Quadratic equations Questions and Answers

Consider the first six terms of this sequence 6 12 24 48 96 Which equation below recursively defines the sequence O an 67 A 6 ax 1 ax 3 2 ax 2 ax 1

Consider the pattern Which function represents the sequence that represents the number of unit squar in the pattern after each step Oa 4 x 1 O 4 2 1 9 a 41 2 a ax

Find mzz 5 mZZ X Write your answer as an integer or as a decimal rounded to the nearest tenth

And UV V70 Write your answer as an integer or as a decimal rounded to the nearest tenth Submit

Solve the right triangle H 3 10 H m I m H 9 Write your answers as integers or as decimals rounded to the nearest tent O I

Find WX 3 WX V 56 Write your answer as an integer or as a decimal rounded to the nearest tent

1 Find the slopes and the equations in slope intercept form of each line Slope 3 2 Equation Slope intercept form 1 Slope 3 2 1 Equation y A Slope 1 Ay Equation Slope Point form 2 3 XY

5 Find the equation of a line that passes through 5 2 and 1 3 in a point slope form b slope int form c general form

9 passes through the point 4 3 and is parallel to the line y 9 x 5

Find the equation of a line in General Form 8 passes through the points 5 0 and 1 3

5 Graph the following lines A A line goes through the point 2 5 and has a slope of 4 3 b y 2 4 3 2 1 x 4 AX O 1 2 y x 3

m m une m 3 Find the slopes of the lines that go through the points A 2 4 and B 5 1 parallel ml m parallel perpendicular ml perpendicular

Find m2T n 10 T 10 S

How much fencing is required to enclose a circular garden whose radius is 70 m round to the nearest meter 440 m 110 m 140 m 15 386 m

ht each kilogram of a person s weight 20 milligrams of a drug is to be given WE dosage should be given to a person who weighs 200 pounds Use 1 pound 0 45 kg Multiply by 10 for each step to the right X10 km hm dam m dm cm mm Divide by 10 for each step to the left 444 44 mg 4 000 mg 1 800 mg 8888 89 ma 10

Find m B D 10 C m B

Given x 0 simplify Vx27 completely

4 Graph the image of trapezoid EFGH after a dilation with a scale factor of 5 centered at the origin 10 8 6 4 2 104 8 6 4 2 F 24 4 6 8 E G 2 H 4 6 8 10 Vic Ver en esp

Write the coordinates of the vertices after a dilation with a scale factor of centered at the origin 10 d 6C 4 2 8 6 4 2 P 4 9 8 2 B 4 A6 8 AO 10 7

Find the indicated term of the geometric sequence 3 6 12 24 the 11th term The 11th term of the geometric sequence is

Write a formula for the general term the nth term of the arithmetic sequence a a2 a3 a4 Then use the formula for a to find ago the 20th sequence 5 0 5 10 OA 5n 100 OB 5n 100 O c 5n 10 90 OD 5n 10 110

Find the nth or general term for the geometric sequence 4 4 4 Which represents the nth OA 4 1 1 OB 4 1 O c 40 1 OD 4 n 1

Evaluate 8 31 51 O A 56 O B 1D 5040 O c 8 O D 1

Find the Least Common Multiply LCM of 3 4 and z z Do not add spaces in your answer LCM

2 3 X 6 x 5 Select the correct choice below and fill in any answer boxes within your choice Simplify your answer Use integers or fractions for any numbers in the expression Use a comma to separate answers as ne 2 3 OA x 6 x 5 OB 2 3 x 6 x 5 X www no numbers must be excluded

Add and simplify your answer Do not add spaces in your answer 3x 2 5x 7

Evaluate 8 31 51 O A 1 5040 OB 1 C 8 OD 56

Write a formula for the general term the nth term of the arithmetic sequence a a2 a3 a4 Then use the formula for an 5 0 5 10 OA 5n 10 110 B 5n 100 O C 5n 10 90 O D 5n 100 to find a20 the 2

9 9 6b 3b 5b 13b 6 3b 9 5b 22b 8 A B b 3 1 b b 4 7 b 8 b 3 b 9 C 18 D 186 10 10 3a 6 21a 66a 48 A C 2 5 a 8 10 a 1 9 14a 16 5a 40 3a a 8 B D a 1 27a

7 7 2n 8 42n 24n A C n 4 3n 3 4 16 16n 21n 3n 4 5 7n D 7 n 4 B 8 8 8x 28x 7x 25x 12 A C x 7 64x 3 x 2 x 5 70x 30 2x 7 B D 40x x 4 x 8 x 5 10x

A survey approximates the number of Americans that are age 65 and older and projects that by the year 2050 approximately 81 8 million Americans will be at least 65 The bar graph shows the estimated number of Americans with projected figures for the year 2020 and beyond A graphing calculator screen displays an exponential function that models the U S population age 65 and over y in millions x years after 1899 Use this information to solve a d below Click the icon to view the bar graph a Explain why an exponential function was used to model the population data OA An exponential function was used because exponential functions are always more accurate than linear functions OB An exponential function was used because there are too many data points to use a linear function OC An exponential function was used because population is always modeled using exponential functions OD An exponential function was used because the data in the bar graph is increasing more and more rapidly b Use the graphing calculator screen to express the model in function notation with numbers rounded to three decimal places f x c According to the model in part b how many Americans age 65 and over were there in 2010 Use a graphing calculator million Type an integer or a decimal rounded to one decimal place as needed million Does this rounded number overestimate or underestimate the 2010 population displayed by the bar graph By how much Choose the correct answer below and fill in the answer box to complete your choice Type an integer or decimal rounded to one decimal place as needed OA The rounded number overestimates the 2010 population by OB The rounded number underestimates the 2010 population by million ExpReg y a b x a 3 3354487089 b 1 023374183

