Elementar Algebra FALL 200 Review for Eam 2 1) In a surve of 60 students, the students showed these preferences for instructional materials. Answer the questions. Graph the equation. 6) = 4 + 3 7) 3 + 18 = -12 8) = 1 4 9) 9 = -63 ) 4 + = 0 a) What percent of students prefer lecture? b) How man students prefer computers? c) How man more student prefer film than TV? Determine whether the given number is a solution of the inequalit. 2) < 11 a) -1 b) 11 c).9 Graph the inequalit. 3) a) > - b) 0 < 4 Find the coordinates of the -intercept and the coordinates of all -intercepts. 11) - - Find the intercepts, then graph the equation. 12) -2 + = 13) = -4+ 8 Describe the graph using set-builder notation. 4) a) -7-6--4-3-2 1 2 3 4 6 7 b) -7-6--4-3-2 1 2 3 4 6 7 Solve using the addition principle. Graph and write set-builder notation for the answer. ) a) -7n + > -8n + 16 b) - + 13a - 12 12a
Write the equation of the line represented b the graph and state the slope. 14) a) 16) The following graph shows data for a recent train ride from New York to Toronto. What was the average speed of the train? 400 - - 300 200 0 b) 1 2 3 4 Time of Da (PM) - - 1) On March Henr rented a van with a full tank of gas and 12,891.0 miles on the odometer. On March 12 he returned the van with 13,074.4 miles on the odometer. The rental agenc charged Henr $76 for the rental and needed gallons to fill up the tank. What was the van's rate of gas consumption in miles per gallon? Use the graph to solve the problem. 17) The graph depicts a relationship between scores achieved on an unspecified standardized test and famil income. Find the rate of change of test scores with respect to famil income. 40 30 20 00 490 480 Income (in $00's)
Find the slope of the line. If the slope is undefined, state so. 18) 4 3 2 1 - -4-3 -2-1 -1 1 2 3 4-2 -3-4 - Find the slope of the line containing the given pair of points. If the slope is undefined, state so. 19) a) (-6, -) and (, -9) b) (4, -4) and (7, 3) 20) An old house has a basement stairwa that has steps with 7.2 inch risers and inch treads. What is the slope of the stairwa? 21) Over one particular stretch of road, the Whitepoint Highwa rises 47 ft over a horizontal distance of 3800 ft. Find the grade of the road. Draw a line that has the given slope and -intercept. 22) Slope - 1 ; -intercept (0, 6) 2 Find the slope-intercept equation for the line with the indicated slope and -intercept. 26) Slope - 4 ; -intercept (0, ) 7 Graph the linear equation. 27) -4-20 = -4 28) = - 1 4-4 29) A moving firm charges a flat fee of $ 30 plus $2 per hour. Let be the cost in dollars of using the moving firm for hours. Find the slope-intercept form of the equation. Determine whether the pair of equations represents parallel lines. 30) 12 + 4 = 16 21 + 7 = 29 Write a point-slope equation for the line with the given slope that contains the given point. 31) m = -; (, -2) Write the slope-intercept equation for the line containing the given pair of points. 32) (-2, 3) and (2, ) Graph the line. 33) - 3 = - 1 ( - 3) 4 34) + 2 = 2( + 3) Find the slope and the -intercept of the line. 23) = 1 4-4 24) -6 + 8 = 8 2) + 7 = 29
Provide the proper response. 3) Identif whether the slope is positive, negative, zero or undefined. a) - - 37) What can ou sa about the graph of A + B = C if B is equal to zero? 38) What can ou sa about a line if ever point on the line has the same coordinate? 39) Is it possible for the -intercept and the -intercept of a straight line to be at the same point? Eplain our answer. b) 40) What is the -intercept of the line = b? - - 41) Does ever straight line have an -intercept? If not, give an eample of an equation whose graph does not have an -intercept. c) Simplif. Assume that no denominator is zero and that 0 0 is not considered. 42) (3)(63) 43) ( + 2) 8 ( + 2) 9 44) (pq 6 )(pq) - - 4) (p - q)8 (p - q) 2 d) 46) g9 h g 2 h - 47) 32 7-83 - Simplif the epression. 48) 3z 0 when z = 14 Provide an appropriate response. 36) Eplain how ou would find the intercept of a line with an equation of the form A + B = C. 49) (-4) 0 - (-4) 1 Simplif. 0) (r 7 ) 3 1) (-4a)4
