simplify each expression. each expression ... is the sum rational or irrational? is the product of a...

Simplify each expression.

SOLUTION:

13. GEOMETRY The area A of a triangle can be found by using the formula , where b represents the base

and h is the height. What is the area of the triangle shown?

SOLUTION:

The area of the triangle is .

SOLUTION:

26. GEOMETRY Find the perimeter and area of a rectangle with a width of and a length of .

SOLUTION:

The perimeter is units.

The area is 12 square units.

SOLUTION:

33. ROLLER COASTERS The velocity v in feet per second of a roller coaster at the bottom of a hill is related to the

vertical drop h in feet and the velocity v0 of the coaster at the top of the hill by the formula .

a. What velocity must a coaster have at the top of a 225-foot hill to achieve a velocity of 120 feet per second at the bottom?

b. Explain why v0 = v − is not equivalent to the formula given.

SOLUTION: a. Let v = 120 and h = 225.

The coaster must have a velocity of 0 feet per second at the top of the hill. b. Sample answer: In the formula given, we are taking the square root of the difference, not the square root of each term.

34. FINANCIAL LITERACY Tadi invests $225 in a savings account. In two years, Tadi has $232 in his account.

You can use the formula to find the average annual interest rate r that the account has earned. The

initial investment is v0 and v2 is the amount in two years. What was the average annual interest rate that Tadi’s

account earned?

SOLUTION:

Let v0 = 225 and let v2 = 232.

The average annual interest rate that Tadi’s account earned was about 1.5%.

35. ELECTRICITY Electricians can calculate the electrical current in amps A by using the formula , where

w is the power in watts and r the resistance in ohms. How much electrical current is running through a microwave oven that has 850 watts of power and 5 ohms of resistance? Write the number of amps in simplest radical form, and then estimate the amount of current to the nearest tenth.

SOLUTION: Let w = 850 and let r = 5.

There are or about 13 amps of electrical current running through the microwave oven.

36. CHALLENGE Determine whether the following statement is true or false . Provide a proof or counterexample to support your answer.

x + y > when x > 0 and y > 0

SOLUTION: Because x and y are both positive, each side of the inequality represents a positive number. So, you can prove thestatement by squaring each side of the inequality.

Because x > 0 and y > 0, the product 2xy must be a positive number.Thus, 2xy > 0 is always true.

Therefore, is a true statement for all x > 0 and y > 0.

37. CCSS ARGUMENTS Make a conjecture about the sum of a rational number and an irrational number. Is the sum rational or irrational? Is the product of a nonzero rational number and an irrational number rational or irrational? Explain your reasoning.

SOLUTION: Examine the sum of several pairs of rational and irrational numbers:

is in lowest terms, and is irrational.

is in lowest terms and is irrational.

is irrational. Examine the product of several pairs of non-zero rational and irrational numbers:

is irrational

is irrational. From the above examples, we should come up with the conjecture that the sum of a rational number and an irrationalnumber is irrational, and the product of a rational number and an irrational number is irrational.

38. OPEN ENDED Write an equation that shows a sum of two radicals with different radicands. Explain how you could combine these terms.

SOLUTION: Sample answer:

When you simplify , you get . When you simplify , you get . Because these two numbers have thesame radicand, you can add them.

39. WRITING IN MATH Describe step by step how to multiply two radical expressions, each with two terms. Write an example to demonstrate your description.

SOLUTION: For example, you can use the FOIL method. You multiply the first terms within the parentheses. Then you multiply the outer terms within the parentheses. Then you would multiply the inner terms within the parentheses. And, then you would multiply the last terms within each parentheses. Combine any like terms and simplify any radicals. For example:

40. SHORT RESPONSE The population of a town is 13,000 and is increasing by about 250 people per year. This can be represented by the equation p = 13,000 + 250y , where y is the number of years from now and p represents the population. In how many years will the population of the town be 14,500?

SOLUTION: Let p = 14,500.

In 6 years, the population of the town will be 14,500.

41. GEOMETRY Which expression represents the sum of the lengths of the 12 edges on this rectangular solid?

A 2(a + b + c) B 3(a + b + c) C 4(a + b + c) D 12(a + b + c)

SOLUTION: There are 4 edges that have a length of a, 4 edges that have a length of b, and 4 edges that have a length of c. So, the expression 4a + 4b + 4c or 4(a + b + c) represents the sum of the lengths of the 12 edges of the rectangular solid. Choice C is the correct answer.

42. Evaluate and for n = 25. F 4; 4 G 4; 2 H 2; 4 J 2; 2

SOLUTION: Substitute 25 for n in both expressions.

Choice G is correct.

43. The current I in a simple electrical circuit is given by the formula , where V is the voltage and R is the

resistance of the circuit. If the voltage remains unchanged, what effect will doubling the resistance of the circuit have on the current? A The current will remain the same. B The current will double its previous value. C The current will be half its previous value. D The current will be two units more than its previous value.

