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Benchmark #3 Review

Benchmark #3 Review. Step 2 4 x + y = 6. 4 x + ( x + 1) = 6. Step 3. –1 –1. 5 x = 5. 5 x = 5. 5 5. x = 1. 1. Solve the system by substitution. y = x + 1. 4 x + y = 6 . The first equation is solved for y. Step 1 y = x + 1.

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Benchmark #3 Review

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  1. Benchmark #3 Review

  2. Step 2 4x + y = 6 4x+(x + 1) = 6 Step 3 –1 –1 5x = 5 5x = 5 5 5 x = 1 1. Solve the system by substitution. y =x + 1 4x + y = 6 The first equation is solved for y. Step 1y = x + 1 Substitute x + 1 for y in the second equation. 5x + 1 = 6 Simplify. Solve for x. Subtract 1 from both sides. Divide both sides by 5.

  3. Step 4 y = x + 1 y = 1 + 1 y = 2 Step 5 (1, 2) y = x + 1 4x + y = 6 2 1 + 1 4(1)+ 2 6 2 2  6 6  Solve the system by substitution. Write one of the original equations. Substitute 1 for x. Write the solution as an ordered pair. Check Substitute (1, 2) into both equations in the system.

  4. x + 2y = 11 Step 1 –2(–3x + y = –5) x + 2y = 11 +(6x –2y = +10) Step 2 7x = 21 x = 3 2. Solve the system by elimination. x + 2y = 11 –3x + y = –5 Multiply each term in the second equation by –2 to get opposite y-coefficients. Add the new equation to the first equation. 7x + 0 = 21 Simplify and solve for x.

  5. x + 2y = 11 Step 3 –3 –3 2y = 8 Step 4 (3, 4) Write one of the original equations. 3 + 2y = 11 Substitute 3 for x. Subtract 3 from each side. Simplify and solve for y. y = 4 Write the solution as an ordered pair.

  6. 3. Simplify. A. 4–3 B. 70 Any nonzero number raised to the zero power is 1. 7º = 1 C. (–5)–4 D. –5–4

  7. Use the definition 4. Evaluate the expression for the given value of the variables. x–2 for x = 4 Substitute 4 for x.

  8. 5. Evaluate the expression for the given values of the variables. –2a0b-4 for a = 5 and b = –3 Substitute 5 for a and –3 for b. Evaluate expressions with exponents. Write the power in the denominator as a product. Evaluate the powers in the product. Simplify.

  9. B. 6. Simplify. A. 7w–4

  10. and 7. Simplify. C.

  11. 8. Find the value of each power of 10. C. 109 A. 10–6 B. 104 Start with 1 and move the decimal point six places to the left. Start with 1 and move the decimal point four places to the right. Start with 1 and move the decimal point nine places to the right. 0.000001 10,000 1,000,000,000

  12. 9. Write each number as a power of 10. B. 0.0001 C. 1,000 A. 1,000,000 The decimal point is six places to the right of 1, so the exponent is 6. The decimal point is four places to the left of 1, so the exponent is –4. The decimal point is three places to the right of 1, so the exponent is 3.

  13. 10. Find the value of each expression. A. 23.89  108 23.8 9 0 0 0 0 0 0 Move the decimal point 8 places to the right. 2,389,000,000 B. 467  10–3 Move the decimal point 3 places to the left. 4 6 7 0.467

  14. 11. Saturn has a diameter of about km. Its distance from the Sun is about 1,427,000,000 km. Write Saturn’s diameter in standard form. Move the decimal point 5 places to the right. 1 2 0 0 0 0 120,000 km

  15. Saturn has a diameter of about km. Its distance from the Sun is about 1,427,000,000 km. Write Saturn’s distance from the Sun in scientific notation. Count the number of places you need to move the decimal point to get a number between 1 and 10. 1,427,000,000 1,4 2 7,0 0 0,0 0 0 9 places Use that number as the exponent of 10. 1.427  109 km

  16. 12. Order the list of numbers from least to greatest. Step 1 List the numbers in order by powers of 10. Step 2 Order the numbers that have the same power of 10

  17. 13. Simplify. A. Since the powers have the same base, keep the base and add the exponents. B. Group powers with the same base together. Add the exponents of powers with the same base.

  18. 1 14. Simplify. A. Group powers with the same base together. Add the exponents of powers with the same base. B. Group the positive exponents and add since they have the same base Add the like bases.

  19. distance = rate time mi 15. Light from the Sun travels at about miles per second. It takes about 15,000 seconds for the light to reach Neptune. Find the approximate distance from the Sun to Neptune. Write your answer in scientific notation. Write 15,000 in scientific notation. Use the Commutative and Associative Properties to group. Multiply within each group.

