Intermediate Algebra. Exam 1 Review (Chapters 1, 2, and 3)

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1 Eam Review (Chapters,, and ) Intermediate Algebra Name. Epress the set in roster form. { N and 7}. Epress the set in set builder form. {-, 0,,,, }. Epress in set builder notation each set of numbers that are indicated on the number line. a. b. c. d.. Solve for. 7( ) ( ). Solve for. ( ) ( ) 6. Solve for. 7. Solve for. ( 8) (6 ) 8. Solve for. 9. Solve for. ( ) ( 8)

2 0. Solve for. ( ) 6. Solve for. ( 7) ( ) ( ) 6. You are choosing between two long-distance telephone plans. One plan has a monthl fee of $ with a charge of $0.0 per minute. The other plan has a monthl fee of $ with a charge of $0.07 per minute. For how man minutes of long-distance calls will the costs for the two plans be the same? Let = Then = plan A And = plan B Equation:. Solve ( ) for, in m b form.. Solve 6 for, in m b form.. Solve P l w for w. 6. Solve A h( b B) for b.

3 7. Multipl. z 8. Simplif. ( z ) 9. Simplif. ( z) 0. Multipl. ( z ) ( ). Simplif. z 0 6 z. Simplif. ab c a bc. Simplif. z z. Convert the following to scientific notation Convert the following to standard form Multipl. (. 0 )(. 0 7 ) 7. Divide Simplif. (.0 )(. 0 ) 8 (7.0 )

9. There are 67,000,000 square feet of Wal-Mart to 00,000,000 U.S. citizens. how man square feet per U.S. citizen in scientific notation. 0. Determine whether the following relations represent a function.

4 9. There are 67,000,000 square feet of Wal-Mart to 00,000,000 U.S. citizens. how man square feet per U.S. citizen in scientific notation. 0. Determine whether the following relations represent a function. a. b.. Determine if the following graphs represent a function. It does represent a function, then state the domain a range. a. b. c. d.. Let g ( t) t t 6 a. g () b. g (h). If a ball is dropped from the top of a 96-foot building, its height above the ground, h, at an time, t, can be found b the function h ( t) 6t 96, 0 t.. the height of the ball at a. second b. seconds. The graph describes the number of minutes ou get from dollars. a. Does 0 minutes cost $6? b. Does $0 give ou 0 minutes?

5 . Sa the weekl profit, P, of a widget store can be approimated b the formula P ( n) 9n, where n is the number of widgets sold. a. If the store sold 0 widgets would it make a weekl profit of $7? b. If the store sold widgets, how much weekl profit would the store make? c. If the store made a weekl profit of $0, how man widgets did the store sale? 6. the - and -intercepts of. -intercept = (, ) -intercept = (, ) 7. the - and -intercepts of. -intercept = (, ) -intercept = (, ) 8. the - and -intercepts of 6. -intercept = (, ) -intercept = (, )

6 9. Graph 0. Graph 6. Graph. Graph 7

7 Formulas: Slope-intercept Point-slope Slope m b m( ) m. the slope of the line through the points (, ) and (-, 6).. the slope of the line.. the slope of the line =. 6. the slope of the line =. 7. Write an equation of the line with slope, m, and goes through the point (-, ). Give our final answer in function notation, f ( ) m b. 8. Write an equation of the line that goes through the points (-, ) and (, -0). Give our final answer in function notation, f ( ) m b. 9. Write an equation of the line that goes through the point (-, -0) and parallel to the line 0. Give our final answer in function notation, f ( ) m b.

8 0. Write an equation of the line that goes through the point (6, 8) and perpendicular to the line that goes through the points (, ) and (6, 0). Give our final answer in function notation, f ( ) m b.. Determine whether the two lines are parallel, perpendicular, or neither. a. b c. 9. The following graph shows the number of Social Securit beneficiaries, n, from the ears 980 projected through 070. The function n(t), (represented b the dashed line) that can be used to approimate this data. Let t be the number of ears after 980. a. Determine the linear function that can be used to estimate the number of Social Securit beneficiaries, n, from the ears 980 projected through 070. b. Use the function determined in part a) to determine the number of Social Securit beneficiaries in the ear 00. c. Use the function determined in part a) to estimate the ear at which the number of Social Securit beneficiaries will be 60 million.