SOLUTION: The current and the resistance have an inverse relationship. If the resistance is double and the voltage remains the same, the current will be half of its previous value.

Consider an example with the resistance is 4 and voltage is 100. Find I when R doubles.

Choice C is the correct answer.

Simplify.

SOLUTION:

Graph each function. Compare to the parent graph. State the domain and range.

SOLUTION:

The parent function is multiplied by a value greater than 1, so the graph is a vertical stretch of .

Another way to identify the stretch is to notice that the y-values in the table are 2 times the corresponding y-values for the parent function. The domain is x|x ≥ 0 and the range is y |y ≥ 0.

x 0 0.5 1 2 y 0 ≈ 1.4 2 ≈ 2.8

SOLUTION:

The parent function is multiplied by a value less than 1, so the graph is a vertical stretch of and a reflection across the x-axis. Another way to identify the stretch is to notice that the y-values in the table are –3 timesthe corresponding y-values for the parent function. The domain is x|x ≥ 0 and the range is y |y ≤ 0.

x 0 0.5 1 2 y 0 ≈ –2.1 –3 ≈ –4.2

SOLUTION:

The value 1 is being added to the square root of the parent function , so the graph is translated 1 unit left

from the parent graph . Another way to identify the translation is to note that the x-values in the table are 1

less than the corresponding x-values for the parent function. The domain is x|x ≥ –1, and the range is y |y ≥ 0.

x –1 –0.5 0 1 2 3 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 ≈ 2

SOLUTION:

The value 4 is being subtracted from the square root of the parent function , so the graph is translated 4 units

right from the parent graph . Another way to identify the translation is to note that the x-values in the table

are 4 more than the corresponding x-values for the parent function. The domain is x|x ≥ 4, and the range is y |y ≥ 0.

x 4 4.5 5 6 7 8 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 2

SOLUTION:

The value 3 is being added to the parent function , so the graph is translated up 3 units from the parent graph

. Another way to identify the translation is to note that the y-values in the table are 3 greater than the

corresponding y-values for the parent function. The domain is x|x ≥ 0 and the range is y |y ≥ 3.

x 0 0.5 1 2 3 4 y 3 ≈ 3.7 4 ≈ 4.4 ≈ 4.7 5

SOLUTION:

The value 2 is being subtracted from the parent function , so the graph is translated down 2 units from the

parent graph . Another way to identify the translation is to note that the y-values in the table are 2 less than

the corresponding y-values for the parent function. The domain is x|x ≥ 0 and the range is y |y ≥ –2.

x 0 0.5 1 2 3 4 y –2 ≈ –1.3 –1 ≈ –0.6 ≈ –0.3 0

Factor each trinomial.

56. x2 + 12x + 27

SOLUTION:

57. y2 + 13y + 30

SOLUTION:

58. p2 − 17p + 72

SOLUTION:

59. x2 + 6x – 7

SOLUTION:

60. y2 − y − 42

SOLUTION:

61. −72 + 6w + w2

SOLUTION:

62. FINANCIAL LITERACY Determine the value of an investment if $400 is invested at an interest rate of 7.25% compounded quarterly for 7 years.

SOLUTION: Use the formula for calculating compound interest.

The value of the investment after 7 years is about $661.44.

Solve each equation. Round each solution to the nearest tenth, if necessary.

63. −4c − 1.2 = 0.8

SOLUTION:

64. −2.6q − 33.7 = 84.1

SOLUTION:

65. 0.3m + 4 = 9.6

SOLUTION:

68. 3.6t + 6 − 2.5t = 8

SOLUTION:

eSolutions Manual - Powered by Cognero Page 1

10-3 Operations with Radical Expressions

SOLUTION:

account earned?

SOLUTION:

Let v0 = 225 and let v2 = 232.

x + y > when x > 0 and y > 0

is irrational

Simplify.

SOLUTION:

x 0 0.5 1 2 y 0 ≈ 1.4 2 ≈ 2.8

SOLUTION:

x 0 0.5 1 2 y 0 ≈ –2.1 –3 ≈ –4.2

SOLUTION:

x –1 –0.5 0 1 2 3 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 ≈ 2

SOLUTION:

x 4 4.5 5 6 7 8 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 2

SOLUTION:

x 0 0.5 1 2 3 4 y 3 ≈ 3.7 4 ≈ 4.4 ≈ 4.7 5

SOLUTION:

x 0 0.5 1 2 3 4 y –2 ≈ –1.3 –1 ≈ –0.6 ≈ –0.3 0

56. x2 + 12x + 27

SOLUTION:

57. y2 + 13y + 30

SOLUTION:

58. p2 − 17p + 72

SOLUTION:

59. x2 + 6x – 7

SOLUTION:

60. y2 − y − 42

SOLUTION:

61. −72 + 6w + w2

SOLUTION:

63. −4c − 1.2 = 0.8

SOLUTION:

64. −2.6q − 33.7 = 84.1

SOLUTION:

65. 0.3m + 4 = 9.6

SOLUTION:

68. 3.6t + 6 − 2.5t = 8

SOLUTION:

account earned?

