4. [-I2 Points] DETAILS HARMATHAP12 2.1.015.Ml. Solve the equation by using the quadratic formula. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION.) x2 6x = 9 (a) Give real answers exactly. x: (b) Give real answers rounded to two decimal places. x: Need He 9? _ | 5. [-l2 Points] DETAILS HARMATHAP12 2.1.019. Solve the equation using the quadratic formula. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION.) 5 2x x2 = o (a) Give real answers exactly. x: (b) Give real answers rounded to two decimal places. x: Need Help? 7. [-/1 Points] DETAILS HARMATHAP12 5.2.018. Write the equation in logarithmic form. 91/2 = 3 Need Help? Read It 8. [-/1 Points] DETAILS HARMATHAP12 5.2.039.MI. Write the expression as the sum or difference of two logarithmic functions containing no exponents. 109 2 x x + 8 ) Need Help? Read It Master It 9. [-/1 Points] DETAILS HARMATHAP12 5.2.041. Use the properties of logarithms to write the expression as a single logarithm. In(4x) - In(4y) Need Help? Read It Watch It17. [-/2 Points] DETAILS HARMATHAP12 0.7.055. l MY NOTES l PRACTICE ANOTHER A company's average cost per unit when x units are produced is defined to be Total cost x Average cost = Suppose a company's average costs are given by 6000 x Average cost = + 65 + 047x. (a) Express the averagecost formula as a single fraction. Average cost = (b) Write the expression that gives the company's total costs. (Simplify your answer completely) Need Help? i 18. [-/1 Points] DETAILS HARMATHAP120.R.O95. l MY NOTES l PRACTICE ANOTHER Suppose that the total cost of producing and selling x units of a product is 500 + 8x and the total revenue from the sale ofx units is 40X 0.006x2. Find the difference of these expressions (total revenue minus total cost) to nd the profit from the production and sale ofx units of the product. (Simplify your answer completely.) Prot = Need Help? 19. [-/1 Points] DETAILS HARMATHAP12 0.7.028. Perform the indicated operation and simplify. b - 2 b + b2 + 2b 5b + 10 Need Help? Read It10. [-/1 Points] DETAILS HARMATHAP12 5.2.043. Use the properties of logarithms to write the expression as a single logarithm. log5(x + 1) + - 1095(x) Need Help? Read It 11. [-/1 Points] DETAILS HARMATHAP12 5.2.044. Use the properties of logarithms to write the expression as a single logarithm. log(8x + 1) - _ log(x + 1) Need Help? Read ItHARMATHAP12 1.6.050.MI. PRACTICE ANOTHER Stutz Department Store will buy 10 pairs of sunglasses if the price is $81 per pair and 30 pairs if the price is $31. The supplier of the sunglasses is willing to provide 35 pairs if the price is $86 per pair but only 5 pairs if the price is :26. Assuming that the supply and demand functions for the sunglasses are linear, nd the market equilibrium point. (q. p) = ( ) Need Help? ___ 7. [-/1 Points] 8. [-I6 Points] HARMATHAP12 1.5.035.MI. PRACTICE ANOTHER A concert promoter needs to make $85,600 from the sale of 1840 tickets. The promoter charges $40 for some tickets and $60 for the others. Letx represent the number of $40 tickets and y represent the number of $60 tickets. (a) Write an equation that states that the sum of the tickets sold is 1840. (b) Write an expression for how much money is received from the sale of $40 tickets? $ (c) Write an expression for how much money is received from the sale of $60 tickets? s (:1) Write an equation that states that the total amount received from the sale is $85,600, (2) Solve the equations simultaneously to nd how many tickets of each type must he sold to yield the $85,600. X = g] y: 4. [-/1 Points] DETAILS HARMATHAP12 5.2.013. Solve for x by writing the equation in exponential form. (Round your answer to three decimal places.) In(2x + 4) = 2.3 X = Need Help? Read It Watch It 5. [-/1 Points] DETAILS HARMATHAP12 5.2.019. Write the equation in logarithmic form and solve for x. (Round your answer to three decimal places.) e7x + 3 = 0.51 X = Need Help? Read It Watch It3. [/4 Points] HARMATHAP12 1.6.009. PRACTICE