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All Textbook Solutions for High School Math 2012 Common-core Algebra 1 Practice And Problem Solvingworkbook Grade 8/9
Which method (s) would you choose to solve each equation? Justify your reasoning. 4x2144=0Which method (s) would you choose to solve each equation? Justify your reasoning. f22f35=0Writing Explain how the discriminant can be used to determine the number of solutions a quadratic equation has.Find the number of real-number solutions of each equation. x28x+7=0Find the number of real-number solutions of each equation. x26x=0Find the number of real-number solutions of each equation. 2x25x+16=0Find the number of real-number solutions of each equation. 3x24x8=0Find the number of real-number solutions of each equation. 7x2+12x21=0Find the number of real-number solutions of each equation. 2x2+4x+2=0Use any method to solve each equation. If necessary, round answers to the nearest hundredth. 5m23m15=0Use any method to solve each equation. If necessary, round answers to the nearest hundredth. 9y2+6y=12Use any method to solve each equation. If necessary, round answers to the nearest hundredth. 4a2=36Use any method to solve each equation. If necessary, round answers to the nearest hundredth. 6t296=0Use any method to solve each equation. If necessary, round answers to the nearest hundredth. z2+7z=10Use any method to solve each equation. If necessary, round answers to the nearest hundredth. g2+4g+3=0Use any method to solve each equation. If necessary, round answers to the nearest hundredth. x2+11x10=0Use any method to solve each equation. If necessary, round answers to the nearest hundredth. x2+7x+8=0Use any method to solve each equation. If necessary, round answers to the nearest hundredth. 3x2+5x9=0Use any method to solve each equation. If necessary, round answers to the nearest hundredth. 2x2+10x1=0Use any method to solve each equation. If necessary, round answers to the nearest hundredth. 3x2+6x+3=0Use any method to solve each equation. If necessary, round answers to the nearest hundredth. 6x2+x+12=0The weekly profit of a company is modeled by the function w=g2+120g28. The weekly profit, w is dependent on the number of gizmos, g, sold. If the break-even point is when w=0, how many gizmos must the company sell each week in order to break even?Reasoning The equation 4x2+bx+9=0 has no real-number solutions. What must be true about b?Open-Ended Describe three different methods to solve x2x56=0. Tell which method you prefer. Explain your reasoning.For Exercises 1-6, choose the correct letter. Which expression gives the solutions of 5+2x2=6x? 24(4)(6)(5)12 636(4)(2)(5)4 525(4)(2)(6)10 636(4)(2)(5)4For Exercises 1-6, choose the correct letter. What are the approximate solutions of 2x2x+10=0? F. 2,2.5 G. 1.97,2.47 H. 2.5,2 I. no solutionFor Exercises 1-6, choose the correct letter. What are the approximate solutions of 7x2+4x9=0? A. 1.42,0.85 C. 0.88,1.5 B. 1.5,0.88 D. no solutionFor Exercises 1-6, choose the correct letter. Which method is the best method for solving the equation 8x213x+3=0? F. square roots H. graphing G. factoring I. quadratic formulaFor Exercises 1-6, choose the correct letter. How many solutions are there for 5x2+7x4=0? A. 0 B. 1 C. 2 D. 3For Exercises 1-6, choose the correct letter. The perimeter of a rectangle is 54 cm. The area of the same rectangle is 176 cm2. What are the dimensions of the rectangle? F. 11 cm by 16 cm H. 5.5 cm by 32 cm G. 8 cm by 22 cm I. 4 cm by 44 cmThe fight of a baseball that has been hit when it was 4 feet off the ground is modelled by the function h=16t2+75t+4 where h is the height of the baseball in feet after t seconds. Rounding to the hundredth, how long will it take before the ball lands on the ground? Show your work.Graph each set of points. Which model is most appropriate for each set? (3,8),(1,2),(0,1),(1,4),(3,10)Graph each set of points. Which model is most appropriate for each set? (2,0.75),(1,1.5),(0,3),(1,6)Graph each set of points. Which model is most appropriate for each set? (2,1),(1,0),(0,1),(1,4),(2,9)Graph each set of points. Which model is most appropriate for each set? (2,11),(1,5),(0,3),(1,5),(2,11)Graph each set of points. Which model is most appropriate for each set? (4,0),(2,1),(0,2),(2,3),(4,4)Graph each set of points. Which model is most appropriate for each set? (1,0.67),(0,2),(1,6),(2,18)Graph each set of points. Which model is most appropriate for each set? (3,10),(1,2),(0,1),(1,2),(3,10)Graph each set of