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All Textbook Solutions for High School Math 2012 Common-core Algebra 1 Practice And Problem Solvingworkbook Grade 8/9
Solve each system by graphing. Check your solution. y=12x2 y=3x+5Solve each system by graphing. Check your solution. y=32x+6 x+y=1Solve each system by graphing. Check your solution. y=5x y=x6Solve each system by graphing. Check your solution. 3x+y=5 y=7Solve each system by graphing. Check your solution. y=4x6 y=x+9Solve each system by graphing. Check your solution. y=34x5 3x4y=20Solve each system by graphing. Check your solution. y=43x3 y=23x+3Solve each system by graphing. Check your solution. y=25x2 y=x5Reasoning Can there be more than one point of intersection between the graphs of two linear equations? Why or why not?Reasoning If the graphs of the equations in a system of linear equations coincide with each other, what does that tell you about the solution of the system? Explain.Writing Explain the method used to graph a line using the slope and y-intercept.Reasoning If the ordered pair (3,2) satisfies one of the two linear equations in a system, how can you tell whether the point satisfies the other equation of the system? Explain.Writing If the graphs of two lines in a system do not intersect at any point, what can you conclude about the solution of the system? Why? Explain.Reasoning Without graphing, decide whether the following system of linear equations has one solution, infinitely many solutions or no solution. Explain. y=3x56x=2y+10Five years from now, a fathers age will be three times his sons age, and 5 years ago, he was seven times as old as his son was. What are their present ages?The denominator of a fraction is greater than its numerator by 9. If 7 is subtracted from both its numerator and denominator, the new fraction equals 23. What is the original fraction?The sum of the distances two hikers walked is 53 mi, and the difference is 25 mi. What are the distances?The result of dividing a two-digit number by the number with its digits reversed is 74. If the sum of the digits is 12, what is the number?Solve each system by graphing. Tell whether the system has one solution, infinitely many solutions, or no solution. y=3x+5 x+y=3Solve each system by graphing. Tell whether the system has one solution, infinitely many solutions, or no solution. y=2x+1 y=4x+7Solve each system by graphing. Tell whether the system has one solution, infinitely many solutions, or no solution. 2x+y=8 y=12x+12Solve each system by graphing. Tell whether the system has one solution, infinitely many solutions, or no solution. y=2x+1 y=23x+5Solve each system by graphing. Tell whether the system has one solution, infinitely many solutions, or no solution. y=3x+2 3x+y=1Solve each system by graphing. Tell whether the system has one solution, infinitely many solutions, or no solution. y=5x15 y=34x+2Solve each system by graphing. Tell whether the system has one solution, infinitely many solutions, or no solution. y=12x6 y=14xSolve each system by graphing. Tell whether the system has one solution, infinitely many solutions, or no solution. y=6x+4 2+y=6xSolve each system by graphing. Tell whether the system has one solution, infinitely many solutions, or no solution. y=x7 y=2x+5Solve each system by graphing. Tell whether the system has one solution, infinitely many solutions, or no solution. 18x3y=21 y=6x+7Solve each system by graphing. Tell whether the system has one solution, infinitely many solutions, or no solution. y=5x6 x+y=6Solve each system by graphing. Tell whether the system has one solution, infinitely many solutions, or no solution. y=32x3 y=14x+4The measure of one of the angles of a triangle is 35. The sum of the measures of the other two angles is 145 and the difference between their measures is 15. What are the measures of the unknown angles?For Exercises 14, choose the correct letter. Which best describes a system of equations that has no solution? A. consistent, independent C. consistent, dependent B. inconsistent, dependent D. inconsistentFor Exercises 14, choose the correct letter. How many solutions does this system have? 2x+y=3 6x=93y F. 1 G. none H. infinite I. 2For Exercises 14, choose