SOLUTION:

Let v0 = 225 and let v2 = 232.

x + y > when x > 0 and y > 0

is irrational

Simplify.

SOLUTION:

x 0 0.5 1 2 y 0 ≈ 1.4 2 ≈ 2.8

SOLUTION:

x 0 0.5 1 2 y 0 ≈ –2.1 –3 ≈ –4.2

SOLUTION:

x –1 –0.5 0 1 2 3 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 ≈ 2

SOLUTION:

x 4 4.5 5 6 7 8 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 2

SOLUTION:

x 0 0.5 1 2 3 4 y 3 ≈ 3.7 4 ≈ 4.4 ≈ 4.7 5

SOLUTION:

x 0 0.5 1 2 3 4 y –2 ≈ –1.3 –1 ≈ –0.6 ≈ –0.3 0

56. x2 + 12x + 27

SOLUTION:

57. y2 + 13y + 30

SOLUTION:

58. p2 − 17p + 72

SOLUTION:

59. x2 + 6x – 7

SOLUTION:

60. y2 − y − 42

SOLUTION:

61. −72 + 6w + w2

SOLUTION:

63. −4c − 1.2 = 0.8

SOLUTION:

64. −2.6q − 33.7 = 84.1

SOLUTION:

65. 0.3m + 4 = 9.6

SOLUTION:

68. 3.6t + 6 − 2.5t = 8

SOLUTION:

account earned?

SOLUTION:

Let v0 = 225 and let v2 = 232.

x + y > when x > 0 and y > 0

is irrational

Simplify.

SOLUTION:

x 0 0.5 1 2 y 0 ≈ 1.4 2 ≈ 2.8

SOLUTION:

x 0 0.5 1 2 y 0 ≈ –2.1 –3 ≈ –4.2

SOLUTION:

x –1 –0.5 0 1 2 3 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 ≈ 2

SOLUTION:

x 4 4.5 5 6 7 8 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 2

SOLUTION:

x 0 0.5 1 2 3 4 y 3 ≈ 3.7 4 ≈ 4.4 ≈ 4.7 5

SOLUTION:

x 0 0.5 1 2 3 4 y –2 ≈ –1.3 –1 ≈ –0.6 ≈ –0.3 0

56. x2 + 12x + 27

SOLUTION:

57. y2 + 13y + 30

SOLUTION:

58. p2 − 17p + 72

SOLUTION:

59. x2 + 6x – 7

SOLUTION:

60. y2 − y − 42

SOLUTION:

61. −72 + 6w + w2

SOLUTION:

63. −4c − 1.2 = 0.8

SOLUTION:

64. −2.6q − 33.7 = 84.1

SOLUTION:

65. 0.3m + 4 = 9.6

SOLUTION:

68. 3.6t + 6 − 2.5t = 8

SOLUTION:

account earned?

SOLUTION:

Let v0 = 225 and let v2 = 232.

x + y > when x > 0 and y > 0

is irrational

Simplify.

SOLUTION:

x 0 0.5 1 2 y 0 ≈ 1.4 2 ≈ 2.8

SOLUTION:

x 0 0.5 1 2 y 0 ≈ –2.1 –3 ≈ –4.2

SOLUTION:

x –1 –0.5 0 1 2 3 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 ≈ 2

SOLUTION:

x 4 4.5 5 6 7 8 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 2

SOLUTION:

x 0 0.5 1 2 3 4 y 3 ≈ 3.7 4 ≈ 4.4 ≈ 4.7 5

SOLUTION:

x 0 0.5 1 2 3 4 y –2 ≈ –1.3 –1 ≈ –0.6 ≈ –0.3 0

56. x2 + 12x + 27

SOLUTION:

57. y2 + 13y + 30

SOLUTION:

58. p2 − 17p + 72

SOLUTION:

59. x2 + 6x – 7

SOLUTION:

60. y2 − y − 42

SOLUTION:

61. −72 + 6w + w2

SOLUTION:

63. −4c − 1.2 = 0.8

SOLUTION:

64. −2.6q − 33.7 = 84.1

SOLUTION:

65. 0.3m + 4 = 9.6

SOLUTION:

68. 3.6t + 6 − 2.5t = 8

SOLUTION:

account earned?

SOLUTION:

Let v0 = 225 and let v2 = 232.

x + y > when x > 0 and y > 0

is irrational

Simplify.

