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All Textbook Solutions for College Algebra
A prospective buyer wants to know how much grain a specific silo can hold. The area of the floor of the silo is (2x+9)2 . The height of the silo is 10x+10 , where x is measured in feet. Expand the square and multiply by the height to find the expression that shows how much grain the silo can hold.For the following exercises, perform the given operations. 55. (4t7)2(2t+1)(4t2+2t+11)For the following exercises, perform the given operations. 56. (3b+6)(3b6)(9b236)For the following exercises, perform the given operations. 57. (a2+4ac+4c2)(a24c2)Factor x(b2a)+6(b2a) by pulling out the GCF.Factor x27x+6 .Factor. 2x2+9x+9 6x2+x1Factor 49x214x+1Factor 81y2100 .Factor the sum of cubes: 216a3+b3. .Factor the difference of cubes: 1,000x31 .Factor 2(5a1)34+7a(5a1)14 .If the terms of a polynomial do not have a GCF, does that mean it is not factorable? Explain.A polynomial is factorable, but it is not a perfect square trinomial or a difference of two squares. Can you factor the polynomial without finding the GCF?How do you factor by grouping?For the following exercises, find the greatest common factor 4. 14x+4xy18xy2For the following exercises, find the greatest common factor. 5. 49mb235m2ba+77ma2For the following exercises, find the greatest common factor. 6. 30x3y45x2y2+135xy3For the following exercises, find the greatest common factor. 7. 200p3m330p2m3+40m3For the following exercises, find the greatest common factor. 8. 36j4k218j3k3+54j2k4For the following exercises, find the greatest common factor. 9. 6y42y3+3y2yFor the following exercises, factor by grouping. 10. 6x2+5x4For the following exercises, factor by grouping. 11. 2a2+9a18For the following exercises, factor by grouping. 12. 6c2+41c+63For the following exercises, factor by grouping. 13. 6n219n11For the following exercises, factor by grouping. 14. 20w247w+24For the following exercises, factor by grouping. 15. 2p25p7For the following exercises, factor the polynomial. 16. 7x2+48x7For the following exercises, factor the polynomial. 17. 10h29h9For the following exercises, factor the polynomial. 18. 2b225b247For the following exercises, factor the polynomial. 19. 9d273d+8For the following exercises, factor the polynomial. 20. 90v2181v+90For the following exercises, factor the polynomial. 21. 12t2+t13For the following exercises, factor the polynomial. 22. 2n2n15For the following exercises, factor the polynomial. 23. 16x2100For the following exercises, factor the polynomial. 24. 25y2196For the following exercises, factor the polynomial. 25. 121p2169For the following exercises, factor the polynomial. 26. 4m29For the following exercises, factor the polynomial. 27. 361d281For the following exercises, factor the polynomial. 28. 324x2121For the following exercises, factor the polynomial. 29. 144b225c2For the following exercises, factor the polynomial. 30. 16a28a+1For the following exercises, factor the polynomial. 31. 49n2+168n+144For the following exercises, factor the polynomial. 32. 121x288x+16For the following exercises, factor the polynomial. 33. 225y2+120y+16For the following exercises, factor the polynomial. 34. m220m+100For the following exercises, factor the polynomial. 35. 25p2120p+144For the following exercises, factor the polynomial. 36. 36q2+60q+25For the following exercises, factor the polynomial. 37. x3+216For the following exercises, factor the polynomial. 38. 27y38For the following exercises, factor the polynomial. 39. 125a3+343For the following exercises, factor the polynomial. 40. b38d3For the following exercises, factor the polynomial. 40. 64x3125For the following exercises, factor the polynomial. 42. 729q3+1331For the following exercises, factor the polynomial. 43. 125r3+1,728s3For the following exercises, factor the polynomial. 44. 4x(x1)23+3(x1)13For the following exercises, factor the polynomial. 45. 3c(2c+3)145(2c+3)34For the following exercises, factor the polynomial. 46. 3t(10t+3)13+7(10t+3)43For the following exercises, factor the polynomial. 47. 14x(x+2)25+5(x+2)35For the following exercises, factor the polynomial. 49. 9y(3y13)152(3y13)65For the following exercises, factor the polynomial. 49. 5z(2z9)32+11(2z9)12For the following exercises, factor the polynomial. 50. 