Algebra Questions

mative com formatives 63580800 1 Sketch the graph of each linear inequality 1 y2x 3 A B D 2 2 5x y S s A B D 13 1

A3 4 3 3 2x 5ps 10 M 5 6 4 5x 3p 9 7

5 Algebra Prep 1032 Kuli Software lur SUM 2 Q2 Solve each system by elimination 5 6y 42 18x 4x 8 3y A 4 1 B 4 1 reserved 6 6 3y 3x 15 9 3x 2y A 7 5 B 7 8 ZOO

Solve the equation by graphing x 14x 49 0 First graph the associated parabola by plotting the vertex and four additional points two on each side of the vertex Then use the graph to give the solution s to the equation If there is more than one solution separate them with commas 30 B Ho 6 X Solution s x 0 DO No solution X 03

B 3 4 44 Y 7 y x 2 5 y 2x 6 7 8 B 11 Show the solution to the following system FOLLOW D 9 10

Use the ALEKS graphing calculator to find all the real zeros of the quadratic function f x 3x 2x 2 Round to the nearest hundredth If there is more than one answer separate them with commas If there are no real zeros click on None real zero s 0 0 None

A 4 1 C 1 4 Sketch the solution to each system of inequalities 7 y x y2 2x 3 B D r 2 B A P B 4 D 1 4 AN 100 Y C2822 Kule Software LLC All sighis roser cel A 7 5 C 7 10 8 2x 3y2 3 x 3y 6 A B O D 4 2 Made with 17 222 Inti a ste B 7 8 D 1 6 Algebre 2

g x x Plot five points on the graph of the function one point with x 0 two points with negative x values and two points with positive x values Then click on the graph a function button 32 EG 21x 10 8 13 10 X

9 10 10 ys y2 x 7 zoom in

14 Given f x and g x x find the following expressions x 5 a fog 4 b gof 2 c fof 1 d gog 0 a fog 4 Type an exact answer using radicals as needed Simplify your answer

12 When police officers investigate a car crash they can estimate the speed the car was travelling by measuring the skid distance Skid Distance of a Car Skid distance m 160 120 d 80 40 0 S 40 80 120 Speed km h a Why are the points on the graph connected b Estimate the domain and range of the graph Are there any restrictions on the domain an range Explain

Evaluate each expression using the values given in the table 1 0 2 3 1 6 0 1 27 X f x g x a fog 1 d gof 0 3 9 7 a fog 1 1 b fog 1 1 c gof 1 7 d gof 0 2 6 2 b fog 1 e gog 2 1 3 0 3 9 c gof 1 f fof 1

Find functions f and g so that fog H x 9x 1 5 Choose the correct pair of functions OA 5 f x x g x 9x 1 C 5 f x 9x 1 g x x O B f x x g x 1 9 O D x 1 f x g x x 9

Evaluate each expression using the values given in the table 1 2 3 3 6 9 0 2 7 X f x g x a fog 1 d gof 0 3 2 9 6 7 2 a fog 1 1 b fog 1 1 FV 0 1 1 b fog 1 e gog 2 1 3 0 c gof 1 f fof 1

Evaluate each expression using the graphs of y f x and y g x shown below a gof 1 b gof 0 c fog 1 d fog 4 a gof 1 4 Simplify your answer b gof 0 Simplify your answer C 8 yg x 6 4 y f x

X 3 or f x x 3 and g x x 4 b gof a fog x 5 find the following composite functions and state the domain of each X 6 d gog c fof a fo ky Factor completely Simplify your answer

Find functions f and g so that fog H H x 8x 5 Choose the correct pair of functions OA f x 8x 5 g x x O B f x x g x 8x 5 O C f x x g x 5 8 O D f x X 5 8 g x x

2 If f x x 3 and g x then which of the following does fog x equal X Choose the correct answer below O O O 2 x 3 2 X N 2 3 3 2

Evaluate each expression using the graphs of y f x and y g x shown below a gof 1 b gof 0 c fog 1 d fog 4 a gof 1 Simplify your answer I y g x 6 di y f x

If H f og and H x 64 9x which of the following cannot be the component functions f and g Choose the correct answer below O A f x 64 x g x 9x OB f x x g x 64 9x OC f x 64 9x g x x OD f x 64 x g x 9x

Evaluate each expression using the values given in the table 3 2 1 2 9 6 3 6 7 2 0 2 X f x g x a fog 1 d gof 0 a fog 1 0 3 1 0 1 b fog 1 e gog 2 3 9 7 c gof 1 f fof 1

State whether the following statement is true or false If f x x and g x x 9 then fo g 2 3 Choose the correct answer below O A True because g 2 2 9 and f 2 9 3 OB True because f 2 2 and g 2 3 OC False because f 2 2 and g 2 3 OD False because g 2 2 9 and f 2 9 3

3 4B Exit Ticket Divide the following polynomials using any method of your choosing 77x 5x 57x 71 x 10 x x 10

Divide the following polynomials using any method of your choosing 2 16x 3 x 4 11 x x 4

Find the least squares solution of the system Ax b 2 1 2 1 1 3 12 0 X A 26 11 29 11 b

