Algebra Questions

Use exact numbers y x 9 8 7 6 5 4 3 2 9 876 6 6 SK 5 4 3 2 14 23 Y 2 8788 3 4 5 6 7 8 9 HE 1 2 3 4 5 6 7 8 9

in a triangle one leg measures 14 km and the other leg measures 48 km what is the length of the hypotenuse

question Use the Mathematician s Plan to answer each question Show all work and attempt every 1 Determine the coordinates of each point below E 10 9 0 A 70 6 5 B 2 2 3 4 5 6 y 8 G H 2 State the coordinates of each of the points below YA A 7 6 B 5 C 4 3 D 2 E 1 F A 7 6 5 4 3 2 1 0 2 3 40 5 6 7 F 1 E 2 3 B 4 A B C D E F G H 1 5 6 D 7 x

5 If f x 2x 3 g x x x 21 find x when a f x 7 b g x

5 Distance miles 0 10 9 8 765 3 1 3 ate 2 3 19 Gulliver s Travels 4 5 6 Time hours 7 endent 8 9 10 read as 711 The function d represents Gulliver s distance from home after t hours 1 Use the graph to evaluate the function at each value Explain what each means in terms of the problem a d 2 4 b d 5 11 c d 2 9 4 d d 10 2 Calculate the value of t that makes each equation true Explain what each means in terms the problem a d t 2 c d t 4 b d t 5 d d t 0

Put the function P 7 1 2 in the form P Poekt NOTE Round your answer to four decimal places if required P

A turbo prop plane flying with the wind flew 1400 mi in 5 h Flying against the wind the plane required 7 h to travel the same distance Find the rate of the wind and the rate of the plane in calm air

F The position of a particle moving along a coordinate line is s 25 4t with s in meters and t in seconds Find the rate of change of the particle s position at t 6 sec The rate of change of the particle s position at t 6 sec is Type an integer or a simplified fraction m sec CL

Given s t 2t 4t where s t is in feet and t is in seconds find each of the following a v t b a t c The velocity and acceleration when t 2 sec a v t b a t c When t 2 sec the velocity is Simplify your answer When t 2 sec the acceleration is

Describe how the graph of the following function can be obtained from one of the basic graphs 1 g x x 2 Start with the graph of y Shift it unit s it by multiplying each by and then reflect it across the

Lena invested 400 in a fund for 3 years and was paid simple interest The total interest that she received on the investment was 36 As a percentage what was the annual interest rate of her investment If necessary refer to the list of financial formulas n

To be able to take her dream vacation Kaitlin decides to save for 3 years She opens a savings account with 800 The account pays simple interest a annual rate of 4 She doesn t make any more deposits Answer the following questions If necessary refer to the list of financial formulas a How much total interest will Kaitlin earn b What will the total amount in the account be including interest X

Use the quadratic formula to solve the equation 2x x 1 TER The solution set is Type an exact answer using radicals as needed Type your answer in the form a bi Use a comma to sep answers as needed

A jogging track has a length of 1496 yards yd How long is this in miles mi First fill in the blank on the left side of the equation using one of the ratios Then write your answer on the right side of the equation Ratios 1 ft 12 in 1496 yd 12 in 1 ft 1 mi 5280 ft 0 5280 ft 1 mi 1760 yd 1 mi 1 mi 1760 yd ft 00 X yd in S mi

have real solutions tell whether they are rational or irrational Do not actually solve the equation 10x 10x 7 0 The discriminant is 180 Simplify your answer Determine the number of real solutions of the equation If the equation does have real solutions tell whether they are rational or irrational Choose the correct answer below OA There is one real irrational solution B The are two real irrational solutions C There are no real number solutions D The are two real rational solutions

3 Using the table of values find the following 9 4 X f x a f 3 c f 8 0 1 e If f x 9 what is x g If f x 0 what is x 8 4 P A 3 2 9 3 2 b f 20 d f 1 f If f x 4 what is x h If f x 5 what is x 5 8 20 0

olve the equation For an equation with real solutions support the answer graphically x 8x 9 ewrite the equation in factored form E x 9 x 1 0 Factor completely he solution set is Type an integer or a simplified fraction Type an exact answer using radicals and i as needed Use a c eparate answers as needed

