Quadratic equations Questions and Answers

A building is 1 ft from a 7 ft fence that surrounds the property A worker wants to wash a window in the building 10 ft from the ground He plans to place a ladder over the fence so it rests against the building See the figure He decides he should place the ladder 7 ft from the fence for stability To the nearest tenth of a foot how long a ladder will he need He will need a ft ladder 7 ft 7 ft 1 ft to the nearest tenth as needed 3 ft

The difference of the squares of two positive consecutive even integers is 52 Find the integers Use the fact that if represents an even integer then x 2 represents the next consecutive even integer Use a comma to separate answers as needed

Solve by completing the square 2 6x 4 0 The solution set is Simplify your answer Type an exact answer using radicals as needed Use a comma to separate answers as needed

Find the product 8 3i 8 31 Simplify your answer Type your answer in the form a b

Section 2 2 10 find at least four ordered pairs but you do not need to Sumit a graph

An astronaut on the moon throws a baseball upward The astronaut is 6 ft 6 in tall and the initial velocity of the ball is 40 ft per sec The heights of the ball in feet is given by the equation s 2 7t2 40t 6 5 where t is the number of seconds after the ball was thrown Complete parts a and b a After how many seconds is the ball 12 ft above the moon s surface After seconds the ball will be 12 ft above the moon s surface Round to the nearest hundredth as needed Use a comma to separate answers as needed b How many seconds will it take for the ball to hit the moon s surface It will take seconds for the ball to hit the moon s surface Round to the nearest hundredth as needed

Sally can paint a room in 9 hours while it takes Steve 7 hours to paint the same room How long would it take them to paint the room if they worked together It would take hours Simplify your answer Type an integer or a fraction

Margaret drove to a business appointment at 30 mph Her average speed on the return trip was 1 20 mph The return trip took hr longer 2 because of heavy traffic How far did she travel to the appointment She traveled miles Morning Afternoon r 30 20 t X X 1 2

Find the solution set Then indicate whether the equation is contradiction 14 x 1 7 2 x 7x Select the correct choice below and fill in any answer boxes present in your choice O A The solution set is OB The solution is the set of all real numbers OC The solution is the empty set Indicate whether the equation is conditional an identity or a contradiction Choose the correct answer O conditional equation O identity O contradiction

B BC CD 6cm AC 8 8cm A Show Transcribed Text 6 D

ind an equation of the plane through the point 3 2 5 and perpendicular to the vector 1 4 4 Do this problem in the standard way or WebWork may no ecognize a correct answer X y Z

Find the APPROXIMATE area of each sector Round your answers to the nearest tenth 24 1200

120 8 m Arc Length and Sector Area Find the APPROXIMAT area of each sector Round your answers to the nearest tenth

ndicated Assume that lines which appear tangent are tangent 21 Find PQ P x 3 10 R 2 x 1

A doctor has found that over the years 95 of the babies he has delivered weighed x pounds where x 7 7 s1 6 What range of weights corresponds to this inequality The range of weights that corresponds to the given inequality is Simplify your answer Type your answer in interval notation Use integers or decimals for any numbers in the expression

Solve the quadratic inequality Write the solution set in interval notation x 4x 5 2 Select the correct choice below and if necessary fill in the answer box to complete you choice OA The solution set is Use integers or fractions for any numbers in the expression OB The solution set is the empty set

Line segments about circles Find the measure of the line segme indicated 8 Find CA D 27 30 3x 9 U 20 B

Find the LCD for 5 3q 4q 7g 36 4q 27g 81

20 Find m RZY R X 110x 93x 1 Z Y 66x

19 Find m XVW 8x 2 V W 4x 14 X

9 K M L 114

Solve the equation 7x 1 3 X 2 1 6 X x 1 2 2x Select the correct choice below and if necessary fill in the answer box to complet choice OA The solution set is Use a comma to separate answers as needed Type an integer or a simplified fraction OB The solution is the empty set

Graph f x 2 1 and g x x 5 on the same coordinate plane What is the solution to the equation f x g x Enter your answer in the box X

Find the measure of the arc or angle indicated 6 Y X 115 L Z 130 200

In 1993 the sports league introduced a salary cap that limits the amount of money spent on players salaries The quadratic model y 0 2313x 2 600x 35 17 approximates this cap in millions of dollars for the years 1993 2009 where x 0 represents 1993 x 1 represents 1994 and so on Complete parts a and b a Approximate the sports league salary cap in 2008 The approximate sports league salary cap in 2008 is million Round to the nearest tenth as needed

At a point on the ground 15 ft from the base of a tree the distance to the top of the tree is 1 ft more than 2 times the height of the tree Find the height of the tree The height of the tree is ft Simplify your answer Round to the nearest foot as needed

If there are n teams in a league and each team plays each other twice in a season the total number of games is given by the polynomial n n N A women s basketball league plays a total of 156 games How many teams are in the league

Solve the equation 2x 3 3x 2 x 3 X Select the correct choice below and if necessary fill in the answer box to complete choice O A The solution set is Simplify your answer Use a comma to separate answers as needed OB The solution is the empty set

