Quadratic equations Questions and Answers

Use a graphing calculator to approximate the partition numbers of f x Then solve the inequalities A f x 0 and B f x 0 f x x 6x 3x 7 What are the partition number s of f x Type an integer or decimal rounded to four decimal places as needed Use a comma to separate answers as needed

A department store wants to send codes for 15 off a 75 purchase to the subscribers of its e mail list The coupon code will have three letters followed by one digit followed by one letter The letters P Q and R will not be used So there are 23 letters and 10 digits that will be used Assume that the letters can be repeated How many such coupon codes can be generated

The sides of a triangle ABC are AB 15 cm BC 18 cm and CA 24 cm Determine the distance from the point of intersection of the angular bisectors to the line AB in cm

Kylie walked for 2 1 2 hours at a rate that varied between 3 and 4 miles per hour Of the following which is NOT a possible number of miles that she could have walked during that time period

Fule to solve the system 6x 6y 12 If there is a solution write your answer in the format x y option will display any text boxes needed to complete your answer O No Solution O One Solution Solution Set Ofinitely Many Solutions ER

nk by performing the indicated elementary row operation s 1 1 2 8 1 8 11 4 8 10 5 10 R R 2R1 R3

1 Students Faculty Administrators T TOTAL Importance of Interacting With People via Social Media Very Important 64 16 9 89 Somewhat Important 84 30 5 14 128 X Not Important TOTAL 52 200 34 17 103 80 40 320 Given that a participant said social media is somewhat important what is the probability the participant is an administrator You can draw on the table to show your thinking F Submit

T iles ke iles 5 Like Skateboards 80 45 8 125 S Do Not Like Skateboards 25 10 35 Totals 105 55 X 160 Mothlins com In general two events A nu b P A P A B Use this definition to verify if liking snowmobiles and liking skateboards are independent events for the people in the table given Yes They are independent events No They are not independent events

2 To make toy trucks Babyco Corporation s variable costs were 800 000 and their fixed costs were 4 per truck How many trucks must be sold at 20 each to break even

Find an equation for the hyperbola described Graph the equation Center at 1 1 focus at 10 1 vertex at 2 1 Write an equation for the hyperbola 0 0 1 Type exact answers for each term using fractions as needed Select the graph which correctly describes the hyperbola O A B G G F 16

9 7 mm GIT TEST All work must be shown on this page for full credit 17 Find the volume of the figure below 3 mm 7 2 mm 9 14 A 52 38 mm B 70 2 mm C 84 5 mm D 104 76 mm h

Graph Label identify at least four points with integer coordinates on the graph 19 f x 3 x 7 5 8 7 6 5 7 wo 8 99 W A 6 1 7 was tw 00 Q 4 5 n 7

Solve the following inequality 4x 15 x 6 Give your answer in interval notation For example if you found a 20 y you would enter 20

Solve the following absolute value inequality Select the correct answer below O 5 2 O 2 5 O 5 U 2 00 O 2 U 5 00 2x 3 7

C 14 points Given the graph and the equation complete the table below Property 1 point each Opening Vertex Axis of Symmetry x intercept s y intercept s Domain Rang f x 2x 4 3 3 000 10 6 41 IN 2 4 6 8 10 3 6 9

Find the volume of the triangular prism b 12 ft 10 ft 14 ft

7 Find the area of the shaded region All work must be shown on this page for full credit 18 cm 5 14 4 A 34 77 cm B 40 24 cm C 88 56 cm D 106 75 cm

2 2 0 6 2 The graph of a cubic function is shown above

on this page for full credit 2 Find the area of the figure below 24 in 20 8 in 19 2 In 16 In A 832 in B 768 in C 416 in D 384 in HEL DE

Find the Surface Area of the rectangular prism 3 i Base 4 in Base 6 in Base 6 in Base 3 in

9 K 3 k 1 10k 4k 6 k 1 10k 4k 6 1 1 K 1 10K 4K 6

10 m 6 m 2 9m 18 9m 18 m 6 m 2 4m 18

Use interval notation to express the following The set of all numbers greater than 8 Select the correct answer below O 8 O 8 O 8 00 01 8 00

The graph below is of the form f x Acos Bx D Use the graph to answer the following questions a What is the amplitude of the function b What is the period of the function c What is the vertical shift of the function d What is the equation of the function a 2 1 0 1 n 4 3 n 1 3 4 3

3 ft 9 ft classlink The figure below is a net for a right rectangular prism Its surface area is 342 ft and the area of some of the faces are filled in below Find the area of the missing faces and the missing dimension 27 ft2 9 ft OER Project Home 36 ft2 2 9 ft A 27 ft2 A A 21ST century libr m HBO Max JThe Juice Daily Ju 9 ft 36 ft2 3 ft Infinit

