Algebra Questions

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 2 4 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

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

USE SALT A report set a goal of 0 541 for the proportion of babies still being breastfed one year after birth The organization also used the survey data to estimate the proportion who were still being breastfed one year after birth to be 0 351 for babies born in a particular year Suppose that the survey used a random sample of 1 000 parents and that you want to use the survey data to decide if there is evidence that the goal is not being met Let p denote the population proportion of all babies born in that particular year who were still breastfeeding at 12 months Hint See Example 10 10 Hp The shape of the sampling distribution is approximately normal The sampling distribution is centered at 0 0224 x a Describe the shape center and variability of the sampling distribution of p for random samples of size 1 000 if the null hypothesis Ho p 0 541 is true Round your standard deviation to four decimal places 0 541 MY NOTES PRACTICE ANOTHER b Would you be surprised to observe a sample proportion as small as p 0 532 for a sample of size 1 000 if the null hypothesis Ho P 0 541 were true Explain why or why not Round your answer to four decimal places Consider the event surprising if the probability the event occurs when Ho P 0 541 is true is less than 0 05 Since the probability of a sample proportion this small or smaller is 0 met The standard deviation of the sampling distribution is We would not B be surprised to observe a sample proportion of p 0 532 for a sample of size 1 000 if the null hypothesis Ho P 0 541 is true The probability of a sample proportion this small or smaller is 0 0132 X which is greater than 0 05 c Would you be surprised to observe a sample proportion as small as p 0 507 for a sample of size 1 000 if the null hypothesis Ho p 0 541 were true Explain why or why not Round your answer to four decimal places Consider the event surprising if the probability the event occurs when Ho P 0 541 is true is less than 0 05 0 05 there is 0 We would B be surprised to observe a sample proportion of p 0 507 for a sample of size 1 000 if the null hypothesis Ho p 0 541 is true The probability of a sample proportion this small or smaller is 0 05 which is less than d The actual sample proportion observed in the study was p 0 351 Based on this sample proportion is there convincing evidence that the goal is not being met or is the observed sample proportion consistent with what you would expect to see when the null hypothesis is true Round your answer to four decimal places Consider the evidence that the goal is not being met convincing if the probability the event occurs when Ho P 0 541 is true is less than 0 05 which is less than O convincing evidence that the goal is not being

3 20 points Evaluate the following functions using the graphs shown f x 3 0 2 3 1 4 i g f 1 ii f g 0 1 0 14 N 3 0 3 9 D iii f f 3 1 0 0 2 1 3 0 10 5 01 0 1 g x 3 6

a Assuming that L 3 in the figure below sketch the function to which the Fourier e series converges for 0 x 3 g x 3 if 0 x 1 0 if 1 x 2 1 if 2 x 3

3N a101 b 22 c 34 Submit Answer 3 57 Points DETAILS STITZTRIG3 2 3 006 ASK YOUR TEACHER Use the Law of Cosines to find the angles if possible Round your answers to two decimal places If an answer does not exist enter ONE MY NOTES PRACTICE ANOTHER

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

You may need to use the appropriate appendix table or technology to answer this question The average U S daily internet use at home is two hours and twenty minutes A sample of 81 homes in a certain city showed an average usage of one hour and 40 minutes with a standard deviation of 90 minutes We are interested in determining whether or not the average usage in that city is significantly different from the U S average a State the null and alternative hypotheses in minutes to be tested Enter for as needed 1 00 Your answer cannot be understood or graded More Information Ho H 1 00 X X b Compute the test statistic 0 65 X Your answer cannot be understood or graded More Information c The null hypothesis is to be tested using a 0 05 Determine the critical value s for this test Round your answer s to two decimal places If the test is one tailed enter NONE for the unused tail test statistic 2 58 test statistic 2 2 58 X X d What do you conclude O Reject Ho We can conclude that the average usage in that city is significantly different from the U S average O Do not reject Ho We can conclude that the average usage in that city is significantly different from the U S average O Do not reject Ho We cannot conclude that the average usage in that city is significantly different from the U S average Reject Ho We cannot conclude that the average usage in that city is significantly different from the U S average X

