Quadratic equations Questions and Answers

e 32 P and Q can do a piece of work in 15 days and 20 days respectively They work for 5 days and left then in how many days Q alone can finish the remaining work 8 days 7 days 8 days 8 days c e 33 The area of a square is 144 cm What is the perimeter of the square formed with the diagonal the original square as its side 48 2cm 24 2cm 48 cm 24 cm

The diameter of a circle is 8 mm Answer the parts below Make sure that you use the correct units in your answers If necessary refer to the list of geometry formulas a Find the exact area and circumference of the circle Write your answers in terms of Exact area 0 b Approximate the area and circumference of the circle To do the approximations use the button on the ALEKS calculator and round your answers to the nearest hundredth Approximate area Exact circumference 0 Approximate circumference 00 mm 8 mm X J mm mm

To purchase 12 200 worth of machinery for her business Donna made a down payment of 1600 and took out a business loan for the rest After 2 years of paying monthly payments of 469 81 she finally paid off the loan a What was the total amount Donna ended up paying for the machinery including the down payment and monthly payments 12875 44 b How much interest did Donna pay on the loan X

Write a quadratic function f whose zeros are 4 and 3 f x

A fruit company packages its fruit into two types of boxes large and small This morning the company made two deliveries The table below shows the number of boxes in each delivery and the total weight in kilograms First delivery Second delivery Number of large boxes 2 5 Number of small boxes 12 3 Let x be the weight in kilograms of each large box Let y be the weight in kilograms of each small box x y 0 x y 0 Total weight in kilograms 199 133 a Write a system of equations that could be used to find the weight in kilograms of each type of box b How much does each type of box weigh in kilograms Weight of each large box kilograms Weight of each small box kilograms X

Find all real zeros of the function g x 2 x 5 x 36 x 5 If there is more than one answer separate them with commas zero s 8 0 0 None

Graph the equation y 6 x 6 10 F 10 X Ex

Graph the parabola y 3 x 2 1 Plot five points on the parabola the vertex two points to the left of the vertex and two points to the right of the vertex Then click on the graph a functio button 10 8 6 12 10 8 6 10 12 10 12 X

1 Fill in the missing values for the weekly time card Mon Tues IN 8 15 8 30 OUT 12 00 12 30 IN 12 30 1 10 OUT 4 30 5 10 HOURS 7 75

Graph the parabola y x 10x 28 Plot five points on the parabola the vertex two points to the left of the vertex and two points to the right of the vertex Then click on the graph a function button 10 8 12 10 N 6 22 2 8 10 12 10 12 X

Graph the line y x 3 3 2 10 6 10 N 6 10 X

f x x g x x 3 G Choose the correct graph below O A 20 O C 20 OB O D 20 20 Q Q Q

Determine the domain and the range of the function shown below 6 4 2 6 4 2 2 6 2 Select the correct choice below and fill in the answer box to complete your choice A The domain is an interval The domain of the function is Type your answer in interval notation OB The domain is a list of values The domain of the function is Type an integer or a simplified fraction Use a comma to separate answers as needed

Determine whether the graph is that of a function An open dot indicates that the point does not belong on the graph CIT Is the graph the graph of a func No OYes

Determine if a graph is a function Is this the graph of a function OYes O No THE 2

2 B Show that the Borel algebra B is also generated by the collection of all half open intervals a b x R a x b Also show that B is generated by the collection of all half rays x e R x a ER

13 1 point 49 the only possible answer for x is 7 True False If x Previous

9 1 point Multiply 5k 2 2k 3 O 10k 11k 6 O10k 19k 6 10k 11k 6 6 O10k 11k

5 1 point The degree of the monomial is 3 3z y True

Solve the following systems of equations using the A b construct as well as the Gauss Seidel method with a tolerance of 10 7 in some cases convergence may not occur a 2x x 3x3 8 4X1 2x2 5x3 9 6x 3x2 x3 12 b 10x1 x2 2x3 3 X1 10X2 X3 1 5 2X1 X2 10x3 9 5 5

Which value or values satisfy the absolute value inequality y 4 3 select all that apply

Let G be a group and let Z G be its centre Prove that if G Z G is cyclic then G is abelian Hint If G Z G is cyclic prove that a generator gives rise to an element outside Z G which commutes with all elements of G

1 15 marks For each of the following three dimensional integrals re order the integral so that the x integration is first the y integration is second and the z integration third That is dx dy dz a b c 1 pln 2 fm f x y z dy o r2 3 0 da dz f x y z dy dz dz 1 dy de 2

Consider three vectors d 1 2 2 b 3 5 1 7 0 2 3 Part a 4 points Find the area of the triangle formed by the vectors a and 2 Prove that a and do not lie in the same plane Suppose a 1 0 4 y1 is perpendicular to both a and b Find a Part b 3 points Part c 5 points and y

