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The course begins with an in-depth study of function families, with a focus on connecting multiple representations, followed by an advanced investigation of trigonometry and its applications, including polar graphs, parametric equations, and vectors. The course continues with a unit on sequences and series followed by an accessible and engaging introduction to the big ideas of Calculus. The unit overviews and learning targets for the Math Medic Precalculus course can be found here .

## Math Medic Help

## 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

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## Eureka Math Grade 8 Module 5 Lesson 11 Answer Key

Engage ny eureka math 8th grade module 5 lesson 11 answer key, eureka math grade 8 module 5 lesson 11 example answer key.

→ Could the sphere have a radius of 8 inches? Explain. No. If the sphere had a radius of 8 inches, then it would not fit into the cylinder because the height is only 14 inches. With a radius of 8 inches, the sphere would have a height of 2r, or 16 inches. Since the cylinder is only 14 inches high, the radius of the sphere cannot be 8 inches.

→ What size radius for the sphere would fit into the cylinder? Explain. A radius of 7 inches would fit into the cylinder because 2r is 14, which means the sphere would touch the top and bottom of the cylinder. A radius of 7 means the radius of the sphere would not touch the sides of the cylinder, but would fit into it.

→ Now that we know the radius of the largest sphere is 7 inches, what is the volume of the sphere? Sample student work: V = \(\frac{4}{3}\) πr 3 = \(\frac{4}{3}\) π(7 3 ) = \(\frac{4}{3}\) π(343) = \(\frac{1372}{3}\) π = 457 \(\frac{1}{3}\) π The volume of the sphere is 457 \(\frac{1}{3}\) π cm 3 .

## Eureka Math Grade 8 Module 5 Lesson 11 Exercise Answer Key

Exercises 1–3

Exercise 1. What is the volume of a cylinder? Answer: V = πr 2 h

Exercise 2. What is the height of the cylinder? Answer: The height of the cylinder is the same as the diameter of the sphere. The diameter is 2r.

Exercise 3. If volume(sphere) = 2/3 volume(cylinder with same diameter and height), what is the formula for the volume of a sphere? Answer: Volume(sphere) = \(\frac{2}{3}\) (πr 2 h) Volume(sphere) = \(\frac{2}{3}\) (πr 2 2r) Volume(sphere) = \(\frac{4}{3}\) (πr 3 )

Exercises 4–8

Exercise 5. The average basketball has a diameter of 9.5 inches. What is the volume of an average basketball? Round your answer to the tenths place. Answer: V = \(\frac{4}{3}\) πr 3 V = \(\frac{4}{3}\) π(4.75 3 ) V = \(\frac{4}{3}\) π(107.17) V ≈ 142.9π The volume of an average basketball is about 142.9π in 3 .

Exercise 6. A spherical fish tank has a radius of 8 inches. Assuming the entire tank could be filled with water, what would the volume of the tank be? Round your answer to the tenths place. Answer: V = \(\frac{4}{3}\) πr 3 V = \(\frac{4}{3}\) π(8 3 ) V = \(\frac{4}{3}\) π(512) V ≈ 682.7π The volume of the fish tank is about 682.7π in 3 .

b. Use the diagram to find the volume of each, and determine which has the greater volume. Answer: V = \(\frac{1}{3}\) πr 2 h V = \(\frac{1}{3}\) π(2.5 2 )(12.6) V = 26.25π The volume of the cone is 26.25π mm 3 . V = \(\frac{4}{3}\) πr 3 V = \(\frac{4}{3}\) π(2.8 3 ) V = 29.269333…π The volume of the sphere is about 29.27π mm 3 . The volume of the sphere is greater than the volume of the cone.

## Eureka Math Grade 8 Module 5 Lesson 11 Problem Set Answer Key

The volume of the sphere: V = \(\frac{4}{3}\) πr 3 = \(\frac{4}{3}\) π(2 3 ) = \(\frac{32}{3}\) π = 10 \(\frac{2}{3}\) π The cone has volume 37 \(\frac{1}{3}\) π in 3 and the sphere has volume 10 \(\frac{2}{3}\) π in 3 . The sphere has the lesser volume.

The volume of the sphere: V = \(\frac{4}{3}\) πr 3 = \(\frac{4}{3}\) π(5 3 ) = \(\frac{500}{3}\) π = 166 \(\frac{2}{3}\) π The cylinder has volume 55.8π mm 3 and the sphere has volume 166 \(\frac{2}{3}\) π mm 3 . The sphere has the greater volume.

b. Determine which choice is the best value for her money. Explain your reasoning. Answer: Student answers may vary. Checking the cost for every in 3 of each choice: \(\frac{2}{4.19}\) ≈ 0.47723… \(\frac{2}{6.8}\) ≈ 0.29411… \(\frac{3}{8.37}\) ≈ 0.35842… \(\frac{4}{12.56}\) ≈ 0.31847… \(\frac{4}{14.13}\) ≈ 0.28308… The best value for her money is the cup filled with ice cream since it costs about 28 cents for every in 3 .

## Eureka Math Grade 8 Module 5 Lesson 11 Exit Ticket Answer Key

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Eureka Math Grade 8 Module 2 Lesson 11 Exercise Answer Key. Exercise 1. The mass of a proton is. 0.000 000 000 000 000 000 000 000 001 672 622 kg. In scientific notation it is. Answer: 1.672622×10 -27 kg. Exercise 2. The mass of an electron is.

