Q4 Week 2 HW Exponents and Equations

Name: lass: ate: I: Q4 Week 2 HW Exponents and Equations Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Write (b)(b)(b)(b)(b) in exponential form. a. 5 b c. b 5 b. b 5 d. b 6 2. Write 2 2 2 2 in exponential form. a. 4 2 c. 2 5 b. 2 3 d. 2 4 3. Write 3 in exponential form. a. 3 0 c. 3 1 b. 1 3 d. 3 2 4. Evaluate ( 2) 2. a. 0 c. 4 b. 22 d. 4 5. Evaluate a x (b c) d for a = 7, b = 3, c = 2, d = 6, and x = 2. a. 35 c. 7.5 b. 48 d. 7.2 6. Evaluate (6) 2. a. 36 c. 1 36 b. 1 36 d. 36 7. Evaluate a x (b + c) y for a = 4, b = 2, c = 8, x = 1, and y = 2. a. b. 1 24 c. 96 3 25 d. 6 25 8. Simplify 6w0 r 5 t 7. a. 6r 5 t 7 b. 6t 7 r 5 c. 6wr 5 t 7 d. 6 r 5 t 7 9. Multiply. Write the product as a power. 12 5 12 2 a. 12 10 c. 12 7 b. annot combine d. 12 3 1

Name: I: 10. ivide. Write the quotient as a power. 13 9 13 5 a. 13 4 c. 13 14 b. annot combine d. 52 11. Simplify (9 9 ) 8. a. 9 1 c. 81 8 b. 9 72 d. 9 17 12. Simplify (x 2 ) 4 x 4. 1 a. b. x 32 x 4 c. x 4 d. x 8 13. Write the number 6.54 10 7 in standard notation. a. 0.000000654 c. 65,400,000 b. 6,540,000 d. 654,000,000 14. Write the number 9.91 10 6 in standard notation. a. 0.0000991 c. 0.00000991 b. 9,910,000 d. 0.000000991 15. Write the number 230,000 in scientific notation. a. 0.230 10 6 c. 2.3 10 5 b. 2.30 10 6 d. 23.0 10 4 16. Write the number 0.000000001 in scientific notation. a. 0.01 10 6 c. 0.001 10 6 b. 00.1 10 8 d. 1.0 10 9 17. Suppose a sheet of 100 stamps is 0.77 millimeters thick. If a stack of sheets contains 100,000 stamps, how many millimeters thick is the stack? Write the answer in scientific notation. a. 7.7 10 4 mm c. 77.0 10 1 mm b. 7.7 10 2 mm d. 0.77 10 3 mm 18. If an average grape weighs 4.87 grams and a company purchases 1,000,000 grapes, how much will the grape shipment weigh in kilograms? Write the answer in scientific notation. a. 4.87 10 6 kg c. 4.87 10 3 kg b. 48.7 10 2 kg d. 0.487 10 4 kg 19. The attendance at a parade was 6.73 10 4 people. The attendance at a rally was 6.75 10 4 people. Which event had the higher attendance? a. rally b. parade 2

Name: I: 20. The attendance at a college football game was 1.27 10 5 people. The attendance at a World up soccer match was 1.22 10 5 people. Which event had the higher attendance? a. soccer match b. football game 21. Find the two square roots of the number 144. a. 36, 36 c. 11, 11 b. 72, 72 d. 12, 12 22. square room has a tiled floor with 81 square tiles. How many tiles are along an edge of the room? a. 9 tiles c. 40 tiles b. 11 tiles d. 20 tiles 23. square mosaic is made of small glass squares. If there are 196 small squares in the mosaic, how many are along an edge? a. 98 squares c. 14 squares b. 49 squares d. 16 squares 24. Evaluate the expression 4 14 + 50. If necessary, round your answer to the nearest tenth. a. 50 c. 32 b. 24 d. 28.3 25. The square root 103 is between two integers. Name the integers. a. 102, 104 c. 10, 11 b. 15, 16 d. 25, 26 26. Elena needs to cut a square piece of wood with an area of 69 square inches. How long should the sides of the square be, rounded to the nearest tenth of an inch? a. 7 in. c. 34.5 in. b. 8.3 in. d. 17.3 in. 27. chessboard is made of 64 small squares. Suppose a single square on a chessboard has an area of 6 square centimeters. How long is one side of the entire board, rounded to the nearest tenth of a centimeter? a. 2.4 cm c. 9.8 cm b. 156.8 cm d. 19.6 cm 28. Use a calculator to find 304. Round your answer to the nearest tenth. a. 17.44 c. 17.02 b. 13.2 d. 17.4 16 29. lassify the number as rational or irrational. 2 a. irrational b. rational 43 30. lassify the number as rational, irrational, or not a real number. 8 a. irrational b. not a real number c. rational 3