SOLUTION:

x 0 0.5 1 2 y 0 ≈ 1.4 2 ≈ 2.8

SOLUTION:

x 0 0.5 1 2 y 0 ≈ –2.1 –3 ≈ –4.2

SOLUTION:

x –1 –0.5 0 1 2 3 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 ≈ 2

SOLUTION:

x 4 4.5 5 6 7 8 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 2

SOLUTION:

x 0 0.5 1 2 3 4 y 3 ≈ 3.7 4 ≈ 4.4 ≈ 4.7 5

SOLUTION:

x 0 0.5 1 2 3 4 y –2 ≈ –1.3 –1 ≈ –0.6 ≈ –0.3 0

56. x2 + 12x + 27

SOLUTION:

57. y2 + 13y + 30

SOLUTION:

58. p2 − 17p + 72

SOLUTION:

59. x2 + 6x – 7

SOLUTION:

60. y2 − y − 42

SOLUTION:

61. −72 + 6w + w2

SOLUTION:

63. −4c − 1.2 = 0.8

SOLUTION:

64. −2.6q − 33.7 = 84.1

SOLUTION:

65. 0.3m + 4 = 9.6

SOLUTION:

68. 3.6t + 6 − 2.5t = 8

SOLUTION:

account earned?

SOLUTION:

Let v0 = 225 and let v2 = 232.

x + y > when x > 0 and y > 0

is irrational

Simplify.

SOLUTION:

x 0 0.5 1 2 y 0 ≈ 1.4 2 ≈ 2.8

SOLUTION:

x 0 0.5 1 2 y 0 ≈ –2.1 –3 ≈ –4.2

SOLUTION:

x –1 –0.5 0 1 2 3 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 ≈ 2

SOLUTION:

x 4 4.5 5 6 7 8 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 2

SOLUTION:

x 0 0.5 1 2 3 4 y 3 ≈ 3.7 4 ≈ 4.4 ≈ 4.7 5

SOLUTION:

x 0 0.5 1 2 3 4 y –2 ≈ –1.3 –1 ≈ –0.6 ≈ –0.3 0

56. x2 + 12x + 27

SOLUTION:

57. y2 + 13y + 30

SOLUTION:

58. p2 − 17p + 72

SOLUTION:

59. x2 + 6x – 7

SOLUTION:

60. y2 − y − 42

SOLUTION:

61. −72 + 6w + w2

SOLUTION:

63. −4c − 1.2 = 0.8

SOLUTION:

64. −2.6q − 33.7 = 84.1

SOLUTION:

65. 0.3m + 4 = 9.6

SOLUTION:

68. 3.6t + 6 − 2.5t = 8

SOLUTION:

account earned?

SOLUTION:

Let v0 = 225 and let v2 = 232.

x + y > when x > 0 and y > 0

is irrational

Simplify.

SOLUTION:

x 0 0.5 1 2 y 0 ≈ 1.4 2 ≈ 2.8

SOLUTION:

x 0 0.5 1 2 y 0 ≈ –2.1 –3 ≈ –4.2

SOLUTION:

x –1 –0.5 0 1 2 3 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 ≈ 2

SOLUTION:

x 4 4.5 5 6 7 8 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 2

SOLUTION:

x 0 0.5 1 2 3 4 y 3 ≈ 3.7 4 ≈ 4.4 ≈ 4.7 5

SOLUTION:

x 0 0.5 1 2 3 4 y –2 ≈ –1.3 –1 ≈ –0.6 ≈ –0.3 0

56. x2 + 12x + 27

SOLUTION:

57. y2 + 13y + 30

SOLUTION:

58. p2 − 17p + 72

SOLUTION:

59. x2 + 6x – 7

SOLUTION:

60. y2 − y − 42

SOLUTION:

61. −72 + 6w + w2

SOLUTION:

63. −4c − 1.2 = 0.8

SOLUTION:

64. −2.6q − 33.7 = 84.1

SOLUTION:

65. 0.3m + 4 = 9.6

SOLUTION:

68. 3.6t + 6 − 2.5t = 8

SOLUTION:

account earned?

SOLUTION:

Let v0 = 225 and let v2 = 232.

x + y > when x > 0 and y > 0

is irrational

Simplify.

SOLUTION:

x 0 0.5 1 2 y 0 ≈ 1.4 2 ≈ 2.8

SOLUTION:

x 0 0.5 1 2 y 0 ≈ –2.1 –3 ≈ –4.2

SOLUTION:

x –1 –0.5 0 1 2 3 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 ≈ 2

SOLUTION:

x 4 4.5 5 6 7 8 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 2

SOLUTION:

x 0 0.5 1 2 3 4 y 3 ≈ 3.7 4 ≈ 4.4 ≈ 4.7 5

SOLUTION:

x 0 0.5 1 2 3 4 y –2 ≈ –1.3 –1 ≈ –0.6 ≈ –0.3 0

56. x2 + 12x + 27

SOLUTION:

57. y2 + 13y + 30

SOLUTION:

58. p2 − 17p + 72

SOLUTION:

59. x2 + 6x – 7

SOLUTION:

60. y2 − y − 42

SOLUTION:

61. −72 + 6w + w2

SOLUTION:

63. −4c − 1.2 = 0.8

SOLUTION:

64. −2.6q − 33.7 = 84.1

SOLUTION:

65. 0.3m + 4 = 9.6

SOLUTION:

68. 3.6t + 6 − 2.5t = 8

SOLUTION:

account earned?