6d(2d+3)16+5(2d+3)56For the following exercises, consider this scenario: Charlotte has appointed a chairperson to lead a city beautification project. The first act is to install statues and fountains in one of the city’s parks. The park is a rectangle with an area of 98x2+105x27m2 ,as shown in the following figure. The length and width of the park are perfect factors of the area. 51. Factor by grouping to find the length and width of the parkREAL-WORLD APPLICATIONS Charlotte has appointed a chairperson to lead a city beautification project. The first act is to install statues and fountains in one of the city’s parks. The park is a rectangle with an area of 98x2+105x27m2 ,as shown in the following figure. The length and width of the park are perfect factors of the area. 52. A statue is to be placed in the center of the park. The area of the base of the statue is 4x2+12x+9m2 . Factor the area to find the lengths of the sides of the statue.For the following exercises, consider this scenario: Charlotte has appointed a chairperson to lead a city beautification project. The first act is to install statues and fountains in one of the city’s parks. The park is a rectangle with an area of 98x2+105x27m2 ,as shown in the following figure. The length and width of the park are perfect factors of the area. 53. At the northwest corner of the park, the city is going to install a fountain. The area of the base of the fountain is 9x225m2 . Factor the area to find the lengths of the sides of the fountain.For the following exercise, consider the following scenario: A school is installing a flagpole in the central plaza. The plaza is a square with side length 100 yd as shown in the figure below. The flagpole will take up a square plot with area x26x+9yd2. 54. Find the length of the base of the flagpole by factoring.For the following exercises, factor the polynomials completely. 56. 16x4200x2+625For the following exercises, factor the polynomials completely. 56. 81y4256For the following exercises, factor the polynomials completely. 57. 16z42,401a4For the following exercises, factor the polynomials completely. 58. 5x(3x+2)24+(12x+8)32For the following exercises, factor the polynomials completely. 59. (32x3+48x2162x243)1Simplify x6x236 .Multiply the rational expressions and show the product in simplest form: x2+11x+30x2+5x+6x2+7x+12x2+8x+16Divide the rational expressions and express the quotient in simplest form: 9x2163x2+17x283x22x8x2+5x14Subtract the rational expressions: 3x+51x3Simplify: xyyxyHow can you use factoring to simplify rational expressions?How do you use the LCD to combine two rational expressions?Tell whether the following statement is true or false and explain why: You only need to find the LCD when adding or subtracting rational expressions.For the following exercises, simplify the rational expressions. 4. Y13 x216x25x+4For the following exercises, simplify the rational expressions. 5. y2+10y+25y2+11y+30For the following exercises, simplify the rational expressions. 6. 6a224a+246a224For the following exercises, simplify the rational expressions. 7. 9b2+18b+93b+3For the following exercises, simplify the rational expressions. 8. m12m2144For the following exercises, simplify the rational expressions. 9. 2x2+7x44x2+2x2For the following exercises, simplify the rational expressions. 10. 6x2+5x43x2+19x+20For the following exercises, simplify the rational expressions. 11. a2+9a+18a2+3a18For the following exercises, simplify the rational expressions. 12. 3c2+25c183c223c+14For the following exercises, simplify the rational expressions. 13. 12n229n828n25n3For the following exercises, multiply the rational expressions and express the product in simplest form. 14. x2x62x2+x62x2+7x15x29For the following exercises, multiply the rational expressions and express the product in simplest form. 15. c2+2c24c2+12c+36c210c+24c28c+16For the following exercises, multiply the rational expressions and express the product in simplest form. 16. 2d2+9d35d2+10d+213d2+2d213d2+14d49For the following exercises, multiply the rational expressions and express the product in simplest form. 17. 10h29h92h219h+24h216h+645h237h24For the following exercises, multiply the rational expressions and express the product in simplest form. 18. 6b2+13b+64b296b2+31b3018b23b10For the following exercises, multiply the rational expressions and express the product in simplest form. 19. 2d2+15d+254d2252d215d+2525d21For the following exercises, multiply the rational expressions and express the product in simplest form. 20. 6x25x5015x244x2020x27x62x2+9x+10For the following exercises, multiply the rational expressions and express the product in simplest form. 21. t21t2+4t+3t2+2t15t24t+3For the following exercises, multiply the rational expressions and express the product in simplest form. 22. 2n2n156n2+13n512n213n+34n215n+9For the following exercises, multiply the rational expressions and express the product in simplest form. 23. 36x2256x2+65x+503x2+32x+2018x2+27x+10For the following exercises, divide the rational expressions. 24. 3y27y62y23y9y2+y22y2+y3For the following exercises, divide the rational expressions. 25.6p2+p128p2+18p+96p211q+42p2+11p6For the following exercises, divide the rational expressions. 26.q29q2+6q+9q22q3q2+2q3For the following exercises, divide the rational expressions. 27.18d2+77d1827d215d+23d2+29d449d215d+4For the following exercises, divide the rational expressions. 28.16x2+18x5532x236x112x2+17x+304x2+25x+6For the following exercises, divide the rational expressions. 