plane from point A distance from A mi Find the elevation of the plane height mi Enter your answer as a number your answer should be accurate to 2 decimal places Question Help Worked Example 1

In the circle below suppose m VUX 204 and mZUVW 95 Find the following a mZVUX b m ZUXW ZVUX 0 ZUXW

Which of these is an equation of one of the asymptotes of the function f x 7 sec X x X X x 32 8 2 1 2 4 sec 1 2 xXx 1 x 4 None of the above

Complete each proof 18 Given 3 2x 7 29 4x Prove x 4 Statements Reasons

1 point Given the function f x 3x 4x 1 find the following a the average rate of change of f on 2 6 b the average rate of change of f on x x h

Use the following problem to answer questions 48 50 Find the dilation image AA B C of AABC with center at the origin 1 and k 48 A a 1 2 b 9 18 c 18 9 d 2 1 49 B a 0 1 b 9 0 c 1 0 d 0 9 50 C a 18 0 b 2 0 c 0 18 d 0 2

Find the central angle which subtends an arc of length 2 centimeters of a circle of radius 12 centimete 0 radians Type on intogor

Sketch a graph of y 2 7 6 5 4 3 Clear All Draw 6 54321 4 5 6 7 x 1 4 1 1 2 3 4 5 6 7 no XX

1 2 3 Graph the function h x 2x 1 4 5 6 X

Set A is the set of factors of 24 set B is the set of even natural numbers less than 25 and set C is t set of even natural numbers less than 13 The universal set U is the set of natural numbers less than 24 Use the sets given below to answer questions a g A 1 2 3 4 6 8 12 24 B 2 4 6 8 10 12 14 16 18 20 22 24 C 2 4 6 8 10 12 U 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 What is An B

Use the complement of calculate the indicated probabilities One pile of cards contains the number 2 through 6 in red hearts A second pile of cards contains the numbers 4 through 8 in black spades Each pile of cards has been randomly shuffled If one card from each pile is chosen at the same time what is the probability that the sum will be less than 12

If the radius of a circle is 6 Inches then the area of a sector bounded by a 100 arc is Round the answer to the nearest tenth of a square Inch square inches

Graph the hyperbola x 4y 6x 24y 63 0 12 4 124 0 a 9 S 4 NO 10 2 2 12 23 41 4 14 OX X V

V Find an equation of the line L The equation is Tyne an equation Simplify your answer

points A supplier is late with a delivery which has caused a delay in completion of Derek and Addison s project In which part of their project status report would Derek and Addison discuss this Problems encountered Project overview Impact on budget The delay should not be mentioned

Multiple Concept Example 9 deals with the concepts that are important in this problem A grasshopper makes four jumps The displacement vectors are 1 33 0 cm due west 2 28 0 cm 44 0 south of west 3 20 0 cm 63 0 south of east and 4 23 0 cm 60 0 north of east Find a the magnitude and b direction of the resultant displacement Express the direction as a positive angle with respect to due west a Number i b Number i 72 73 8 Units Units TA 0 7 W Start N S E

Show that the equation sin x X x 0 has a solution Provide all the necessary ju

A Bolat leaves a port traveling due east at 12 mi hr At the same time another boat leaves the same port traveling northeast at 15 mi hr The angle of the line between the boals is measured relative to due north see the figure to the right What is the rate of change of this angle 30 min after the boats leave the port 3 hr after the boats leave the port Purt Let x be the distance from the port to the eastbound boat and let z be the distance from the port to the northeast bound boat Write an equation relating x z and 2 2 x Z 2 tan 2 Type an exact answer Type any angle measures in radians The rate of change of this angle 30 min after the boats leave the port is Round to the nearest thousandth as needed 15 mih 12 mih

A circle with a diameter of 10 cm and a central angle of 30 is drawn below 10 cm 30 What is the area to the nearest tenth of a square centimeter of the sector formed by the 30 angle 1 5 2 2 6 5 3 13 1 4 26 2

Find the area of the sector created below Round to the nearest tenth 120 4 cm B

3 A ball is rolling in a circular path that has a radius of 10 inches as shown in the accompanying diagram What distance has the ball rolled when the subtended arc is 54 F Express your answer to the nearest hundredth of an inch 10 in 54

ect the correct answer from each drop down menu BC has vertices at A 11 6 B 5 6 and C 5 17 YZ has vertices at X 10 5 Y 12 2 and Z 4 15 NO has vertices at M 9 4 N 3 4 and O 3 15 KL has vertices at J 17 2 K 12 2 and L 12 7 PQR has vertices at P 12 3 Q 12 2 and R 3 2 can be shown to be congruent by a sequence of reflections and transl can be shown to be congruent by a single rotation

solve the following equation for 0 where 0 0 180degree sec 20 3degree csc 20 51degree

1 Use the parallelogram to answer each of the following questions a Find the height 5

2 A man who is 6 feet tall stands in front of a flagpole His shadow is 10 feet long and the distance from the flagpole to the tip of his shadow is 85 ft How tall is the flagpole 6 ft ft