Algebra Questions

Write the Roman numeral as a Hindu Arabic numeral MMDCLXVI OA 2 656 OB 2 666 OC 2 565

1 Use the Rational Zero Theorem to find al real zeros Enter your answers as a comma separated list 4x 7x 10x 3 0 X

6 4 2 8 6 4 0 0 0 2 y 4 6 8 2 2 2 4 6 X Graph the circle x y 4x 4y 8 0

6 2 2 4 8 6 4 2 2 0 2 6 4 0 0 2 4 16 8 X large points to move the center and change the radius so that x 3 y 4 16 4

a Find the center radius form of the equation of the circle with center 3 5 and radius 4 b Graph the circle a The center radius form of the equation of the circle is x 3 y 5 16 Type an equation b Use the graphing tool to graph the circle Click to enlarge graph 4 10 B Ay 10 8 6 4 2 2 8 40 x

Use the graph below to determine the equation of the circle in a center radius form and b general form 10 46 8 2 4 2 10 C a Type the equation in center radius form x 4 y 2 16 Simplify your answer b Type the equation in general form Simplify your answer

Give the center and radius of the circle represented by the equation 4x 16x 4y 4y 127 0 The center of the circle is The radius of the circle is Type an ordered pair using integers or fractions Type an integer or a simplified fraction

Use the graph below to determine the equation of the circle in a center radius form and b general form 10 40 0 2 46 4 2 a Type the equation in center radius form Simplify your answer

Consider the equation z 1 i Find the value of z which satisfies this equation and which has the second smallest positive argument 0 0 0 2 Express your answer as z reie where r and 0

Use the graph below to determine the equation of the circle in a center radius form and b general form 10 16 3 6 32 5 a Type the equation in center radius form Simplify your answer

a Find the center radius form of the equation of the circle with center 4 2 and radius 5 b Graph the circle SACHCICH a The center radius form of the equation of the circle is Type an equation 15 12 9 6 B 15 12 Q 6 13 B Ay

Find the center radius form of the equation of the circle described and graph it center 0 2 radius 2 Type the center radius form of the equation of the circle Type an equation Simplify your answer 10

5 A trigonometric equation in the form a sinx b c sinx d 0 where a b c d E N has 3 solutions in 0 2 The conditions that are required are A a b c d B a b c d C a b c d D a b c d

The table contains price demand and total cost data for the production of extreme cold sleeping bags where p is the wholesale price in dollars of a sleeping bag for an annual demand of x sleeping bags and C is the total cost in dollars of producing x sleeping bags Complete parts A through C below CLOS X 950 1 150 1 900 2 050 B Find a linear regression equation for the cost data using x as the independent variable C x 46 864 x 92 868 217 Round to three decimal places as needed profit P 230 220 160 125 A Find a quadratic regression equation for the price demand data using x as the independent variable p x 0 000084 0 163134 x 148 0621 Round the constant to four decimal places as needed Round all other values to six decimal places as needed C 135 000 150 000 180 000 190 000 C What is the form of the equation for profit Write the profit function in terms of the variables from the table x p and C

1 Determine the amplitude period phase shift and midline of the given function Clearly label your answers 1 y cos 3x 6

Write in logarithmic form 5 25 What is the equivalent logarithmic form log Simplify your answers Type integers or fraction

According to 2010 U S census the population of Sebastian was 21 749 The 2020 U S census found that the population of Sebastian had grown to 26 186 Use the exponential growth model Y Yekt where t is the number of years after 2010 to write an exponential growth function for the city of Sebastian Round the growth constant k to four significant figures The exponential growth function that models the population of Sebastian is Use the population growth model to predict the population of Sebastian in year 2032 Round the solution to the nearest whole number The model predicts that the population of Sebastian in 2032 will be Determine the year when model predicts the population of Sebastian will be 39 032 Round the solution to the nearest whole number According to the model the population of Sebastian will be 39 032 in the year

Match the logarithm in Column I with its value in Column II Remember that log ax is the exponent to which a must be raised in order to obtain x 2 1 a log 2 16 b log 31 c log 100 1 d log 2 2 e log e 1 f log 1 28 B www

2 Choose the correct graph on the right C Q O

For the function f x 6x 7 determine whether f x is one to one If so a write an equation for the inverse function in the form y f x b graph fand f1 on the same axes and c give the domain and the range of f and f If the function is not one to one say so G OA The domain off is and the range of fis Type your answers in interval notation c Give the domain and range of f and f1 Begin by finding the domain and range of f x Select the correct choice below and if necessary fill in any answer boxes to complete your choice OA The domain of f is and the range of f Type your answers in interval notation OB The function is not one to one Give the domain and the range of f1 Select the correct choice below and if necessary fill in any answer boxes to complete your choice B The function is not one to one d 4

For the function f x 6x 7 determine whether f x is one to one If so a write an equation for the inverse function in the form y f x b graph f and f on the same axes and c give the domain and the range of f and f If the function is not one to one say so 1 a Write an equation for the inverse function in the form y f x Select the correct choice below and if necessary fill in any answer boxes to complete your choice O A The function f x is one to one and f x Simplify your answer OB The function is not one to one b Choose the correct graph off and f below O A O B Q www OA The domain of f is and the range of fis OC O D The function f x is not one to one c Give the domain and range of f and f Begin by finding the domain and range of f Select the correct choice below and if necessary fill in any answer boxes to complete your choice

