Quadratic equations Questions and Answers

Question 3 25 points Planar Graphs Is the graph at the right planar Yes No It is not because it contains a K5 subgraph

Find the maximum value of the function z 3x 8y subject to the following constraints x23 y23 3x 4y 45 Note that the ALEKS graphing calculator can be used to make computations easier 8 08

2 f x log3 x 1 2 f x X Domain Range Asymptotes Graph 3 Use change of base formula to evaluate the function log3 7 4 Evaluate log 7343 5 Use the log properties to expand these funcitons x y a log2 5 b log3 3 7

Find the following matrix product if possible 3 1 8 3 9 1 OA 5 9 5 Select the correct choice below and if necessary fill in the answer box to complete your choice 3 1 8 3 9 1 5 9 5 B The product is not possible

Find k so that the line through 2 4 and k 1 is a parallel to 3x 2y 4 b perpendicular to 4x 3y 2 a k Type an integer or a simplified fraction b k Type an integer or a simplified fraction

Let A 3 4 6 10 12 B 3 4 8 12 C 4 8 12 D 3 8 E 6 and U 3 4 6 8 10 12 14 Which pairs of sets are disjoint Select all that apply A A and B E C and E 1 B and U C and D M B A and D F C and U J E and U N A and U C A and C G A and E K B and D O D and E D D and U H B and E L B and C P None of the sets are disjoint

Find the values of the variables H a 2 5z 1 7m 12k 5 N m 11 1 k 11 2 10a 11z 12m 0 10k 3 35 15 57 66 8 2

The shortest leg of a triangle is 7 meters shorter than the other leg The hypotenuse of this triangle is 17 meters What are the lengths of the two legs of this triangle The shortest leg is meters long The other leg is meters long

If the perimeter of a rectangle is 36 cm and the area is 72 square cm then what are the dimensions of the rectangle The width or shorter side is The length or longer side is cm cm

The length of a rectangle is 7 inches longer than it is wide If the area is 144 square inches what are the dimensions of the rectangle The width or shorter side is The length or longer side is inches inches

The equation x 2 3x 4 0 has two solutions One is an integer the other is a fraction The integer solution is The fraction solution is

Solve the equation p 10p 0 Enter any solution as an integer or reduced fraction not a mixed number or decimal using a comma if there is more than one solution If there is no solution click No solution Suggestion Check any solution s in the original equation before submitting answer No solution

Find x Round your answer to the nearest tenth of a degree 6 5

ind x the angle of depression from the top of a lighthouse that is 184 ft above water level to the waterline of a ship 955 ft off shore Round your answer to the earest tenth of a degree 955 L 184 X 0

A ramp 27 ft long rises to a platform The bottom of the platform is 12 ft from the foot of the ramp Find x the angle of elevation of the ramp Round your answer to the nearest tenth of a degree 27 RX 12 Platform Ground X 0 X S

A 7 ft ladder leans against the side of a house How far is the bottom of the ladder from the side of the house when the angle of elevation of the ladder is 69 Round your answer to the nearest tenth 69 ft X

Find x Round your answer to the nearest tenth of a degree 22

sun is 63 above the horizon find the length of the shadow cast by a building 77 ft tall Round your answer to the nearest tenth 000 X

Factor the expression 4x 25x 21

Factor the expression completely 22 24z 54

Factor the expression completely 7x 28x315

Factor the expression 5x 29x 42

Factor the expression 2x 11x 15

Match each radical expression with the equivalent exponential expression 3 3 3 2 2

Prev Graph the following function by considering how the function x2 has been shifted reflected stretched or compressed x 2 2 Answer 2 Points f x 3 Keypad Keyboard Shortcuts Points can be moved by dragging or using the arrow keys Points whose positions are related to a moved point will be updated automatically Any lines or curves will be drawn once all required points are plotted and will update whenever a point is moved Enable Zoom Pan NA N

Consider the following function Prev u x Answer 2 Points 5x 10 6 2 if x 2 if x 2 Step 2 of 3 Identify the general shape and direction of the graph of this function on the interval 2 00 f Keyb

Prev Consider the following equation x 2 0 Step 3 of 3 Plot the point on the line with the y coordinate y 2 Answer 2 Points Keyboard Points can be moved by dragging or using the arrow keys Any lines or curves will be drawn once all required points are plotted and will updat whenever a point is moved 107 5 Enable Zoom Pan x

