Quadratic equations Questions and Answers

Establish the identity 1 tan 0 cos 0 1 Rewrite the left side expression by expanding the product Do not simplify

f x 7 3 e 4 solve f x 8

A wooden artifact from an ancient tomb contains 35 percent of the carbon 14 that is present in living trees How long ago to the nearest year was the artifact made The half life of carbon 14 is 5730 years years

Solve the given system of equations If the system has no solution say that is it inconsistent y 2 4z 8 2y z 4 X 2x and z A The solution is x Type integers or simplified fractions O B There are infinitely many solutions Using ordered triplets they can be expressed as z any real number x y z x y Simplify your answers Type expressions using z as the variable as needed O C There are infinitely many solutions Using ordered triplets they can be expressed as

Solve the system of equations If the system has no solution say that it is inconsistent Graph the lines of the system 6x 48 x 4y 0 Click to enlarge graph 10 8 6 4 2 10 8 go 6 4 2 2 4 y

7 3x 22x 35 A 3x 7 x 5 B 2x 7 x 7 C 3 x 7 x 5 D 3x 7 x 5 8 8 15x65x 70 A 5 3x 7Xx 2 B 5 3x 7 x 2 C x 7 3x 2 D al3x 7

5 2n 24m 54 A n 6Xx 10 B 4 n 3 2 C 2 n 3 9 D 2 n 3X 9 6 6 7m 29m 24 A 7m 8Xm 1 B 8 7 3 C Not factorable D 7m 8 m 3

Graph each line a The line passes through T 4 1 and ha slope 3 b The line passes through U 3 4 and ha slope 2 c The line passes through V 2 3 and has 1 slope 2 3 d The line has x intercept 5 and slope

5 Write an equation for the graph of a linear function that a has slope 5 and passes through P 4 2 b has slope 7 and passes through Q 6 8 c has slope and passes through R 7 5 d has slope 0 and passes through S 3 8

1 Given the following examples determine if the function graphed is one to one If the function is one to one graph its inverse If the function is not one to one explain why n 2 points each Function 0 5 5 5 One to One no Graph of Inverse OR Explanation of why Inverse does not exist It is infinite FOR D

3 A line passes through D 3 5 and has slope 4 a Why is y 5 4 x 3 an equation of this line b Why is y 4x 7 an equation of this line

4 Graph the function f x 2x2 1 5 pts What is the y intercept s b What is the x intercept s c What is the domain of f x d What is the range of f x 10 10 10 5 Solve the following three equations without using logarithms 3 pts each 2x 2 82x 5 4 3 27 e4x 1 e

7 3x 22x 35 A 3x 7 x 5 B 2x 7 x 7 C 3 x 7 x 5 D 3x 7 x 5 9 10x 31x 24 A 5 2x 5 5x 3 B 10 x 3 x 8 C 2x 3 5x 8 D 2 5x 3 x 4 11 12n 2n 30 A 2 3n 5 2n 3 B 12 n 5 n 3 C 2 3n 5 2n 3 D 3 2n 5 n 1 8 10 12 8 15x 65x 70 A 5 3x 7 x 2 B 5 3x 7 x 2 C x 7 3x 2 D x 3x 7 10 60n 162n 108 A 6 2n 3 5n 6 B 6 2n 3 5n 6 C 2 5n 3 n 3 D 60 n 3 n 6 12 9 33r 10 A 6r 3r 4 B r 10 4r 3 C 2 r 2 9r 10 D 3r 1 3r 10

1 oftwa Factoring Quadratic Factor each completely 1 m 18m 81 A m 9 B m 10 m 7 C m 9 D m 10 m 3 3 r 4r 60 A r 6 r 10 B r 10 4 C Not factorable

2022 Kuta Software LLC All rights reserved Factoring Quadratics Factor each completely 1 m 18m 81 A m 9 B m 10 m 7 C m 9 D m 10 m 3 3 r 4r 60 A r 6 r 10 B r 10 4 C Not factorable D 6 r 8 r 1 5 2n 24n 54 A n 6 n 10 B 4 n 3 n 2 C 2 n 3 n 9 D 2 n 3 n 9 2 4 6 2 k 3k A k k 3 B k 4 k 10 C Not factorable D 2 k 9 k 7 4 x 11x 28 A x 4 x 7 B x 4 x 7 C x 4 x 7 D x 8 x 6 6 7m 29m 24 A 7m 8 m 1 B m 8 7m 3 C Not factorable D 7m 8 m 3

Factoring Quadratics Factor each completely 1 m 18m 81 A m 9 B m 10 m 7 C m 9 D m 10 m 3

Consider the function Which graph below corresponds to the following traces 18 2 B f x y m 1 0 2x xy 6 1 The trace for z 1 35 2 The trace for y 0 75 3 The trace for x 0 3 4 The trace for y 2 C 2 118 D

14 Solve the following logarithmic equation If multiple solutions exist enter solutions using a comma separated list In 10t 10 In 2 ln 5t 6