  20. 16. Simplify. Use the Power of a Power Property. Simplify. Use the Power of a Power Property. Zero multiplied by any number is zero Any number raised to the zero power is 1. 1

  21. 16. Simplify. Use the Power of a Power Property. C. Simplify the exponent of the first term. Since the powers have the same base, add the exponents. Write with a positive exponent.

  22. 17. Simplify. A. Use the Power of a Product Property. Simplify. B. Use the Power of a Product Property. Simplify.

  23. 17. Simplify. C. Use the Power of a Product Property. Use the Power of a Product Property. Simplify.

  24. 18. Simplify. A. B.

  25. 18. Simplify. C. D.

  26. Simplify and write the answer in scientific notation Write 0.5 in scientific notation as 5 x 10 . 19. Write as a product of quotients. Simplify each quotient. Simplify the exponent. The second two terms have the same base, so add the exponents. Simplify the exponent.

  27. The Colorado Department of Education spent about dollars in fiscal year 2004-05 on public schools. There were about students enrolled in public school. What was the average spending per student? Write your answer in standard form. 20. To find the average spending per student, divide the total debt by the number of students. Write as a product of quotients.

  28. The Colorado Department of Education spent about dollars in fiscal year 2004-05 on public schools. There were about students enrolled in public school. What was the average spending per student? Write your answer in standard form. To find the average spending per student, divide the total debt by the number of students. Simplify each quotient. Simplify the exponent. Write in standard form. The average spending per student is $5,800.

  29. 21. Simplify. Use the Power of a Quotient Property. Simplify.

  30. Use the Power of a Product Property: Simplify and use the Power of a Power Property: 22. Simplify. Use the Power of a Product Property.

  31. Use the Power of a Product Property: Use the Power of a Product Property: 23. Simplify. Use the Power of a Product Property.

  32. Use the Power of a Product Property: Simplify.

  33. and 24. Simplify. Rewrite with a positive exponent. Use the Powers of a Quotient Property .

  34. 25. Simplify.

  35. 26. Simplify. Rewrite each fraction with a positive exponent. Use the Power of a Quotient Property. Use the Power of a Product Property: (3)2 (2n)3 = 32  23n3 and (2)2  (6m)3 = 22  63m3

  36. Since this function is in the form f(x) = , you can graph it as a horizontal translation of the graph of f(x) = Graph f(x) = and then shift the graph 3 units to the right. 27. Graph .

  37. Graph . This is not a horizontal or vertical translation of . Step 1 Find the domain of the function. x ≥ 0 The expression under the radical sign must be greater than or equal to 0. The domain is the set of all real numbers greater than or equal to 0.

  38. 28. Simplify each expression. B. A.

  39. 29. Simplify. All variables represent nonnegative numbers. Factor the radicand using perfect squares. Product Property of Square Roots. Simplify.

  40. Since x is nonnegative, . 30. Simplify. All variables represent nonnegative numbers. Product Property of Square Roots. Product Property of Square Roots.

  41. 31. Simplify. All variables represent nonnegative numbers. A. B. Simplify. Quotient Property of Square Roots. Quotient Property of Square Roots. Simplify. Simplify.

  42. 32. Simplify. All variables represent nonnegative numbers. Product Property. Quotient Property. Write 108 as 36(3). Simplify.

  43. 33. Simplify. All variables represent nonnegative numbers. Quotient Property. Product Property. Simplify.

  44. A. 34. Add or subtract. The terms are like radicals. B. The terms are unlike radicals. Do not combine.

  45. the terms are like radicals. 35. Add or subtract. A. B. Identify like radicals. Combine like radicals.

  46. 36. Simplify each expression. Factor the radicands using perfect squares. Product Property of Square Roots. Simplify. Combine like radicals.

  47. 37. Simplify each expression. Factor the radicands using perfect squares. Product Property of Square Roots. Simplify. The terms are unlike radicals. Do not combine.

  48. 38. Simplify each expression. Factor the radicands using perfect squares. Product Property of Square Roots. Simplify. Combine like radicals.

  49. 49. Multiply. Write the product in simplest form. Product Property of Square Roots. Multiply the factors in the radicand. Factor 16 using a perfect-square factor. Product Property of Square Roots Simplify.

  50. 40. Multiply. Write the product in simplest form. Expand the expression. Commutative Property of Multiplication. Product Property of Square Roots. Simplify the radicand. Simplify the Square Root. Multiply.

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