2 Use the key features to sketch the graph Use graph paper or a coordinate plane to earn credit a x intercept 5 0 y intercept 0 2 Linearity linear Continuity continuous Positive for values x 5 Decreasing for all values of x End Behavior As x o f x and as x f x b x intercept 1 0 and 1 0 y intercept 0 1 Linearity nonlinear Continuity continuous 810 Symmetry symmetric about the line x 0 Positive for values 1 x 1 Negative for values of x 1 and x 1 Increasing for all values of x 0 Decreasing for all values of x 0 Extrema maximum at 0 1

The conversion between Celsius x and Fahrenheit y can be expressed as a linear equation When it is O degrees Celsius it is 32 degrees Fahrenheit When it is 100 degrees Celsius it is 212 degrees Fahrenheit Which of the following equations represents the relationship between degrees Celsius and Fahrenheit

Sketch 3 Cycles of the function represented by f t 12 2 1 1 t if Cos 3Mt if 0 2 12 t 1 100 t 1 if 17 1 2

1 1 Explain how to complete each diagram so that it shows a 1 2 A student shows a as What is wrong with the diagram b Question 2 Vraag 2 2 1 Match each application with a fraction model Fraction Model 1 Part of a whole 2 Point on a number line Application a Your height in inches b Fraction of those surveyed who jog c The fraction of the day for which you are asleep d Evenly sharing 3 pizzas among 5 people 3 Division 4 Part of a group 2 1 4

Identify whether graph represents a polynomial function that has a degree that is even or odd and whether the leading term is positive or negative 244 18 15 12 9 6 3 6 9 12 15 18 21 even and leading term is positive odd and leading term is positive even and leading term is negative

Find the area of the shaded portion of the flag below Show or explain how you got your answer 8 in 6 in

Replace the with the correct symbol 59 6 11 6 11

Round the given number to the nearest hundredth 518 006 518 006 rounded to the nearest hundredth is

ill in the blank AAY AXD XAY XXD

Solve for y in the equation below Round your answer to the nearest hundredth Do not round any intermediate computations 9 6 11

3 When riding on a Ferris wheel your height h in meters above the ground in terms of time t in seconds can be represented by the graph shown below 15 Th 10 50 100 125 150 175 a Determine the diameter of the Ferris wheel b Determine the height of the center of the Ferris wheel c Determine a sine function and cosine modeled by this sketch show calculations 200 225 1 1 3 EN 1

12 Sketch period graphs to satisfy the given properties Shape 45 Period 135 1 Amplitude Equation of Axis 225 315 405 y 1 y 3 State the period amplitude and the equation of the axis for the given function Number of Cycles 2

1 Approximately plot the locus of roots using the basic rules 2 Describe in detail the application of the basic rules

Write the letter of the statement in the Agree or Disagree column Explain why you put it there and justify your answer mathematically A radar is used to measure speeds of cars on Interstate 85 The speeds are normally distributed with a mean of 75 mi hr and a standard deviation of 5 mi hr What approximations can be made about the drivers on 1852 A 50 of drivers drive 75 mi hr or less on 185 C If you drive 69 mph you are in the 16th percentile E 50 of drivers are between 72 and 78 miles per hour Agree B 80 of drivers drive between 65 and 80 miles per hour D Only 0 47 of drivers are going faster than 88 mi hr F If an officer only pulls over the top 5 of speeders they will pull over everyone going 83 mph or higher Disagree

not to scale Solve the triangle round to the nearest tenth drawing 24 a C C 36 16

1 Each of the following equations establishes a linear relationship between M and t i 2 81 10 t 1 10 10 M 4 14 10 M 3 14 ii 3 11 10 M t iii aM yt 3t c a y c 0 For each of the equations above identify the gradient and M intercept of the linear relationships

b State the transformations and write the equation of the transformed cubic function Transformations reflec harizantel 1 0 to M 6 5 4 3 10 0 8 0 2 34 4 5 6 7 8 N 1 2 Hver Vest Crimso Equation Explain how you got the numbers for your equation Two possible correct equations can be written for the above transformed cubic function Why are there two possible equations for this function t JOT L

f x h f x h 0 when f x 2x 4x 4 h C 2x 4 2h D 2x 4 2h E 4x 4 9 Simplify the difference quotient A 4x 4 2h B 4x 4 2h

Find the following difference and write it in lowest terms 7 16 7 1 16 16 1 16 Type an integer or a simplified fraction

The graph of h is shown 14 13 12 11 10 9 8 7 6 5 4 3 2 1 In interval notation the domain of his In interval notation the range of his 16 5 4 32 24 1234 a

3 Bellamy is attending a business conference in another state She must pay for her airfare and 139 per night at the hotel She calculates that if she stays for 3 nights she will have to spend a total of 914 for airfare and hotel but she is considering extending her stay Write an equation that relates the total cost of her trip airfare and hotel C to the number of nights in her stay n

nd the following sum 48 38 93 73 48 38 93 73 Type an integer or a decimal

Evaluate and write in lowest terms 3 7 30

Find the reciprocal of the fraction 12 5 12 The reciprocal of is 5

6 Rewrite the fraction with 33 as the denominator

56 40 56 40 Type an integer or a simplified fraction