Quadratic equations Questions and Answers
![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](https://media.kunduz.com/media/sug-question-candidate/20230502222559460091-3893389.jpg?w=256)
Algebra
Quadratic equations2 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](https://media.kunduz.com/media/sug-question-candidate/20230502235155469650-3694319.jpg?w=256)
Algebra
Quadratic equationsFind 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](https://media.kunduz.com/media/sug-question-candidate/20230502234135453941-3694319.jpg?w=256)
Algebra
Quadratic equationsFind 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](https://media.kunduz.com/media/sug-question-candidate/20230502224056044532-3694319.jpg?w=256)
Algebra
Quadratic equationsLet 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](https://media.kunduz.com/media/sug-question-candidate/20230502224330188048-3694319.jpg?w=256)
Algebra
Quadratic equationsFind 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](https://media.kunduz.com/media/sug-question-candidate/20230502204533539866-4116583.jpg?w=256)
Algebra
Quadratic equationsThe 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](https://media.kunduz.com/media/sug-question-candidate/20230502204450232947-4116583.jpg?w=256)
Algebra
Quadratic equationsIf 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](https://media.kunduz.com/media/sug-question-candidate/20230502204435066438-4116583.jpg?w=256)
Algebra
Quadratic equationsThe 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](https://media.kunduz.com/media/sug-question-candidate/20230502203104522274-4116583.jpg?w=256)
Algebra
Quadratic equationsThe 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](https://media.kunduz.com/media/sug-question-candidate/20230502203153697847-4116583.jpg?w=256)
Algebra
Quadratic equationsSolve 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](https://media.kunduz.com/media/sug-question-candidate/20230502200532598162-5593977.jpg?w=256)
![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](https://media.kunduz.com/media/sug-question-candidate/20230502200313518102-5593977.jpg?w=256)
Algebra
Quadratic equationsind 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](https://media.kunduz.com/media/sug-question-candidate/20230502200155749708-5593977.jpg?w=256)
Algebra
Quadratic equationsA 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](https://media.kunduz.com/media/sug-question-candidate/20230502200335285394-5593977.jpg?w=256)
Algebra
Quadratic equationsA 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](https://media.kunduz.com/media/sug-question-candidate/20230502200124626790-5593977.jpg?w=256)
![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](https://media.kunduz.com/media/sug-question-candidate/20230502195944788144-5593977.jpg?w=256)
Algebra
Quadratic equationssun 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](https://media.kunduz.com/media/sug-question-candidate/20230502194122232881-4116583.jpg?w=256)
![Factor the expression completely 22 24z 54](https://media.kunduz.com/media/sug-question-candidate/20230502194220133075-4116583.jpg?w=256)
![Factor the expression completely 7x 28x315](https://media.kunduz.com/media/sug-question-candidate/20230502194204512660-4116583.jpg?w=256)
![Factor the expression 5x 29x 42](https://media.kunduz.com/media/sug-question-candidate/20230502194002791345-4116583.jpg?w=256)
![Factor the expression 2x 11x 15](https://media.kunduz.com/media/sug-question-candidate/20230502193721343984-4116583.jpg?w=256)
![Match each radical expression with the equivalent exponential expression 3 3 3 2 2](https://media.kunduz.com/media/sug-question-candidate/20230502185802255420-5593741.jpg?w=256)
Algebra
Quadratic equationsMatch 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](https://media.kunduz.com/media/sug-question-candidate/20230502181042786361-3694319.jpg?w=256)
Algebra
Quadratic equationsPrev 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](https://media.kunduz.com/media/sug-question-candidate/20230502181334384767-3694319.jpg?w=256)
Algebra
Quadratic equationsConsider 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](https://media.kunduz.com/media/sug-question-candidate/20230502181208209357-3694319.jpg?w=256)
Algebra
Quadratic equationsPrev 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](https://media.kunduz.com/media/sug-question-candidate/20230502180157401692-4083857.jpg?w=256)
Algebra
Quadratic equationsIn 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](https://media.kunduz.com/media/sug-question-candidate/20230502175619551786-3694319.jpg?w=256)
Algebra
Quadratic equationsev 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](https://media.kunduz.com/media/sug-question-candidate/20230502175858138903-3694319.jpg?w=256)