In this question we will use a spreadsheet to approximate the root of f x x5 3x 9 using Newton s method with o 1 The picture below shows a spreadsheet being used to perform the calculation A downwards arrow indicates the contents from the cell above will be copied down a Which entry should go in cell A1 O 5 B1 4 9 B1 2 O A1 5 3 A1 3 9 00 O 5 A1 4 9 A1 2 O B1 5 3 B1 3 9 01 b Which entry should go in cell B1 00 A1 5 3 A1 3 9 1 O 5 B1 4 9 B1 2 O B1 5 3 B1 3 9 5 A1 4 9 A1 2 c Which entry should go in cell C1 O A1 5 3 A1 3 9 B1 5 3 B1 3 9 5 B1 4 9 B1 2 5 A1 4 9 A1 2 1 1234 AC 2 A1 B1 C1 B C

15 Solve the following logarithmic equation If multiple solutions exist enter solutions using a comma separated list log3u log3 4u 12 2

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

11 Solve the following logarithmic equation If multiple solutions exist enter solutions using a comma separated list log 6x 17 log 4x 18 1

12 Solve the following logarithmic equation If multiple solutions exist enter solution using a comma separated list log x 8 log x 12 5

10 Solve the following logarithmic equation log 12t 4 1

9 Rewrite the following logarithmic equation in exponential form Then solve the logarithmic equation Rewrite the following logarithmic equation in exponential form log y 6 6 is equivalent to Put work reasoning here Solve the logarithmic equation y log y 6 6 No Solution Put work reasoning here

8 Solve the following exponential equation Use logarithms to express the solution in its exact form In addition use a calculator to approximate the solution 7 8 775 The exact solution is given by

6 Solve the following exponential equation 42 3 82 4

5 Solve the following exponential equation 1 25 55 6

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

Find the unknown angles in triangle ABC for the following triangle if it exists A 29 1 b 44 1 ft a 26 9 ft Select the correct choice below and if necessary fill in the answer boxes to complete your choice Round to the nearest tenth as needed A There is only one possible set of remaining angles The measurements for the remaining angles are B and C B There are two possible sets of remaining angles The measurements for when B is smaller are B 52 9 and C 98 The measurements for when B is larger are C 23 8 C No such triangle exists

d Convert 325 ft min to m h

3 Solve the following exponential equation 64 1024

2 Solve the following exponential equation e72 6 e If multiple solutions exist enter solutions using a comma separated list

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

1 Solve the following exponential equation 1 625 54 3

6 Rewrite the given expression using natural logarithms only Ing 17

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

3 Use the properties of logarithms to condense the following logarithmic expression solution should be a single logarithm with a coefficient of 1 Where possible evaluate logarithmic expressions log 5 25 log 5 9

1 Use the properties of logarithms to expand the following logarithmic expression as much as possible Where possible evaluate logarithmic expressions W203 215 logs

7 Without using a calculator find the exact value of the following expression in reduced form log 8 logo 001 log1 log12144

6 Find the exact value of the following logarithmic expression In e

Tu upus untry 1 Which figure shows ray AB O O A Line A Line B 557 A B B

If in air at 30 C will cool from 100 C to 70 C in 1 minute find its temperature at the end of 2 minutes

Make up a problem that simplifies to this answer 3 N 3 C 3 1 p q mn5

5 If sin a 5 13 a in QII and tan a sin a 3 b cos a b 3 8 in QIII find 4

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

4 Find the exact value of the following logarithmic expression logi 81

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 n log and transformation techniques to graph A z log x 7 Als indicate which transformation s is are applied Determine the domain range and vertical asymptote of Select all transformations that apply DReflect the graph of f about the n axis Horizontally stretch the graph off by a factor of 7 O Horizontally compress the graph of f by a factor of 7 Dvertically compress the graph of f by a factor of 7 Shift the graph of f 7 units down Oshift the graph of f 7 units to the left Vertically stretch the graph of f by a factor of 7 Reflect the graph of about the y axis shift the graph of f 7 units up shift the graph of f 7 units to the right

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