Name: I: 31. Graph the numbers 5, 1.7, 25, 1, and π on a number line. Then, order the numbers from least to 2 greatest. a. b. 25, 5, 1, π, and 1.7 2 c. 1, 1.7, 5, π, and 25 2 d. 25, π, 5, 1.7, and 1 2 1, 5, 25, 1.7, and π 2 32. Harry and Selma start driving from the same location. Harry drives 42 miles north while Selma drives 144 miles east. How far apart are Harry and Selma when they stop? a. 1,764 mi c. 22,500 mi b. 150 mi d. 20,736 mi 33. community is building a square park with sides that measure 80 meters. To separate the picnic area from the play area, the park is split by a diagonal line from opposite corners. etermine the approximate length of the diagonal line that splits the square. If necessary, round your answer to the nearest meter. a. 12,800 m c. 160 m b. 80 m d. 113 m 34. ombine like terms. 2z + 9 z + 3 a. 2z + 27 c. z + 12 b. 3z + 6 d. z + 6 35. ombine like terms. 8x + 5z 4x + 3z + 6. a. 4x + 8z c. 4x + 8z + 6 b. 32x + 15z + 6 d. 12x + 2z + 6 4

Name: I: 36. Simplify. 9(4t + 6) + 3t a. 33t + 54 c. 39t 54 b. 39t + 54 d. 39t + 6 37. Solve. 10y 2y = 64 a. y = 56 c. y = 5 1 3 b. y = 8 d. y = 72 38. Simplify and solve. 3(9 8x 4x) + 8(3x + 4) = 11 a. x = 3 c. x = 24 b. x = 4 d. x = 5 39. Solve. 2z + 3 + 7z = 12 a. z = 3 c. z = 1 b. z = 15 d. z = 1.8 40. Solve. z + 5 = 13 32 8 16 a. z = 13 c. z = 46 b. z = 6 d. z = 1 4 41. The Sanchez family had dinner at their favorite restaurant. 9% sales tax was added to their bill. my paid the bill with a $10 gift certificate plus $30.60. How much did the family s dinner cost before tax? Round your answer to the nearest penny. a. $43.25 c. $35.95 b. $37.25 d. $36.95 42. arlos works part time as a salesperson for an electronics store. He earns $7.50 per hour plus a percent commission on all of his sales. Last week arlos worked 15 hours and earned a gross income of $270.63. If his total sales for the week were $2,750, what percent commission does arlos earn? If necessary, round your answer to the nearest hundredth of a percent. a. 0.06% c. 6.75% b. 5.75% d. 1.04% 43. Solve 3.8y + 4 x + 2 = 0 for y. 7 a. y = 4 7 76 x 2 c. y = x 38 35 5 b. y = 20 x 10 d. y = 10 133 19 19 44. Solve. 8a 10 = 6a a. a = 0.3 c. a = 2 b. a = 5 d. a = 0 5

Name: I: 45. Solve. 4v 13 10v = 12 24v + 5 a. v = 1 2 3 c. v = 18 29 b. v = 18 31 d. v = 3 5 46. Solve. y 3 + 8y 4 3 6 = y + 7 2 a. y = 16 49 c. y = 3 b. y = 1 3 d. y = 17 48 47. local water park has two types of season passes. Plan costs a one-time fee of $142 for admission plus $10 for parking every trip. Plan costs a one-time fee of $48 for parking plus $22 for admission every trip. How many visits must a person make for plan and plan to be equal in value? a. 8 c. 16 b. 7 d. 3 48. Solve the system of equations. Ï Ô y = 5x + 4 Ì ÓÔ y = 7x + 6 a. ( 1, 11) c. ( 1, 1) b. ( 1, 1) d. ( 4, 1) 49. Solve the system of equations. Ï Ô x + 2y = 2 Ì ÓÔ x + y = 1 a. Ê Ë Á 4, 3 ˆ c. Ê Ë Á 4,3 ˆ b. Ê Ë Á 4,3 ˆ d. Ê Ë Á 4, 3 ˆ 6