29. 144b22572b26b1018b221b+536b218b10For the following exercises, divide the rational expressions. 30.16a224a+94a2+17a1516a294a2+11a+6For the following exercises, divide the rational expressions. 31.22y2+59y+1012y2+28y511y2+46y+824y210y+1For the following exercises, divide the rational expressions. 32.9x2+3x203x27x+46x2+4x10x22x+1For the following exercises, add and subtract the rational expressions, and then simplify. 33.4x+10yFor the following exercises, add and subtract the rational expressions, and then simplify. 34.122q63pFor the following exercises, add and subtract the rational expressions, and then simplify. 35.4a+1+5a3For the following exercises, add and subtract the rational expressions, and then simplify. 36.c+23c44For the following exercises, add and subtract the rational expressions, and then simplify. 37.y+3y2y3y+1For the following exercises, add and subtract the rational expressions, and then simplify. 38.x1x+12x+32x+1For the following exercises, add and subtract the rational expressions, and then simplify. 39.3zz+1+2z+5z2For the following exercises, add and subtract the rational expressions, and then simplify. 40.4pp+1p+14pFor the following exercises, add and subtract the rational expressions, and then simplify. 41.xx+1+yy+1For the following exercises, simplify the rational expression. 42. 6y4xyFor the following exercises, simplify the rational expression. 43. 2a+7bbFor the following exercises, simplify the rational expression. 44. x4p8pFor the following exercises, simplify the rational expression. 45. 3a+b62b3aFor the following exercises, simplify the rational expression. 46. 3x+1+2x1x1x+1For the following exercises, simplify the rational expression. 47. abbaa+babFor the following exercises, simplify the rational expression. 48. 2x3+4x7x2For the following exercises, simplify the rational expression. 49. 2cc+2+c1c+12c+1c+1For the following exercises, simplify the given expression. 50. xyyxxy+yxBrenda is placing tile on her bathroom floor. The area of the floor is 15x28x7ft2 . The area of one tile is x22x+1ft2 . To find the number of tiles needed,simplify the rational expression: 15x28x7x22x+1.The area of Sandy’s yard is 25x2625ft2 . A patch of sod has an area of x210x+25ft2 . Divide the two areas and simplify to find how many pieces of sod Sandy needs to cover her yard.Aaron wants to mulch his garden. His garden is x2+18x+81ft2 . One bag of mulch covers x281ft2 . Divide the expressions and simplify to find how many bags of mulch Aaron needs to mulch his garden.For the following exercises, perform the given operations and simplify. 54.x2+x6x22x32x23x9x2x210x2+27x+18x2+2x+1For the following exercises, perform the given operations and simplify. 55. 3y210y+33y2+5y22y23y202y2y15y4For the following exercises, perform the given operations and simplify. 56. 4a+12a3+2a32a+34a2+9aFor the following exercises, perform the given operations and simplify. 57.x2+7x+12x2+x63x2+19x+288x24x242x2+x33x2+4x7For the following exercises, perform the given operations. 1.(532)26For the following exercises, perform the given operations. 2.64(28)+147For the following exercises, perform the given operations. 3.252+62For the following exercises, solve the equation. 4.5x+9=11For the following exercises, solve the expression. 5. 2y+42=64For the following exercises, simplify the expression. 6.9(y+2)32+1For the following exercises, simplify the expression. 7.3m(4+7)mFor the following exercises, identify the number as rational, irrational, whole, or natural. Choose the most descriptive answer. 8.11For the following exercises, identify the number as rational, irrational, whole, or natural. Choose the most descriptive answer. 9.0For the following exercises, identify the number as rational, irrational, whole, or natural. Choose the most descriptive answer. 10.56For the following exercises, identify the number as rational, irrational, whole, or natural. Choose the most descriptive answer. 11.11For the following exercises, simplify the expression. 12.2224For the following exercises, simplify the expression. 13.4543For the following exercises, simplify the expression. 4.( a 2 b 3 )4For the following exercises, simplify the expression. 15.6a2a02a4For the following exercises, simplify the expression. 16.(xy)4y32x5For the following exercises, simplify the expression. 17.42x3y32x0For the following exercises, simplify the given expression. 18.( 2 x 2 y)2For the following exercises, simplify the expression. 19.(16a3b2)(4ab1)2For the following exercises, simplify the expression. 20. Write the number in standard notation: 2.1314106For the following exercises, simplify the expression. 