Algebra Questions

What is the expression in radical form 5ab 312 O 125a b3 O 5a 6 212

Solve the equation Check your solution 5k 4 5 3

Solve and check the linear equation 10 X N 2 11 x3 X

Solve the equation Check your solution 3x 4 1 7 12 The solution set is Simplify you or Tune Integ o fre

if dilating a shape maps it onto another shape then the two shapes are similar In this activity you will use dilation to determine whether the shapes in these graphs are similar Graph 1 Question 1 3 5 D 7 Hi A 3 Graph 2 III a

Select the value of the y intercept in the graph below 2 8 7 99 6 5 4 3 2 L 2 1 N 2 4 5

Identify the value of the zero s in the graph below Select all that apply 5 4 3 2 A 2 B 0 C 1 D 1 E F 12 3 10 086 4 42 2 2 4 6 B 12 14 16 18 20 1 3 4 5

10 8 6 6 The function is I There is function is 2 I 0 5 10 15 x 2 There is a I 20 25 3 35 40 interval 2 x 6 8 on the interval on the at 32 at 4 and at 2 The positive negative zero

Choose the statement s that is are TRUE about the graph below Select all that apply Y 5 4 3 2 1 A B C D y 3 2 1 0 14 3 4 5 1 2 3 The function has three zeros 4 The function is positive on two intervals X 5 The value of the y intercept is 2 The function is negative on two intervals

An integer a 40 it said to be divide integer b if there exists an integer k such that b ak it le denoted by a b Ex 02 8 8 2 4 3 24 24 3 8 It a does not divides b denoted by a b It a b a 6 3 It a b a b Properties of dinsibility It a b then P T a bx where x ie an integer Pt Guven a b b ak kez Note x B Sx bx ak x k x K 2

Evaluate each function for the given value 11 f x x 6x 7 Find 0 A 7 B 2 C 6 D 2 3 3 f x 4x 4 Find f 3 B 7 D 8 A 9 C 2 2 2 f x 3x 4 4 Find 2 B 2 D 8 A 4 C 9 4 4 f x x 2x 4 Find 0 A 1 B 3 C 0 D 4

Choose the correct values from the dropdown menu to identify the domain and range of the graph below 5 4 3 2 1 LO The range is 4 3 2 4 2 3 5 1 2 3 4 5 The domain is x y

notation 5 4 3 2 1 A B C D 5 4 3 2 H 4 2 3 5 1 2 3 4 5 5 y 4 5 y 3 3 y 4 3 y 2

Which of the following graphs are functions Select all t apply A B 64444 12345 5482 11145 C D E F

Identify each graph as discrete or continuous Drag the correct answer to match with each graph situation The weight of a horse The number of TV sets in your house 31 5 4 3 2 1 1 2 3 4 5 5 4 3 2 1 2 4 1 2 3 4 1 2 3 4 5 I I I I

It r 0 then ri b therefore from 0 0 9 2 9 5 a 1 22 1 51 0 hot s a s b 5 a 69 from GCD a b 0 GCDa b exists It r to we repeat the process in finite steps n This process terminates In this any ex will arrive at vero remainde after th step we have sequence of integers of such that ostat recrub re n2 n23 p Shume To ser Foster rn b and on Wri n a

Consider the following f x 2x 7 a Write the formula for f x dx b Write the formula for 2 16x dx f x dx f x dx Use C for the constant of integration X 10x dx f x dx

oblem 7 Use Gaussian elimination to find a row echelon form not reduced row echelon form of the augmented matri for the following system and then use it to determine for which value of a the following system has infinitel many solutions x 2y 3z 1 x 2y 7 2x 3y az 0

A car is driving away from a crosswalk The formula d t 2t expresses the car s distance from the crosswalk in feet d in terms of number of seconds t since the car started moving a Suppose t varies from t 2 tot 5 i Does the car travel at a constant speed over this interval of time No ii What is the car s average speed over this interval of time feet per second Preview b Suppose t varies from t 1 7 to t 2 5 i Does the car travel at a constant speed over this interval of time No ii What is the car s average speed over this interval of time feet per second Preview

Each graph represents a relation Determine if the relation is a function DIS 14 3 A The relation is not a function B The relation is a function 10 HO The A The relation is a function B The relation is not a function 2 4 E 41 DEL 19 M Blind HIND 100 10 SHALI PEN A The relation is a function B The relation is not a function IN A The relation is a function B The relation is not a function FOM

9 A Domain x 5 Range All real numbers B Domain x 4 11 Range All real numbers C Domain x 6 Range All real numbers D Domain x 5 Range All real numbers 10 10 A Domain 3 x 5 Range 6 y 6 B Domain 3 x 4 Range 4 y 4 C Domain 1 x 3 Range 6y 6 D Domain 2 x 6 Range 7 ys5 12