I: Q4 Week 2 HW Exponents and Equations nswer Section MULTIPLE HOIE 1. NS: Identify how many times (b) is a factor. (b)(b)(b)(b)(b) = b 5 heck that you are not using the base as the exponent. heck the sign on the exponent. The exponent tells the number of times the base is used as a factor. PTS: 1 IF: asic REF: Page 162 OJ: 4-1.1 Writing Exponents NT: 8.5.3.c TOP: 4-1 Exponents KEY: exponent write 2. NS: Identify how many times (?? ) is a factor. 2 2 2 2 = 2 4 heck that you are not using the base as the exponent. The exponent tells the number of times the base is used as a factor. ount the factors. PTS: 1 IF: asic REF: Page 162 OJ: 4-1.1 Writing Exponents NT: 8.5.3.c TOP: 4-1 Exponents KEY: exponent write 3. NS: Identify how many times (3) is a factor. 3 = 3 1 Use the correct exponent. heck that you are not using the base as the exponent. The exponent represents how many times the base is used as factor. PTS: 1 IF: verage REF: Page 162 OJ: 4-1.1 Writing Exponents NT: 8.5.3.c TOP: 4-1 Exponents KEY: exponent write 1

I: 4. NS: The exponent tells the number of times to multiply the base by itself. ( 2) 2 = 4 Multiply the base by itself instead of adding. Multiply the base to find the answer. The exponent tells how many times to multiply the base by itself. The exponent tells the number of times to multiply the base by itself. PTS: 1 IF: verage REF: Page 162 OJ: 4-1.2 Evaluating Powers NT: 8.5.3.c TOP: 4-1 Exponents KEY: exponent power evaluate 5. NS: First, substitute a = 7, b = 3, c = 2, d = 6, and x = 2. Then, multiply inside the parentheses. Next, evaluate the exponent. Then, divide from left to right. Finally, subtract from left to right. 7 2 (3 2) 6 = 7 2 6 6 = 49 6 6 = 48 First, substitute the given values. Then, use the order of operations and simplify. Use the order of operations. Multiply and divide before subtracting. PTS: 1 IF: verage REF: Page 163 OJ: 4-1.3 Using the Order of Operations NT: 8.5.3.c TOP: 4-1 Exponents 6. NS: ny number except 0 with a negative exponent equals its reciprocal with the opposite exponent. power with a negative exponent equals 1 divided by that power with its opposite exponent. heck the sign of the exponent. First, write the reciprocal, and change the sign of the exponent. Then, find the product and simplify. The reciprocal of a number is 1 divided by that number. PTS: 1 IF: verage REF: Page 167 OJ: 4-2.2 Evaluating Negative Exponents TOP: 4-2 Look for a Pattern in Integer Exponents NT: 8.5.3.c KEY: negative exponent evaluate 2

I: 7. NS: First, substitute a = 4, b = 2, c = 8, x = 1, and y = 2. Then, add inside the parentheses. Next, evaluate the exponents. Finally, subtract from left to right. 4 1 (2 + 8) 2 = 4 1 (10) 2 = 1 4 1 100 = 6 25 Use the order of operations. First, substitute the given values. Then, use the order of operations and simplify. Write the number with a negative exponent as the reciprocal with an opposite exponent. PTS: 1 IF: verage REF: Page 167 OJ: 4-2.3 Using the Order of Operations NT: 8.5.3.c TOP: 4-2 Look for a Pattern in Integer Exponents 8. NS: 6w 0 r 5 t 7 = 6 1 r 5 1 t 7 Rewrite 6w0 r 5 t 7 without negative or zero exponents. = 6 1 1 r 5 1 t 7 Simplify each part of the expression. r 5 = 1 r 5. = 6 1 1 r 5 t7 1 t 7 = t7. = 6t7 r 5 ny number to the zero power is equal to 1. negative exponent in the numerator becomes positive in the denominator. ny number to the zero power is equal to 1. negative exponent in the numerator becomes positive in the denominator. negative exponent in the denominator becomes positive in the numerator. PTS: 1 IF: dvanced NT: 8.1.3.a TOP: 4-2 Look for a Pattern in Integer Exponents 3