the correct letter. What is the approximate solution of the linear system represented by the graph at the right? A. (4,3) B. (6,1) C. (1,4) D. (4,1)For Exercises 14, choose the correct letter. Which cannot describe a system of linear equations? F. no solution H. infinite solutions G. exactly two solutions I. exactly one solutionFor Exercises 1-4, choose the correct letter. A farmer feeds his cows 200 pounds of feed each day and has 700 pounds of feed in his barn. Another farmer feeds his cows 350 pounds of feed each day and has 1000 pounds of feed in his barn. a. In how many days will the two farmers have the same amount of feed left? ___________________________________________________________________ b. Does your answer make scans? Explain. ____________________________________________________________________________________________________________________________________________________________________ c. How would your answer change if both farmers got an additional 1000 pounds of feed? __________________________________________________________________________________Solve each system by substitution. Check your solution. x=y x+2y=3Solve each system by substitution. Check your solution. y=x+4 y=3xSolve each system by substitution. Check your solution. y=2x10 2y=x8Solve each system by substitution. Check your solution. 2y=x+1 2xy=7Solve each system by substitution. Check your solution. x+2y=14 y=3x14Solve each system by substitution. Check your solution. 2x3y=13 y=12x72Solve each system by substitution. Check your solution. 3x2y=5.5 x+3y=7.5Solve each system by substitution. Check your solution. 6x4y=54 9x+2y=69Solve each system by substitution. Check your solution. y=x24 2xy=5Writing How do you know that substitution gives the answer to a system of equations? Explain.Reasoning With the substitution method, which variable should you solve for first? Explain.Writing How can you use substitution method to solve a system of equations that does not have a variable with a coefficient of 1 or -1?6y+2x=3 Writing When solving the system of equations 2x+y=8 using substitution, which variable will you solve for and which equation will you use to substitute into?Reasoning Can you tell that there is no solution for a system by just looking at the equations? Explain and give an example.If the difference in the side lengths of two squares is 10, and the sum of the side lengths is 18, what are the side lengths?A shopper purchased 8 T-Shirts and 5 pairs pants for $220. The next day, he purchased 5 T-shirts and 1 pair of pants for $112. How much does each T-shirt and each pair of pants cost?A student bought 1 box of crayons and 5 reams of paper for $54. She bought 5 boxes of crayons and 3 reams of paper for $50. What is the cost of each box of crayons and each ream of paper?Suppose you got 8 mangoes and 3 apples for $18 and 3 mangoes and 5 apples for $14.50. How much does each mango and each apple cost?A shopper purchased 4 tables and 2 chairs for $200 and 2 tables and 7 chairs for $400. What is the cost of each table and each chair?If the length of the rectangle is twice the width, and the perimeter of the rectangle is 30cm, what is length and width of the rectangle?The population of a city is 2,500. If the number of males is 240 more than the number of females, how many males and females are there in the city?Solve each system by substitution. Tell whether the system has one solution, infinitely many solutions, or no solution. 7x+2y=13 3x8y=23Solve each system by substitution. Tell whether the system has one solution, infinitely many solutions, or no solution. x9y=10 6x+y=5Solve each system by substitution. Tell whether the system has one solution, infinitely many solutions, or no solution. x=y4+1 y=4x5Solve each system by substitution. Tell whether the system has one solution, infinitely many solutions, or no solution. x2y1=0 y5x+14=0Solve each system by substitution. Tell whether the system has one solution, infinitely many solutions, or no solution. y=8x37 x+3y=4Solve each system by substitution. Tell whether the system has one solution, infinitely many solutions, or no solution. 3x+6y=18 3y=32x+9Solve each system by substitution. Tell whether the system has one solution, infinitely many solutions, or no solution. 