ANOTHER Let C(X) = 5X + 550 and R(x) = 23x. (3) Write the prot function P(x). P(x) : (b) What is the slope m of the profit function? me: (c) What is the marginal prot ? (d) Interpret the marginal profit. O Each additional unit sold increases the prot by this much. 0 This is the smallest number of units that can be sold in order to make a prot. 0 Each additional unit sold decreases the profit by this much. 0 The prot is maximized when this many units are sold. Need Help? _' 4. [-12 Points] HARMATHAP12 1.6.011.Ml. MY NOTES PRACTICE ANOTHER A company charting its profits notices that the relationship between the number of units sold, x, and the prot, P, is lineal: If 190 units sold results in $2140 prot and 240 units sold results in $4940 profit, write the prot function for this company. in : Find the marginal profit. e: N... Help? @ 12. [-I8 Points] HARMATHAP12 5.3.001 .MI.SA. MY NOTE This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise Solve the equation. 96" = 4,782,969 We want to solve the equation 96" = 4,782,969 for x, and give the answer correct to three decimal places. The first step in solving an exponential equation is to the exponential, which has already been done in this equation. The next step is to take the logarithm either base e or base 10 of both sides of the equation. We will choose base e. This gives us |n( ) = ln(4,782,969). Submit _S_k_ip_(you cannot come back) Need Help? _' 13. [-I1 Points] HARMATHAP12 5.3.005. MY NOTE Solve the equation. Give your answer correct to 3 decimal places. 85,000 = 10,000(1.02)9X Need Help? _ 9. [-/7 Points] DETAILS HARMATHAP12 0.6.061.MI.SA. MY NOTES PRACTICE This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise The consumer expenditure, in dollars, for a commodity is the product of its market price, p, and the number of units demanded, x. Suppose that for a certain commodity, the consumer expenditure is given by 8,000p - 130p. (a) Factor this in order to find an expression for the number of units demanded. (b) Use (a) to find the number of units demanded when the market price is $37. Step 1 (a) Factor this in order to find an expression for the number of units demanded. The consumer expenditure, in dollars, for a commodity is the product of its market price, p, and the number of units demanded, x. The product of the values p and x is written as ---Select--- V] . Submit Skip_ (you cannot come back). Need Help? Read It 10. [-/2 Points] DETAILS HARMATHAP12 0.6.063. MY NOTES PRACTICE Revenue R from the sale of x units of a product is found by multiplying the price by the number of items sold. (a) Factor the right side of R = 200x - x2. R= (b) What is the expression for the price of the item? Need Help? Read It14. [-I2 Points] DETAILS HARMATHAP12 2.1.051. Suppose the prot from the sale of X units of a product is P = 6400x 18x2 400. (a) What level(s) of production will yield a profit of $318,800? (Enter your answers as a comma-separated list. Round your answers to two decimal places.) x: (b) Can a prot of more than $318,800 be made? 0 Yes ONO Need Help? _" 15. [-I1 Points] DETAILS HARMATHAP12 2.1.053.M|. If a ball is thrown upward at 96 feet per second from the top of a building that is 120 feet high, the height of the ball is given by s = 120 + 961' 16t2 feet where t is the number of seconds after the ball is thrown. How long after it is thrown is the height 120 feet? Need Help? 16. [-I1 Points] DETAILS HARMATHAP12 2.1.054.M|. A tennis ball is thrown into the air from the top of a hotel that is 90 feet above the ground. The height of the ball from the ground is given by D(t) = 16t2 + 18t + 90 feet where t is the time, in seconds, after the ball is thrown. How long after the ball is thrown does it hit the ground? Need Help? 11. [-/1 Points] DETAILS HARMATHAP12 0.7.005. Simplify the fraction. x2 - 2x + 1 x2 - 5x + 4 Need Help? Read It Watch It 12. [-/1 Points] DETAILS HARMATHAP12 0.7.009. Perform the indicated operation and simplify. 