I: 9. NS: To multiply powers with the same base, keep the base and add the exponents. To multiply powers with the same base, keep the base and add the exponents. heck whether the bases are the same. To multiply powers with the same base, keep the base and add the exponents. PTS: 1 IF: asic REF: Page 170 OJ: 4-3.1 Multiplying Powers with the Same ase NT: 8.5.3.c TOP: 4-3 Properties of Exponents KEY: exponent power multiplication base 10. NS: To divide powers with the same base, keep the base and subtract the exponents. heck whether the bases are the same. To divide powers with the same base, keep the base and subtract the exponents. To divide powers with the same base, keep the base and subtract the exponents. PTS: 1 IF: asic REF: Page 171 OJ: 4-3.2 ividing Powers with the Same ase NT: 8.5.3.c TOP: 4-3 Properties of Exponents KEY: exponent power division base 11. NS: (9 9 ) 8 = 9 9 8 Multiply the exponents. = 9 72 Multiply the exponents, not add. To raise a power to a power, keep the base and multiply the exponents. Multiply the exponents, not subtract. PTS: 1 IF: verage REF: Page 171 OJ: 4-3.3 Raising a Power to a Power NT: 8.5.3.c TOP: 4-3 Properties of Exponents 4

I: 12. NS: (x 2 ) 4 x 4 = x 2( 4) x 4 Multiply the exponents. = x 8 x 4 = x 8 + 4 dd the exponents. = x 4 When you write the reciprocal, the sign of the exponent changes. To raise a power to a power, keep the base and multiply the exponents. To multiply powers with the same base, keep the base and add the exponents. PTS: 1 IF: dvanced NT: 8.5.3.c TOP: 4-3 Properties of Exponents 13. NS: positive exponent means move the decimal point to the right. negative exponent means move the decimal point to the left. positive exponent means move the decimal point to the right. Move the decimal point the correct number of places. Move the decimal point the correct number of places. PTS: 1 IF: verage REF: Page 174 OJ: 4-4.1 Translating Scientific Notation to Standard Notation NT: 8.1.1.f TOP: 4-4 Scientific Notation KEY: scientific notation standard notation 14. NS: positive exponent means move the decimal point to the right. negative exponent means move the decimal point to the left. Move the decimal point the correct number of places. negative exponent means move the decimal point to the left. Move the decimal point the correct number of places. PTS: 1 IF: verage REF: Page 174 OJ: 4-4.1 Translating Scientific Notation to Standard Notation NT: 8.1.1.f TOP: 4-4 Scientific Notation KEY: scientific notation standard notation 5

I: 15. NS: To write a number in scientific notation, write it as the product of a power of ten and a number greater than or equal to 1 but less than 10. The first part is a number greater than or equal to 1 but less than 10. ount how many places the decimal point is moved. The first part is a number greater than or equal to 1 but less than 10. PTS: 1 IF: verage REF: Page 175 OJ: 4-4.2 Translating Standard Notation to Scientific Notation NT: 8.1.1.f TOP: 4-4 Scientific Notation KEY: scientific notation standard notation 16. NS: To write a number in scientific notation, write it as the product of a power of ten and a number greater than or equal to 1 but less than 10. number less than 1 will have a negative exponent when written in scientific notation. ount how many places the decimal point is moved. The first part is a number greater than or equal to 1 but less than 10. The first part is a number greater than or equal to 1 but less than 10. PTS: 1 IF: verage REF: Page 175 OJ: 4-4.2 Translating Standard Notation to Scientific Notation NT: 8.1.1.f TOP: 4-4 Scientific Notation KEY: scientific notation standard notation 17. NS: To write a number in scientific notation, write it as the product of a power of ten and a number greater than or equal to 1 but less than 10. The stack will be 7.7 10 2 mm thick. There are 100 stamps per sheet. alculate the thickness correctly. The first part is a number greater than or equal to 1 but less than 10. The first part is a number greater than or equal to 1 but less than 10. PTS: 1 IF: verage REF: Page 175 OJ: 4-4.3 pplication NT: 8.1.1.f TOP: 4-4 Scientific Notation KEY: scientific notation standard notation expression evaluate 6