5x9y=29 12x+y=47Solve each system by substitution. Tell whether the system has one solution, infinitely many solutions, or no solution. 2x=3y9 3x+y=10Solve each system by substitution. Tell whether the system has one solution, infinitely many solutions, or no solution. 5y=7x+22 x=6y+17Solve each system by substitution. Tell whether the system has one solution, infinitely many solutions, or no solution. x=6y+16 9x2y=12Solve each system by substitution. Tell whether the system has one solution, infinitely many solutions, or no solution. 4xy4=0 3x+2y14=0Solve each system by substitution. Tell whether the system has one solution, infinitely many solutions, or no solution. x+3y=5 2xy=5Solve each exercise and enter your answer on the grid provided. For the following system of equations, what is the x-value of the solution? x+2y=6 6y=x+18Solve each exercise and enter your answer on the grid provided. The sum of the measures of angle X and angle Y is 90. If the measure of angle X is 30 less than twice the measure of angle Y, what is the measure of angle X?Solve each exercise and enter your answer on the grid provided. One number is 4 less than 3 times a second number. If 3 more than two times the first number is decreased by 2 times the second number, the result is 11. Use the substitution method. What is the first number?Solve each exercise and enter your answer on the grid provided. An investor bought 3 shares of stock A and 2 shares of stock B for a total of $41. Stock A costs $2.00 more per share than stock B. What is the cost of a share of stock A in dollars?Solve each exercise and enter your answer on the grid provided. Solve the following system of equations using substitution. What is the value of y? 2x+3y=105x+2y=65Solve each system using elimination. x+y=2 xy=4Solve each system using elimination. x+2y=3 xy=6Solve each system using elimination. 2xy=4 3xy=2Solve each system using elimination. x2y=2 x+y=3Solve each system using elimination. x3y=3 2x+3y=5Solve each system using elimination. x+2y=4 x+y=2Solve each system using elimination. 3x2y=8 2x2y=5Solve each system using elimination. x2y=3 3xy=2Solve each system using elimination. 2x4y=6 xy=13x5y=9 Writing For the system 2x+y=3 which variable should you eliminate first and why? How will you eliminate that variable?Open-Ended If you do not have equal coefficients for both variables, can you still use the elimination method? Explain.In a class, 45 students take the SAT exam. The number of boys is 8 more than the number of girls. a. Write a system that models the above situation. b. Do you need to multiply any of the equations by a constant? If so, which equation and what is the constant?Open-Ended Write a system for which using the elimination method to solve the system is easier than the substitution method. Explain.Error Analysis A student solved a system of linear equations using the elimination method as follows. Describe and correct the error made by the student. 3x5y=4 2x+3y=2 6x10y=8 6x+3y=67y=14 y=2 Multiply equation 1 by 2. Multiply equation 2 by 3. Add the equations. Divide by -7A farm raises a total of 220 chickens and pigs. The number of legs of the stock in the farm totals 520. How many chickens and pigs are at the farm?You drive a car that runs on ethanol and gas. You have a 20-gallon tank to fill and you can buy fuel that is either 25 percent ethanol or 85 percent ethanol. How much of each type of fuel should you buy to fill your tank so that it is 50 percent ethanol?Your math test has 38 questions and is worth 200 points. The test consists of multiple-choice questions worth 4 points each and open-ended questions worth 20 points each. How many of each type of question are there?A student bought 3 boxes of pencils and 2 boxes of pens for $6. He then bought 2 boxes of pencils and 4 boxes of pens for $8. Find the cost of each box of pencils and each box of pens.Solve each system using elimination. Tell whether the system has one solution, infinitely many solutions, or no solution. x3y=7 2x=6y14Solve each system using elimination. Tell whether the system has one solution, infinitely many solutions, or no solution. 