points. Which model is most appropriate for each set? (2,4),(1,2),(0,0),(1,2),(2,4)Which type of function best models Is the data in each table? Use differences or ratios.Which type of function best models Is the data in each table? Use differences or ratios.Which type of function best models Is the data in each table? Use differences or ratios.Which type of function best models the ordered pairs (1,6),(0,1),(1,2), and (2,9)? Use differences or ratios.Which type of function best models the ordered pairs (1,0.25),(0,0.5),(1,1), and (2,2)? Use differences or ratios.Which type of function best models the data in each table? Write an equation to model the data.Which type of function best models the data in each table? Write an equation to model the data.Which type of function best models the data in each table? Write an equation to model the data.Which type of function best models the data in each table? Write an equation to model the data.Which type of function best models the data in each table? Write an equation to model the data.Which type of function best models the data in each table? Write an equation to model the data.Which type function best models the data in each ordered pair? Write an equation to model the data. (3,33),(1,21),(0,15),(1,9),(3,3)Which type function best models the data in each ordered pair? Write an equation to model the data. (2,16),(1,8),(0,4),(1,2),(2,1)Which type function best models the data in each ordered pair? Write an equation to model the data. (2127),(119),(0,13),(1,1),(2,3)Which type function best models the data in each ordered pair? Write an equation to model the data. (2,2),(1,3.5),(0,4),(1,3.5),(2,2)Which type function best models the data in each ordered pair? Write an equation to model the data. (6,5),(3,4.5),(0,4),(3,3.5),(6,3)Which type function best models the data in each ordered pair? Write an equation to model the data. (1,10),0,3),(1,0),(2,1)The population of a city for years since 2000 is shown below. Which kind of function best models the data? Write an equation to model the data.For Exercises 1-4, choose the correct letter. Which kind of function best models the set of data points (1,22),(0,6),(1,10),(2,26),(,42)? Linear B. quadratic C. exponential D. none of the aboveFor Exercises 1-4, choose the correct letter. Which kind of function best models the set of data points (3,18),(2,6),(1,2),(0,11),(1,27)? F. linear G. quadratic H. exponential I. none of the aboveFor Exercises 1-4, choose the correct letter. What function can be used to model data pairs that have a common ratio? A. linear B. quadratic C. exponential D. none of the aboveFor Exercises 1-4, choose the correct letter. The attendances at the high school basketball games seemed to be effected by the success of the team. The graph at the right models the attendance over the first half of the season. Which function would also represent the data shown in the graph where a represents the attendance and g represents the number of games the team has won? F. a=25(3)g H. a=25g2+100 G. a=25g+100 I. a=25g2+100The data in the table show the population growth of a city since the year 2000. What kind of function models the data? How do you know?Solve each system by graphing. y=x2+2 y=x+2Solve each system by graphing. y=x2 y=2xSolve each system by graphing. y=x25 y=x3Solve each system by graphing. y=x2+1 y=x+1Solve each system by graphing. y=x24x2 y=x2Solve each system by graphing. y=x26x7 y=x+1Solve each system by graphing. y=x2 y=x+2Solve each system by graphing. y=x24 y=x2Solve each system by graphing. y=x22x+2 y=2x2Solve each system by graphing. y=x2+4x3 y=x+1Solve each system by graphing. y=x2+2x+4 y=x+4Solve each system by graphing. y=x2x6 y=2x2The weekly profits of two different companies selling similar items that opened for business at the same time are modeled by the equations shown below. The profit is represented by y and the number of weeks the companies have been in business is represented by x. According to the projections, what week(s) did the companies have the same profit? What was the profit of both companies during the week(s) of equal profit? Company A: y=x270x+3341 Company X: y=50x+65The populations of two different cities are modeled by the equations shown below. The population (in thousands) is represented by y and the number of years since 1970 is represented by x. What year(s) did the cities have the same population? What was the population of both cities during the year(s) of equal population? Baskinville: y=x222x+350 