I: 18. NS: To write a number in scientific notation, write it as the product of a power of ten and a number greater than or equal to 1 but less than 10. The shipment would weigh 4.87 10 3 kg. There are 1000 grams in a kilogram. alculate the weight correctly. The first part is a number greater than or equal to 1 but less than 10. The first part is a number greater than or equal to 1 but less than 10. PTS: 1 IF: verage REF: Page 175 OJ: 4-4.3 pplication NT: 8.1.1.f TOP: 4-4 Scientific Notation KEY: scientific notation standard notation expression evaluate 19. NS: ompare the powers of 10. Then compare the values between 1 and 10. 6.73 10 4 < 6.75 10 4 First, compare the powers of 10. Then, compare the values between 1 and 10. PTS: 1 IF: asic REF: Page 176 OJ: 4-4.4 pplication NT: 8.1.1.f TOP: 4-4 Scientific Notation 20. NS: ompare the powers of 10. Then compare the values between 1 and 10. 1.27 10 5 > 1.22 10 5 First, compare the powers of 10. Then, compare the values between 1 and 10. PTS: 1 IF: asic REF: Page 176 OJ: 4-4.4 pplication NT: 8.1.1.f TOP: 4-4 Scientific Notation 7

I: 21. NS: The square root of a number is another number that, when multiplied by itself, equals the first number. 12 is a square root, since 12 12 = 144. 12 is also a square root, since 12 12 = 144. Multiply these numbers by themselves to see if they equal the original number. The square root of a number is another number that, when multiplied by itself, equals the first number. heck your calculations. PTS: 1 IF: asic REF: Page 182 OJ: 4-5.1 Finding the Positive and Negative Square Roots of a Number NT: 8.5.3.b TOP: 4-5 Squares and Square Roots KEY: square square root positive negative 22. NS: Find the square root of 81. 81 = 9, since 9 9 = 81. There are 9 tiles along the edge. heck your calculations. Find the square root of the number of tiles in the room. Multiply this number by itself to check your answer. PTS: 1 IF: verage REF: Page 183 OJ: 4-5.2 pplication NT: 8.5.3.b TOP: 4-5 Squares and Square Roots KEY: square square root perfect square 23. NS: Find the square root of 196. 196 = 14, since 14 14 = 196. There are 14 squares along the edge. Find the square root of the number of glass squares in the mosaic. Multiply this number by itself to check your answer. heck your calculations. PTS: 1 IF: verage REF: Page 183 OJ: 4-5.2 pplication NT: 8.5.3.b TOP: 4-5 Squares and Square Roots KEY: square square root perfect square 8

I: 24. NS: First, evaluate the square root. Use the order of operations, and add the numbers under the square root symbol. Then, take the square root of the sum, and multiply the result by the number outside the square root. Use the order of operations, and evaluate everything under the square root symbol first. Evaluate everything under the square root symbol first. Use the order of operations. PTS: 1 IF: verage REF: Page 183 OJ: 4-5.3 Evaluating Expressions Involving Square Roots NT: 8.5.3.c TOP: 4-5 Squares and Square Roots KEY: square square root expression evaluate 25. NS: Find two perfect squares close to 103. 10 2 = 100 11 2 = 121 So, 103 is between 10 and 11. Think of two perfect squares close to the number. heck your calculations. Think of two perfect squares close to the number. PTS: 1 IF: asic REF: Page 186 OJ: 4-6.1 Estimating Square Roots of Numbers NT: 8.1.2.d TOP: 4-6 Estimating Square Roots KEY: square square root estimate 26. NS: Use the square root of the area to find the length of the sides. 69 8.3 The sides should be 8.3 inches long. heck your calculations. Find the square root of the area. Use the square root of the area to find the length of the sides. PTS: 1 IF: verage REF: Page 186 OJ: 4-6.2 Problem-Solving pplication NT: 8.1.2.d TOP: 4-6 Estimating Square Roots KEY: square square root estimate 9