3x5y=2 x+3y=4Solve each system using elimination. Tell whether the system has one solution, infinitely many solutions, or no solution. x+2y=6 2x4y=12Solve each system using elimination. Tell whether the system has one solution, infinitely many solutions, or no solution. 5x+y=15 3y=15x+6Solve each system using elimination. Tell whether the system has one solution, infinitely many solutions, or no solution. 3x=4y5 12y=9x+15Solve each system using elimination. Tell whether the system has one solution, infinitely many solutions, or no solution. 3xy=2 2x+2y=8Solve each system using elimination. Tell whether the system has one solution, infinitely many solutions, or no solution. x+2y=4 3x+2y=4Solve each system using elimination. Tell whether the system has one solution, infinitely many solutions, or no solution. x+y=2 xy=4Solve each system using elimination. Tell whether the system has one solution, infinitely many solutions, or no solution. 3x2y=3 6y=9x+9Solve each system using elimination. Tell whether the system has one solution, infinitely many solutions, or no solution. 4x3y=5 3x2y=8Solve each system using elimination. Tell whether the system has one solution, infinitely many solutions, or no solution. x3y=1 2x+2y=10Solve each system using elimination. Tell whether the system has one solution, infinitely many solutions, or no solution. 4x2y=20 2x+y=19How is the multiplication or division property of equality used in the elimination method? Are the properties always needed? Explain.For Exercises 15, choose the correct letter. What is the solution for the following system of equations? 5x+7y=3 2x+3y=1For Exercises 15, choose the correct letter. The perimeter of a rectangle is 24 in. and its length l is 3 times the width w. What is the length and width (l,w) of the rectangle? F. (3,9) G. (14.4,4.8) H. (12,4) I. (9,3)For Exercises 15, choose the correct letter. What do both dependent and inconsistent systems have in common? A. no solution C. same slope B. same y-intercept D. same slope and y-interceptFor Exercises 15, choose the correct letter. Two linear equations have the same y-intercept and different slopes. How would you classify the system? F. consistent, independent H. dependent, inconsistent G. consistent, dependent I. independent, inconsistentFor Exercises 15, choose the correct letter. What is the solution of the following system of equations? 5x+7y=3 2x=3y+1 A. (11,17) B. (2,1) C. (11.5,8) D. (2,1)A hotel is offering the two weekend specials described below. Plan 1: 3 nights and 4 meals for $233. Plan 2: 3 nights and 3 meals for $226.50. For accounting purposes, the hotel will record income for the stay and the meals separately. So the cost per night for each special must be the same, and the cost per meal for each special must be the same. a. What is a system of equations for the situation? b. Solve the system. What is the cost per night and the cost per meal?Solve each word problem You have $6000 to invest in two stock funds. The first fund pays 5 annual interest and the second account pays 9 annual interest. If after a year you have made $380 in interest, how much money did you invest in each account?Solve each word problem During a sale at the local department store, you buy three sweatshirts and two pairs of sweatpants for $85.50. Later you return to the same store and buy three more sweatshirts and four more pairs of sweatpants for $123. What is the sale price of each sweatshirt and each pair of sweatpants?Solve each word problem The sum of two numbers is 27. The larger number is 3 more than the smaller number. What are the two numbers?Solve each word problem One plane at 520 feet is ascending at a rate of 40 feet per minute, while another plane at 3800 feet is descending at a rate of 120 feet per minute. How long will it take the two planes to be at the same altitude?Solve each word problem The perimeter of a rectangle is 24 in. and its length is 3 times its width. What are the length and the width of the rectangle?Solve each word problem You are getting ready to move and have asked some friends to help. For lunch, you buy the following sandwiches at the local deli for $30: six tuna sandwiches and six turkey sandwiches. Later at night, everyone is hungry again and you buy four tuna sandwiches and eight turkey sandwiches for $30.60. What is the price of each sandwich?Solve each word problem You have a cable plan that costs $39 a month for a basic plan plus one movie channel. Your friend has the same basic plan plus two movie channels for $45.50. What is the basic plan charge that you both pay?Solve each word problem At an all-you-can-eat barbeque fundraiser that you are sponsoring, adults pay $6 for a dinner and children pay $4$ for a dinner. 