Determine whether the following statement is true or false The equation 3 p 2 p 2 3 0 is quadratic in form Choose the correct answer below 2 O A True because the given equation is of the form au bu c 0 by letting up OB True because the given equation is of the form au bu c 0 by letting up O C False because the given equation is of the form ax b 0 by letting up 2 O D False because the given equation is of the form ax b 0 by letting u p 2

For the equation 5w 23 w 12 0 determine the appropriate substitution and write the equation in the form au bu c 0 The appropriate substitution is u The equation with substitution is Tyne an equation in terms of u

Describe how the graph of the following function can be obtained from one of the basic graphs 1 g x 3 3x 13 To obtain the graph of g x 3 start with the graph of y it by dividing each by Then shift it

Write an equation for a function that has a graph with the given characteristics The shape of y x but upside down and shifted right 4 units Which of the following is the equation of the function O A y x 4 2 OB y x 4 OC y x 4 2 OD y x 4

Describe how the graph of the function can be obtained from one of the basic graphs g x x 5 7 Start with the graph of h x x Shift it units Then reflect it across the and shift it units

Find a polynomial f x of degree 3 with real coefficients and the following zeros 4 2 i f x

Describe how the given function can be obtained from one of the basic graphs Then graph the function g x x 1 5 Describe how the given function can be obtained from one of the basic graphs Start with the graph of f x Shift it 1 unit and then shift it 5 units

Simplify 6w 8w 2 21 16w 0

Write an equation for a function that has a graph with the given characteristics The shape of y x but upside down and shifted right 6 units and up 8 units Which of the following is the equation of the function O A y x 6 8 OB y x 6 8 OC y x 6 8 OD y x 6 8

Given that f x x 6 match the function g with a transformation of f g x x 4 6 What is the transformation O A g x f x 4 OC g x f x 4 O E g x 4f x O B g x f 4x O D g x f x 4 OF g x f x 4

Write an equation for a function that has a graph with the given characteristics The shape of y x but shifted left 9 units and up 6 units Which of the following is the equation of the function OA y x 91 6 O B y x 91 6 OC y x 91 6 OD y x 91 6

By transforming each point on f x determine the resulting set of ordered pairs that define g x f x 4 Submit your answer is the form a b Do Not use any spaces in your answers Point 2 5 transforms to Point 0 4 transforms to Point 1 3 transforms to

The heights of a ball after t seconds when thrown straight up with an initial speed of 70 feet per second from an height of 5 feet can be modeled by the equation s 16t 70t 5 a When will the height of the ball be 40 feet b When will the height of the ball be 70 feet c Will the ball ever reach a height of 130 feet a The height of the ball will be 40 feet after approximately seconds Use a comma to separate answers as needed Round to the nearest tenth as needed b The height of the ball will be 70 feet after approximately seconds Use a comma to separate answers as needed Round to the nearest tenth as needed c Will the ball ever reach a height of 130 feet Choose the correct answer below O A Yes because both solutions of the equation when s 130 are irrational O B No because one of the solutions of the equation when s 130 is negative O C No because both solutions of the equation when s 130 are rational

Zero is the smallest integer True False

sting for Symmetry Graphically In Exercises 23 and 24 test the graph for symmetry with respect to the given axis or the origin 23 Origin 0 0 14 412 2 2 244 2 2 4 4 24 y Axis 4 2 1 2 2 6 1 0 4 6 2 2 3 6

Use a vertical format to find the product x 3x 6 4x 8

Ive the following equation using the quadratic formula 2 5x 3x 2

To help with her retirement savings Jina has decided to invest Assuming an interest rate of 3 47 compounded quarterly how much would she have to to have 147 200 after 20 years Do not round any intermediate computations and round your final answer to the nearest dollar If necessary refer to the list of financial formulas sm