I: 27. NS: Take the square root of the area to get the length of a single square. There are side of a chessboard, so multiply the side length of a single square by 8. 6 2.4495 2.4495 8 19.6 64 = 8 squares along the The sides are 19.6 cm long. Include all of the squares along the edge of a chessboard. heck your calculations. First, take the square root of the area to get the length of a single square. Then, multiply the result by the side length of a single square. PTS: 1 IF: verage REF: Page 186 OJ: 4-6.2 Problem-Solving pplication NT: 8.1.2.d TOP: 4-6 Estimating Square Roots KEY: square square root estimate 28. NS: 304 17.435596 17.4 Round your answer to the correct place. Use a calculator to help you. Use a calculator to help you. PTS: 1 IF: asic REF: Page 187 OJ: 4-6.3 Using a alculator to Estimate the Value of a Square Root NT: 8.1.2.d TOP: 4-6 Estimating Square Roots KEY: square square root estimate calculator 29. NS: rational number can be written as a fraction. Rational numbers include integers, fractions, terminating decimals, and repeating decimals. n irrational number can only be written as decimals that do not terminate or repeat. rational number will terminate or repeat, but an irrational number will not. PTS: 1 IF: asic REF: Page 191 OJ: 4-7.1 lassifying Real Numbers NT: 8.1.1.b TOP: 4-7 The Real Numbers KEY: real number classify rational number irrational 10

I: 30. NS: Fractions with a denominator of 0 and square roots of negative numbers are not real numbers. rational number can be written as a fraction with a non-zero denominator. Rational numbers include integers, fractions, terminating decimals, and repeating decimals. n irrational number cannot be expressed as a terminating decimal or repeating decimal. Irrational numbers cannot be expressed with a finite number of digits. ividing by a 0 or taking the square root of a negative number will not produce a real number. PTS: 1 IF: verage REF: Page 192 OJ: 4-7.2 etermining the lassification of ll Numbers NT: 8.1.1.b TOP: 4-7 The Real Numbers KEY: real number classify rational number irrational 31. NS: Write all the numbers in decimal form, and then graph them. From left to right on the number line, the numbers appear from least to greatest. Write all the numbers in decimal form, and then graph them. Order the numbers from least to greatest, not greatest to least. Write all the numbers in decimal form, and then graph them. PTS: 1 IF: dvanced NT: 8.1.1.b TOP: 4-7 The Real Numbers 32. NS: Use the Pythagorean Theorem: a 2 + b 2 = c 2. First, substitute for a and b. Then, simplify the powers, and add. Finally, find the square root. a 2 + b 2 = c 2 42 2 + 144 2 = c 2 22,500 = c 2 22,500 = c 150 = c Harry and Selma are 150 miles apart. Substitute for a and b in the Pythagorean Theorem, and then simplify. There is one more step before the getting the answer. Take the square root of this number. Use the Pythagorean Theorem. PTS: 1 IF: verage REF: Page 197 OJ: 4-8.3 Using the Pythagorean Theorem for Measurement TOP: 4-8 The Pythagorean Theorem NT: 8.3.3.d 11

I: 33. NS: Since the park is square and the diagonal line stretches between opposite corners, the length of the diagonal line is the hypotenuse of a right triangle. Use the Pythagorean Theorem, a 2 + b 2 = c 2, to solve this problem. Let c = the length of the diagonal. 80 2 + 80 2 = c 2 12,800 = c 2 113 c The diagonal is about 113 meters long. Take the square root after you add the squares of the lengths of the legs. Use the Pythagorean Theorem to find the length of the diagonal. Use the Pythagorean Theorem to find the length of the diagonal. PTS: 1 IF: dvanced NT: 8.3.3.d TOP: 4-8 The Pythagorean Theorem KEY: Pythagorean Theorem right triangle diagonal 34. NS: Example: 7k + 5 k 2 (7k k) + (5 2) Group like terms. 6k + 3 dd or subtract the coefficients. id you multiply the numbers together, rather than adding them? id you use the proper signs for all the numbers? id you use the proper signs for the terms with no variables? PTS: 1 IF: asic REF: Page 584 OJ: 11-1.1 ombining Like Terms to Simplify TOP: 11-1 Simplifying lgebraic Expressions NT: 8.5.3.c KEY: like terms simplify combine 12