Solve the equation 813x 3 729x 2

Use the definition of inverses to determine whether f and g are inverses 1 f x 3x 11 g x 3X 11 Are the given functions inverses O Yes No

Use the definition of inverses to determine whether f and g are inverses f x 2x 8 g x 4 Are the f and g inverses of each other O No OYes

Each letter of the alphabet is assigned a numerical value according to its position in the alphabet Encode the message NEED HELP using the one to one function defined f x x 4 Give the inverse function that the decoder would need when the message is received Write the encoded message Use space to separate the numbers

Find a set of parametric equations to represent the graph of the rectangular equation using t x and t 1 x Enter your answers as comma separated lists of equations x 3y 2 a c x x 4 y 1 2 3 b 7 1 x x 1 4 y 2 t 3 Very nice

Without using a calculator find the exact value of the following expression in reduced form log 1 log 0 0001 logs 25 log53 75

Rewrite the following logarithmic equation in exponential form Then solve the logarithmic equation log v 5 3 Rewrite the following logarithmic equation in exponential form log4 v 5 3 is equivalent to

Find the partial fraction decomposition for the following rational expressic 2 2 x 18x 81

Rewrite the expression In 39 In 6 so that it includes the expressions In 3 and 39 and 6 do not appear inside a natural logarithm Expression

Rewrite the given expression using natural logarithms only log129 log129 Use a calculator to approximate the value of log129 Round the solution to four decimal places necessary 4 log129

Graph the function f x log 1 2 x 3 1 Use the graphing tool to graph the equation Click to enlarge graph Ay

Use the properties of logarithms to rewrite the expression Simplify the result as much as possible Assume all variables represent positive real numbers 5r7 25 log2 Select the correct choice below and if necessary fill in the answer box to complete your choice log2 5r cannot be simplified

g x logg 1 1 The domain of g is

Determine the remaining sides and angles of the triangle ABC A 26 36 B 26 48 c 10 68 m C 127 16 a 5 95 m Round to the nearest hundredth as needed Question 7 7 1 Part 3 of 3 b m Round to the nearest hundredth as needed

f log 8 4x The domain of f is 2 00 X

Question 5 7 1 15 Part 2 of 3 Determine the remaining sides and angles of the triangle ABC What is the measure of angle B O 44 6 Simplify your answer Type an integer or a decimal What is the length of side a Simplify your answer Type an integer or a decimal Round to the nearest tenth as needed CIL B HW Score 25 O Points 0 of 62 6 ft 20 2 115 2

Solve the logarithmic equation X 10log 6

in exponential form log 636 2 Write the equivalent exponential equation Type an equation Type your answer using exponential notation Do not sim

Solve the logarithmic equation x log 5 125

Find the area of the triangle ABC a 12 62 in b 5 16 in C 13 73 Question 12 7 1 55 What is the area of the triangle 7 8 in2 Simplify your answer Type an integer or decimal rounded to the nearest tenth as needed

If 12 g of a radioactive substance are present initially and 8 yr later only 6 0 g remain how much of the substance to the nearest tenth of a gram will be present after 15 yr After 15 yr there will beg of the radioactive substance Do not round until the final answer Then round to the nearest tenth as needed HID

Write in logarithmic form 35 243 What is the equivalent logarithmic form log 3 Simplify your answers Type integers or fractions

Find the half life of a radioactive element which decays according to the function 0 0304t A t Ape where t is the time in years 2 The half life of the element is years Round to the nearest tenth

ample of 400 g of radioactive lead 210 decays to polonium 210 according to the function A t 400e 0 032t where t is time in years Find the amount of radioactive lead remaining af 4 yr b 8 yr c 10 yr d Find the half life The amount of radioactive lead remaining after 4 yr will be und to the nearest integer as needed g

Find the doubling time of an investment earning 3 interest if interest is compounded continuously The doubling time of an investment earning 3 interest if interest is compounded continuously is years Round to the nearest tenth of a year

value of a large copy machine during the first 5 years of use a What is the value of the copier after 2 years and 3 months After 2 years and 3 months the copier is worth b What is the salvage value of the copier if it is replaced after 5 years After 5 years the salvage value of the copier is 500 O c State the domain of this function o 0 d Sketch the graph of this function 18000 16000 14000 12000 t 3500t 18000 where Vis value and it is time in years can be used te 10000 8000 6000 4000 2000 Clear All Draw What is the range of the function After how many years will the copier be worth only years the copier will be worth only After 1800 Round to 2 decimal place

In a mountain range of California the percent of moisture that falls as snow rather than rain can be approximated by the function p h 76 In h 602 where h is the altitude in and p h is the percent of an annual snow fall at the altitude h Use the function to approximate the amount of snow at the altitudes 5000 feet and 7000 feet The percent of annual precipitation that falls as snow at 5000 feet is approximately Round to the nearest integer

How much time will be needed for 21 000 to grow to 24 371 36 if deposited at 6 kt compounded quarterly For calculating use the formula A P 1 P 1 7 year s The amount 21 000 will grow to 24 371 36 in Do not round until the final answer Then round to the nearest tenth as neede

Solve the equation Give the solution in exact form log 3 6x 1 1 Rewrite the given equation without logarithms Do not solve for x