Eureka Math Grade 2 Module 8 Lesson 10 Answer Key; Eureka Math Grade 2 Module 8 Lesson 11 Answer Key; Eureka Math Grade 2 Module 8 Lesson 12 Answer Key; EngageNY Math Grade 2 Module 8 Topic D Application of Fractions to Tell Time. Eureka Math Grade 2 Module 8 Lesson 13 Answer Key; Eureka Math Grade 2 Module 8 Lesson 14 Answer Key; Eureka Math ...

Answer Key 2• 8 Set E 1. 9 11. 8 21. 12 31. 17 2. 7 12. 9 22. 13 32. 20 3. 14 13. 14 23. 18 33. 9 4. 4 14. 13 24. 6 34. 9 5. 15 15. 13 25. 9 35. 7 6. ... Lesson 4 Answer Key 2• 8 Homework 1. 2 parallel lines of different lengths drawn 2. 2 parallel lines of the same length drawn 3. Parallelogram drawn and named

Lesson 8.2 Problem Solving Use Multiplication COMMON CORE STANDARD CC.5.NF.7b Apply and extend previous understandings of multiplication and division to multiply and divide fractions. 1. Sebastian bakes 4 pies and cuts each pie into ... (Lesson 7.1) @ 11 @ 33 66 @ 99 P172 4. 6. Title: Go Math! Practice Book (TE), G5

11. 14. 65 2,210 34 1,280 -z- 25 51 r5 44 2,910 66 r6 5. 9. 2,961 63 47 6. 10. 86 6,290 73 r12 Problem Solving REAL WORLD 13. A copier prints 89 copies in one minute. ... (Lesson 2.6) @ 33,792 @ 352 34 Christy buys 48 barrettes. She shares the barrettes equally between herself and her 3 sisters. Which expression represents the

Lesson 11.4. Section 11.5: Lesson 11.5. Exercise 1. Exercise 2. Exercise 3. Exercise 4. Exercise 5. Exercise 6. Exercise 7. ... you'll learn how to solve your toughest homework problems. Our resource for McDougal Littell Algebra 2 Practice Workbook includes answers to chapter exercises, as well as detailed information to walk you through the ...

Assessments, Answer Keys, and Sample Questions. Follow. This section includes helpful information about assessments, including where to locate answer keys for module problem and homework sets as well as the location of sample questions for state assessments that are released to the public. When will the Grades 3-8 ELA and mathematics Common ...

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Selected Answers. 2-8. U.S. Traditional Multiplication, Part 4 ... Home Link 2-11 English Español Selected Answers. 2-12. Strategies for Choosing Partial Quotients ... With a login provided by your child's teacher, access resources to help your child with homework or brush up on your math skills.

Answer Key Chapter 2 - College Algebra | OpenStax. Our mission is to improve educational access and learning for everyone. OpenStax is part of Rice University, which is a 501 (c) (3) nonprofit. Give today and help us reach more students.

The unit overviews and learning targets for the Math Medic Precalculus course can be found here. Units. Unit 0: Prerequisites. Unit 1: Functions. Unit 2: Polynomial and Rational Functions. Unit 3: Exponential and Logarithmic Functions. Unit 4: Trigonometric Functions. Unit 5: Applications of Trigonometry. Unit 6: Systems of Equations.

Homework: Lesson 11.1 Lesson 11.2 Lesson 11.3 Lesson 11.4 Lesson 11.5 Lesson 11.6 Lesson 11.7 Lesson 11.8 Lesson 11.9 Lesson 11.10 Lesson 11.11 Lesson 11.12 Extra Practice. Powered by Create your own unique website with customizable templates.

Exercise 8. Exercise 9. Exercise 10. Exercise 11. Exercise 12. Exercise 13. Exercise 14. Exercise 15. Find step-by-step solutions and answers to Algebra 2 Common Core - 9780133186024, as well as thousands of textbooks so you can move forward with confidence.

Jeromy drove at a speed of 80 mph and his mother drove 60 mph. 2.87. Christopher's speed was 50 mph and his parents' speed was 40 mph. 2.88. Ashley's parents drove 55 mph and Ashley drove 62 mph. 2.89. Pierre and Monique will be 429 miles apart in 3 hours. 2.90. Thanh and Nhat will be 330 miles apart in 2.2 hours.

Our resource for Algebra 1: Homework Practice Workbook includes answers to chapter exercises, as well as detailed information to walk you through the process step by step. With Expert Solutions for thousands of practice problems, you can take the guesswork out of studying and move forward with confidence. Find step-by-step solutions and answers ...

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View Homework Help - Signing Naturally Lesson 2.8-2.12 from C D 374 at New Mexico State University. Homework #5: Lessons 2:8-2:12_LAPAGE.K Lesson 2:8 c Lesson 2:9 Minidialogue 1 Male Identified by

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Our resource for Algebra 1: Homework Practice Workbook includes answers to chapter exercises, as well as detailed information to walk you through the process step by step. With Expert Solutions for thousands of practice problems, you can take the guesswork out of studying and move forward with confidence. Find step-by-step solutions and answers ...

Eureka Math Grade 8 Module 5 Lesson 11 Example Answer Key. Example 1. Compute the exact volume for the sphere shown below. Provide students time to work; then, have them share their solutions. The volume of the sphere is 85 13 π cm 3. Example 2. A cylinder has a diameter of 16 inches and a height of 14 inches.