algebra 2 unit 2 lesson 2 homework answers

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• Big Ideas Math Algebra 2, Virginia Edition, 2019

• Big Ideas Math Algebra 2, 2014

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• Big Ideas Math Algebra 2 A Bridge to Success

• Core Connections Algebra 2, 2013

• Houghton Mifflin Harcourt Algebra 2, 2015

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• McGraw Hill Glencoe Algebra 2, 2017

• Pearson Algebra 2 Common Core, 2011

• Pearson Algebra 2 Common Core, 2013

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Algebra 2 (Eureka Math/EngageNY)

Unit 1: module 1: polynomial, rational, and radical relationships, unit 2: module 2: trigonometric functions, unit 3: module 3: exponential and logarithmic functions, unit 4: module 4: inferences and conclusions from data.

Algebra 2 Worksheets with answer keys

Enjoy these free printable math worksheets . Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. Plus each one comes with an answer key.

• Absolute Value Equations
• Simplify Imaginary Numbers
• Adding and Subtracting Complex Numbers
• Multiplying Complex Numbers
• Dividing Complex Numbers
• Dividing Complex Number (advanced)
• End of Unit, Review Sheet
• Exponential Growth (no answer key on this one, sorry)
• Compound Interest Worksheet #1 (no logs)
• Compound Interest Worksheet (logarithms required)
• Simplify Rational Exponents
• Solve Equations with Rational Exponents
• Solve Equations with variables in Exponents
• Factor by Grouping
• 1 to 1 functions
• Evaluating Functions
• Composition of Functions
• Inverse Functions
• Operations with Functions
• Functions Review Worksheet
• Product Rule of Logarithms
• Power Rule of Logarithms
• Quotient Rule of Logarithms
• Logarithmic Equations Worksheet
• Dividing Polynomials Worksheet
• Solve Quadratic Equations by Factoring
• Solve Quadratic Equations by Completing the Square
• Quadratic formula Worksheet (real solutions)
• Quadratic Formula Worksheet (complex solutions)
• Quadratic Formula Worksheet (both real and complex solutions)
• Discriminant Worksheet
• Sum and Product of Roots
• Radical Equations
• Rationalizing the Denominator
• Simplify Rational Expressions Worksheet
• Dividing Rational Expressions
• Multiplying Rational Expressions
• Adding and Subtracting Rational Expressions (with like denominators)
• Adding and Subtracting Ratioal Expressions with Unlike Denominators
• Mixed Review on Rational Expressions

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Be Prepared

18 x + 30 18 x + 30

3 − 2 n 3 − 2 n

2 x − 6 2 x − 6

0.045 0.045

w − 3 w − 3

0.35 x + 0.4 0.35 x + 0.4

2 c + 3 2 c + 3

0.042 0.042

15 15 is greater than x x .

15 < x 15 < x

2 5 x + 4 2 5 x + 4

− x + 4 − x + 4

a. >; b. >; c. >; d. >

m = 2 m = 2

a = 0 a = 0

u = 2 u = 2

x = 4 x = 4

p = −2 p = −2

q = −8 q = −8

y = − 17 5 y = − 17 5

z = 0 z = 0

identity; all real numbers

conditional equation; q = − 9 11 q = − 9 11

conditional equation; k = 201 14 k = 201 14

contradiction; no solution

x = 1 2 x = 1 2

x = −2 x = −2

x = 12 x = 12

u = −12 u = −12

n = 2 n = 2

m = −1 m = −1

r = 1 r = 1

s = −8 s = −8

n = 9 n = 9

d = 16 d = 16

He bought two notebooks.

He did seven crosswords puzzles.

−15 , −8 −15 , −8

−29 , 11 −29 , 11

−33 , −32 , −31 −33 , −32 , −31

−13 , −12 , −11 −13 , −12 , −11

−10 , −8 , −6 −10 , −8 , −6

The average cost was $5,000.

The median price was $19,300.

ⓐ 36 ⓑ $26 ⓒ 125 % 125 %

ⓐ 33 ⓑ $36 ⓐ 175 % 175 %

8.8 % 8.8 %

ⓐ $600 ⓑ $1,800

ⓐ $2,975 ⓑ $11,475

He will earn $2,500.

She earned $7,020.