6 Solve the following exponential equation 42 3 82 4

4 Solve the following exponential equation 5x 4 56x 2 If multiple solutions exist enter solutions using a comma separated 1

d Convert 325 ft min to m h

1 2 x 5 2 27x 1 3 3 2x 1 2x 2 2x 2 5 40 52x 3x 5 5 log x 3x 1 6 4 log 3x 1 1 7 log25 x 1 1

2 Use the properties of logarithms to expand the following logarithmic expression as much as possible Where possible evaluate logarithmic expressions 100000 log

A 30 20 10 10 20 30

1 Georgia wants to go to the skating rink with her friends If the tickets cost 12 and they all spent a total of 72 how many people p went skating 2 Bill wants to split up his remaining Halloween candy c so that his 7 friends get 4 pieces each How much candy must Bill have 3 John had a group of friends attend his birthday party After 5 friends left the party 16 were left How many friends were there at the beginning 4 In a basketball game the Raiders scored p points in the first half and added 35 in the second half They scored a total of 77 points How many points did they score in the first half

5 The temperature is 36 degrees in the morning and rises d degrees by the afternoon and falls 7 degrees at night If the temperature is 42 degrees at night how much did the temperature rise in the afternoon 6 Tricia went to the library with b books and returned 5 but took out 2 If Tricia has a total of 8 books out how many did she start with 7 Blaine is going bowling and will need to pay 4 for shoes and then 3 for every game Write an equation for the situation if g represents the games played and C represents the total cost 3 Stan bought 8 fish for f dollars each and a fish tank for 60 Write an equation to represent the situation if T represents the total cost

6 17 subtracted from a number squared 7 A number cubed is at least 125 8 4 times the quantity of a number plus 10 equals 80 9 The difference of 9x and x to the fifth power 10 Half of a number is more than 16 11 The quotient of twice a number and 5 is 12 12 16 reduced by triple a number is smaller than 22

1 The quotient of a number and 5 2 The sum of 8 and a number is 14 3 The product of 9 and a number is no more than 27 4 14 less than x is 22 5 8 less than the product of 6 and a number 6 17 subtracted from a number squared

Find the area of the triangle ABC a 105 8 m b 74 7 m c 99 8 m What is the area of the triangle 2 3565 6 m Round to the nearest square meter as needed

Use log 20 335 log 30 621 and log 50 794 to approximate the value of the given logarithm to 3 decimal places Assume that b 0 and b log 12 X

5 Find the exact value of the following logarithmic expression Jog 1296

is the midpoint of DF DE 6x 1 and EF 7x 4 Find DE EF and DF

Use the parent function f x b and transformation techniques to graph g z 5 1 Also indicate which transformation s is are applied Determine the domain range and horizontal asymptote of g Select all transformations that apply Horizontally stretch the graph of f by a factor of 1 Shift the graph of f 1 unit down Shift the graph of f 1 unit to the right Shift the graph of f 1 unit up Horizontally compress the graph of f by a factor of 1 Shift the graph of f 1 unit to the left Reflect the graph of f about the y axis vertically compress the graph of f by a factor of 1 Vertically stretch the graph of f by a factor of 1 Reflect the graph of f about the z axis

Use the parent function f z b and transformation techniques to graph g x e 6 5 Also indica which transformation s is are applied Determine the domain range and horizontal asymptote of g Select all transformations that apply Reflect the graph of f about the y axis Shift the graph of f 5 units down Shift the graph of f 6 units to the left Horizontally compress the graph of f by a factor of 6 Horizontally stretch the graph of f by a factor of 5 Vertically stretch the graph of f by a factor of 5 Shift the graph of f 6 units to the right Shift the graph of f 5 units up Vertically compress the graph of f by a factor of 6 Reflect the graph of f about the z axis

Use the parent function f x log and transformation techniques to graph g z log z 6 8 Also indicate which transformation s is are applied Determine the domain range and vertical asymptote of g Select all transformations that apply Horizontally compress the graph of f by a factor of 6 Reflect the graph of f about the y axis Shift the graph of f 8 units down Vertically compress the graph of f by a factor of 8 Shift the graph of f 8 units up Shift the graph of f 6 units to the left shift the graph of f 6 units to the right Reflect the graph of f about the z axis Horizontally stretch the graph of f by a factor of 6 Vertically stretch the graph of f by a factor of 8

Let the polynomial function g be a function of The graph of the polynomial has four zeros a 5 3 0 7 Select all the expressions that could represent g a b C d e 4x x 5 4x 3 x 7 4x x 5 4x 3 x 7 4x x 5 x x 7 4x x 5 3x4 x 7 x x 5 x x 7

6 While walking to school you pass a barn with a silo If you are standing at about 40 m from the base of the silo and the silo is 33 5 m tall Using this information and your knowledge of trigonometric ratios calculate the angle of elevation to the top of the silo 33 5 m 40 m

Date Name Ceme This do now must be submitted by the end of class for grade and must be done b starting assignment 20 Do Now 1 Martha has 5 dollars Kelvin has 3 less than twice what Martha has Write an expression to represent how much money Kelvin has 2 What is 30 percent of 60