What is the y intercept of the function 10 07 05 5 5 256 10 X

Prime numbers An integer pyl which has no divisor except one and the number itself is called a prime number An integer p71 il called 7 prime number if it e not divisible by any other member except II and IP Ex 2 3 5 7 11 13 composte number Composite number an integer which i not a prime number 96 An integer axt called o called a composite number it it has a divisor other than II or a Ex 4 6 8 9 10

The graph shows a linear function What is the y intercept of the function y 15 14 5 10 5 5 10 X

From 6 we get 1 A k my By which gives 1 Ak and 1 N or A and B Hence 1 y k my ky Thus the given differential equation can be rewritten as 1 Bk m or ky k my dx for y0 and k my 0 In the integration of Eqn 7 the signs of y and k my play an important role We now discuss the following possible cases Case 1 y 0 and k my 0 0 y m For the case under consideration Eqn 7 can be expressed as d ny In k my m k k my my 1 7 which on integrating yields Iny In k my x c where c is a constant of integration The above equation can be further express as In y In k my x c 1 k exp x c k my Case II y 0 When y 0 then k my 0 because m 0 k 0 In this case Eqn 7 on integration can be written as In y In k my x c

MODELING WITH MATHEMATICS A repair bill for your car is 553 The parts cost 265 The labor cost is 48 per hour Write and solve an equation to find the number of hours t of labor spent repairing the car

Problem 1 Find the exact values of the other five trigonometric functions of t by using information 7 25 a cos t b tan t c csc t 1 7 2 5 2 such that the terminal s Quadrant II such that sec t 0 such that cot t 0

Describe how the graph of the function g x x1 2 can be obtained from the basic graph Then graph the function Start with the graph of h x x Then Type an integer or a simplified fraction it vertically by a factor of Finally shift it 12121 unit s

Describe how the graph of h x 2x 3 can be obtained from one of the basic graphs Then graph the function Fill in the blanks To obtain the graph of h x 2x 3 start with the graph of y by multiplying each and shift it units it by Then reflect it across the

Describe how the graph of g x x 9 can be obtained from one of the basic graphs Then graph the function Select the correct choice below and fill in the answer box to complete your choice O A Start with the graph of y Shrink it horizontally by a factor of 9 B Start with the graph of y Shift it left 9 units OC Start with the graph of y OD Start with the graph of y Shift it up 9 units Shift it down 9 units

5 Shown on the right is the graph of y X Determine its symmetries if any This graph is O A symmetric to the origin B symmetric to the x axis OC symmetric to the y axis D not symmetric to the x axis y axis or origin C P 49 B B q

Decide whether f is even odd or neither f x x 2x 7 Choose the correct statement A The function is even B The function is odd OC The function is neither even nor odd

Determine visually whether the function is even odd or neither even nor odd Is the function odd even or neither O A Even OB Odd OC Neither MAA 2 Ay 2 2x Q

Determine whether the function is even odd or neither Then determine whether the function s graph is symmetric with respect to the y axis the origin or neither 6 g x x 4x Determine whether the function is even odd or neither Choose the correct answer below even odd neither

63 Cost of Private College Education The table lists average annual cost in dollars of tuition and fees at private four year colleges for selected years Year 2013 2014 2015 2016 2017 Data from National Center for Education Statistics Cost in dollars 24 523 25 707 26 739 27 942 29 478 a Determine a linear function f x ax b that models the data where x 0 represents 2013 x 1 represents 2014 and so on Use the points 0 24 523 and 4 29 478 to graph f and a scatter diagram of the data on the same coordinate axes What does the slope of the graph indicate b Use the function from part a to approximate average tuition and fees to the nearest dollar in 2016 Compare the approximation to the actual figure given in the table 27 942 c A graphing calculator is required Use the linear regression feature of a graphing calculator to find the equation of the line of best fit

a Given that 1 where n Z n 1 Find the roots of the equations for the various values of n and complete the table below 77 3 4 5 6 7 750 51 1 Roots 73 Sum of the roots What conclusion can you make b Find the roots of the equation 1 0 where n 2 Represent these roots on the Argand 2 7 diagram Suppose w e is the root with the smallest positive argument express the other roots in terms of w Show that 1 w w w w 0 using i the sum of geometric series the expansion of z 1 1 z 2 2 c For any two complex numbers and w use the properties of a complex conjugate to establish the relationship wf z wf 2 P wf Sketch and was vectors on an Argand plane If the vectors and w form a parallelogram find the length of the diagonals of the parallelogram in terms of and w Give a geometric interpretation of