Cryersport: y=55x950Solve each system using substitution. y=x2+x60 y=2x4Solve each system using substitution. y=x23x+7 y=4x3Solve each system using substitution. y=x22x5 y=x5Solve each system using substitution. y=x22x4 7x+7=2Solve each system using substitution. y=x2+6x xy=4Solve each system using substitution. y=x2+4x15 y25=xSolve each system using substitution. y=x2+5x+13 y=5x+3Solve each system using a graphing calculator. y=x2x+82 y=2x+50Solve each system using a graphing calculator. y=x212x+150 y=15x20Solve each system using a graphing calculator. y=x22x+2.5 y=2x1.25Solve each system using a graphing calculator. y=x20.9x1 y=0.5x+0.76Solve each system using a graphing calculator. y=x268 y=5x+25.75Reasoning What are the solutions of the system y=2x211 and y=x2+2x8? Explain how you solved the system.Writing Explain why a system of linear and quadratic equations can only have 0,1, or two possible solutions.Reasoning the graph at the right shows a quadratic function and the linear function x=b. How many solutions does this system have? If the linear function were changed to y=b , how many solutions would the system have? If the linear function were changed y=b+3, how many solutions would the system have?For Exercises 1-4, choose the correct letter. Which system of equations represents the graph shown? y=x+3 y=x+3 y=x29 y=2x218 y=x3 y=x3 y=x29 y=2x218For Exercises 1-4, choose the correct letter. What is the solution of the equations shown below? y=x2 y=x28x+6 F. (1,3) and (8,10) H. (0,2) and (5,3) G. (2,0) and (8,10) I. (1,1) and (8,6)For Exercises 1-4, choose the correct letter. What is the solution of the system of equations shown below? y=x25x+18 y=4x+4 (2,4) and (7,24) C. (2,12) and (7,32) (0,4) and (2,12) D. (4,20), and (5,24)For Exercises 1-4, choose the correct letter. An architect makes a drawing of a parabolic-shaped arch with a linear support intersecting it in two places. The parabola can be modelled by the function y=x25x+10. The line intersects the parabola when x=2 and x=4. What is the equation of the line? F. y=x6 G. y=x2 H. y=x+2 I. y=x+6Graph the following system of equations. How many solutions does this system have? Explain your reasoning. y=2x2+2 y=2x2Use the triangle at the right. Find the length of the missing side. If necessary, round to the nearest tenth. a=9,b=12Use the triangle at the right. Find the length of the missing side. If necessary, round to the nearest tenth. a=7,c=25Use the triangle at the right. Find the length of the missing side. If necessary, round to the nearest tenth. b=12,c=13Use the triangle at the right. Find the length of the missing side. If necessary, round to the nearest tenth. a=35,b=45Use the triangle at the right. Find the length of the missing side. If necessary, round to the nearest tenth. b=2,c=2.5Use the triangle at the right. Find the length of the missing side. If necessary, round to the nearest tenth. a=12,c=37Use the triangle at the right. Find the length of the missing side. If necessary, round to the nearest tenth. a=20,b=21Use the triangle at the right. Find the length of the missing side. If necessary, round to the nearest tenth. a=3.2,b=13Use the triangle at the right. Find the length of the missing side. If necessary, round to the nearest tenth. a=1.8,c=8.2Use the triangle at the right. Find the length of the missing side. If necessary, round to the nearest tenth. b=20,c=25Use the triangle at the right. Find the length of the missing side. If necessary, round to the nearest tenth. a=65,b=85Use the triangle at the right. Find the length of the missing side. If necessary, round to the nearest tenth. a=0.8,b=1.5A quilter is cutting along the diagonal of a rectangular piece of fabric 34 yard wide by 1 yard long. What will be the length of the cut?How long is the diagonal of a 12 mm-by-16 mm face of a rectangular prism?A pilot flies a plane south and then 600 miles west, where she lands the plane. How far south did the pilot fly the plane if she lands 610 miles from her starting point?A builder divides a rectangular plot of land in half along the diagonal. If the plot is 1310 mile wide and the diagonal measures 1^-miles long, what is the length of the plot?Determine whether the given lengths can be side lengths of a right triangle. 16 cm, 30 cm, 34 cmDetermine whether the given lengths can be side lengths of a right triangle. 0.8 m, 1.5 m, 1.7 mDetermine whether the given lengths can be side lengths of a right triangle. 60 in., 91 in., 110 in.Determine whether the given lengths can be side lengths of a right triangle. 