21. Write the number in scientific notation: 16,340,000For the following exercises, find the principal square root. 22.121For the following exercises, find the principal square root. 23.196For the following exercises, find the principal square root. 24.361For the following exercises, find the principal square root. 25.75For the following exercises, find the principal square root. 26.162For the following exercises, find the principal square root. 27.3225For the following exercises, find the principal square root. 28.8081For the following exercises, find the principal square root. 29.491250For the following exercises, find the principal square root. 30.24+2For the following exercises, find the principal square root. 31.43+63For the following exercises, find the principal square root. 32.125135For the following exercises, find the principal square root. 33.2435For the following exercises, find the principal square root. 34.250383For the following exercises, perform the given operations and simplify. 35.(3x3+2x1)+(4x22x+7)For the following exercises, perform the given operations and simplify. 36.(2y+1)(2y22y5)For the following exercises, perform the given operations and simplify. 37.(2x2+3x6)+(3x24x+9)For the following exercises, perform the given operations and simplify. 38.(6a2+3a+10)(6a23a+5)For the following exercises, perform the given operations and simplify. 39.(k+3)(k6)For the following exercises, perform the given operations and simplify. 40.(2h+1)(3h2)For the following exercises, perform the given operations and simplify. 41.(x+1)(x2+1)For the following exercises, perform the given operations and simplify. 42.(m2)(m2+2m3)For the following exercises, perform the given operations and simplify. 43.(a+2b)(3ab)For the following exercises, perform the given operations and simplify. 44.(x+y)(xy)For the following exercises, find the greatest common factor. 45.81p+9pq27p2q2For the following exercises, find the greatest common factor. 46.12x2y+4xy218xyFor the following exercises, find the greatest common factor. 47.88a3b+4a2b144a2For the following exercises, factor the polynomial. 48.2x29x18For the following exercises, factor the polynomial. 49.8a2+30a27For the following exercises, factor the polynomial. 50.d25d66For the following exercises, factor the polynomial. 51.x2+10x+25For the following exercises, factor the polynomial. 52.y26y+9For the following exercises, factor the polynomial. 53.4h212hk+9k2For the following exercises, factor the polynomial. 54.361x2121For the following exercises, factor the polynomial. 55.p3+216For the following exercises, factor the polynomial. 56.8x3125For the following exercises, factor the polynomial. 57.64q327p3For the following exercises, factor the polynomial. 58.4x(x1)14+3(x1)34For the following exercises, factor the polynomial. 59.3p(p+3)138(p3)43For the following exercises, factor the polynomial. 60.4r(2r1)235(2r1)13For the following exercises, simplify the expression. 61.x2x12x28x+16For the following exercises, simplify the expression. 62.4y2254y220y+25For the following exercises, simplify the expression. 63.2a2a32a26a85a219a410a213a3For the following exercises, simplify the expression. 64.d4d29d3d216For the following exercises, simplify the expression. 65.m2+5m+62m25m32m2+3m94m24m3For the following exercises, simplify the expression. 66.4d27d26d217d+108d2+6d+16d2+7d10For the following exercises, simplify the expression. 67.10x+6yFor the following exercises, simplify the expression. 68.12a2+2a+13a21For the following exercises, simplify the expression. 69.1d+2c6c+12ddcFor the following exercises, simplify the expression. 70. 3x7y2xFor the following exercises, identify the number as rational, irrational, whole, or natural. Choose the most descriptive answer. 1.13For the following exercises, identify the number as rational, irrational, whole, or natural. Choose the most descriptive answer. 2.2For the following exercises, evaluate the equations. 3.2(x+3)12=18For the following exercises, evaluate the equations. 4.y(3+3)226=10For the following exercises, evaluate the equations. 5. Write the number in standard notation: 3.1415106For the following exercises, evaluate the equations. 6. Write the number in scientific notation: 0.0000000212.For the following exercises, simplify the expression. 7.2(2+32)2+144For the following exercises, simplify the expression. 8.4(x+3)(6x+2)For the following exercises, simplify the expression. 9. 3533For the following exercises, simplify the expression. 10.(23)3For the following exercises, simplify the expression. 11.8x3(2x)2For the following exercises, simplify the expression. 12.(16y0)2y2For the following exercises, simplify the expression. 13.441For the following exercises, simplify the expression. 14.490For the following exercises, simplify the expression. 15.9x16For the following exercises, simplify the expression. 16.121b21+bFor the following exercises, simplify the expression. 17.624+754126For the following exercises, simplify the expression. 18.836254For the following exercises, simplify the given expression. 19.