Quadratic equations Questions and Answers

6 Solve the system of equations by elimination 3x y 6 5x 2y 14 1

4 Solve the system of equations by substitution y 2x 5 y 3x 10 X y

3 Which is a solution to the system of equations below 6x 2y 50 y x 11 O 7 4 O 1 12 O 4 0 O 4 6

Make sure your answer is in degrees You should be able to find this without a calculator sin sin 17

Find the following in radians You should be able to do this without a calculator cos 0 T

8 State the number of solutions for the linear system equations 10x 2y 40 3y 78 12x O One solution O Infinite solutions solutions

12 State the number of solutions without graphing 14x 7y 35 28x 42 7y O No solutions OTwo solutions O One solution Many solutions

6 On a separate piece of paper solve the system of equations by graphing and check each solution with the feedback after submission y x 4 3y x 3 X y

State the type of system of equation y 42 3 16x 4y 12 Inconsistent O Consistent and dependent O Consistent and independent O None of the above

House Find the domain of the function Write your answer as a compound inequality involving x Domain of A x Figure 1 Figure 2 sa has 60 ft of fencing available to construct fence that will divide her garden into two rectangular sections Her house forms one side of the garden and x represents the width as show Figure 1 Express the total area of the two sections as a function of x A x Using the graph of A x shown in Figure 2 determine the dimensions that yield the maximum area Width ft A x 18 308

2 State whether the linear system of equations is consistent or inconsistent independent or dependent 8y 96x 48 2y 24x 28 O Consistent and dependent O Consistent and independent O Inconsistent

2K where m is the mass of the The velocity v in metres per second of an object can be defined as v object in kilograms and K is the kinetic energy in joules J What is the mass of an object travelling at 10 m s with a kinetic energy of 750 J

Now that we know how to use 1 rand 1 r to write percent growth and decay equations we can use this to determine the rate of change of a given equation 1 You make an investment where the balance over time can be modeled by the equation y 32000 1 035 where x represents the number of years since the investment started and y represents your total balance after x years a What is the starting balance of your investment b What is the rate of growth of your investment 2 y 100 0 96 is an equation that can be used to represent the purchasing power of 100 after x years of inflation What is the rate of inflation used to make this calculation

6 A woman spends 7 42 at the drug store If she had NOT bought the mouthwash costing 1 19 she would have spent A B C D 6 23 6 27 6 33 8 61

the b value is 1 then no growth or decay happens If you are told that the initial value changes by a percent then we can represent the b value as growth or decay where 1 Growth is 1 r Decay is 1 r r is the decimal form of the percent Write an equation that represents the following situation Starting value 125 O O Rate 6 growth per year Years 10 years www ngpf org Last updated 12 2 21 2 Write an equation that represents the following situation O Starting value 200 O Rate 2 5 decay per year

The numbers of polio cases in the world are shown in the table for various years Year Number of Polio Cases thousands 1988 1992 1996 2000 2005 2007 350 138 33 2 Find an equation of f Hint f t Let f t be the number of polio cases in thousands t years since 1980 3 2 1 3 Predict the number of polio cases in 2020 16 16 Round the coefficients to 4 decimal places Hint Predict in which year there will be 1 case of polio Hint

Condense each expression to a single logarithm 5 log3 x log3 y 3 log 3 z log2 x y 2 6 5log 5 log48 2

Expand each logarithm 1 log z x 5 2 1099 10993 510ga 2log xl Z 2015 x x 2 logg xy M

3 i 4 PN 2 1 1 2 3 Determine the period 2 4 B 10 12 14 Enter

NW 2 1 1 2 3 4 Determine the period 2 6 8 10 12 14 Enter

1 Determine the period MAAA 12 Enter

Use the drawing tool s to form the correct answer on the provided number line Consider the given functions Function 1 f x 5x 1 10 6 Represent the interval where both functions are decreasing on the number line provided Function 2 g x 2 30 20 10 10 20 30 N 6 4

Find the partial fraction decomposition 4x 3x 25 tr 50 Find the following values A B B 4 2 1 C x 5

Use cylindrical coordinates to find the volume of the object represented in the following figure which is the region where the following inequalities are satisfied x y z 4 x y 1 x 0 y 0 and z 0 K

synthetic division 3 2 f x 2x 3 x 2 9x 18 e whet

A y cos x 2 C y cos x Find the equation 1 EN 2 B y cos x TT 2 D y cos x TT m

Find the equation A y 2 sin x TI C y 2 sin x 2 75 KIN 2 B y 2 sinx D y 2 sin x TT 2

x 2 A 0 1 1 B 0 1 1 C 4 1 1 D 0 0 0 E 2 0 3 Q4 Find the intersection of the line 2 y 2 and the sphere x 2 y z 3 9 2 3 2