I: 35. NS: Example: Simplify 8a + 5t 4a 4t 2 (8a 4a) + (5t 4t) 2 Group like terms. 4a + t 2 dd or subtract the coefficients. id you forget to put one of the terms in your answer? id you multiply the coefficients together, rather than adding them? id you use the proper signs for all the coefficients? PTS: 1 IF: asic REF: Page 585 OJ: 11-1.2 ombining Like Terms in Two-Variable Expressions NT: 8.5.3.c TOP: 11-1 Simplifying lgebraic Expressions KEY: like terms simplify combine two-variable expression 36. NS: Example: Simplify 9(10a 7) + 5a. 90a 63 + 5a Multiply. (90a + 5a) 63 Group like terms. 95a 63 dd or subtract the coefficients. fter grouping like terms did you add and subtract the coefficients correctly? id you use the proper sign for the number that has no variable? id you multiply through for all the terms in the parentheses? PTS: 1 IF: verage REF: Page 585 OJ: 11-1.3 Using the istributive Property to Simplify TOP: 11-1 Simplifying lgebraic Expressions KEY: like terms simplify combine algebraic expression NT: 8.1.5.e 13

I: 37. NS: Example: Solve 9x + 2x = 77 11x = 77 11x = 77 11 11 ombine like terms. ivide both sides by 11 to isolate x. x = 7 id you use division to solve this problem? Should you be adding or subtracting the coefficients? How do you undo multiplication? PTS: 1 IF: verage REF: Page 585 OJ: 11-1.4 ombining Like Terms to Solve lgebraic Equations NT: 8.5.3.c TOP: 11-1 Simplifying lgebraic Expressions KEY: like terms simplify combine equation 38. NS: 3(9 8x 4x) + 8(3x + 4) = 11 27 24x 12x + 24x + 32 = 11 istributive Property 59 12x = 11 ombine oefficients. 27 + 32 = 59 24 12 + 24 = 12 59 12x = 11 Subtract 59 from both 59 59 sides. 12x = 48 Simplify. 12x 48 = 12 12 ivide both sides by 12. x = 4 Simplify. fter removing the parenthesis and combining like terms, isolate the variable x. negative number minus a negative number is the sum of two negative numbers. First use the distributive property to remove the parentheses. PTS: 1 IF: dvanced NT: 8.5.4.a TOP: 11-1 Simplifying lgebraic Expressions 14

I: 39. NS: To solve this equation, combine like terms and use the inverse operation to isolate the variable from the addition/subtraction. Then use division as the inverse operation to isolate the variable from the multiplication. How do you combine like terms? id you use inverse operations to solve? How do you solve multi-step equations? PTS: 1 IF: asic REF: Page 588 OJ: 11-2.1 Solving Equations That ontain Like Terms NT: 8.5.4.a TOP: 11-2 Solving Multi-Step Equations KEY: equation like terms solving 40. NS: To solve this equation, multiply both sides of it by the least common denominator to clear the fraction. Use the inverse operation to isolate the variable from the addition/subtraction. Then use division as the inverse operation to isolate the variable from the multiplication. How do you solve multi-step equations? id you use inverse operations to solve the equation? id you clear the fractions? PTS: 1 IF: verage REF: Page 588 OJ: 11-2.2 Solving Equations That ontain Fractions NT: 8.5.4.a TOP: 11-2 Solving Multi-Step Equations KEY: fraction multi-step equation solving 15

I: 41. NS: price of dinner + (price of dinner % sales tax) = amount of gift certificate + amount paid Substitute values and solve. Example: The family paid 8% sales tax and paid with a $25 gift certificate plus $39.30. Let p represent the price of the dinner. p + Ê Ë Á p 0.08ˆ = 25.00 + 39.30 1.08p = 64.30 1.08p = 64..30 1.08 1.08 p = 59.53703 59.54 How do you find the percent? id you remember to account for the gift certificate? id you account for the sales tax? PTS: 1 IF: verage REF: Page 589 OJ: 11-2.3 pplication NT: 8.5.4.a TOP: 11-2 Solving Multi-Step Equations KEY: multi-step equation solving 16

I: 42. NS: Sample: aron earns $5.25 per hour. Last week he worked 25 hours, had sales of $1,700, and earned a gross income of $195. Set up an equation relating the hourly income, the commission, and the total income: hourly income + commission = total income Let p represent the percent commission and substitute known values: 5.25(25) + 1,700p = 195 131.25 + 1,700p = 195 1,700p = 63.75 p = 0.0375 p = 3.75% He earns a 3.75% commission on sales. How do you convert a decimal to a percent? How are the hourly income, the amount of commission, and the gross income related? id you remember to check your addition? PTS: 1 IF: verage REF: Page 589 OJ: 11-2.3 pplication NT: 8.5.4.a TOP: 11-2 Solving Multi-Step Equations KEY: multi-step equation solving 17