A population of fish in a newly dug pond grows according to the equation P Find the initial number of fish in the pond X fish What is time 9000 1 8e 0 6t where time t is given in years

1 Sketch each angle in standard position a 1350 b 210 c 30

Perform the indicated operations and simplify 36x 49 X 7

1 Algebra 2 Name Izzy Unit 5 Complex s Rational Exponents Period 1 Practice Lesson 3 4 3 3 2 Unit 3 Lesson 3 Cumulative Practice Problems 1 Complete the table Use powers of 64 in the top row and radicals or rational numbers in the bottom row 64 64 64 edge length ft 3 volume ft a a b C Date 2023 11 28 4 d 64 Select all the expressions equivalent to 4 0 Explain show why below 25 2 t 5 16 b 220 4 4 d 47 0 Unit 3 Lesson 4 Cumulative Practice Problems 5 Evaluate 8 without a calculator 64 85 istrative The table shows the edge length and volume of several different cubes Complete the table using exact values 100 Select all items equivalent to 24 Explain your selected answers the area of a square with side length 24 units the side length of a square with area 24 square units the positive number x where x x 24 the positive number y where y 24 24 Mathematics 125 2 Select all expressions that are equal to 64 Explain your chosen answers a 96 b 8 c 512 d 4 e 64 f 64 e 64 1 147

Simplify completely O x 23 Ox 23 Ox 8 Ox 8 x 15x 56 X 7

Simplify completely x 2 X 9 x 10X 24 x 3x 108 X 2 x 9 x 2 X 9 x 12 X 9 X 2 OX 2 x 2 x 9 X 9 y 9 y 12 and find the restrictions on the variable

x 4 x 4x 9x 36x 4 x 4 a 9ab 20b a 8ab 7b a 7b a 8ab 16b

6x5 x 11x 18 15x x 7x 18 8 a ab 12b 2a 7ab 3 16a 8b 12

Which function below has an asymptote at y b f x a b c g x c b a Oh x b a c k x a c b

nger 1 Should a golfer try to hit the ball long or hit it straight off the tee Recent golfers have been able to hit the ball thanks to better equipment However this extra distance can come at the price of not being as accurate as to where the ball lands Below is data for ten golfers average driving distance yards and driving accuracy Percent where driving distance impacts the driving accuracy 260 163 Driving Distance Driving Accuracy 246 82 Miles 22 Price 266 72 XMonth January Feb Precip 4 45 254 4 01 76 Missing 0 1 Grade 90 91 March 3 26 264 1 96 71 44 14 600 a Write the linear regression equation of your line b Use your equation to predict the price for a car driven 40 thousand miles a Write the linear regression equation of your line g x 0 53 210 30 x b Use your equation to predict the driving accuracy for an average driving distance of 260 yards 8 260 2 Is there an association between the price of a used car and the number of miles it has been driven The table shows the number of miles driven 1 000 s and price for a sample of Honda CR V s 40 40 43 36 38 30 18 000 16 500 15 000 14 000 2 85 p 40 3 The table shows the monthly normal precipitation P in inches for San Francisco CA April May 1 17 256 3 83 73 0 38 268 50 15 000 6 89 66 June 0 11 270 65 July 0 03 248 75 8 13 83 76 54 56 70 70 14 500 12 000 13 600 14 600 p x 85 90x 18777 98X August Sept 0 07 0 20 Oct 14 79 1 40 248 81 Let x represent the month with x 1 corresponding to January Find an appropriate quadratic regression model for the data 3 4 Do students with more missing assignments have lower grades in math Below is data for an Algebra 1 class showing how many missing assignments the student has and their grade in the class 7 18 68 64 53 246 Nov a Write the linear regression equation of your line g x b Use your equation to predict the grade for a student who has ten missing assignments g 10 77 2 49 86 11 000 Dec 2 89 20 25 25 28 32 33 55 52 46 51

Be sure to fully justify your responses when appropriate Round percentages proportions to 4 decimal places and values of confidence interval bounds to 2 decimal places Don t forget Units anytime you give a non probability number and use complete sentences when asked to interpret your confidence intervals 1 4 pts If we are given the confidence interval 36 1 39 5 estimating the average number of credits earned by students in their third term of school What are the sample mean and margin of error for this confidence interval

Find m2B D 4 C m B 11 Lear

The given equation represents a conic section nondegenerative case a Use rotation of axes to eliminate the xy term to write the equation in the form A x2 C y2 D x E y F 0 b Write the equation in standard form and sketch the graph x 6xy 9y 9 10x 17 10y 90 0

3 Solve the equation 9x 116 3 DC 3 13 0 13 13 13 0 13 3 O 13 13 11 53Enter all real soluti

9 2 x 4 6 11 10 3x 1 10 6 10 x 12 2 10 4x

Find an equation of the circle that has center 6 2 and passes through 2 6 0 0 3 X 0 0

Find the unknown angles in triangle ABC for each triangle that exists B 155 9 c 8 7 b 15 4 Select the correct choice below and if necessary fill in the answer boxes to complete your choice OA There are two possible sets of remaining angles The measurements for when A is larger are A and C The measurements for when A is smaller are A Round to the nearest tenth as needed OB There is only one possible set of remaining angles The measurements for the remaining angles are A Round to the nearest tenth as needed OC No such triangle exists and C 0

5 10 2 X 2 x 2 7 3 11x 19 6 5 3 2x 8 10 5x 15

Review What would be the next step in solving the following equation for x 2x 3 6 Divide both sides of the equation by 2 Multiply both sides of the equation by 2 Add 3 to both sides of the equation Subtract 3 from both sides of the equation