Solve by completing the square x 3x 18 0 The solution set is Simplify your answer comma to separate an as needed

Answer the questions about the following function f x 2x x 1 a Is the point 2 9 on the graph of f b If x 2 what is f x What point is on the graph of f c If f x 1 what is x What point s are on the graph of f d What is the domain of f e List the x intercept s if any of the graph of f f List the y intercept if there is one of the graph of f

Expand each logarithm 1 log 7 2 7 6 2log 5 3 log 6 5 11 5 log 34 2 7 log s logs log 36 10 2 log 5 11 109 312511 4 log ab 6 log x y 8 log 4 10 log 19

Condense each expression to a single logarithm 11 2log 12 2log3 11 log 5 2 1093 12 11 5 13 16log a 4log b 4log c 15 log 6 log 11 log 8 log 6 3 log 3 17 2log 5 log 11 og 8 log 7 log 3 log 11 3 3 3 7 12 log w 4log2 u 6log v 14 6log a log 4 c 5log 4 b 16 log w 4log 4 4log 4 v 18 25log 7 25log 10 5log 11 20 6log z 6log x 3log y

At a local play student tickets cost 5 each and adult tickets cost 11 each If ticket sales were 3 000 for 300 tickets how many students attended the play 050 O 150 O250

32 What quantity should be added to both sides of this equation to complete the square x 4x 5 a 1 b 2 c 3 d 4 33 What is the solution set of the quadratic equation 8x 2x 1 0 a b 1 2 1 2 4 1 7 1 7 8 8 d no real solutions

Find the following for the function f x 2 X 1 a f 0 e f x TA g f 3x X b f 5 f f x 2 0 c f 5 g f 3x Simplify your answer Use integers or fractions for any numbers in the expression d f x h f x h 3x 2 9x 1 Simplify your answer Use integers or fractions for any numbers in the expression h f x h Simplify your answer Use Integers or fractions for any numbers in the expression

30 Which expression shows the complete factorization of 12x 147 a 3x 7 4x 2 b 4x 21 3x 7 c 12 x 7 x 7 d 3 2x 7 2x 7 31 What quantity should be added to both sides of this equation to complete the square x 8x a 4 b 64 c 16 d

38 Identify which of the following tables represent a linear function Select ALL options a b 341 c X y X 2 7 4 8 1 0 4 3 3 6 2 4 1 4 2 7 1 0 2 0 3 12 1 2 d X y X y 2 1 0 1 1 0 1 2 3 0 1 2 3 4 1 2 2 4 3 8 4 5 16 32

34 Identify a b and c for the following equation 2x 4x 2 A a 2 B a 2 b 4 b 4 c 2 c 2 a 2x a 2 b 4x b 4 c 2 c 2 C 35 How many real number solutions does the quadratic equation a 12a 36 0 have HINT you need to use the discriminant The formula for the discriminant is b 4ac b 4ac 0 b 4ac 0 No real solution One real solution no x intercepts one x intercept a 0 D b 1 c 2 b 4ac 0 Two real solutions Two x intercepts d 3

36 Which statement best explains why there are two real solutions to the quadratic equation x 4x 8 0 a The value of 4 2 4 1 8 is positive b The value of 4 4 1 8 is equal to 0 c The value of 4 4 1 8 is negative d The value of 4 4 1 8 is not a perfect square 37 Solve the equation 3x 2 4 What is the value of x a x 2 b x 0 c x 12 d x 6

17 Graph the quadratic y x 2x 8 and answer the following questions using the graph a What is the vertex b What is the axis of symmetry c Minimum Maximum circle one Value d What is the y intercept e What is the function s domain f What is the functions range

29 Which of the following is not a difference of 2 squares a x 25 b 9 x c m 9 d m 16n

Multiple Choice Practice Select the best answer option for the given problem 28 a b is equivalent to A a b B a 2ab b C 2a 2b D a a b b

Solve for the variable If necessary leave answers in radical form 22 3m 9m 0 23 x 6x 5 0

Simplify Rationalize denominators if necessary 18 5 25 iate techviques 19 24

Factor completely using the appropriate technique s 14 x 3x 15 x 81 16 k 7k 8

In the xy plane above line k not shown is perpendicular to line What is the slope of line k 05 1 5 of 0 1 0 5

1 2 Ex3 Now let s look at how to graph the exponential function y G 727 y y TO V 6 6

Number of Dots T Linear X X Quadratic S Tr Stage Number 3 4 5 Choose the function family that describes the dot pattern Provide a justification Complete the table Find the number of dots in stage 4 of Dot Pattern F Stage Number x Number of Dots 0 2 T 1 4 2 10 Define a function to describe the dot pattern j x 3 21 How many dots are in stage 21 Show your work in the sketch below For which stage are there 100 dots Show your work in the sketch below 4 Submit X

he table and graph below show the number of minutes ft on your cell phone plan over the course of the month What is the y intercept of the best fit line Day Minutes 3 5 70 60 45 40 30

Write the number in standard form 3 27 3 3 27 3 Simplify your answer Type your answer in the form a bi Type an exact answer u radicals as needed