20 ft, 24 ft, 26 ftDetermine whether the given lengths can be side lengths of a right triangle. 12cm, 36cm, 37cmDetermine whether the given lengths can be side lengths of a right triangle. 18 mi, 81 mi, 82 miDetermine whether the given lengths can be side lengths of a right triangle. 2.0 km, 2.1 km, 2.9 kmDetermine whether the given lengths can be side lengths of a right triangle. 13yd,14yd,15ydAny set of three positive integers that satisfies the equation a2+b2=c2 is a Pythagorean triple. Determine whether each set of numbers is a Pythagorean triple. 36, 77, 85Any set of three positive integers that satisfies the equation a2+b2=c2 is a Pythagorean triple. Determine whether each set of numbers is a Pythagorean triple. 40, 96, 104Any set of three positive integers that satisfies the equation a2+b2=c2 is a Pythagorean triple. Determine whether each set of numbers is a Pythagorean triple. 9, 16, 25Any set of three positive integers that satisfies the equation a2+b2=c2 is a Pythagorean triple. Determine whether each set of numbers is a Pythagorean triple. 25, 72, 85Any set of three positive integers that satisfies the equation a2+b2=c2 is a Pythagorean triple. Determine whether each set of numbers is a Pythagorean triple. 70, 240, 250Any set of three positive integers that satisfies the equation a2+b2=c2 is a Pythagorean triple. Determine whether each set of numbers is a Pythagorean triple. 12, 60, 61A landscaper attaches a guy wire 10 ft up the trunk of a newly planted sapling. He stakes the wire between 20 and 25 feet from the tree. What could be the length of the guy wire if it forms a right triangle with the tree?Writing Summarize the method for finding the measure of the hypotenuse of a right triangle if you are given the measure of both legs.The area of a square is 625 cm2. What is the measure of the diagonal to the nearest tenth?Open-Ended Draw a right triangle with side lengths that are whole numbers. What equation can you use to prove that you have drawn a right triangle? What theorem will you use to help make your proof?For Exercises 1-6, choose the correct letter. What is the length of the missing side? A. 21.8 B. 26 C. 28 D. 34For Exercises 1-6, choose the correct letter. What is the length of the missing side? F. 16mm G. 28 mm H. 42 mm I. 69.5 mmFor Exercises 1-6, choose the correct letter. Which set of lengths could be the side lengths of a right triangle? A. 20 cm, 22cm, 29 cm B. 10 ft, 12 ft, 15 ft C. 7 km, 24 km, 28 km D. 13 in., 84 in., 85 in.For Exercises 1-6, choose the correct letter. A right triangle has a side length that measures 4 m and a hypotenuse that measures 8.5 m. What is the measure of the other side of the triangle? F. 7.5 m G. 8.1 m H. 9.4 m 1.9.8 mFor Exercises 1-6, choose the correct letter. How long is the diagonal of a 12 ft-by-16 ft rectangular garden? A. 6ft B. 14 ft C. 18 ft D. 20 ftFor Exercises 1-6, choose the correct letter. You want to divide a square piece of paper into two equivalent triangles. If the square measures 20 cm on each side, what will the third side of each triangle measure? F. 8.9 cm G. 20 cm H. 28.3 cm I. 40 cmJoe is cutting three risers for a set of stairs. Each riser is a right triangle with legs 712 in. and 10 in. What equation could you use to find the length of the third side of a riser? How long will the staircase measure when the 3 risers are installed? Explain.Simplify each radical expression. 169Simplify each radical expression. 200Simplify each radical expression. 125Simplify each radical expression. 5112Simplify each radical expression. 68Simplify each radical expression. 3121Simplify each radical expression. 63t4Simplify each radical expression. 48n3Simplify each radical expression. 60m7Simplify each radical expression. x150x5Simplify each radical expression. 345y3Simplify each radical expression. 2b136b2Simplify each product. 630Simplify each product. 570Simplify each product. 2396Simplify each product. 4742Simplify each product. 4a12a5Simplify each product. 2n230nSimplify each product. 340x256x5Simplify each product. 3412t320t3Simplify each product. 414d21228d3A pool is shaped like a rectangle with a length 4 times its width w. What is an expression for the distance between opposite corners of the pool?Evelyn rode her horse along a triangular path. The distance she traveled south was five times the distance she traveled east. Then she rode directly back to her starting point. What is an expression for the total distance she rode?Simplify each radical expression. 