What statistic did you use O sample proportion O population proportion An article about the relative priorities of protecting the environment and the economy in America summarized a survey of 1 700 adult U S citizens When asked if they expect to feel the effects of climate change in their lifetime 1 037 of the survey participants responded yes The article states that participants were selected to be representative of all adult U S citizens a Estimate the proportion of adult U S citizens who think that they will feel the effects of climate change in their lifetime 0 61 b Use the sample data to estimate the standard error of p Round your answer to three decimal places MY NOTES c Calculate the margin of error associated with the estimate in Part a Hint See Example 9 3 Round your answer to three decimal places PRACTICE ANOTHER I Interpret the margin of error in the context of this problem OIt is unlikely that the estimated proportion of adult U S citizens who think that they will feel the effects of climate change in their lifetime differs from the true population proportion by less than the calculated value It is likely that the estimated proportion of adult U S citizens who think that they will feel the effects of climate change in their lifetime differs from the true population proportion by the calculated value It is impossible that the estimated proportion of adult U S citizens who think that they will feel the effects of climate change in their lifetime differs from the true population proportion by more than the calculated value It is impossible that the estimated proportion of adult U S citizens who think that they will feel the effects of climate change in their lifetime differs from the true population proportion by less than the calculated value O It is unlikely that the estimated proportion of adult U S citizens who think that they will feel the effects of climate change in their lifetime differs from the true population proportion by more than the calculated value

An article included data from a survey of 1 015 hiring managers and human resource professionals The article noted that many employers are using social networks to screen job applicants Of the 1 015 people who participated in the survey 699 indicated that they use social networking sites to research job applicants For the purposes of this exercise assume that the sample can be regarded as a random sample of hiring managers and human resource professionals a Suppose you are interested in learning about the value of p the proportion of all hiring managers and human resource managers who use social networking sites to research job applicants This proportion can be estimated using the sample proportion p What is the value of p for this sample Round your answer to four decimal places p b Based on what you know about the sampling distribution of p is it reasonable to think that this estimate is within 0 02 of the actual value of the population proportion Explain why or why not Round your answer to four decimal places X In addition We know the sampling distribution of p will be centered at the population proportion px and the standard deviation of this distribution can be estimated as 0 02 the sampling distribution is not mound shaped and symmetric X So we cannot say our value of p is likely to be within 0 02 of the actual value because of the following fact The Empirical Rule implies about 95 of our sampling distribution s values will fall within two standard deviations of the center but two standard deviations is greater than 0 02 The Empirical Rule implies about 95 of our sampling distribution s values will be at most one standard deviation away from the center and our standard deviation is less than 0 02 The Empirical Rule implies about 95 of our sampling distribution s values will be at most one standard deviation away from the center but our standard deviation is greater than 0 02 We cannot make use of the Empirical Rule since our sampling distribution isn t mound shaped and symmetric O The Empirical Rule implies about 95 of our sampling distribution s values will fall within two standard deviations of the center and two standard deviations is less than 0 02 X

nd a set of parametric equations to represent the graph of the rectangular equation using t x and t 5 x Enter your answers as comma separated lists of equation y x 1 a t x x t ty t b t 5 X t 2 3

1 3 x y 3 27y4x 4

Find the domain of the logarithmmic function y log x Write your answer only as an interval in the space below For infinity write inf Do not 1 4 add any spaces An example of the correctly written answer inf 12 4

Solve for x and check for any extraneous roots a log x 1 2 b log10 x 3 log 0 x 1 10

8 Use the properties of logarithms to express the following as sum difference or constant multiple In x x 1 x 1

2 Re arrange the following formulas to solve for the indicated variable SHOW YOUR WORK 5 marks a P D 8PY solve for Y

Given that f x x 8x and g x x 2 calculate a fog 3 b go f 3

7 nin l s nedir A 37 C 143 B 53 D 127 53

On April 3 the Mears Flag Company borrowed 14 000 to pay for start up costs for its new Showroom The loan ha a simple interest rate of 8 75 and was for 290 days The company was able to make partial payments of 5000 o May 28 and 2500 on October 12 How much will the company owe on the date of maturity Assume 360 days in a year Click the icon to view a table of the number of the day of the year for each date The company will owe on the date of maturity Round to the nearest cent as needed

PREVIOUS ANSWERS PECKSTAT3 8 3 503 XP MI An article included data from a survey of 2 183 hiring managers and human resource professionals The article noted that many employers are using social networks to screen job applicants and that this practice is becoming more common Of the 2 183 people who participated in the survey 1 311 indicated that they use social networking sites such as Facebook MySpace and LinkedIn to research job applicants For the purposes of this exercise assume that the sample can be regarded as a random sample of hiring managers and human resource professionals MY NOTES a Suppose you are interested in learning about the value of p the proportion of all hiring managers and human resource professionals who use social networking sites to research job applicants This proportion can be estimated using the sample proportion p What is the value of p for this sample Round your answer to two decimal places b Based on what you know about the sampling distribution of p is it reasonable to think that this estimate is within 0 02 of the actual value of the population proportion Explain why or why not eatona The sampling distribution of f