I: 43. NS: 3.8y + 4 7 x + 2 = 0 3.8y + 4 x = 2 Subtract 2 from both sides. 7 3.8y = 4 x 2 Subtract the 4 x term from both sides. 7 7 38 x 2 10 7 38 Rewrite 3.8 as y = 10 Ê 4 x 2 ˆ 38 7 Ë Á Multiply by 10 38 y = 40 266 38 istribute. y = 20 133 x 10 19 Simplify. 10. ivide all terms by 3.8. Multiply by the reciprocal of 3.8. Keep the x term in the equation. PTS: 1 IF: dvanced NT: 8.5.4.a TOP: 11-2 Solving Multi-Step Equations 44. NS: Use inverse operations to group terms with variables on the same side of the equation, and simplify by using addition/subtraction. fter the like terms are on one side of the equation and the equation is simplified, divide by the like terms to get the correct value for the variable. id you combine like terms? id you divide the like terms correctly? id you use the correct inverse operations to solve? PTS: 1 IF: asic REF: Page 593 OJ: 11-3.1 Solving Equations with Variables on oth Sides TOP: 11-3 Solving Equations with Variables on oth Sides NT: 8.5.4.a KEY: equation solving 18

I: 45. NS: Use inverse operations to group terms with variables on the same side of the equation and to group the constant values on the opposite side of the equation. Then use division as the inverse operation to isolate the variable from the multiplication. Should your first step be to combine like terms? id you combine like terms properly? id you use the correct inverse operations to solve? PTS: 1 IF: verage REF: Page 594 OJ: 11-3.2 Solving Multi-Step Equations with Variables on oth Sides NT: 8.5.4.a TOP: 11-3 Solving Equations with Variables on oth Sides KEY: multi-step equation solving 46. NS: To solve multi-step equations with variables on both sides, clear the fractions by multiplying the entire equation by the Least ommon enominator. ombine the like terms. dd or subtract variable terms to both sides of the equation so the variable occurs on only one side of the equation. Use division as the inverse operation to isolate the variable from the multiplication. id you combine the like terms correctly? id you correctly isolate the variable? id you combine the fractions correctly? PTS: 1 IF: verage REF: Page 594 OJ: 11-3.2 Solving Multi-Step Equations with Variables on oth Sides NT: 8.5.4.a TOP: 11-3 Solving Equations with Variables on oth Sides KEY: multi-step equation solving 19

I: 47. NS: Let n represent the number of trips to the park. admission + (parking n) = parking + (admission n) Use inverse operations to group terms with variables on the same side of the equation and to group the constant values on the opposite side of the equation. Then use division as the inverse operation to isolate the variable from the multiplication. Should your first step be to combine like terms? id you combine like terms properly? id you use the correct inverse operations to solve? PTS: 1 IF: verage REF: Page 595 OJ: 11-3.3 pplication NT: 8.5.4.a TOP: 11-3 Solving Equations with Variables on oth Sides KEY: multi-step equation solving 48. NS: To solve a system of equations that are already simplified, you must substitute the first equation into the second equation. Then you can simplify the resulting equation by combining the like terms. Once the value of x has been found, you can substitute it into either of the two original equations in order to determine the y-value. Once you have an x- and y-value determined, you then put the values in the form (x, y). id you combine the like terms correctly? id you insert the x-value into an original equation to solve for y? id you combine the two equations correctly? PTS: 1 IF: asic REF: Page 608 OJ: 11-6.1 Solving Systems of Equations KEY: solving system of equations TOP: 11-6 Systems of Equations 20

I: 49. NS: Solve the first equation for either variable x or y. Then substitute the result into the second equation, thus eliminating one of the variables, and simplify. Once the value of x or y has been found, you can substitute it into either of the two original equations in order to determine the other value. Then write the solution in the form (x, y). id you use the correct equation? re you paying attention to the signs? oes the ordered pair solve both equations? PTS: 1 IF: verage REF: Page 609 OJ: 11-6.2 Solving Systems of Equations by Solving for a Variable TOP: 11-6 Systems of Equations KEY: solving system of equations MTHING 21