36 Evaluate the expression without using calculator cx x R Sin II tan I CSc

7 In the hyperbola shown below one focus is at F1 2 12 and the other at F2 2 8 The points A 2 8 and B 2 4 lie on the graph of the hyperbola F 2 12 A 2 8 B 2 4 M F 2 8 13 12 11 10 9 8 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 7 6 5 4 3 2 2 5 6 5 6 7 8 9 10 11 12 13 14 Use the locus definition of a hyperbola and either point A or B to determine the differenc in the distance from any point on this hyperba to each foci Difference

Use vectors to find the interior angles in degrees of the triangle with the given vertices Round your answers to two decimal places 2 4 3 8 6 4 smallest value largest valu

Identify the vertex and axis of symmetry of each Then sketch the graph 3 y x 5 4 y x 6

4 Prove the identity sin x cos x cot x tan t

Given the graph below provide the requested information 12 8 4 Requested info Equation Domain Range Critical Point Increasing 12 8 4 4 8 12 y 1 1 4 1 E E 8 12 x

Write the transformed equation of the parent functions shown below keep it simple f x h x 6 3 3 g x j x 3 6 3

Find A B and C for the partial decomposition 2x x 2 x 1 x 4 A Bx C x 4 x 1

2 A batter hit a baseball whose height in feet can be modeled by the function h t 161 641 3 where t is the time in seconds Construct a table of values to graph the function and answer the questions below Ke F 3 S 6431 3 3 S O 1 2 From the table and or graph a Find the maximum height of the baseball 64m b Find the time it takes the baseball to reach its maximum height 2 minuits

From the table and or graph a Find the maximum height of the golf ball b Find the time it takes the golf ball to reach its maximum height c How long does it take the golf ball to return to the ground

Assume that acid rain has lowered the pH of a particular lake to pH 5 0 What is the hydroxide ion concentration of this lake O 5 0 x 105 mol of hydroxide ions per liter of lake water O 1 x 105 mol of hydroxide ions per liter of lake water O 1 x 109 mol of hydroxide ions per liter of lake water O 5 0 M hydroxide ion

2 A scientist records the motion of a dolphin as it jumps from the water The function below models the height feet above the water after 1 seconds h t 16x 32t y a Find the axis of symmetry b Graph the function from 0 t 2 with a scale of 0 5 seconds X Y c What is the maximum height of the dolphin

In a piggy bank the numer of nickels is 8 nore than one half the number of quarters The value of the coins is 21 85

When y e x 2 y Thus in terms of x 2y y Need Help 2 Points Read It y e x 2 Viewing Saved Work Revert to Last Response DETAILS ZILLDIFFEQ9 1 1 013 Verify that the indicated function is an explicit solution of the given differential equation Assume an appropriate interval I of definition for each solution y 8y 25y 0 y ex cos 3x When y ex cos 3x y

WXY is a rectangle Select the statements used to prove that its diagonals are congruent Select two Y V N AWWY AWXY by the side angle side criterion AVWY AWVX by the side angle side criterion Opposite sides of a parallelogram are congruent Adjacent sides of a parallelogram are congruent AWWY AVWX by the angle side angle criterion X W

1 point Given m A 61 a 16 b 17 Find m B First answer not a triangle not a triangle Secon

13 Consider y y 3 cos T 2 4 a What is the period of this function b What is the vertical shift of this function c What is the horizontal shift of this function left right up down

72K A A 2 is the period 2 The equation of the graph is of the form f x Asin Bx C D where A B C and D are real numbers 1 A is the amplitude 360 2 B 3 y D is the midline 4 D is the vertical shift A 2T Using the above information write the positive values for A B C and D

5 Graph y 2 cos z 2 To make sure you get the correct graph use the following steps Step 1 Choose the correct graphing choice Step 2 Plot a point at the midline Step 3 Plot a point at either the max or the min POINT 4R 7 72 2 k SEGMENT 71 A COS 3T 5 2T 77 2 312 E 70 SIN 75 70 2 0 2 TAN FI2 71 312 T 2 27 532 2 3T 7 72 2 k 4T 72 9 2 5T

12 What is the phase shift represented by in the function below f x cos x T B 2T 2 77 k

7 Which equation is graphed in the diagram below Ay 2 sin x 2 3 y 2 sin x 7 2 2 y 2 sin x 2 2 75 62 WZ 312

Analyze the equation to determine the features of the graph of the function y 2 sin 2x 3 Amplitude Period 2 IT It 4rt 5 201 Vertical Shift

Solve the quadratic equation by completing the square k 14k 41 19 Give the equation after completing the square but before taking the square root Your answer should look like k a b The equation is Give all solutions to the equation including any non real solutions The solutions are k

8 John wants to measure the heigh exactly 100 feet from the base of the tree and looks up The angle from the ground to the top of the tree is 33 How tall is the tree 10 Kelly is flying a kite to which the angle of elevation is 70 The string on the kite is 65 meters long How far is the kite above the ground

7 A man is in a boat that is floating 175 feet from the base of a 200 foot cliff What is the angle of depression between the cliff and the boat 9 The flagpole in front of CB East casts a shadow 40 feet long when the measurement of the angle of elevation to the sun is 31 How tall is the flagpole