The rate of simple interest was 6%.

The rate of simple interest was 5.5%.

He paid $17,590.

She deposited $9,600.

b = 2 A h b = 2 A h

h = 2 A b h = 2 A b

C = 5 9 ( F − 32 ) C = 5 9 ( F − 32 )

b = 2 A − B h h b = 2 A − B h h

t = A − P P r t = A − P P r

r = A − P P t r = A − P P t

y = 9 − 4 x 7 y = 9 − 4 x 7

y = 1 − 5 x 8 y = 1 − 5 x 8

The window’s height is 12 meters.

The length of the base is 6 feet.

The measures of the angles are 20°, 70°, and 90°.

The measures of the angles are 30°, 60°, and 90°.

The length of the leg is 8.

The length of the leg is 12.

The length is 39 inches and the width is 16 inches.

The length is 17 yards and the width is 26 yards.

The lengths of the sides of the triangle are 5, 11 and 12 inches.

The lengths of the sides of the triangle are 4, 7 and 9 feet.

The length of the swimming pool is 70 feet and the width is 30 feet.

The length of the garden is 90 yards and the width is 60 yards.

The ladder reaches 12 feet.

He should attach the lights 8 feet from the base of the mast.

Jess has 41 nickels and 18 quarters.

Elane has 22 nickels and 59 dimes.

Eric bought thirty-two 49-cent stamps and twelve 35-cent stamps.

Kailee bought twenty-six 49-cent stamps and ten 20-cent stamps.

84 adult tickets, 31 student tickets

615 children’s tickets and 195 adult tickets

Orlando mixed five pounds of cereal squares and 25 pounds of nuts.

Becca mixed 21 gallons of fruit punch and seven gallons of soda.

The speed of the local train is 48 mph and the speed of the express train is 60 mph.

Jeromy drove at a speed of 80 mph and his mother drove 60 mph.

Christopher’s speed was 50 mph and his parents’ speed was 40 mph.

Ashley’s parents drove 55 mph and Ashley drove 62 mph.

Pierre and Monique will be 429 miles apart in 3 hours.

Thanh and Nhat will be 330 miles apart in 2.2 hours.

Suzy’s speed uphill is 1.8 1.8 mph and downhill is three mph.

The boat’s speed upstream is eight mph and downstream is12 mph.

Hamilton drove 40 mph in the city and 70 mph in the desert.

Phuong rode uphill at a speed of 12 mph and on the flat street at 20 mph.

Angie can buy 7 packs of juice.

Daniel can have 11 people at the party.

Sergio and Lizeth can travel no more than 500 miles.

Rameen can use no more than 76 therms.

Caleb must work at least 96 hours.

Elliot must work at least 85 jobs.

Brenda must babysit at least 27 hours.

Josue must shovel at least 20 driveways.

The homeowner can use 5–20 hcf and still fall within the “conservation usage” billing range.

The homeowner can use 16–40 hcf and still fall within the “normal usage” billing range.

ⓐ ± 2 ± 2 ⓑ no solution ⓒ 0

ⓐ ± 11 ± 11 ⓑ no solution ⓒ 0

x = 4 , x = − 2 3 x = 4 , x = − 2 3

x = −1 , x = 5 2 x = −1 , x = 5 2

x = 8 , x = 0 x = 8 , x = 0

x = 8 , x = 2 x = 8 , x = 2

No solution

x = − 2 5 , x = − 2 5 , x = 5 2 x = 5 2

x = 3 , x = 3 , x = 1 9 x = 1 9

The diameter of the rod can be between 79.991 and 80.009 mm.

The diameter of the rod can be between 74.95 and 75.05 mm.

Section 2.1 Exercises

y = 5 y = 5

w = −18 w = −18

q = 3 q = 3

x = 14 x = 14

c = 4 c = 4

c = 5 2 c = 5 2

y = −5 y = −5

s = 10 s = 10

p = −4 p = −4

c = −4 c = −4

h = 3 4 h = 3 4

m = 6 m = 6

conditional equation; j = 2 5 j = 2 5

conditional equation; m = 16 5 m = 16 5

x = −1 x = −1

y = −1 y = −1

a = 3 4 a = 3 4

w = 9 4 w = 9 4

b = 12 b = 12

p = −41 p = −41

x = − 5 2 x = − 5 2

n = −3 n = −3

u = 3 u = 3

x = 18 x = 18

x = 20 x = 20

d = 8 d = 8

L = 19.75 L = 19.75 feet

Answers will vary.