ny In k my 1 which on integrating yields Iny In k my x c where c is a constant of integration The above equation can be further express In y k In k my k x c or my 1 k 1 exp x c

tions of Case III y 0 and k my 0 y In this case Eqn 7 after integration gives In y In k my x c k or th ex c k my You may now try the following exercises E1 Solve the following equations a 1 x dy 1 y dx 0 0 c y x a y x dx dx d 3e tan ydx 1 ex sec ydy 0

ky my2 dx Now we will try to decompose the coefficient of into partial fractions dy dx 1 A B Let y k my yk my where A and B are constants to be determined From 6 we get 1 A k my By which gives 1 Ak and 1 or A Hence and B 1 y k my ky Bk m m 1 k k my Thus the given differential equation can be rewritten as 1 1 m dy 1 ky kk my or For the case under consideration Eqn 7 can be expressed as ny In k my 1 for y0 and k my 0 In the integration of Eqn 7 the signs of y and k my play an important role We now discuss the following possible cases Case 1 y 0 and k my 0 0 y k which on integrating yields 6 7 Iny In k my x C where e is a constant of integration The above equation can be further express as In y In k my x c 1 4 my exp x c Case II y 0 When y 0 then k my 0 because m 0 k 0 In this case Eqn 7 on integration can be written as

The manager of a large apartment complex knows from experience that all 120 units will be occupied if the rent is 420 dollars per month A market survey suggests that on average one additional unit will become vacant for each 20 dollar increase in rent Let a represent the number of times that rent is increased by 20 Express the monthly revenue R as a function of x R x What rent should the manager charge to maximize revenue rent month max revenue month What is the maximum possible revenue

D for the matrix A 01 4 1 is No Decomposition possible NO Find pumutation matrix P such tha PA LU for come lower I upper triangular makine 13 3 PAZLU mu

For the following system to be consistent 6y 31y 20y CT CT 34 z kz E 43 Ma

A farmer has 600 meters of wire fence with which to build two identical rectangular pens that share one side as shown below Note you can move the point to alter the rectangles Let be the length in meters of the shared side Express the combined area of the two pens as a function of x A x For what value of x is the combined area maximized Round your answer to two decimal places m What is the maximum combined area of such an enclosure Round your answer to two decimal places

Divide the following and round to the nearest hundredth 29 432 0 0012

to the point In the image below you can slide the point along the curve to visualize this scenario 5 0 5 3 3 5 Enter the coordinates of the closet point Round each coordinate to two decimal places

f x x x 2 a Use the four step procedure to find the following derivatives of f x Notes unless spec ified you can directly apply rules of differentiation to find derivatives This is the only problem in this quiz that requires you to calculate the derivative from the limit definition b Use rules of differentiation to find f x and compare the results in a and b

Exercise 4 4 1 For each set of vectors use the most efficient method to determine if it is linearly independent or not 0 2 1 U i S ii S v1 iii S3 2 2 1 2 22 W 1 1 1 Uz V3 0 G W4 5 100 101 2 1

For each of the series below select the letter from A to C that best applies and the letter from D to K that best applies A possible answer is AF for example A The series is absolutely convergent B The series converges but not absolutely C The series diverges D The alternating series test shows the series converges E The series is a p series or a constant multiple of a p series F The series is a geometric series G We can decide whether this series converges by comparison with a p series but the series is not a p series or a constant multiple of one H We can decide whether this series converges by comparison with a geometric series I Partial sums of the series telescope J The terms of the series do not have limit zero K We can decide using the integral test NOTE Make sure that you can provide the proper arguments to support your answers 818181818 1 4n ln n cos nn NT 2n 5 n n n 6 sin n n cos n Activa Go to S

1 Dan has to pay 2 each time he takes the city bus Write an equation for the cost y of Scenario 1 taking x bus trips Y ax 2 One week Dan s bus bill is 34 How many times did he ride the bus X 1 34 2 17 17 timet 3 Dan can buy a monthly bus pass for 39 50 If Dan takes the bus an average of 25 times per month should he buy the pass No because he ll only becible 39 50 2 ride 19 75 to 19 Jimes with the Padd without GP Of The Pass if 38 so the past y a 30 2 25 4 Write an equation for x in terms of y 17y x Scenario 2 1 At Cayla s cookie decorating business she can decorate a dozen cookies in 2 minutes Write an equation for the number of cookies decorated d after m minutes 2 How long would it take Cayla to decorate 30 cookies doporoto 4 cookies per minute write an equation for how

3 5 points each Find the Area and Perimeter of the following sector A P 128 12 ft radius