212 people attend and you raise $1128. What is the total number of adults and the total number of children attending? a. What is a system of equations that you can use to solve this problem? b. What method would you use to solve the system? Why?Solve each system. Explain why you chose the method you used. 2y=x+1 2xy=7Solve each system. Explain why you chose the method you used. 6x4y=54 9x+2y=69Solve each system. Explain why you chose the method you used. 3x2y=8 2x2y=5Solve each system. Explain why you chose the method you used. 2xy=4 3xy=2Solve each system. Explain why you chose the method you used. 2x3y=13 y=12x72Solve each system. Explain why you chose the method you used. x3y=3 2x+3y=5Open-Ended What are three differences between an inconsistent system and a consistent and independent system? Explain.Reasoning One number is 4 less than 3 times a second number. If 3 more than two times the first number is decreased by two times the second, the result is 11. What are both numbers?Error Analysis In Exercise 16, what kind of errors are likely to occur when solving the problem?A plane leaves Chicago and flies 750 miles to New York. It it takes 2.5 hours to get to New York flying against the wind, but only 2 hours to fly back to Chicago, what is the planes rate of speed and what is the wind speed?A coin bank has 250 coins, dimes and quarters, worth $39.25. How many of each type of coin are there?In 4 years, a mother will be 5 times as old as her daughter. At present, the mother is 9 times as old as the daughter. How old are the mother and the daughter today?For Exercises 15, choose the correct letter. You solved a linear system with two equations and two variables and got the equation 6=6. How many solutions does the system of equations have? A. no solution C. exactly 1 solution B. infinitely many solutions D. 2 solutionsFor Exercises 15, choose the correct letter. The sum of two numbers is 12. The difference of the same two numbers is 4. What is the larger of the two numbers? F. 4 H. 7 G. 5 I.8For Exercises 15, choose the correct letter. You solved a linear system and got the equation 6=0. How many solutions does the system of equations have? A. no solution C. exactly 1 solution B. infinitely many solutions D. 2 solutionsFor Exercises 15, choose the correct letter. y+3x=6 What is the solution of the system of equations? y=6x+12 F. (2,0) H. (2,0) G. (0,2) I. (0,2)For Exercises 15, choose the correct letter. A kayaker paddles upstream for 1.5 hours, then turns his kayak around and returns to his tent in 1 hour. He travels 3 miles each way. What is the rate of the rivers current? A. 0.5mi/h B. 2 mi/h C. 1mi/h D. 1.5mi/hRectangle EFGH has a perimeter of 24 inches, and triangle BCD has a perimeter of 18 inches. a. What is a system of equations for the perimeters of the figures? b. Without solving, what method you would use to solve the system? Explain.Graph each linear inequality. x4Graph each linear inequality. y2Graph each linear inequality. 3xy6Graph each linear inequality. 4x+5y3Graph each linear inequality. 3x+2y6Graph each linear inequality. yxGraph each linear inequality. 3x5y6Graph each linear inequality. x44y3Graph each linear inequality. x44y3Error Analysis A student graphed y4x+3 as shown. Describe and correct the students error.Writing How do you decide which half-plane to shade when graphing an inequality? Explain.Determine whether the ordered pair is a solution of the linear inequality. 