Quadratic equations Questions and Answers

4 Kent can paint a certain room in 6 hours but Kendra needs 4 hours to paint the same room How long does it take them to paint the room if they work together

In Exercises 11 14 use zeros to graph the function 11 y x 1 x 3 13 g x g x x 10x 21 12 f x 2 x 2 x 6 14 y x x 6

2 A plane flies 910 miles with the wind in the same time it can go 660 miles against the wind The speed of the plane in still air is 305 miles per hour What is the speed of the wind Against With Distance Rate Time

6 If s varies inversely as t2 and s 10 when t 2 find s when t is 10

3 A person swims 11 miles downriver in the same time they can swim 7 miles upriver The speed of the current is 4 miles per hour Find the speed of the person in still water Rate Time Distance Upstream Downstream X C x c

EVALUATE without a calculator log 35 logs 125 9 11 log 6 log 8 10 log 2 9 12 2 0923 5 logs6 logs 7

5 Marco can build a lap top twice as fast as Cliff Working together it takes them 5 hours How long would it have taken Marco working alone

In Exercises 1 and 2 find the x intercepts and axis of symmetry of the graph of the function 1 2 2 y X y x 2 x 2 2 y 2 x 1 x 4 4 A 6 2 X 8

In Exercises 7 10 find the zero s of the function 7 y 4 x 5 x 9 9 g x x 7x 30 8 f x 1 x 3 x 2 10 y 2x x 10

4 Solve the following system of linear equations using a Gaussian Elimination method b Guass Jordan Method x2 2x3 x4 1 x 2x x3 2 2x x x3 3

Ian is decorating the outside of a box in the shape of a right rectangular prism The figure below shows a net for the box 8 cm 7 cm 7 cm 12 cm 7 cm 7 cm What is the surface area of the box in square centimeters that Ian decorates

Convert the following quadratic function to vertex form by completing the square Identify the vertex and the axis of symmetry w z 3z 15z 5 The vertex is The axis of symmetry is x

10 8 6 a b 6 y Identify a and b for the hyperbola with equation IE 6 8 10 2 a 62 D 1

Using the Integral Test In Exercises 29 32 use t Integral Test to determine the convergence or divergence of t p series 29 31 AL nl 4 30 32 12 12 n 2 27 10 11T

What is the value of y OA 2 B 3 O C 4 OD 8 Show Transcribed Text Which side lengths form an acute triangle A 5 12 13 OB 8 10 14 C 6 7 11 6

A small plane flew 888 miles in 4 hours with the wind Then on the return trip flying against the wind it traveled only 528 miles in 4 hours What were the wind velocity and the speed of the plane Note The speed of the plane means how fast the plane would be flying with no wind Answer How to enter your answer opens in new window speed of the plane wind velocity mph mph Keypa Keyboard Shortc

Find the mean median and mode Round to the nearest tenth when necessary 3 4 11 15 4 OA mean 7 4 median 4 no mode OB mean 8 3 median 4 no mode OC mean 7 4 median 4 mode 4 OD mean 6 4 median 4 mode 11

Find the mean and standard deviation of the of data Round to the nearest tent 20 16 18 14 9 20 16 OA mean 16 standard deviation 3 6 OB mean 16 standard deviation 12 7 OC mean 16 1 standard deviation 3 6 OD mean 16 1 standard deviation 12 7

The Luxor Hotel in Las Vegas is a square base pyramid that is 646 feet wide at the base and 350 feet tall If the outer walls of the hotel are covered in glass what was the minimum amount of glass used for the exterior

Answer x 5y 3z 11 4x 4y 62 36 Indicate the number of solutions to this system State the solution if one exists and if there are infinitely many solutions express the solution set in t variables Selecting an option will display any text boxes needed to complete your answer O No Solution O One Solution 2023 Hawkes Learning O Infinitely Many Solutions

Solve the following exponential equation Express your answer as a decimal approximation rounded to two decimal places e 9 7 14

Answer x 5y 14 Keyboar Indicate the number of solutions to this system State the solution if one exists and if there are infinitely many solutic the solution set in terms of one of the variables Selecting an option will display any text boxes needed to complete your answer O One Solution O No Solution Solution Set Infinitely Many Solutions E z ZER

struct the augmented matrix that corresponds to the following system of equations 5x 3y 2 3 4 swer 2 7z 3x y 8 2 x 6 z 6y