SOLUTION:

Let v0 = 225 and let v2 = 232.

x + y > when x > 0 and y > 0

is irrational

Simplify.

SOLUTION:

x 0 0.5 1 2 y 0 ≈ 1.4 2 ≈ 2.8

SOLUTION:

x 0 0.5 1 2 y 0 ≈ –2.1 –3 ≈ –4.2

SOLUTION:

x –1 –0.5 0 1 2 3 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 ≈ 2

SOLUTION:

x 4 4.5 5 6 7 8 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 2

SOLUTION:

x 0 0.5 1 2 3 4 y 3 ≈ 3.7 4 ≈ 4.4 ≈ 4.7 5

SOLUTION:

x 0 0.5 1 2 3 4 y –2 ≈ –1.3 –1 ≈ –0.6 ≈ –0.3 0

56. x2 + 12x + 27

SOLUTION:

57. y2 + 13y + 30

SOLUTION:

58. p2 − 17p + 72

SOLUTION:

59. x2 + 6x – 7

SOLUTION:

60. y2 − y − 42

SOLUTION:

61. −72 + 6w + w2

SOLUTION:

63. −4c − 1.2 = 0.8

SOLUTION:

64. −2.6q − 33.7 = 84.1

SOLUTION:

65. 0.3m + 4 = 9.6

SOLUTION:

68. 3.6t + 6 − 2.5t = 8

SOLUTION:

account earned?

SOLUTION:

Let v0 = 225 and let v2 = 232.

x + y > when x > 0 and y > 0

is irrational

Simplify.

SOLUTION:

x 0 0.5 1 2 y 0 ≈ 1.4 2 ≈ 2.8

SOLUTION:

x 0 0.5 1 2 y 0 ≈ –2.1 –3 ≈ –4.2

SOLUTION:

x –1 –0.5 0 1 2 3 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 ≈ 2

SOLUTION:

x 4 4.5 5 6 7 8 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 2

SOLUTION:

x 0 0.5 1 2 3 4 y 3 ≈ 3.7 4 ≈ 4.4 ≈ 4.7 5

SOLUTION:

x 0 0.5 1 2 3 4 y –2 ≈ –1.3 –1 ≈ –0.6 ≈ –0.3 0

56. x2 + 12x + 27

SOLUTION:

57. y2 + 13y + 30

SOLUTION:

58. p2 − 17p + 72

SOLUTION:

59. x2 + 6x – 7

SOLUTION:

60. y2 − y − 42

SOLUTION:

61. −72 + 6w + w2

SOLUTION:

63. −4c − 1.2 = 0.8

SOLUTION:

64. −2.6q − 33.7 = 84.1

SOLUTION:

65. 0.3m + 4 = 9.6

SOLUTION:

68. 3.6t + 6 − 2.5t = 8

SOLUTION:

account earned?

SOLUTION:

Let v0 = 225 and let v2 = 232.

x + y > when x > 0 and y > 0

is irrational

Simplify.

SOLUTION:

x 0 0.5 1 2 y 0 ≈ 1.4 2 ≈ 2.8

SOLUTION:

x 0 0.5 1 2 y 0 ≈ –2.1 –3 ≈ –4.2

SOLUTION:

x –1 –0.5 0 1 2 3 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 ≈ 2

SOLUTION:

x 4 4.5 5 6 7 8 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 2

SOLUTION:

x 0 0.5 1 2 3 4 y 3 ≈ 3.7 4 ≈ 4.4 ≈ 4.7 5

SOLUTION:

x 0 0.5 1 2 3 4 y –2 ≈ –1.3 –1 ≈ –0.6 ≈ –0.3 0

56. x2 + 12x + 27

SOLUTION:

57. y2 + 13y + 30

SOLUTION:

58. p2 − 17p + 72

SOLUTION:

59. x2 + 6x – 7

SOLUTION:

60. y2 − y − 42

SOLUTION:

61. −72 + 6w + w2

SOLUTION:

63. −4c − 1.2 = 0.8

SOLUTION:

64. −2.6q − 33.7 = 84.1

SOLUTION:

65. 0.3m + 4 = 9.6

SOLUTION:

68. 3.6t + 6 − 2.5t = 8

SOLUTION:

account earned?

SOLUTION:

Let v0 = 225 and let v2 = 232.

x + y > when x > 0 and y > 0

is irrational

Simplify.