7x+2y5,(1,1)Determine whether the ordered pair is a solution of the linear inequality. xy3,(2,1)Determine whether the ordered pair is a solution of the linear inequality. y+2x5,(4,1)Determine whether the ordered pair is a solution of the linear inequality. x+4y2,(8,2)Determine whether the ordered pair is a solution of the linear inequality. yx+4,(9,5)Determine whether the ordered pair is a solution of the linear inequality. y3x+2,(3,10)Determine whether the ordered pair is a solution of the linear inequality. x12y3,(9,12)Determine whether the ordered pair is a solution of the linear inequality. 0.3x2.4y0.9,(8,0.5)Write an inequality that represents each graph.Write an inequality that represents each graph.You and some friends have $30. You want to order large pizzas (p) that are $9 each and drinks (d) that cost $1 each. Write and graph an inequality that shows how many pizzas and drinks can you order?Tickets to a play cost $5 at the door and $4 in advance. The theater club wants to raise at least $400 from the play. Write and graph an inequality for the number of tickets the theater club needs to sell. If the club sells 40 tickets in advance, how many do they need to sell at the door to reach their goal?Reasoning Two students did a problem as above, but one used x for the first variable and y for the second variable and the other student used x for the second variable and y for the first variable. How did their answers differ and which one, if either, was incorrect?For Exercises 15, choose the correct letter. What point on the axes satisfies the inequality yx? A. (0,1) B. (1,0) c. (1,0) D. (0,0)For Exercises 15, choose the correct letter. For the graph of the inequality x2y4, what is a value of x for a point that is on the boundary line and the axes? F. 4 G. 2 H. 2 I. 4For Exercises 15, choose the correct letter. If x0 and y0, then which quadrant holds the solutions? A. IV B. III C. I D. IIFor Exercises 15, choose the correct letter. Which is the y-value of a boundary point that is an intersecting point not on the axes for this region: x0,y0,x4 and y3? F. 4 G. 0 H. 1 I. 3For Exercises 15, choose the correct letter. How do you decide where to shade an inequality whose boundary does not go through the origin? A. For , shade above the boundary. B. If (0,0) is a solution, shade where (0,0) is. C. For , shade below the boundary. D. If (0,0) is a solution, shade the boundary.A school fundraiser sells holiday cards and wrapping paper. They are trying to raise at least $400. They make a profit of $1.50 on each box of holiday cards and $1.00 on each pack of wrapping paper. a. What is an inequality for the profit the school wants to make for the fundraiser? b. If the fundraiser sells 100 boxes of cards and 160 packs of wrapping paper, will they reach their goal? Show your work.Solve each system of inequalities by graphing. 3x+y1 xy3Solve each system of inequalities by graphing. 5xy1 x+3y2Solve each system of inequalities by graphing. 4x+3y1 2xy2Writing What is the difference between the solution of a system of linear inequalities and the solution of a system of linear equations? Explain.Open-Ended When can you say that there is no solution for a system of linear inequalities? Explain your answer and show with a system and graph.Error Analysis A student graphs the system below. Describe and correct the students error. xy3 y2 x1Determine whether the ordered pair is a solution of the given system. (0,1); 1x3y 3y12xDetermine whether the ordered pair is a solution of the given system. (2,3) 2x+3y2 3x+5y1Determine whether the ordered pair is a solution of the given system. (1,4) 2x+y3 3xy5Mark is a student, and he can work for at most 20 hours a week. He needs to earn at least $75 to cover his weekly expenses. His dog-walking job pays $5 per hour and his job as a car wash attendant pays $4 per hour. Write a system of inequalities to model the situation, and graph the inequalities.Britney wants to bake at most 10 loaves of bread for a bake sale. She wants to make banana bread that sells for $1.25 each and nut bread that sells for $1.50 each and make at least $24 in sales. Write a system of inequalities for the given situation and graph the inequalities.Write a system of inequalities for the following graph.Solve each system of inequalities by graphing. 