(13q3+2q23)(6q2+5q3)For the following exercises, simplify the expression. 20.(6p2+2p+1)+(9p21)For the following exercises, simplify the given expression. 21.(n2)(n24n+4)For the following exercises, simplify the expression. 22.(a2b)(2a+b)For the following exercises, factor the polynomial. 23.16x281For the following exercises, factor the polynomial. 24.y2+12y+36For the following exercises, factor the polynomial. 25.27c31331For the following exercises, factor the polynomial. 26.3x(x6)14+2(x6)34For the following exercises, simplify the expression. 27.2z2+7z+3z294z215z+94z21For the following exercises, simplify the expression. 28. xy+2xFor the following exercises, simplify the expression. 29. a2b2b9a3a2b6aConstruct a table and graph the equation by plotting points: y=12x+2.Find the intercepts of the equation and sketch the graph: y=34x+3.Find the distance between two points: (1,4) and (11,9) .Find the midpoint of the line segment with endpoints (2,1) and (8,6) .Is it possible for a point plotted in the Cartesian coordinate system to not lie in one of the four quadrants? Explain.Describe the process for finding the x-intercept and the y-intercept of a graph algebraically.Describe in your own words what the y-intercept of a graph is.When using the distance formula d=(x2x1)2+(y2y1)2 , explain the correct order of operations that are to be performed to obtain the correct answer.For each of the following exercises, find the x-intercept and the y-intercept without graphing. Write the coordinates of each intercept. 5. y=3x+6For each of the following exercises, find the x-intercept and the y-intercept without graphing. Write the coordinates of each intercept. 6.4y=2x1For each of the following exercises, find the x-intercept and the y-intercept without graphing. Write the coordinates of each intercept. 7.3y2y=6For each of the following exercises, find the x-intercept and the y-intercept without graphing. Write the coordinates of each intercept. 8.4x3=2yFor each of the following exercises, find the x-intercept and the y-intercept without graphing. Write the coordinates of each intercept. 9.3x+8y=9For each of the following exercises, find the x-intercept and the y-intercept without graphing. Write the coordinates of each intercept. 10.2x23=34y+3For each of the following exercises, solve the equation for yin terms of x. 11.4x+2y=8For each of the following exercises, solve the equation for yin terms of x. 12.3x2y=6For each of the following exercises, solve the equation for yin terms of x. 13.2x=53yFor each of the following exercises, solve the equation for yin terms of x. 14.x2y=7For each of the following exercises, solve the equation for yin terms of x. 15.5y+4=10xFor each of the following exercises, solve the equation for yin terms of x. 16.5x+2y=0For each of the following exercises, find the distance between the two points. Simplify your answers, and write the exact answer in simplest radical form for irrational answers. 17.(4,1)and(3,4)For each of the following exercises, find the distance between the two points. Simplify your answers, and write the exact answer in simplest radical form for irrational answers. 18.(2,5)and(7,4)For each of the following exercises, find the distance between the two points. Simplify your answers, and write the exact answer in simplest radical form for irrational answers. 19.(5,0)and(5,6)For each of the following exercises, find the distance between the two points. Simplify your answers, and write the exact answer in simplest radical form for irrational answers. 20.(4,3)and(10,3)For each of the following exercises, find the distance between the two points. Simplify your answers, and write the exact answer in simplest radical form for irrational answers. 21. Find the distance between the two points given using your calculator, and round your answer to the nearest hundredth. (19,12)and(41,71) .For each of the following exercises, find the coordinates of the midpoint of the line segment that joins the two given points. 22.(5,6)and(4,2)For each of the following exercises, find the coordinates of the midpoint of the line segment that joins the two given points. 23.(1,1)and(7,4)For each of the following exercises, find the coordinates of the midpoint of the line segment that joins the two given points. 24.(5,3)and(2,8)For each of the following exercises, find the coordinates of the midpoint of the line segment that joins the two given points. 25.(0,7)and(4,9)For each of the following exercises, find the coordinates of the midpoint of the line segment that joins the two given points. 26.(43,17)and(23,34)For each of the following exercises, identify the information requested. 27. What are the coordinates of the origin?For each of the following exercises, identify the information requested. 28. If a point is located on the y-axis, what is the x-coordinate?For each of the following exercises, identify the information requested. 