2) (w 8 z) 4 (w 4 z 2 ) Simplif. Assume that no denominator is zero and that 0 0 is not considered. 3) 3 3a 4) ) z 2 2 3 4 7z 6 2 Identif the terms in the polnomial. 6) -2t 7 + t 4-2t 2 + 3 Determine the coefficient and the degree of each term in the polnomial. 7) 3w 7-4w 3 - w Determine the leading term, leading coefficient, and the degree of the polnomial. 8) - 2 2-6 3-4 + Evaluate the polnomial. 9) 32 + 9-9 for = 2 60) -22 + 6-3 for = -2 61) The position of an object moving in a straight line is given b s = t2-2t, where s is in meters and t is the time in seconds the object has been in motion. How far will an object move in 3 seconds? Add. 62) a) (6a + 8a2) + (8a - 6a2) b) (-7 + 4n7-6n) + (9n7 + 4n - 8) c) (-9 + 42 + 94-93) + (33-72 - + 34) Subtract. 63) a) (17a4-9a2) - (-6a4-17a2) b) (8n - 16n3 + 16) - (4n3 + 2n + 14) c) (4 + 77 - - 6) - (-7-26 + 27 + 6) 64) Charlie purchased a digital camera. The cost of the camera, including 7. percent sales ta was $33.40. What was the cost of the camera before ta? 6) In a local election, 24,138 people voted. This was an increase of 8% over the last election. How man people voted in the last election? 66) A chemical solution contains 9% salt. How much salt is in 1. ml of solution? Solve using the five-step problem-solving process. 67) The second angle of a triangle is 3 times as large as the first. The third angle is 3e more than the first. Find the measure of all three angles of the triangle. 68) A rectangular window has a perimeter of 22 inches. The length of the window is 30 inches more than the width. What are the dimensions of the window? 69) A triangular lake-front lot has a perimeter of 1,0 feet. One side is 200 feet longer than the shortest side, while the third side is 300 feet longer than the shortest side. Find the lengths of all three sides. 70) The sum of three consecutive odd integers is 171. Find the integers.
Answer Ke Testname: EA EXAM 2 REVIEW F0 1) a) 18% b) 234 students c) 2 students 2) Yes, No, Yes 3) a) -8-7-6--4-3-2-1 0 1 2 3 4 6 7 8 - - b) -7-6 - -4-3 -2-1 0 1 2 3 4 6 7 4) a) {v 4} b) {v > -3} ) a) {n n > 11} 8) 9) 8 9 11 12 13 14 b) {a a 6} 3 4 6 7 8 9 - - ) - - 6) 7) - - - - 11) (0, 2), (-, 0) 12) (-, 0), (0, 2)
Answer Ke Testname: EA EXAM 2 REVIEW F0 13) (0, 8), (2, 0) 26) = - 4 7 + 27) - - - 14) a) = -4, Slope is undefined b) = 6, Slope is 0 1) 18.3 miles/gallon 16) 0 miles per hour 17) 4 points per thousand dollars 3-18) - 1 2-19) a) - 4 11 b) 7 3-20) 0.73 21) 12.% 22) 28) 29) = 2 + 30 30) Yes 31) + 2 = -( - ) 32) = 1 2 + 4 33) - - 23) 1 4 ; (0, -4) - - 24) 3 ; (0, 1) 4 2) - 7 ; (0, 29 7 )
Answer Ke Testname: EA EXAM 2 REVIEW F0 34) - - 3) a) Positive b) Undefined c) Negative d) Zero 36) Let = 0 and solve for. 37) The graph is a vertical line. 38) The line is vertical. 39) Yes. If the line passes through the origin, then both the -intercept and the -intercept are at (0, 0). 40) (0, b) 41) The -intercept is the point where the line crosses the -ais. Lines parallel to the -ais do not intercept the -ais. Thus the graph of an equation of the form = b where b 0 has no -intercept. 42) 306 43) ( + 2) 17 44) p 6 q 11 4) (p-q) 6 46) g 7 h 4 47) -44 48) 3 49) 0) 12r 21 1) (-4)4a20 2) w 36 z 6 3) 12 27a 3 4) 2 z ) 46 8 49z 12 6) -2t 7, t 4, -2t 2, 3 7) Coefficients: 3, -4, -1; degrees: 7, 3, 1 8) -4, -4, 9) 21 60) -23 61) 39 meters 62) a) 14a + 2a2 b) 13n7-2n - 1 c) 124-63 - 32-14 63) a) 23a4 + 8a2 b) 6n - 20n3 + 2 c) 7-36 - 2 + 2 64) $312 6) 22,30 people 66) 0.13 ml 67) 29e, 87e, 64e 68) 48 in., 78 in. 69) 200 ft, 400 ft, 00 ft 70), 7, 9