Algebra Questions

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

4 A sailboat is approaching a cliff The height of the cliff is known to be about 2000 m and the boat is about 3464 m from the cliff Determine the angle of elevation from the sailboat to the top of the cliff CLIFF

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

Julio deposits 1500 in a savings account that pays 2 4 interest per year compounded monthly The amount in the account after n months is given by An 1500 1 0 024 0 024 12 a Find the first six terms of the sequence Round your answers to the nearest cent A A A3 A4 A5 A6 S b Find the amount in the account after 5 years Round your answers to the nearest cent Aso

Module 1 For the function f x 4 3x 1 2 x 5 find the followin y intercept x intercept s leading coefficient degree of the polynomial

e Rudy Meangru Solve for x and check for any extraneous roots log x 6 log x 4

16 x y x y 5 A 51 F X B 380 C 9 D 19 E 22

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

P The shortest distance between the curves 2y2 x and 3 2 9x 9y 60y 91 0 is

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

that exists B 147 7 c 8 124 b 14 121 Select the correct choice below and if necessary fill in the answer boxes with in the choice A There is only one possible solution for the triangle The measurements for the remaining angles A and C and side a are as follows A 14 4 C 18 a 6 6 Round to the nearest tenth as needed A B There are two possible solutions for the triangle The measurements for the solution with the longer side a are as follows O C 0 A O Round to the nearest tenth as needed Round to the nearest tenth as needed The measurements for the solution with the shorter O O Round to the nearest tenth as needed C Round to the nearest tenth as needed Round to the nearest tenth as needed C There are no possible solutions for the triangle Round to the nearest thousandth as needed a Round to the nearest thousandth as needed side a are as follows a Round to the nearest thousandth as needed

KSJ between 12 00 noon and 1 00 pm are the minute and hour hands of a

1 Find the area of the triangle using the formula A bh and then verify that Heron s formula gives the same result 1 bh Use the formula A 2b The area is 48 Use Heron s formula The area is C 10 16 10

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 m Round to the nearest square meter as needed Question 12

Question 10 7 3 65 Use an appropriate area formula to find the area of the triangle with the given side lengths a 17 m b 9m c 12 m The area of the triangle is m Round your answer to the nearest tenth

1 3 x y 3 27y4x 4

K Find the measure of 0 in the triangle Do not use a calculator 0 B A B 0 1 C

Diyagram enine izgilerle kesilen iki paralel izgi a ve b yi g stermektedir x in de eri nedir 490 to 380 a b

11 ABC geni gen DBE ye benzer B l m A X in de erini bulmak i in bir denklem kurun ve z n A 4x 3 7x 30 B E

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

Diyagram enine kesilen iki paralel izgiyi g stermektedir 22 3y 10 l s ve 28 7y 30 l s B l m A Bir denklem yaz n ve y nin de erini bulmak i in z n 1 3 re 2 7 5 6 8

Using the graph and table as a reference identify the Domain of the function f x Write your answer in Interval Notation 5 4 3 10 1 2 3 4 f x 1 4 f x 0 11111111111111 0 14285714285714 0 16666666666667 0 2 0 25 0 33333 3333333 Undefined Domain of f x 2 S 32 1 L 44 PL 31 EJ D

2 Solve for x use log where necessary 41 8 a b 22 x 3x

Problem 5 Let W be the subspace of R spanned by the vectors u 1 0 1 0 u2 0 1 1 0 and u3 0 0 1 1 Use the Gram Schmidt process to transform the basis u u2 u3 into an orthonormal basis 4 v 2 0 2 0 v2 V V V 0 v3 3 V3 6 3 6 2 0 2 0 v V6 NE V6 0 V3 13 13 13 V2 3 3 D v 2 0 2 0 v2 V6 V6 6 0 v3 2 0 0 v 6 16 16 0 1 13 13 13 v3 E v V2 B v1 C v 2 0 2 0 v2 V6 V6 N 0 v3 V 3 6 F v 2 0 2 0 v2 V6 v6 6 0 v3 3 6 v3 13 2 0 2 0 v NE VE 0 13 3 V 0 6 6 G v H v 0 2 0 v2 v v 0 v3 6 3 6

Problem 4 Let v 3 1 0 1 v2 0 1 3 1 and b 1 6 1 4 Let W be the subspace or R4 spanned by v and V2 Find projw b Problem 4 Enter your answer symbolically as in these examples Enter the four components separated with commas

Problem 3 Which of the following sets of polynomials form a basis for P2 P1 1 3x 5x P2 5 x ii P 1 x P2 10x x P3 1 11x x iii P 1 P2 1 6x P3 x P4 x Problem 3 A all of them B i only C i and ii only D iii only E none of them F ii and iii G i and iii only H ii only Select

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

Prof Rudy Meangru 1 Evaluate the following without a calculator a log1000 b log 10 3 2 FI 2023 Due Monday 11 27 c In e

Find the exact values for the six trigonometric functions of the angle 0 in the figure O For the given triangle which of the following ratios represents the trigonometric function sin 0 BC AB O AC BC AB BC BC AB Find the value of sin 0 sin 0 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression For the given triangle which of the following ratios represents the trigonometric function cos 0 BC AC 11 5 AB AC B Find the value of cos 8 cos 0 Simplify your answer including any radicals Use integers or fractions for any num 2

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

Problem 6 Let S 1 4x 1 3x2 Which of the following polynomials could be added to the set S to form a basis for P2 Problem 6 1 2 4x 3x 11 5 4x12x 111 8 12x 15x s A none of them B all of them C i only D ii and iii only E ii only F iii only G i and ii only H i and iii only Select

Problem 1 Which of the following sets of vectors are independent 1 1 2 1 3 2 0 2 4 1 11 1 2 1 3 2 0 5 6 0 ii 1 2 1 3 2 0 7 10 2 A none of them B ii only C i only D i and iii only E ii and iii only F iii G all of them H i and ii only

Problem 2 Let p 8x 6x 3 Find the coordinate vector of p relative to the following basis for P2 P1 1 P2 1 x P3 1 x x Problem 2 Enter the coordinates separated with commas

Determine the exponential regression of the data below using either a calculator or spreadsheet program 21 6 19 23 13 33 8 47 5 54 2 62 Select the correct answer below Of x 93 264 1 106 Of x 93 264 1 106 O f x 93 264 1 106 O f x 93 264 1 106

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