In the START 0 0 0 D 5 6 F 14 14 18 In the EST graph how long does it take to do just task E 3 FINISH 21

ev Find the value of the following function at x 6 and x between these two x values Answer 2 Points 7 Does the Intermediate Value Theorem guarantee that the function has a real zero f x x 5x 6x 9 f 6 7 Does the intermediate Value Theorem guarantee that there is a real zero between 6 and 7 VES Keypad Keyboard Shortcuts Nex

Consider the following functions Step 3 of 4 Find f g 3 AnswerHow to enter your answer opens in new window 2 Points 2 5 3 2 0 0 and 8 2 5 3 1

The half life of nitrogen 13 is approximately 9 97 minutes Step 1 of 3 Determine a so that A t Apa describes the amount of nitrogen 13 left after t minutes where Ao is the amount at time t 0 Round to six decimal places window 2 Points Keypad

Symmetry Skewness Outlier Shape QUESTION 2 Using information from the Tour de France describe each variable as categorical or quantitative or both a Variable county of origin b C Variable total time Variable total distance QUESTION 3 For Blank 3 Information that is recorded numerically for example height age income O Qualitative data O Quantitative data

Question 2 25 points Chromatic Numbers Use graph coloring to find the minimum number of colors needed to color the graph 2 3 4 5 A B E C D

Time Tak B B B B Q D D D D E 5 colors E 4 Colors E 3 colors E 2 colors

Question 4 25 points Use graph coloring to find the minimum number of colors needed to color the map m J C B

number of colors needed to color the map

Solve each equation by rewriting it in factored form and using the zero product property 1 x2 12x 11 0 2 x 3 11 3 x 6x 7 2 x 1 and r 11 x 1 and x 5 2 2 and z 2 2 2 3 7 and x 0 x 1 and x 11 x 9

Write each expression in factored form If it is not possible write not possible 36 49 25x2 x 9 10000 16 2 4x 0 4x 7 5x 75x Not Possible x 6 x 6

As with other types of equations you can solve exponential functions for any variable In this section we will solve for the exact initial value but only estimate the exponent since solving for exponents is beyond what we have learned so far 1 Sari makes an investment with the goal of having 20 000 after 30 years If the growth factor is 1 12 how much money will she need to invest to reach her goal 2 Charlotte has 12 000 to invest and would like this investment to grow to 18 000 If the growth factor is 1 09 how many years will it take to reach her goal Use guess and check to find an approximate answer

A 300 pair of shoes is 35 off What s the price with tax 8 fill in your answer X 15 6

17 7 In Exercises 9 16 find the inverse of the function Then graph the function and its inverse 9 f x 6x 10 f x 3x 11 f x 2x 5 13 f x x 4 X R 2 1 0 14 f x x 1 REASONING In Exercises 17 and 18 f and g are inverse functions Complete the 1 2 15 f x 3x 1 1 38 18 X 2

In Exercises 43 46 determine whether the functions are inverse functions See Example 5 43 f x 2x 9 g x 9 x 1 5 5 45 f x 3 x 9 5 rs g x 5x5 9 5 44 f x g x 5x 1 46 f x 7x 2 4 g x x 4 7

eller 1 2 2x 8 3 4 X2 20 6 x 7 14 6 5 3 11 5 7 X5 8 20 25 5 15 8 16 5 X 3 9 5 18 10 5 5x 10 1 x m 5 17 12 6 16 6x 18 4 4 3 2 12 12 X 6 x 5 9 2 17 9 16 x 7 5 8 10 15 12 20 2x 13 10 9 8

20 Given 21 22 23 24 Prove AZXY is isosceles W ALCA

Calculator Reference A mountaineer climbed 1 000 feet at a rate of x feet per hour He dimbed an additional 5 000 feet at a different rate This rate was 10 feet per hour less than twice the first rate Which expression represents the number of hours the mountaineer climbed OA 6 000 3x 10 OB O C OD 6 000 3x 10 1 000 5 000 x 2x 10 1 000 5 000 10 X 14 of Atag for Revi

Solve the equation I log 1 3 log 1 7x 12

Use the like bases property to solve the equation 8 64 I

Use the like bases property to solve the equation 5 653n 10 n

Choose the graph of y loga z 2 O O 10 for k fr ty 5 6 a q 16 33 Y Fo O 139 25 k ty Or 6459a cy S Fr 679

sider the function y x 3 The vertical asymptote of the graph is The horizontal asymptote of the graph is The domain is all real numbers except The range is all real numbers except QUESTION 4 Which equation is graphed 8 6 CO 4 4 3 2 1 2 21 ME 6 4x 1 X f x 1 x f x X 3 4 5 6 7 8 9 10 f x x 2 x 4 2 2