SOLUTION:

x 0 0.5 1 2 y 0 ≈ 1.4 2 ≈ 2.8

SOLUTION:

x 0 0.5 1 2 y 0 ≈ –2.1 –3 ≈ –4.2

SOLUTION:

x –1 –0.5 0 1 2 3 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 ≈ 2

SOLUTION:

x 4 4.5 5 6 7 8 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 2

SOLUTION:

x 0 0.5 1 2 3 4 y 3 ≈ 3.7 4 ≈ 4.4 ≈ 4.7 5

SOLUTION:

x 0 0.5 1 2 3 4 y –2 ≈ –1.3 –1 ≈ –0.6 ≈ –0.3 0

56. x2 + 12x + 27

SOLUTION:

57. y2 + 13y + 30

SOLUTION:

58. p2 − 17p + 72

SOLUTION:

59. x2 + 6x – 7

SOLUTION:

60. y2 − y − 42

SOLUTION:

61. −72 + 6w + w2

SOLUTION:

63. −4c − 1.2 = 0.8

SOLUTION:

64. −2.6q − 33.7 = 84.1

SOLUTION:

65. 0.3m + 4 = 9.6

SOLUTION:

68. 3.6t + 6 − 2.5t = 8

SOLUTION:

account earned?

SOLUTION:

Let v0 = 225 and let v2 = 232.

x + y > when x > 0 and y > 0

is irrational

Simplify.

SOLUTION:

x 0 0.5 1 2 y 0 ≈ 1.4 2 ≈ 2.8

SOLUTION:

x 0 0.5 1 2 y 0 ≈ –2.1 –3 ≈ –4.2

SOLUTION:

x –1 –0.5 0 1 2 3 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 ≈ 2

SOLUTION:

x 4 4.5 5 6 7 8 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 2

SOLUTION:

x 0 0.5 1 2 3 4 y 3 ≈ 3.7 4 ≈ 4.4 ≈ 4.7 5

SOLUTION:

x 0 0.5 1 2 3 4 y –2 ≈ –1.3 –1 ≈ –0.6 ≈ –0.3 0

56. x2 + 12x + 27

SOLUTION:

57. y2 + 13y + 30

SOLUTION:

58. p2 − 17p + 72

SOLUTION:

59. x2 + 6x – 7

SOLUTION:

60. y2 − y − 42

SOLUTION:

61. −72 + 6w + w2

SOLUTION:

63. −4c − 1.2 = 0.8

SOLUTION:

64. −2.6q − 33.7 = 84.1

SOLUTION:

65. 0.3m + 4 = 9.6

SOLUTION:

68. 3.6t + 6 − 2.5t = 8

SOLUTION:

account earned?

SOLUTION:

Let v0 = 225 and let v2 = 232.

x + y > when x > 0 and y > 0

is irrational

Simplify.

SOLUTION:

x 0 0.5 1 2 y 0 ≈ 1.4 2 ≈ 2.8

SOLUTION:

x 0 0.5 1 2 y 0 ≈ –2.1 –3 ≈ –4.2

SOLUTION:

x –1 –0.5 0 1 2 3 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 ≈ 2

SOLUTION:

x 4 4.5 5 6 7 8 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 2

SOLUTION:

x 0 0.5 1 2 3 4 y 3 ≈ 3.7 4 ≈ 4.4 ≈ 4.7 5

SOLUTION:

x 0 0.5 1 2 3 4 y –2 ≈ –1.3 –1 ≈ –0.6 ≈ –0.3 0

56. x2 + 12x + 27

SOLUTION:

57. y2 + 13y + 30

SOLUTION:

58. p2 − 17p + 72

SOLUTION:

59. x2 + 6x – 7

SOLUTION:

60. y2 − y − 42

SOLUTION:

61. −72 + 6w + w2

SOLUTION:

63. −4c − 1.2 = 0.8

SOLUTION:

64. −2.6q − 33.7 = 84.1

SOLUTION:

65. 0.3m + 4 = 9.6

SOLUTION:

68. 3.6t + 6 − 2.5t = 8

SOLUTION:

account earned?

SOLUTION:

Let v0 = 225 and let v2 = 232.

x + y > when x > 0 and y > 0

is irrational

Simplify.

SOLUTION:

x 0 0.5 1 2 y 0 ≈ 1.4 2 ≈ 2.8

SOLUTION:

x 0 0.5 1 2 y 0 ≈ –2.1 –3 ≈ –4.2

SOLUTION:

x –1 –0.5 0 1 2 3 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 ≈ 2

SOLUTION:

x 4 4.5 5 6 7 8 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 2

SOLUTION:

x 0 0.5 1 2 3 4 y 3 ≈ 3.7 4 ≈ 4.4 ≈ 4.7 5

SOLUTION:

x 0 0.5 1 2 3 4 y –2 ≈ –1.3 –1 ≈ –0.6 ≈ –0.3 0

56. x2 + 12x + 27

SOLUTION:

57. y2 + 13y + 30

SOLUTION:

58. p2 − 17p + 72

SOLUTION:

59. x2 + 6x – 7

SOLUTION:

60. y2 − y − 42

SOLUTION:

61. −72 + 6w + w2

SOLUTION:

63. −4c − 1.2 = 0.8

SOLUTION:

64. −2.6q − 33.7 = 84.1

SOLUTION:

65. 0.3m + 4 = 9.6

SOLUTION:

68. 3.6t + 6 − 2.5t = 8

SOLUTION:

account earned?