5x+7y6 x+3y1Solve each system of inequalities by graphing. x+4y20 2xy+12Solve each system of inequalities by graphing. x256y 3x+y2For Exercises 14, choose the correct letter. You and a friend both would like a salad and a small drink. Between the two of you, you have $8.00. A salad costs $2.49 and a small drink is $.99. Can either of you have a second salad or drink? A. yes, 1 salad B. yes, 1 of each c. yes, 1 drink D. no, you cannotWhich of the following systems of inequalities represents the graph? F. y2x+4 G. 2xy4 yx+2 yx+2 H. y2x+4 ।. 2x+y4 x+y2 x+y2For the graph above, what is the approximate y-value of the point of intersection? A. 1 B. 4 C. 3 D. 2A student spends no more than 2 hours on his math and English homework. If math takes about twice as long as English, what is the maximum time that the student can spend on English? F. 13 hour G. 12 hour H. l hour I. 23 hourA young woman wants to make at least $200 a week and can work no more than 30 hours a week. She works at the library for $8 an hour and babysits for $6 an hour. a. What system of inequalities shows the possible combination of hours and jobs she can work? b. Why did you exclude points to the left of the y-axis and below the x-axis?Simplify each expression. 130Simplify each expression. 53Simplify each expression. 334Simplify each expression. 241Simplify each expression. (7)2Simplify each expression. 461Simplify each expression. 6Simplify each expression. (12x)2Simplify each expression. 180Simplify each expression. 6bc0Simplify each expression. (11x)0Simplify each expression. 292Simplify each expression. 3m8p0Simplify each expression. 5a42cSimplify each expression. 3k3(mn)3p8Simplify each expression. 2m3n3Simplify each expression. 82q3r5Simplify each expression. (10a)4b0Simplify each expression. 11xy1z0v3Simplify each expression. 5m19(ab)4c7Evaluate each expression for a=4,b=3, and c=2. 3a1Evaluate each expression for a=4,b=3, and c=2. b3Evaluate each expression for a=4,b=3, and c=2. 4a2b2c3Evaluate each expression for a=4,b=3, and c=2. 9a0c4Evaluate each expression for a=4,b=3, and c=2. a2Evaluate each expression for a=4,b=3, and c=2. (c)2Write each number as a power of 10 using negative exponents. 11000Write each number as a power of 10 using negative exponents. 110Write each expression as a decimal. 103Write each expression as a decimal. 8104The number of people who vote early doubles every week leading up to an election. This week 1200 people voted early. The expression 12002w models the number of people who will vote early w weeks after this week. Evaluate the expression for w=3. Describe what the value of the expression represents in the situation.A pizza shop makes large pizzas with a target diameter of 16 inches. A pizza is acceptable if its diameter is within 322 in. of the target diameter. Let d represent the diameter of a pizza. Write an inequality for the range of acceptable large pizza diameters in inches.Open-Ended Choose a fraction to use as a value for the variable c. Find the values of c1,c3, and c3.For Exercises 16, choose the correct letter. What is the simplified form of 3a4b2c3? A. 81a4c3b2 B. 81a4b2c3 C. 3a4b2c3 D. 3a4c3b2For Exercises 16, choose the correct letter. What is a2 if a=5? F. -25 G. 25 H. 125 I. 125For Exercises 16, choose the correct letter. Which of the following simplifies to a negative number? A. 44 B. (4)4 C. 44 D. 144For Exercises 16, choose the correct letter. What is the simplified form of (14x)0y7z? F. 14zy7 G. 14zy7 H. zy7 I. zy7For Exercises 16, choose the correct letter. What is (m)3n if m=2 and n=24? A. 3 B. – 3 C. 4 D. -4For Exercises 16, choose the correct letter. What is the simplified form of 5a33? F. 27125a3 G. 27125a3 H. 125a327 I 125a327The number of bacteria in a culture quadruples every hour. There were 65,536 bacteria in the culture at 8: 00 A.M. The expression 65,5364h models the number of bacteria in the culture h hours after 8: 00 A.M. a. What is the value of the expression for h=4? b. What does the value of the expression in part a represent?Rewrite each expression using each base only once. 4543Rewrite each expression using each base only once. 242622Rewrite each expression using each base only once. 565251Rewrite each expression using each base only once. 104104102Rewrite each expression using each base only once. 7973710Rewrite each expression using each base only once. 929896Simplify each expression. z8z5Simplify each expression. 