3649Simplify each radical expression. 8116Simplify each radical expression. 100225Simplify each radical expression. 18y36y3Simplify each radical expression. 49x525xSimplify each radical expression. 16a24b4Simplify each radical expression. 52Simplify each radical expression. 1215Simplify each radical expression. 7240Simplify each radical expression. 25b5b3Simplify each radical expression. 243nSimplify each radical expression. 830m2You are making a mosaic design on a square table top. You have already covered half of the table top with 150 1-inch square tile pieces. What are the dimensions of the table top? What is the measure of the diagonal from one corner to the opposite corner of the tabletop?The equation r=SA4 gives the radius r of a sphere with surface area SA What is the radius of a sphere with the given surface area? Use 3.14 for . a. 1256 in2 b. 200.96 cm2 c. 379.94 ft2Open-Ended What are three radical expressions that simplify to 2x3?For Exercises 1-5, choose the correct letter. What is the simplified form of 140? A. 435 B. 1014 C. 270 D. 235For Exercises 1-5, choose the correct letter. What is the simplified form of 48n9? F. 4n33 G. 4n43n H. 3n4n8 I. 43n9For Exercises 1-5, choose the correct letter. What is the simplified form of 35c15c3? A. 15c23 B. 6c25 C. 5c23 D. 12c45For Exercises 1-5, choose the correct letter. Which is radical expression is in simplified form? A. 11y3 B. 85y C. 174 D. 2581For Exercises 1-5, choose the correct letter. A gardener is mowing a 20 yd-by-40 yd rectangular pasture using a diagonal pattern. He mows from one comer of the pasture to the corner diagonally opposite. What is the length of this pass with the mower? Give your answer in simplified form. A. 1020 B. 202 C. 4005 D. 205Suppose the height of the freight elevator in your building is half its width w when the doors are all the way open. a. What is an expression for the maximum side length of a sheet of metal that will fit through the elevator doors? b. if the height of the elevator is 3 meters, what is the maximum length that will fit through the doors?Simplify each sum or difference. 37+57Simplify each sum or difference. 83+3Simplify each sum or difference. 11545Simplify each sum or difference. 211611Simplify each sum or difference. 413+413Simplify each sum or difference. 747Simplify each sum or difference. 4763Simplify each sum or difference. 83+248Simplify each sum or difference. 68250Simplify each sum or difference. 320245Simplify each sum or difference. 518+432Simplify each sum or difference. 12725Simplify each product. 312+4Simplify each product. 83+3Simplify each product. 772Simplify each product. 342Simplify each product. 23+56543Simplify each product. 7+35735Simplify each quotient. 12117Simplify each quotient. 83+1Simplify each quotient. 3273Simplify each quotient. 2157Simplify each quotient. 305+2Simplify each quotient. 12837+5A painting is shaped like a golden rectangle. Its length is 24 cm What is the paintings width to the nearest tenth ol a cm?A tomato fits into a l0-in.-long golden rectangle. What is the tomatos width to the nearest tenth of an inch?The length of a golden rectangle is 4+45. Use the ratio of length to width 1+5:2 to find the width of the golden rectangle.Error Analysis A student multiplied the radical expressions shown at the right. What mistake did the student make? What is the simplified form of the radical? 33+6=9+18=62Writing What is the conjugate of 837? What is the product of the conjugates? Show your work to explain your answer.Find the length of the hypotenuse of the right triangle to the right. Write your answer in simplified radical form.Open-Ended Make up three differences that are greater than or equal to 10. Use the square roots of 2,3,5, or 7 and whole numbers less than or equal to 10. For example, 1032710.A large park is designed as two 10-km squares connected at the corner and with diagonals aligned. If Riley jogs along the diagonal from one end of the park to the other end, how many total kilometers will he jog? Give your answer as a simplified radical and to the nearest tenth of a kilometer.For Exercises 1-6, choose the correct letter. What is the simplified form of 85+55? A 35 B. 135 C. 405 D 200For Exercises 1-6, choose the correct letter. What is the simplified form of 2112? F 102 G. 112 H. 122 I 22For Exercises 1-6, choose the correct letter. What is the simplified form of 4327? A 53 B. 73 C. 3 D 9For Exercises 1-6, choose the correct letter. What is