Tony is going to invest to help with a down payment on a home How much would he have to invest to have 36 800 after 10 years assuming an interest rate of 1 61 compounded monthly Do not round any intermediate computations and round your final answer to the nearest dollar If necessary refer to the list of financial formulas

Solve 8 sin n 7x x 3 for the four smallest positive solution

Thus 1 1 2 s 3yo s ds 1 8ds 81 1 y 1 2 s y s ds 2 f s 2 ds 2 2t 2 x 1 L3 1 8r 1 21 2 Next x 1 1 2x s 3y s ds 1 8 11 8 1 Y 1 2 f s y s ds 2 2 1 3 1 2 21 3 2 2 1 8 2 25 2 3 ds dr 3 2 21 2 6 2

A C b 2 21 30 O C sin 21 30 OD sin 21 30 cos 21 30 a C 6 What is the length of c in the right angle triangle shown O A sin 21 30 O B 2cos 21 30

Write the interval notation for this compound inequality Explain why parenthesis brackets etc Lesson 1 05 x 4 or x 8

For the function below a find the vertex b find the axis of symmetry c determine whether there is a maximum or a minimum value and find that value and d graph the function 2 f x x 4x 5 a The vertex is 2 1 Type an ordered pair using integers or fractions b The axis of symmetry is x 2 Type an equation Use integers or fractions for any numbers in the equation c Does f x have a maximum or a minimum value The parabola has a minimum value The parabola has a maximum value The minimum maximum value is Type an integer or a fraction 10 8 6 4 Ay 10 8 6 4 2 2 4 6 8

1 4

2 Anton 10 B i Mostres a 10 10 x x 8x 13 KOCAELO swyckel CERNISERI KAGAME DRE NT PETER BARE MA SAAN MAINE BAGES SEMENTAREDIMIES HERBERA COMPRUERENT THESTATE 11 11 3x x 1

f x 5 4 3 2 N 1 4 3 2 1 0 1 2 1 2 ge of the piecewise function above 3 4 X

8 Describing end behavior Sketch the graph of each function 8 y x 4x 8 24 T

7 4 1

2x 8 x 2 f x x 3 2 x 3 x 3 Evaluate f 3 in the piecewise function above Evaluate f 2 in the piecewise function above Evaluate f 1 in the piecewise function above Dovers x 3

Given the following function a find the vertex b determine whether there is a maximum or a minimum value and find the value c find the range and d find the intervals on which the function is increasing and the intervals on which the function is decreasing f x x 10x 21 B The parabola opens upward and has a minimum value of 4 c What is the range of f x The range of f x is 4 00 Type your answer in interval notation Use integers or fractions for any numbers in the expression d On what interval is the function increasing A The function is increasing on 5 00 Type your answer in interval notation Use integers or fractions for any numbers in the expression On what interval is the function decreasing The function is decreasing on Type your answer in interval notation Use integers or fractions for any numbers in the expression

Given the following function a find the vertex b determine whether there is a maximum or a minimum value and find the value c find the range and d find the intervals on which the function is increasing and the intervals on which the function is decreasing f x 4x 4x 3 Select the correct choice below and fill in the answer box within your choice Type an integer or a fraction A The parabola opens downward and has a maximum value of 4 B The parabola opens upward and has a minimum value of c What is range of f x The range of f x is 4 Type your answer in interval notation Use integers or fractions for any numbers in the expression d On what interval is the function increasing The function is increasing on for any numbers in the expression

Given the following function a find the vertex b determine whether there is a maximum or a minimum value and find the value c find the range and d find the intervals on which the function is increasing and the intervals on which the function is decreasing f x x 1 10x 21 L JPY RAY O A The parabola opens downward and has a maximum value of B The parabola opens upward and has a minimum value of 4 c What is the range of f x The range of f x is 4 00 Type your answer interval otation Use integers or fractions for any numbers the expression d On what interval is the function increasing The function is increasing on Type your answer in interval notation Use integers or fractions for any numbers in the expression