29. If a point is located on the x-axis, what is the y-coordinate?For each of the following exercises, plot the three points on the given coordinate plane. State whether the three points you plotted appear to be collinear (on the same line). 30.(4,1)(2,3)(5,0)For each of the following exercises, plot the three points on the given coordinate plane. State whether the three points you plotted appear to be collinear (on the same line). 31.(1,2)(0,4)(2,1)For each of the following exercises, plot the three points on the given coordinate plane. State whether the three points you plotted appear to be collinear (on the same line). 32.(3,0)(3,4)(3,3)For each of the following exercises, plot the three points on the given coordinate plane. State whether the three points you plotted appear to be collinear (on the same line). 33. Name the coordinates of the points graphed.For each of the following exercises, plot the three points on the given coordinate plane. State whether the three points you plotted appear to be collinear (on the same line). 34. Name the quadrant in which the following points would be located. If the point is on an axis, name the axis. a. (3,4) b. (5,0) c. (1,4) d. (2,7) e. (0,3)For each of the following exercises, construct a table and graph the equation by plotting at least three points. 35.y=13x+2For each of the following exercises, construct a table and graph the equation by plotting at least three points. 36.y=3x+1For each of the following exercises, construct a table and graph the equation by plotting at least three points. 37.2y=x+3For each of the following exercises, find and plot the x-and y-intercepts, and graph the straight line based on those two points. 38.4x3y=12For each of the following exercises, find and plot the x-and y-intercepts, and graph the straight line based on those two points. 39.x2y=8For each of the following exercises, find and plot the x-and y-intercepts, and graph the straight line based on those two points. 40.y5=5xFor each of the following exercises, find and plot the x-and y-intercepts, and graph the straight line based on those two points. 41.3y=2x+6For each of the following exercises, find and plot the x-and y-intercepts, and graph the straight line based on those two points. 42.y=x32For each of the following exercises, use the graph in the figure below. 43. Find the distance between the two endpoints using the distance formula. Round to three decimal places.For each of the following exercises, use the graph in the figure below. 44. Find the coordinates of the midpoint of the line segment connecting the two points.For each of the following exercises, use the graph in the figure below. 45. Find the distance that (3,4) is from the origin.For each of the following exercises, use the graph in the figure below. 46. Find the distance that (5,2) is from the origin. Round to three decimal places.For each of the following exercises, use the graph in the figure below. 47.Which point is closer to the origin?For the following exercises, use your graphing calculator to input the linear graphs in the Y= graph menu. After graphing it, use the 2ndCALC button and l:valuebutton, hit ENTER. At the lower part of the screen you will see x= and a blinking cursor. You may enter any number for x and it will display the yvalue for any x value you input. Use this and plug in x=0 , thus finding the y-intercept, for each of the following graphs. 48.Y1=2x+5For the following exercises, use your graphing calculator to input the linear graphs in the Y= graph menu. After graphing it, use the 2ndCALC button and l:valuebutton, hit ENTER. At the lower part of the screen you will see x= and a blinking cursor. You may enter any number for x and it will display the yvalue for any x value you input. Use this and plug in x=0 , thus finding the y-intercept, for each of the following graphs. 49.Y1=3x84For the following exercises, use your graphing calculator to input the linear graphs in the Y= graph menu. After graphing it, use the 2ndCALC button and l:valuebutton, hit ENTER. At the lower part of the screen you will see x= and a blinking cursor. You may enter any number for x and it will display the yvalue for any x value you input. Use this and plug in x=0 , thus finding the y-intercept, for each of the following graphs. 50.Y1=x+52For the following exercises, use your graphing calculator to input the linear graphs in the Y= graph menu. After graphing it, use the 2ndCALC button and 2:zero button, hit ENTER. At the lower part of the screen you will see “left bound?” and a blinking cursor on the graph of the line. Move this cursor to the left of the x-intercept, hit ENTER. Now it says “right bound?" Move the cursor to the right of the x-intercept, hit ENTER. Now it says “guess?” Move your cursor to the left somewhere in between the left and right bound near the x-intercept. Hit ENTER. At the bottom of your screen it will display the coordinates of the x-intercept or the “zero" to the y-value. Use this to find the x-intercept. Note: With linear/straight line functions the zero is not really a “guess,” but it is necessary to enter a “guess” so it will search and find the exact x-intercept between your right and left boundaries. With other types of functions (more than onex-intercept), they may be irrational numbers so “guess” is more appropriate to give it the correct limits to find a very close approximation between the left and right boundaries. 