Section 2.2 Exercises

58 hardback books

−11 , −12 , −13 −11 , −12 , −13

−69 , −71 , −73 −69 , −71 , −73

ⓐ 54 ⓑ 108 ⓐ 30%

ⓐ 162.5 162.5 ⓑ $35 ⓐ 150%

$ 11.88 $ 11.88

−2.5 % −2.5 %

−11 % −11 %

ⓐ $ 26.97 $ 26.97 ⓑ $ 17.98 $ 17.98

ⓐ $576 ⓑ 30%

ⓐ $ 7.20 $ 7.20 ⓑ $ 23.20 $ 23.20

ⓐ $ 0.20 $ 0.20 ⓑ $ 0.80 $ 0.80

3.75 % 3.75 %

21.2 % 21.2 %

Section 2.3 Exercises

d = C π d = C π

L = V W H L = V W H

d 1 = 2 A d 2 d 1 = 2 A d 2

b 1 = 2 A h − b 2 b 1 = 2 A h − b 2

a = 2 h − 108 t t 2 a = 2 h − 108 t t 2

a = 180 − b − c a = 180 − b − c

p = 2 A − 2 B l p = 2 A − 2 B l

L = P − 2 W 2 L = P − 2 W 2

y = 15 − 8 x y = 15 − 8 x

y = −6 + 4 x y = −6 + 4 x

y = 4 + x y = 4 + x

y = 7 − 4 x 3 y = 7 − 4 x 3

y = 12 − 2 x 3 y = 12 − 2 x 3

y = 18 − 3 x −2 y = 18 − 3 x −2

45 ° , 45 ° , 90 ° 45 ° , 45 ° , 90 °

30 ° , 60 ° , 90 ° 30 ° , 60 ° , 90 °

18 meters, 11 meters

13.5 13.5 m, 12.8 12.8 m

25 ft, 50 ft

12 ft, 13 ft, 14 ft

3 ft, 6 ft, 8 ft

120 yd, 160 yd

40 ft, 85 ft

104 ° F 104 ° F

ⓐ Answers will vary. ⓑ The areas are the same. The 2 × 8 2 × 8 rectangle has a larger perimeter than the 4 × 4 4 × 4 square. ⓒ Answers will vary.

Section 2.4 Exercises

nine nickels, 16 dimes

ten $10 bills, five $5 bills

63 dimes, 20 quarters

16 nickels, 12 dimes, seven quarters

330 day passes, 367 tournament passes

40 postcards, 100 stamps

15 $10 shares, five $12 shares

34 general, 61 youth

114 general, 246 student

Four pounds of macadamia nuts, eight pounds almonds

3.6 3.6 lbs Bermuda seed, 5.4 5.4 lbs Fescue seed

$33,000 in Fund A, $22,000 in Fund B

5.9 % 5.9 %

Kathy 5 mph, Cheryl 3 mph

commercial 550 mph, private plane 340 mph

Violet 65 mph, Charlie 55 mph

Ethan 22 mph, Leo 16 mph

DaMarcus 16 mph, Fabian 22 mph

uphill 1.6 1.6 mph, downhill 4.8 4.8 mph

light traffic 54 mph, heavy traffic 30 mph

freeway 67 mph, mountain road 22.3 mph

running eight mph, walking three mph

ⓐ 15 minutes ⓑ 20 minutes ⓒ one hour (d) 1:25

Section 2.5 Exercises

A maximum of 14 people can safely ride in the elevator.