2x - 14 4x - 28 X - 7 6x - 42 Need Help? Read It Watch It 13. [-/1 Points] DETAILS HARMATHAP12 0.7.012. Perform the indicated operation and simplify. 4x + 4 x2 - 6x+ 9 x - 3 8 x-+ 8x Need Help? Read It7. [-/1 Points] DETAILS HARMATHAP12 0.6.030. MY NOTES Factor completely. 2x2 + 13x + 6 Need Help? Read It 8. [-/2 Points] DETAILS HARMATHAP12 0.6.061.MI. MY NOTES The consumer expenditure, in dollars, for a commodity is the product of its market price, p, and the number of units demanded, x. Suppose that for a certain commodity, the consumer expenditure is given by 9,000p - 90p. (a) Factor this in order to find an expression for the number of units demanded. (Simplify your answer completely.) X = units (b) Use (a) to find the number of units demanded when the market price is $26. X = units17. [-/1 Points] DETAILS HARMATHAP12 2.1.057.MI. The time t, in seconds, that it takes a car to accelerate to x mph can be described by t = 0.001(0.732x2 + 15.417x + 609.738). How fast, in mph, is the car going after 8.63 seconds? Give your answer to the nearest tenth. mph Need Help? Read It Master It 18. [-/1 Points] DETAILS HARMATHAP12 2.1.059. For the years since 2001, the percent p of high school seniors who have tried marijuana can be considered as a function of time t according to p = f(t) = 0.17t2 - 2.61t + 52.64 where t is the number of years past 2000. t In what year after 2000 is the percent predicted to reach 55%, if this function remains valid? Need Help? Read It 19. [-/1 Points] DETAILS HARMATHAP12 2.1.062. The global spending on travel and tourism (in billions of dollars) can be described by the equation y = 1.48x2- 25.23x + 416.91 where x equals the number of years past 1990.+ Find the year after 1990 in which spending is projected to reach $1,768 billion. (Round your answer to the nearest year.) Need Help? Read It6. [-/2 Points] DETAILS HARMATHAP12 2.1.020. Solve the equation using the quadratic formula. (Enter your answers as a commaseparated list. If there is no real solution, enter NO REAL SOLUTION.) 18x 4 = 9X2 (a) Give real answers exactly. x: (b) Give real answers rounded to two decimal places. x: Need Help? 7. [-l1 Points] DETAILS HARMATHAP12 2.1.021.M|. Find the exact real solutions to the equation, if they exist. (Enter your answers as a comma-separated list.) y2=2 y: Need Help? 4. [-/1 Points] DETAILS HARMATHAP12 0.6.013. Factor the expression as a product of binomials. x2 - 18x + 81 Need Help? Read It 5. [-/1 Points] DETAILS HARMATHAP12 0.6.019.MI. Factor completely. 16x2 - X Need Help? Read It Watch It Master It 6. [-/1 Points] DETAILS HARMATHAP12 0.6.022. Factor completely. x3 - 2x2 - 3x + 6 Need Help? Read It1. [-18 Points] DTA|LS HARMATHAP12 1.6.005. A linear cost function is C(x) = 8x + 950. (Assume C is measured in dollars.) (a) What are the slope and the Cintercept? :1 Ci ntercept (b) What is the marginal cost WC? What does the marginal cost mean? 0 Each additional unit produced costs this much (in dollars). 0 If production is increased by this many units, the cost decreases by $1. Q If production is increased by this many units, the cost increases by $1. 0 Each additional unit produced reduces the cost by this much (in dollars). (c) What are the xed costs? $:l (d) How are your answers to parts (a), (b), and (c) related? 0 slope = fixed costs, and C-intercept = marginal cost 0 CIntercept = marginal cost slope O slope = marginal cost, and Cintercept = fixed costs 0 slope = marginal cost C-intercept (e) What is the cost of producing one more item if 50 are currently being produced? $:l What is the cost of producing one more item if 100 are currently being produced? $:l 1. [-/1 Points] DETAILS HARMATHAP12 5.2.003. Use the definition of a logarithmic function to rewrite the equation in exponential form. 2 = 109 49(7) Need Help? Read It 2. [-/1 Points] DETAILS HARMATHAP12 5.2.005.MI. Solve for x by writing the equation in exponential form. log 5(x) = 2 X = Need Help? Read