9 . The number of calories burned in hour of swimming, when swimming between 0 and 0 ards per minute, is a linear function of the speed of the swimmer. A person swimming at 0 ards per minute will burn about 89 calories in hour. While swimming at 0 ards per minute a person will burn about calories in hour. This information is shown in the following graph. a. Determine a linear function that can be used to estimate the number of calories, C, burned in hour when a person swims at r ards per minute. b. Use the function determined in part a) to determine the number of calories burned in hour when a person swims at 0 ards per minute. c. Use the function determined in part a) to estimate the speed at which a person needs to swim to burn 600 calories in hour.. Let f ( ) and g ( ) a. ( f g)( ) b. ( f g)( a) c. ( f g)() d. ( f g)( ) e. ( f g)( ) f. ( f g)( ) g. ( f g)() h. ( f / g)() i. ( f / g)()

10 . The double line graph below compare high temperatures in Honolulu and Miami in August. From the das listed, use the graph to answer the following questions. a. Use the graph to find the combined temperature on August th. b. Use the graph to find the difference in temperatures on August 6 th. Solve the following linear sstem b graphing. 6. Solve the following linear sstem b graphing. 7. 6

11 Solve the following linear sstems b the method of our choice z z z z z z

12 6. Sa ou sold boes of peanut butter cookies for $.0 and boes of chocolate chip cookies for $.. One da ou sold 7 boes and made $. How man boes of each did ou sell? 6. A rowing team, while practicing, rowed an average of 7.9 miles per hour with the current and 0.7 miles per hour against the current. Determine the team s rowing speed in still water and the speed of the current. 6. You invested $8000 in two funds paing % and % annual interest. At the end of the ear, the interest from the % investment eceeded the interest from the % investment b $8. How much mone was invested at each rate? 6. The manager of a gardening center needs to mi a plant food that is % nitrogen with one that is 8% nitrogen to obtain 0 gallons of a plant food that is 6% nitrogen. How man gallons of each of the plant foods must be used?

13 66. A compan that produces and sells radios has an annual cost of producing radios at $0,000 with a $0 production cost for each radio produced. The annual cost for producing the radios, C(), is the functionc ( ) , where is the number of radios produced. The annual revenue of selling the radios is $0 for each radio sold. The annual revenue, R(), is the function R( ) 0, where is the number radios sold. Solve the sstem of equations to determine the number of radios that must be produced and sold to break even. What will be the cost and revenue for producing and selling that man radios? 67. Three kinds of tickets for a Sogg Bottom Bos concert are available: up-front, main-floor, and balcon. The most epensive tickets, the up-front tickets, are twice as epensive as balcon tickets. Balcon tickets are $0 less than main-floor tickets and $0 less than up-front tickets. Determine the price of each kind of ticket? 68. The largest angle of a triangle has a measure that is 0 less than three times the measure of the second smallest angle. The measure of the smallest angle is equal to the difference between the measure of the largest angle and twice the measure of the second smallest angle. Determine the measures of the three angles of the triangle.

14 69. A garden store owner needed to keep track of the number of -pound bags, 0-pound bags, and 0- pound bags of soil he sold during the week, which sell for $7.0, $9, and $.0, respectivel. He completel forgot to keep track, but he knew he could figure it out. The register tape revealed that a total of bags were sold, which brought in a total of $.0. He also could tell from the depleted dirt pile that he sold a total of 80 pounds of dirt. How man bags of each size did the owner sell? 70. A person invested $,000 among three different investments. With some of the mone, he purchased a municipal bond paing.% simple interest. He invested twice the amount of mone that he paid for the municipal bond in a certificate of deposit paing.% simple interest. He placed the balance of the mone in a mone market account paing.7% simple interest. If the total interest for ear was $69.0, how much was placed in each account? 7. A % solution, an 8% solution, and a 6% solution of saline are to be mied to get liters of a % solution. How man liters of each must be mied if the volume of the 6% solution must be liters less than twice the volume of the % solution?

Identify the domain and the range of the relation from the graph. 8)

Identify the domain and the range of the relation from the graph. 8) INTERMEDIATE ALGEBRA REVIEW FOR TEST Use the given conditions to write an equation for the line. 1) a) Passing through (, -) and parallel to = - +. b) Passing through (, 7) and parallel to - 3 = 10 c)