five drinks

260 messages

62 necklaces

seven lawns

Section 2.6 Exercises

5 ≤ n ≤ 24 5 ≤ n ≤ 24

6 ≤ w ≤ 12 6 ≤ w ≤ 12

ⓐ answers vary ⓑ answers vary

Section 2.7 Exercises

ⓐ x = 4 , x = −4 x = 4 , x = −4 ⓑ no solution ⓒ z = 0 z = 0

ⓐ x = 3 , x = −3 x = 3 , x = −3 ⓑ no solution ⓒ z = 0 z = 0

x = 1 , x = − 1 2 x = 1 , x = − 1 2

x = −1 , x = − 5 2 x = −1 , x = − 5 2

x = 7 , x = 1 x = 7 , x = 1

x = 1 , x = −5 x = 1 , x = −5

no solution

x = −1 , x = − 2 3 x = −1 , x = − 2 3

x = −3 , x = 3 x = −3 , x = 3

x = 2 , x = 1 4 x = 2 , x = 1 4

x = 3 , x = 2 x = 3 , x = 2

x = 3 , x = − 11 3 x = 3 , x = − 11 3

x = 3 2 , x = − 1 2 x = 3 2 , x = − 1 2

The minimum to maximum expected production is 207,500 to 2,225,000 bottles

The acceptable weight is 22.5 to 25.5 ounces.

Review Exercises

s = −22 s = −22

m = −14 m = −14

q = 18 q = 18

k = 3 4 k = 3 4

k = 23 k = 23

x = 5 x = 5

There are 116 people.

−3 , −10 −3 , −10

$ 3.89 $ 3.89

ⓐ $105 ⓑ 52.5 % 52.5 %

d 2 = 2 A d 1 d 2 = 2 A d 1

y = 4 x 3 − 4 y = 4 x 3 − 4

22.5 ° , 67.5 ° , 90 ° 22.5 ° , 67.5 ° , 90 °

24.5 24.5 cm, 12.5 12.5 cm

9 ft, 14 ft, 12 ft

nine pennies, six dimes, 12 quarters

57 students, 68 general admission

2.2 2.2 lbs of raisins, 7.8 7.8 lbs of nuts

9.7 % 9.7 %

Louellen 65 mph, Tracy 66 mph

upstream 3 mph, downstream 5 mph

heavy traffic 32 mph, light traffic 68 mph

$33 per day

at least $300,000

at least 112 jobs

x = 2 , x = 2 3 x = 2 , x = 2 3

x = 9 , x = −3 x = 9 , x = −3

The minimum to maximum expected usage is 210,000 to 220,000 bottles

Practice Test

x = −5 x = −5

a = 41 a = 41

x = 6 x = 6

x = −2 , x = − 1 3 x = −2 , x = − 1 3

−57 , −55 −57 , −55

12 dimes, seven quarters

2.5 2.5 hours

At most $55.56 per costume.

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Access for free at https://openstax.org/books/intermediate-algebra-2e/pages/1-introduction

• Authors: Lynn Marecek, Andrea Honeycutt Mathis
• Publisher/website: OpenStax
• Book title: Intermediate Algebra 2e
• Publication date: May 6, 2020
• Location: Houston, Texas
• Book URL: https://openstax.org/books/intermediate-algebra-2e/pages/1-introduction
• Section URL: https://openstax.org/books/intermediate-algebra-2e/pages/chapter-2

© Jan 23, 2024 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.

Alg2.3 Complex Numbers and Rational Exponents

In this unit, students use what they know about exponents and radicals to extend exponent rules to include rational exponents (for example,  \(5^{\frac{1}{3}}=\sqrt[3]{5}\) ), solve various equations involving squares and square roots, develop the concept of complex numbers by defining a new number  \(i\)  whose square is -1, and use complex numbers to find solutions to quadratic equations.

Exponent Properties

• 1 Properties of Exponents
• 2 Square Roots and Cube Roots
• 3 Exponents That Are Unit Fractions
• 4 Positive Rational Exponents
• 5 Negative Rational Exponents

Solving Equations with Square and Cube Roots

• 6 Squares and Square Roots
• 7 Inequivalent Equations
• 8 Cubes and Cube Roots
• 9 Solving Radical Equations

A New Kind of Number

• 10 A New Kind of Number
• 11 Introducing the Number $i$
• 12 Arithmetic with Complex Numbers
• 13 Multiplying Complex Numbers
• 14 More Arithmetic with Complex Numbers
• 15 Working Backwards

Solving Quadratics with Complex Numbers

• 16 Solving Quadratics
• 17 Completing the Square and Complex Solutions
• 18 The Quadratic Formula and Complex Solutions
• 19 Real and Non-Real Solutions

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