It Watch It Master It 3. [-/1 Points] DETAILS HARMATHAP12 5.2.009. Solve for x by writing the equation in exponential form. log-(3x + 7) = 2 X = Need Help? Read It6. [17 Points] HARMATHAP12 1.6.049.EP. PRACTICE ANOTHER A group of retailers will buy 80 televisions from a wholesaler if the price is $375 and 120 if the price is $325, The wholesaler is willing to supply 60 if the price is $305 and 140 if the price is $395. Assume that the resulting supply and demand functions are linear. Let p represent price (in dollars) and q represent quantity. State the two ordered pairs for the demand function in the form (q, p). List your answers from least :1 to greatest 17. W > Mi) Write the demand function in terms of q. p: State the two ordered pairs for the supply function in the form (a, p). List your answers from least q to greatest q. W Mi) Write the supply function in terms of q' p: Find the equilibrium point for the market in the form (a, p). WW) 2. [-5 Points] DETAILS HARMATHAP12 1.6.007. A linear revenue function is R = 66x. (Assume R is measured in dollars.) (a) What is the slope m? M: (b) What is the marginal revenue ? What does the marginal revenue mean? 0 Each additional unit sold yields this many dollars in revenue. 0 Each additional unit sold decreases the revenue by this many dollars. 0 If the number of units sold is increased by this amount, the revenue decreases by $1. 0 If the number of units sold is increased by this amount, the revenue increases by $1. (c) What is the revenue received from selling one more item if 50 are currently being sold? $|:l What is the revenue received from selling one more item if 100 are being sold? $|:l 5. [-/4 Points] HARMATHAP12 1.6.035.EP. PRACTICE ANOTHER Suppose a certain outlet chain selling appliances has found that for one brand of home theater, the monthly demand is 180 when the price is $900. However, when the price is $855, the monthly demand is 210. Assume that the demand function for this system is linear. Let p represent price (in dollars) and q represent quantity. State the two ordered pairs in the form (q, p). List your answers from least q to greatest q. M > M?) Calculate the slope m of the line connecting the two points. m: Write the linear equation for the demand function Use p for price (in dollars) and q for quantity 8. [-/1 Points] DETAILS HARMATHAP12 2.1.023. Find the exact real solutions to the equation, if they exist. (Enter your answers as a comma-separated list. ) 5x2 = 80 X : Need Help? Read It 9. [-/1 Points] DETAILS HARMATHAP12 2.1.025. Find the exact real solutions to the equation, if they exist. (Enter your answers as a comma-separated list. ) (x + 1)2 = 64 X : Need Help? Read It 10. [-/1 Points] DETAILS HARMATHAP12 2.1.029.MI. Use any method to find the exact real solutions, if they exist. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION.) w 2 W - 2 =0 4 2 W Need Help? Read It Watch It Master It11. [-/1 Points] DETAILS HARMATHAP12 2. 1.033.MI. Use any method to find the exact real solutions, if they exist. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION.) (x - 1)(x + 3) = 12 X = Need Help? Read It Watch It Master It 12. [-/1 Points] DETAILS HARMATHAP12 2.1.045. Multiply both sides of the equation by the LCD and solve the resulting quadratic equation. (Enter your answers as a comma-separated list. ) - = 3x + x - 1 x - 1 X : Need Help? Read It 13. [-/1 Points] DETAILS HARMATHAP12 2.1.049.MI. If the profit from the sale of x units of a product is P = 115x - 100 - x2, what level(s) of production will yield a profit of $2150? (Enter your answers as a comma-separated list.) X = units Need Help? Read It Watch It Master It1. [-/1 Points] DETAILS HARMATHAP12 2.1.005. Solve the equation by factoring. (Enter your answers as a comma-separated list. ) x2 - 8X = 48 X = Need Help? Read It 2. [-/1 Points] DETAILS HARMATHAP12 2.1.007.MI. Solve the equation by factoring. (Enter your answers as a comma-separated list. ) 36 - 25x