4k36k4Simplify each expression. 5b33b6Simplify each expression. 13x83x10Simplify each expression. 2h54h3Simplify each expression. 8n11n9Simplify each expression. mn2m2n4mn1Simplify each expression. 6a3b24ab8Simplify each expression. (12mn)m3n2p5(2m)Write each answer in scientific notation. The population of a country in 1950 was 6.2107. The population in 2030 is projected to be 3102 times the 1950 population. If the projection is correct, what will the population of the country be in 2030?Write each answer in scientific notation. The area of land that Rhode Island covers is approximately 1.5103 square miles. The area of land that Alaska covers is a little more than 4.3102 times the land area of Rhode Island. What is the approximate area of Alaska in square miles?Simplify each expression 1614Simplify each expression. 12513Simplify each expression. 24315Simplify each expression 823Simplify each expression. 6443Simplify each expression. 2532Simplify each expression 7q436r357q136r15Simplify each expression. 3h522k342k323h54Simplify each expression. 8p165m128p145m56Complete each equation. 9294=9Complete each equation. 553=52Complete each equation. 282=22Complete each equation. zz5=z3Complete each equation. m13m16m=m2Complete each equation. d7d13d9=dFind the area of each figure.Find the area of each figure.Find the area of each figure.Find the area of each figure.Simplify each expression. Write each answer in scientific notation. 7101781028Simplify each expression. Write each answer in scientific notation. 410110.8107Simplify each expression. Write each answer in scientific notation. 0.910150.1106Simplify each expression. Write each answer in scientific notation. 0.81050.61017Simplify each expression. Write each answer in scientific notation. 0.51030.6100Simplify each expression. Write each answer in scientific notation. 0.210110.41014The diameter of the moon is approximately 3.5103 kilometres. a. The diameter of Earth is approximately 3.7 times the diameter of the moon. Determine the diameter of Earth. Write your answer in scientific notation. b. The distance from the centre of Earth to the centre of the moon is approximately 30 times the diameter of Earth. Determine the distance from the centre of Earth to the centre of the moon. Write your answer in scientific notation.Simplify each expression. 1n8n3Simplify each expression. 1x4x9Simplify each expression. 7k42k6kSimplify each expression. 2x23x12+5Simplify each expression. 4x4x+14Simplify each expression. (n+2)5(n+2)3Writing Explain what moving the decimal point 4 places to the right or to the left does to the value of a number. In scientific notation, what power of 10 would you multiply by to move the decimal point 4 places to the right or to the left?For Exercises 15, choose the correct letter. What is the simplified form of 3x3y25xy1? A. 15x3v2 B. 15x3y2 c. 15x4y D. 15x4yFor Exercises 15, choose the correct letter. What is the simplified form of 9m12n452m13n25? F. 18m16n825 G. 18m56n65 H. 18m5n6m6n5 I. 18mn8m6n25For Exercises 15, choose the correct letter. A rectangular pasture has a fence around the perimeter. The length of the fence is 16x7 and the width is 48x4. What is the area of the pasture? A. 3x3 B. 128x11 C. 768x11 D. 768x28For Exercises 15, choose the correct letter. What is the simplified form of 3.251037.8106 written in scientific notation? F. 2.5351010 G. 2.5351018 H. 2.5351019 I. 25.35109For Exercises 15, choose the correct letter. The size of a certain cell is 2.5109m. Another cell is 1.5103 times larger. How large is the larger cell in scientific notation? A. 41027m B. 41012m C. 3.75106m D. 3.75106mSimplify each expression. z53Simplify each expression. m410Simplify each expression. v712Simplify each expression. k433Simplify each expression x72Simplify each expression. r146Simplify each expression. bb83Simplify each expression. h2h70Simplify each expression. m232n17Simplify each expression. x62y30Simplify each expression. g55g62Simplify each expression. u23w413Simplify each expression. (6a)4Simplify each expression. (5f)3Simplify each expression. (9z)12Simplify each expression. 10m32Simplify each expression. 6j23Simplify each expression. 9d102