Use the graphs for f x and g x to evaluate the expressions below Write your answer as a whole number or a reduced fraction 6 5 4 3 2 1 1 f x 2 1 f 3 g 1 f 3 g 5 CA A 10 X 160 16 5 4 3 2 1 g x 1 1 g 5 f 4 g 1 f 4 2 st X 160

Exam An airplane flew from a town A to a town B 50km away on a bearing of 210 It then flew from town B to another town C on a bearing of 150 If town C is 80km away from town B find a i b ii the distance between A and C correct to the nearest kilometer the bearing of A from C to the nearest degree How far East of B is C

6 end 10th tem The end 8 sequence o the b the third is 39 tem of sun of 230 Find is the first tem of sum of the an the the first arithmetic sequence first to terms sequence 13 terms is of the 416

Use synthetic division and the factor theorem to determine whether x 2 is a factor of f x f x 3x 8x 7x 6 Complete the first row of the synthetic division table 2 3 8 7 6 Is x 2 a factor of f x OA No x 2 is not a factor because when f x is divided by x 2 the remainder is OB Yes x 2 is a factor because when f x is divided by x 2 the remainder is

Divide the following polynomials using any method of your choosing 2x 7x 2x 9 2x 3 2 x 2x 3

the linear programming problem nimize and maximize 10x 30y bject to 2x y 2 48 x y 232 x 2y 40 xyzo Select the correct choice below and fill in any answer boxes pr your choice What is the minimum value of 2 OA Type an integer or a fraction OB There is no minimum value of z

OA a 26 7 b 44 5 c 30 d 45 This question 1 point s possible For the given data set find the a mean b median c mode or state that there is no mode and d midrange The ages of teachers in the mathematics department of a certain high school are shown below 30 55 33 60 30 55 30 46 46 43 OB a 42 8 b 44 5 c 30 d 45 OC a 31 3 b 44 5 c 30 d 45 Some acco available u OD a 42 8 b 44 5 c 46 d 45

True or False The polynomial below satisfies the given graph 3 y A 0 81 O True O False 40 3 f x x 81x 81

Calculate 1 3i Give your answer in a bi form Give the solution with smallest positive angle

1 2 44 9 D 3 ys 33 2 4 A 10 5 6 10 5 J 8 7 8 A zoom in 9

A graphing calculator is recommended A company s marginal cost function is MC x 28e x 5 dollars where x is the number of units Find the total cost in dollars the first hundred units units x 0 to x 100 Round your answer to the nearest cent 7313 05 x

1 point Let f x be the function 3x2 2x 2 Then the difference quotient f 2 h f 2 can be simplified to ah b for 2 h 2 a and b

Please give complete well written solutions to the following exercises and submit via Gradescope 1 2 points Sketch the regions of integration for each iterated integral below and write each as an iterated integral in the opposite order You may need to break the integral into a sum of 2 iterated integrals a b r5 clnx f x y dy dr 4x 5 f x y dy dx

Solve 1 1 cos x sin 2x The smallest positive solution is The next smallest positive solution is

3x An experimental drug changes a patient s temperature at the rate of x 5 degrees Fahrenheit per milligram of the drug where x is the amount of the drug administered Note The rate of change of temperature with respect to dosage is called the drug sensitivity Find the total change in temperature in F resulting from the first 5 milligrams of the drug Round your answer to three decimal places F

Suppose that the monthly cost in dollars of producing x chairs is C x 0 006x 0 07x 19x 700 and currently 70 chairs are produced monthly a What is the current monthly cost b What is the marginal cost when x 70 c Use the result from part b to estimate the monthly cost of increasing production to 72 chairs per month d What would be the actual additional monthly cost of increasing production to 72 chairs monthly

Points A B C D and E are collinear and in that order Find AC if AE 50 and CE x 32 AC

3 The marked price on a box of chocolates is 15 If the after tax price is 16 20 what percent is the sales tax I

COS COS 7x 12 7T given below CTTP 2 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Rationalize all denominators

K Write the expression as a function of x with no angle measure involved 5 55 6 sin 5 sin 5 0 X 6 Simplify your answer including any radicals Use integers or fractions for any num

K Use a sum or difference formula to find the exact value of the trigonometric function sin 11x 12 11T sin 12 Simplify your answer including any radicals Use integers or fractions for any numbers in the

I sin cos value of the expression 5T J 5x cos 3 12 12 T sin COS 5T 5T 3 12 12 Simplify your answer including any radicals Use integers or fractions for any numbers T sin cos sin

In 1 8 match each expression with the correct choice to form an identity Choices may be used once more than once or not at all sin x sin x 1 cos x y 2 cos x y Drag each of the expressions given above into the appropriate area below 3 cos 4 sin 5 cos 6 sin 7 tan 8 cot 7 IN COS X cos x cosy sin x sin y cos x cos y sin x sin y sin x cOS X sin x tan x cos x cos y sin x sin y cotx COS X cotx tan x COS X Question 1 5 3 1 8 cos x cos y sin x sin y

K Find the exact value of the expression by using appropriate identities Do not us sin 84 cos 39 cos 84 sin 39 sin 84 cos 39 cos 84 sin 39 Type a fraction

Write the expression in terms of sine and cosine and simplify so that no quotients appear in the final ex all functions are of 0 only sin 0 sec 0 cot 0 sin 0 sec 0 cot