9 Write an exponential equation for the graph shown below f x 21 18 15 Use this model to evaluate f 6 12 35 3 2 5 2 1 5 1 05 9 6 P 0 3 X 05 1 15 2 25 3 35

11 Which function s graph is the result of shifting the graph of f x x 4 down 3 units a g x x 1 b g x x 4 c g x 4x 4 d g x x 7

Which situation could be modeled by using a linear function 1 a bank account balance that grows at a rate of 2 per year compounded annually 2 a population of fish that doubles every 10 months 3 the cost of cable service that charges a 80 installation fee and then a 110 monthly charge 4 the value of Matt s car if it depreciates at a rate of 15 per year

Graph the following square root function f x 2x 4 dentify the year

4 Solve the system by graphing and check your answer 3y 9 x x y 2

1 Graph f x x 4 2 using 1 x 7 Describe transformation

Describe the transformation between the graph of each of the functions below and the parent function f x x DO NOT GRAPH 3 g x x 2 6 4 g x 2 x 5 5 g x x 4 6 g x x 2

12 Which of the following is true when the graph of f x x 4 is transformed into the graph of g x 2x 4 a b C d The new function has more zeroes than the old function Both functions have the same vertex The function is translated up The axis of symmetry changes

Match each function to its graph 7 f x 4x 3 A 12 ak ANA 8 f x x 3 B 4 NA 2 10 3 9 f x 4x 3 10 x x 3 C 2 0 2 6 2 XA D 21x 0 2 4

Select the values of x that make the inequality true X 1 4 Choose 3 answers A X C 1 1 4 B0 1

3 2 1 1 2 3 Determine the period AA 2 4 6 8 10 12 14 Ent

4 3 2 1 1 2 3 4 Determine the period 4 A 8 12 16 20 24 28 Enter

Which binomial is a factor of the function f x 2x4 2x 4x A B C D X 2 X 2 X 4 X 1

Solve the system of equations by elimination 5x 2y3z 7 2x 6y 3z 4 5x 4y 4z 5

6 Find the axis of symmetry and vertex algebraically graph the function represented by f x x 2x 3 and answer the questions below a Axis of symmetry b Vertex c Is the vertex a maximum or minimum d What is the maximum or minimum value e Construct a table to graph the function f x intercept s g y intercept h Domain 10 points

Multiple Choice Each correct answer will receive 2 points No partial credit will be given For each question write the numeral preceding the word or expression that best completes the question in the space provided 1 Which set of points model a quadratic function 1 2 4 1 6 0 8 1 10 2 12 2 2 4 1 1 0 0 1 1 2 4 3 2 4 1 2 0 1 1 5 2 25 4 2 4 1 2 0 0 1 2 2 4

5 John determined the zeros of a function to be of 5 and 2 What could be John s function 1 g x x 5 x 2 2 g x x 5 x 2 21 x 5XX 21

4 What are the roots of the equation x 10x 21 0 1 1 and 21 2 5 and 5 3 3 and 7 4 3 and 7

What are the vertex and axis of symmetry of the parabola shown in the diagram below 1 vertex 1 4 axis of symmetry x 1 2 vertex 1 4 axis of symmetry x 4 3 vertex 4 1 axis of symmetry x 1 4 vertex 4 1 axis of symmetry x 4

Previous Answer 5 8 Write the equation in standard for Then identify the center of the circle x y 2x 2y 23 0

Previous Answer 0 10 Write the equation in standard form Then identify the center of the circle x y 10x 16y 53 0

Previous Answer 3 14 Write the equation in standard form Then identify the center of the circle x y2 32x 6y 256 0 Math Sunshine 2017 Emily Bracelin M

Previous Answer 2 6 0 0 Write the equation in standard form Then identify the center of the circle x y 20y 91 0

B an b Round to the nearest integer as needed m Round to the nearest integer as needed m Round to the nearest integer as needed CH CDD 965 m b 40 33

5 5 pts Establish the Identity 4 sin u cos u 1 2 sin u sin 4u

Find the value of b that makes quadrilateral TUVW a parallelogram T b 14 U 15b V

If VW u 9 and VY 4u find the value of u that makes quadrilateral WXYZ a parallelogram V N X W