the simplified form of 85+4? F 1610 G. 210+42 H. 410+42 I 210+82For Exercises 1-6, choose the correct letter. What is the simplified form of 4011+7? A 1011107 B. 20112079 C. 302 D 1011+107For Exercises 1-6, choose the correct letter. A golden rectangle is 32 cm long. Hie ratio of length to width is 1+5:2. What is the width of the rectangle in simplest radical form? F. 165+16 G. 858 H. 16516 I. 325323The diagram to the right shows the design of the 12-in. quilt block that a quilter is sewing. a. What are the dimensions of each triangle in the quilt block? Give your answers as simplified radicals. b. What are the dimensions of each triangle to the nearest tenth of an inch?Solve each radical equation. Check your solution. x+4=7Solve each radical equation. Check your solution. 2t3=11Solve each radical equation. Check your solution. 42s=6Solve each radical equation. Check your solution. 6c+4=8Solve each radical equation. Check your solution. 3t2=5Solve each radical equation. Check your solution. 2=3y5Solve each radical equation. Check your solution. 5n4=6Solve each radical equation. Check your solution. b416=16Solve each radical equation. Check your solution. a23=32You decide to install a rope swing at the bend in the river. The time t in seconds for the rope swing to make one swing is given by 213.3 where I is the length of the rope swing in feet. If one swing takes 3.5 seconds, how long is the rope stving? Round your answer to the nearest tenth of a foot.The radius r of a sphere is given by r=SA4 where SA represents the spheres surface area. If a sphere has a surface area of 531 in2. what is the length of its radius? Use =3.14. Round to the nearest hundredth of an inch.The speed V in feet per second that an acorn falls from a tree is given by V=64d, where d is the distance in feet that the acorn has fallen. An acorn hits the ground at a speed of 28 feet per second. How' far did the acorn fall?Harrison bought a 10-foot ramp to load his dirt bike into the back of his truck. The ramp hooks to the 3-foot-high tailgate. How far away from the tailgate does the ramp sit on the ground? Round your answer to the nearest tenth of a foot.Solve each radical equation. Check your solution. 4d+3=7d3Solve each radical equation. Check your solution. x+7=15xSolve each radical equation. Check your solution. 483y=3y6Solve each radical equation. Check your solution. a2+20=9aSolve each radical equation. Check your solution. 2x2+17=x+32Solve each radical equation. Check your solution. d+7=34dSolve each radical equation. Check your solution. 11=12b59Solve each radical equation. Check your solution. f3=f2Solve each radical equation. Check your solution. t4=7t1016Solve each radical equation. Check your solution. If there is no solution, write no solution. x=2x+8Solve each radical equation. Check your solution. If there is no solution, write no solution. m=6m+7Solve each radical equation. Check your solution. If there is no solution, write no solution. n=4n+12Solve each radical equation. Check your solution. If there is no solution, write no solution. x=3x+28Solve each radical equation. Check your solution. If there is no solution, write no solution. y2=5y+244Solve each radical equation. Check your solution. If there is no solution, write no solution. f=f+56Error Analysis A student solved the equation t=5t+14 and found the solutions 7 and -2. Describe and correct the error.The distance d in feet that it takes an automobile to stop if it is traveling S miles per hour is given by S=21d. Find the distance it would take an automobile traveling 60 miles per hour to stop. Round your answer to the nearest tenth of a foot.Open-Ended Write two radical equations that have no solutions. Explain why all the solutions are extraneous.For Exercises 1-6, choose the correct letter. What is the solution of the radical equation t+9=16? A. - 5 B. 7 C. 25 D. 49For Exercises 1-6, choose the correct letter. What is the solution of 6g23=12g? F. 5 G. 7 H. 11 I. 35For Exercises 1-6, choose the correct letter. What are the solutions of d211=5? A, 4, -4 B. 5, -5 C. 5, 6 D 6, -6For Exercises 1-6, choose the correct letter. Which is the extraneous solution of x=2x+15? F. 5 G. -3 H. 3 I. 5For Exercises 1-6, choose the correct letter. The pendulum of a cuckoo clock completes one full swing every t seconds. The variable t is determined by the function t=2l3.3 where I is the length in meters of the pendulum. Each swing takes 0.5 seconds. How many centimeters long is the pendulum? A. 20.625 cm B. 41.25 