SOLUTION:

Let v0 = 225 and let v2 = 232.

x + y > when x > 0 and y > 0

is irrational

Simplify.

SOLUTION:

x 0 0.5 1 2 y 0 ≈ 1.4 2 ≈ 2.8

SOLUTION:

x 0 0.5 1 2 y 0 ≈ –2.1 –3 ≈ –4.2

SOLUTION:

x –1 –0.5 0 1 2 3 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 ≈ 2

SOLUTION:

x 4 4.5 5 6 7 8 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 2

SOLUTION:

x 0 0.5 1 2 3 4 y 3 ≈ 3.7 4 ≈ 4.4 ≈ 4.7 5

SOLUTION:

x 0 0.5 1 2 3 4 y –2 ≈ –1.3 –1 ≈ –0.6 ≈ –0.3 0

56. x2 + 12x + 27

SOLUTION:

57. y2 + 13y + 30

SOLUTION:

58. p2 − 17p + 72

SOLUTION:

59. x2 + 6x – 7

SOLUTION:

60. y2 − y − 42

SOLUTION:

61. −72 + 6w + w2

SOLUTION:

63. −4c − 1.2 = 0.8

SOLUTION:

64. −2.6q − 33.7 = 84.1

SOLUTION:

65. 0.3m + 4 = 9.6

SOLUTION:

68. 3.6t + 6 − 2.5t = 8

SOLUTION:

account earned?

SOLUTION:

Let v0 = 225 and let v2 = 232.

x + y > when x > 0 and y > 0

is irrational

Simplify.

SOLUTION:

x 0 0.5 1 2 y 0 ≈ 1.4 2 ≈ 2.8

SOLUTION:

x 0 0.5 1 2 y 0 ≈ –2.1 –3 ≈ –4.2

SOLUTION:

x –1 –0.5 0 1 2 3 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 ≈ 2

SOLUTION:

x 4 4.5 5 6 7 8 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 2

SOLUTION:

x 0 0.5 1 2 3 4 y 3 ≈ 3.7 4 ≈ 4.4 ≈ 4.7 5

SOLUTION:

x 0 0.5 1 2 3 4 y –2 ≈ –1.3 –1 ≈ –0.6 ≈ –0.3 0

56. x2 + 12x + 27

SOLUTION:

57. y2 + 13y + 30

SOLUTION:

58. p2 − 17p + 72

SOLUTION:

59. x2 + 6x – 7

SOLUTION:

60. y2 − y − 42

SOLUTION:

61. −72 + 6w + w2

SOLUTION:

63. −4c − 1.2 = 0.8

SOLUTION:

64. −2.6q − 33.7 = 84.1

SOLUTION:

65. 0.3m + 4 = 9.6

SOLUTION:

68. 3.6t + 6 − 2.5t = 8

SOLUTION:

account earned?

SOLUTION:

Let v0 = 225 and let v2 = 232.

x + y > when x > 0 and y > 0

is irrational

Simplify.

SOLUTION:

x 0 0.5 1 2 y 0 ≈ 1.4 2 ≈ 2.8

SOLUTION:

x 0 0.5 1 2 y 0 ≈ –2.1 –3 ≈ –4.2

SOLUTION:

x –1 –0.5 0 1 2 3 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 ≈ 2

SOLUTION:

x 4 4.5 5 6 7 8 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 2

SOLUTION:

x 0 0.5 1 2 3 4 y 3 ≈ 3.7 4 ≈ 4.4 ≈ 4.7 5

SOLUTION:

x 0 0.5 1 2 3 4 y –2 ≈ –1.3 –1 ≈ –0.6 ≈ –0.3 0

56. x2 + 12x + 27

SOLUTION:

57. y2 + 13y + 30

SOLUTION:

58. p2 − 17p + 72

SOLUTION:

59. x2 + 6x – 7

SOLUTION:

60. y2 − y − 42

SOLUTION:

61. −72 + 6w + w2

SOLUTION:

63. −4c − 1.2 = 0.8

SOLUTION:

64. −2.6q − 33.7 = 84.1

SOLUTION:

65. 0.3m + 4 = 9.6

SOLUTION:

68. 3.6t + 6 − 2.5t = 8

SOLUTION:

account earned?

SOLUTION:

Let v0 = 225 and let v2 = 232.

x + y > when x > 0 and y > 0

is irrational

Simplify.

SOLUTION:

x 0 0.5 1 2 y 0 ≈ 1.4 2 ≈ 2.8

SOLUTION:

x 0 0.5 1 2 y 0 ≈ –2.1 –3 ≈ –4.2

SOLUTION:

x –1 –0.5 0 1 2 3 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 ≈ 2

SOLUTION:

x 4 4.5 5 6 7 8 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 2

SOLUTION:

x 0 0.5 1 2 3 4 y 3 ≈ 3.7 4 ≈ 4.4 ≈ 4.7 5

SOLUTION:

x 0 0.5 1 2 3 4 y –2 ≈ –1.3 –1 ≈ –0.6 ≈ –0.3 0

56. x2 + 12x + 27

SOLUTION:

57. y2 + 13y + 30

SOLUTION:

58. p2 − 17p + 72

SOLUTION:

59. x2 + 6x – 7

SOLUTION:

60. y2 − y − 42

SOLUTION:

61. −72 + 6w + w2

SOLUTION:

63. −4c − 1.2 = 0.8

SOLUTION:

64. −2.6q − 33.7 = 84.1

SOLUTION:

65. 0.3m + 4 = 9.6

SOLUTION:

68. 3.6t + 6 − 2.5t = 8

SOLUTION:

account earned?