2 1 4 1 Determine the period N COMPOS Enter

3 2 1 1 2 3 Determine the period MA 4 6 8 10 12 14 2 Enter

Rotate the vector 3 5 270 clockwise about the origin

Rotate the given triangle 90 degrees counter clockwise about the origin To 0 7 3 4

Reflect the given triangle over the line y x 6 3 3 33 3 3 3 31 3 I

1 pm 1 Let G and G the aritrary constants The general soutu to the homogeneous offerential equation 2252 255 1y0s the function Caix C 4 G G 2 The unique solution to the metal vanie problem the Button for C

x the time it took Timothy to hike up the mountain 0 5x the time it took Timothy to hike down the mountain Together these expressions give the total time x 0 5x 6 hours 1 5x 6 hours I divide 6 by 1 5 to find x equals 4 hours So it took Timothy 4 hours to hike up the mountain Since the hike was 6 miles his rate is 6 miles divided by 4 hours or 1 5 miles per hour Use the student s solution to complete the statements The student To write his equation the student used the idea of To solve his equation for x the student used The student justified his solution by when he related x to the total time of 6 hours which is the opposite of

2 Enter the correct answer in the box This graph represents a transformation of the parent cube root function 10 8 6 8 y 6 4 2 10 2 2 4 6 8 16 8 X 10

Find the following for the function f x x 4 a f 0 b f 8 e f x f f x 9 c f 8 g f 5x d f x h f x h

The formula for the voltage V of an electrical current is V VPR where P is the power measured in watts and R is the resistance measured in ohms Which equation expresses R in terms of Vand P

Detemine if the following statement is true or false f The domain of consists of the numbers x that are in the domains of both f and g g Choose the correct answer below O A True because f and g exist for any x in the domain of both f and g B False because f may equal zero for some x values in the domain of f O c False because g may equal zero for some x values in the domain of g O D True because f is always defined for any x in the domain of both f and g g

Find the difference quotient of f that is find 6x The difference quotient of f f x Simplify your answer X 2 is f x h f x h h 0 for the function f x 6x X 2

For the given functions f and g complete parts a h For parts a d also find the domain 3 3 f x 5 g x a Find f g x X 6 f g x 5 Simplify your answer X What is the domain of f g Select the correct choice below and if necessary fill in the answer box to complete you choice A The domain is x x 0 Use integers or fractions for any numbers in the expression OB The domain is x x is any real number b Find f g x f g x Simplify your answer

Can 8x and 16xbe rewritten as like terms Justify your answer

Use the methods from this lesson to write the expression in simplest form Assume x 0 6 32x 512x 16x4 Enter the correct answer in the box

x is a function A True B False LA 12 9 f x 3 2 4

a Use a graphing utility to graph f x x 3x 3 on the interval 2 2 and approximate any local maxima an minima b Determine where f is increasing and where it is decreasing The local minimum is y Round to two decimal places b Where is the graph of f increasing and it occurs at x O 2 1 00 and 1 00 2 O 1 00 1 00 O 1 00 5 00 2 1 00 and 1 00 5 00

a Use a graphing utility to graph f x 0 2x 0 2x 0 8x 4 on the interval 3 2 and approximate any local maxima and local minima b Determine where f is increasing and where it is decreasing Use MAXIMUM to find the local maximum of the graph The local maximum occurs at x 0 and has a value of y 4 Round to two decimal places Use MINIMUM to find the local minima of the graph The local minima occur at x and at x and have values of y and y Round to two decimal places Use the smaller x value as x

a Use a graphing utility to graph f x 0 2x4 0 2x 0 8x 4 on the interval 3 2 and approximate any local maxima and local minima b Determine where f is increasing and where it is decreasing OA B Use MAXIMUM to find the local maximum of the graph The local maximum occurs at x Round to two decimal places and has a value of y y 0 O C

a Use a graphing utility to graph f x 0 4x 0 6x 3x 4 on the interval 6 4 and approximate any local maxima and local minima b Determine where f is increasing and where it is decreasing a Using a graphing utility graph the function for 6 x 4 and 25 sys 10 Choose the correct graph below Q The local maximum is y and it occurs at x Round to two decimal places B 12 Q G OC a Q

to graph f x x 5x 4 on the interval 2 2 and approximate any local maxima and local minima b Determine where f is increasing and where it is decreasing a Using a graphing utility graph the function for 2 x 2 and 4sys 10 Choose the correct graph below B The local maximum is y 8 30 and it occurs at x 1 29 Round to two decimal places Q OB The local minimum is y and it occurs at x Round to two decimal places 20 O C Q Q

11 4log 12 9n 9 1 1 In 5x 8 In 7 4 10 log x 10 log 9 1 12 3 log 6 7n 3 9 14 log 3x 8 log 6 2