cm C. 82.5 cm D. 330 cmFor Exercises 1-6, choose the correct letter. A company invests $15,000 in an account that compounds interest annually. After two years, tire account is worth $16,099.44. Use the function A=P1+r2, where r is the annual interest rate, P is the principal, and A is the amount of money after t years. What is the interest rate of the account? F. 1.04% G. 3.6% H. 5.4% I. 7.3%The radius of Earth is about 6378 kilometers. The escape velocity Ve is determined by the function Ve=2gR where g is acceleration due to gravity in m/s2 and R is the radius of Earth in meters, if g for Earth is 9.8 m/s2, what is the escape velocity of Earth? Show your work.Find the domain of each function. y=2xxFind the domain of each function. y=14xFind the domain of each function. y=x+3Find the domain of each function. y=42x+10Find the domain of each function. y=x9Find the domain of each function. y=4x2Find the domain of each function. y=4.3x+5Find the domain of each function. y=3x18Find the domain of each function. 4x7Find the domain of each function. y=1212xFind the domain of each function. y=2x73Find the domain of each function. y=35x4Make a table of value and graph each function. y=x+2Make a table of value and graph each function. y=3xMake a table of value and graph each function. y=x3+1Make a table of value and graph each function. y=5x5Make a table of value and graph each function. y=2x+3+6Make a table of value and graph each function. y=74x+123Make a table of values and graph each function. The distance d a car skids in feet on dry asphalt is modeled by S — S=21d, where S is the speed of the car in miles per hour upon sudden braking. What are the domain and range of the function? Graph the function. What braking distance will indicate a speed equal to or greater than 56 miles per hour?Graph each function by translating the graph of y=x y=x+2Graph each function by translating the graph of y=x y=x2Graph each function by translating the graph of y=x y=x+5Graph each function by translating the graph of y=x y=x4Graph each function by translating the graph of y=x y=x+12Graph each function by translating the graph of y=x y=4x6The distance d in miles that you can see to the horizon when looking out at the ocean is modeled by the function d=1.5a, where a is your altitude in feet. Graph the function. At what altitude can you see 15 miles? 100 miles? Round to the nearest foot.Stacey is designing a soup can. It must hold 32 cubic inches of soup and the radius must be approximately half the height. The function r=32h shows the radius of the can as a function of its height. What are the domain and range of the function? Graph the function. What height should Stacey design die can?Error Analysis A student graphed the function y=6x3+4 at the right. What mistake(s) did the student make? Draw the correct graph.Writing Describe the steps for graphing a function of the form y=axh+k.For Exercisers 1-5, choose the correct letter. What is the domain of the function y=36x+42? A x0 B x7 C x6 D x7For Exercisers 1-5, choose the correct letter. What are the domain and range of the function y=23x+45 F. x43;y5 G. x43;y5 H. x43;y5 I. x43;y5For Exercises 1-5, choose the correct letter. When will the dependent variable in the equation y=x+43 equal or exceed 4? A. x0.17 B. x45 C. x48 D. x53For Exercises 1-5, choose the correct letter. Which function is shown on the graph to the right? Fy=2x61Gy=2x+6+1Hy=2x6+1Iy=2x+61For Exercises 1-5, choose the correct letter. The function t=d16 models the time tin seconds that an object has been falling after the object has fallen d feet. When will the time be more than or equal to 1 minute? A. d16ft B. d225ft C. d3600ft D. d57,600ftAn amusement park ride is a spinning cylinder. At a certain speed the riders are pinned against the walls by the force of the spin and the floor drops out safely. The speed s in meters per second that is needed to pin the riders is given by s - 4,95 Vr where r is the radius of the cylinder in meters. Graph the function. What is an estimate for the radius of the ride if s — 12 meters per second? Round to the nearest hundredth of a meter.For JKLandRST, find the value of each expression. sinJFor JKLandRST, find the value of each expression. cosJFor JKLandRST, find the value of each expression. tanLFor JKLandRST, find the value of each expression. cosLFor JKLandRST, find the value of each expression. tanTFor JKLandRST, find the value of each expression. sinTFor JKLandRST, find the value of each expression. tanJ