SOLUTION:

Let v0 = 225 and let v2 = 232.

x + y > when x > 0 and y > 0

is irrational

Simplify.

SOLUTION:

x 0 0.5 1 2 y 0 ≈ 1.4 2 ≈ 2.8

SOLUTION:

x 0 0.5 1 2 y 0 ≈ –2.1 –3 ≈ –4.2

SOLUTION:

x –1 –0.5 0 1 2 3 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 ≈ 2

SOLUTION:

x 4 4.5 5 6 7 8 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 2

SOLUTION:

x 0 0.5 1 2 3 4 y 3 ≈ 3.7 4 ≈ 4.4 ≈ 4.7 5

SOLUTION:

x 0 0.5 1 2 3 4 y –2 ≈ –1.3 –1 ≈ –0.6 ≈ –0.3 0

56. x2 + 12x + 27

SOLUTION:

57. y2 + 13y + 30

SOLUTION:

58. p2 − 17p + 72

SOLUTION:

59. x2 + 6x – 7

SOLUTION:

60. y2 − y − 42

SOLUTION:

61. −72 + 6w + w2

SOLUTION:

63. −4c − 1.2 = 0.8

SOLUTION:

64. −2.6q − 33.7 = 84.1

SOLUTION:

65. 0.3m + 4 = 9.6

SOLUTION:

68. 3.6t + 6 − 2.5t = 8

SOLUTION:

account earned?

SOLUTION:

Let v0 = 225 and let v2 = 232.

x + y > when x > 0 and y > 0

is irrational

Simplify.

SOLUTION:

x 0 0.5 1 2 y 0 ≈ 1.4 2 ≈ 2.8

SOLUTION:

x 0 0.5 1 2 y 0 ≈ –2.1 –3 ≈ –4.2

SOLUTION:

x –1 –0.5 0 1 2 3 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 ≈ 2

SOLUTION:

x 4 4.5 5 6 7 8 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 2

SOLUTION:

x 0 0.5 1 2 3 4 y 3 ≈ 3.7 4 ≈ 4.4 ≈ 4.7 5

SOLUTION:

x 0 0.5 1 2 3 4 y –2 ≈ –1.3 –1 ≈ –0.6 ≈ –0.3 0

56. x2 + 12x + 27

SOLUTION:

57. y2 + 13y + 30

SOLUTION:

58. p2 − 17p + 72

SOLUTION:

59. x2 + 6x – 7

SOLUTION:

60. y2 − y − 42

SOLUTION:

61. −72 + 6w + w2

SOLUTION:

63. −4c − 1.2 = 0.8

SOLUTION:

64. −2.6q − 33.7 = 84.1

SOLUTION:

65. 0.3m + 4 = 9.6

SOLUTION:

68. 3.6t + 6 − 2.5t = 8

SOLUTION:

account earned?

SOLUTION:

Let v0 = 225 and let v2 = 232.

x + y > when x > 0 and y > 0

is irrational

Simplify.

SOLUTION:

x 0 0.5 1 2 y 0 ≈ 1.4 2 ≈ 2.8

SOLUTION:

x 0 0.5 1 2 y 0 ≈ –2.1 –3 ≈ –4.2

SOLUTION:

x –1 –0.5 0 1 2 3 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 ≈ 2

SOLUTION:

x 4 4.5 5 6 7 8 y 0 ≈ 0.7 1 ≈ 1.4 ≈ 1.7 2

SOLUTION:

x 0 0.5 1 2 3 4 y 3 ≈ 3.7 4 ≈ 4.4 ≈ 4.7 5

SOLUTION:

x 0 0.5 1 2 3 4 y –2 ≈ –1.3 –1 ≈ –0.6 ≈ –0.3 0

56. x2 + 12x + 27

SOLUTION:

57. y2 + 13y + 30

SOLUTION:

58. p2 − 17p + 72

SOLUTION:

59. x2 + 6x – 7

SOLUTION:

60. y2 − y − 42

SOLUTION:

61. −72 + 6w + w2

SOLUTION:

63. −4c − 1.2 = 0.8

SOLUTION:

64. −2.6q − 33.7 = 84.1

SOLUTION:

65. 0.3m + 4 = 9.6

SOLUTION:

68. 3.6t + 6 − 2.5t = 8

SOLUTION:

simplify each expression. each expression ... is the sum rational or irrational? is the product of a...

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