51.Y1=8x+6For the following exercises, use your graphing calculator to input the linear graphs in the Y= graph menu. After graphing it, use the 2ndCALC button and 2:zero button, hit ENTER. At the lower part of the screen you will see “left bound?” and a blinking cursor on the graph of the line. Move this cursor to the left of the x-intercept, hit ENTER. Now it says “right bound?" Move the cursor to the right of the x-intercept, hit ENTER. Now it says “guess?” Move your cursor to the left somewhere in between the left and right bound near the x-intercept. Hit ENTER. At the bottom of your screen it will display the coordinates of the x-intercept or the “zero" to the y-value. Use this to find the x-intercept. Note: With linear/straight line functions the zero is not really a “guess,” but it is necessary to enter a “guess” so it will search and find the exact x-intercept between your right and left boundaries. With other types of functions (more than onex-intercept), they may be irrational numbers so “guess” is more appropriate to give it the correct limits to find a very close approximation between the left and right boundaries. 52.Y1=4x7For the following exercises, use your graphing calculator to input the linear graphs in the Y= graph menu. After graphing it, use the 2ndCALC button and 2:zero button, hit ENTER. At the lower part of the screen you will see “left bound?” and a blinking cursor on the graph of the line. Move this cursor to the left of the x-intercept, hit ENTER. Now it says “right bound?" Move the cursor to the right of the x-intercept, hit ENTER. Now it says “guess?” Move your cursor to the left somewhere in between the left and right bound near the x-intercept. Hit ENTER. At the bottom of your screen it will display the coordinates of the x-intercept or the “zero" to the y-value. Use this to find the x-intercept. Note: With linear/straight line functions the zero is not really a “guess,” but it is necessary to enter a “guess” so it will search and find the exact x-intercept between your right and left boundaries. With other types of functions (more than onex-intercept), they may be irrational numbers so “guess” is more appropriate to give it the correct limits to find a very close approximation between the left and right boundaries. 53.Y1=3x+54 Round your answer to the nearest thousandth.A man drove 10 mi directly east from his home, made a left turn at an intersection, and then traveled 5 mi north to his place of work. If a road was made directly from his home to his place of work, what would its distance be to the nearest tenth of a mile?If the road was made in the previous exercise, how much shorter would the man’s one-way trip be every day?Given these four points: A(1,3),B(3,5),C(4,7),andD(5,4) , find the coordinates of the midpoint of line segments AB and CD.After finding the two midpoints in the previous exercise, find the distance between the two midpoints to the nearest thousandth.Given the graph of the rectangle shown and the coordinates of its vertices, prove that the diagonals of the rectangle are of equal length.In the previous exercise, find the coordinates of the midpoint for each diagonal.The coordinates on a map for San Francisco are (53,17) and those for Sacramento are (123,78) . Note that coordinates represent miles. Find the distance between the cities to the nearest mile.If San Jose’s coordinates are (76,12) , where the coordinates represent miles, find the distance between San Jose and Sail Francisco to the nearest mile.A small craft in Lake Ontario sends out a distress signal. The coordinates of the boat in trouble were (49,64) . One rescue boat is at the coordinates (60,82) and a second Coast Guard craft is at coordinates (58,47) . Assuming both rescue craft travel at the same rate, which one would get to the distressed boat the fastest?A man on the top of a building wants to have a guy wire extend to a point on the ground 20 ft from the building. To the nearest foot, how long will the wire have to be if the building is 50 fttall?If we rent a truck and pay a $75/day fee plus $.20 for every mile we travel, write a linear equation that would express the total cost y, using x to represent the number of miles we travel. Graph this function on your graphing calculator and find the total cost for one day if we travel 70 mi.