Algebra
Quadratic equationsConsider 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](https://media.kunduz.com/media/sug-question-candidate/20230502175344307204-3694319.jpg?w=256)
Algebra
Quadratic equationsThe 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](https://media.kunduz.com/media/sug-question-candidate/20230502174117314935-5373729.jpg?w=256)
Algebra
Quadratic equationsSymmetry 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](https://media.kunduz.com/media/sug-question-candidate/20230502173338788823-4083857.jpg?w=256)
Algebra
Quadratic equationsQuestion 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](https://media.kunduz.com/media/sug-question-candidate/20230502172115535278-4083857.jpg?w=256)
![Question 4 25 points Use graph coloring to find the minimum number of colors needed to color the map m J C B](https://media.kunduz.com/media/sug-question-candidate/20230502172048855484-4083857.jpg?w=256)
Algebra
Quadratic equationsQuestion 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](https://media.kunduz.com/media/sug-question-candidate/20230502172008344044-4083857.jpg?w=256)
![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](https://media.kunduz.com/media/sug-question-candidate/20230502165510603342-4947564.jpg?w=256)
Algebra
Quadratic equationsSolve 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](https://media.kunduz.com/media/sug-question-candidate/20230502165449258438-4947564.jpg?w=256)
Algebra
Quadratic equationsWrite 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](https://media.kunduz.com/media/sug-question-candidate/20230502151808213223-5320867.jpg?w=256)
Algebra
Quadratic equationsAs 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](https://media.kunduz.com/media/sug-question-candidate/20230502143439186662-3746214.jpg?w=256)
Algebra
Quadratic equationsA 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](https://media.kunduz.com/media/sug-question-candidate/20230502132714880563-3418403.jpg?w=256)
Algebra
Quadratic equations17 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](https://media.kunduz.com/media/sug-question-candidate/20230502132700061412-3418403.jpg?w=256)
Algebra
Quadratic equationsIn 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](https://media.kunduz.com/media/sug-question-candidate/20230502095437777297-5477815.jpg?w=256)
Algebra
Quadratic equationseller 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](https://media.kunduz.com/media/sug-question-candidate/20230502094506232574-5590962.jpg?w=256)
![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](https://media.kunduz.com/media/sug-question-candidate/20230502043520066488-4752310.jpg?w=256)
Algebra
Quadratic equationsCalculator 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](https://media.kunduz.com/media/sug-question-candidate/20230502035556505559-3882370.jpg?w=256)
![Use the like bases property to solve the equation 8 64 I](https://media.kunduz.com/media/sug-question-candidate/20230502035416287842-3882370.jpg?w=256)
![Use the like bases property to solve the equation 5 653n 10 n](https://media.kunduz.com/media/sug-question-candidate/20230502035430579247-3882370.jpg?w=256)
![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](https://media.kunduz.com/media/sug-question-candidate/20230502035238324143-3882370.jpg?w=256)
Algebra
Quadratic equationsChoose 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](https://media.kunduz.com/media/sug-question-candidate/20230502033734007201-5373729.jpg?w=256)
Algebra
Quadratic equationssider 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
![Graph the solution set of the system of inequalities x 3y 6 y x 4 Use the graphing tool to graph the system Click to enlarge graph](https://media.kunduz.com/media/sug-question-candidate/20230502034205377318-5560534.jpg?w=256)
Algebra
Quadratic equationsGraph the solution set of the system of inequalities x 3y 6 y x 4 Use the graphing tool to graph the system Click to enlarge graph
![Solve the system of equations by the addition method 15x 3y 75 3x 5y 43 Select the correct choice below and fill in any answer boxes present in your choice OA The solution set is OB There are infinitely many solutions Oc There is no solution Simplify your answer Type an ordered pair](https://media.kunduz.com/media/sug-question-candidate/20230502031142551494-5560534.jpg?w=256)
Algebra
Quadratic equationsSolve the system of equations by the addition method 15x 3y 75 3x 5y 43 Select the correct choice below and fill in any answer boxes present in your choice OA The solution set is OB There are infinitely many solutions Oc There is no solution Simplify your answer Type an ordered pair