lesson 9 homework 4.4 answer key

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Chapter 9, Lesson 4: Compositions of Transformations

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A: ( 5 , 1 ) ( 5 , 1 )  B: ( −2 , 4 ) ( −2 , 4 )  C: ( −5 , −1 ) ( −5 , −1 )  D: ( 3 , −2 ) ( 3 , −2 )  E: ( 0 , −5 ) ( 0 , −5 )  F: ( 4 , 0 ) ( 4 , 0 )

A: ( 4 , 2 ) ( 4 , 2 )  B: ( −2 , 3 ) ( −2 , 3 )  C: ( −4 , −4 ) ( −4 , −4 )  D: ( 3 , −5 ) ( 3 , −5 )  E: ( −3 , 0 ) ( −3 , 0 )  F: ( 0 , 2 ) ( 0 , 2 )

Answers will vary.

ⓐ yes, yes  ⓑ yes, yes

ⓐ no, no  ⓑ yes, yes

x - intercept: ( 2 , 0 ) ( 2 , 0 ) ; y - intercept: ( 0 , −2 ) ( 0 , −2 )

x - intercept: ( 3 , 0 ) ( 3 , 0 ) , y - intercept: ( 0 , 2 ) ( 0 , 2 )

x - intercept: ( 4 , 0 ) ( 4 , 0 ) , y - intercept: ( 0 , 12 ) ( 0 , 12 )

x - intercept: ( 8 , 0 ) ( 8 , 0 ) , y - intercept: ( 0 , 2 ) ( 0 , 2 )

x - intercept: ( 4 , 0 ) ( 4 , 0 ) , y - intercept: ( 0 , −3 ) ( 0 , −3 )

x - intercept: ( 4 , 0 ) ( 4 , 0 ) , y - intercept: ( 0 , −2 ) ( 0 , −2 )

− 2 3 − 2 3

− 4 3 − 4 3

− 3 5 − 3 5

− 1 36 − 1 36

− 1 48 − 1 48

slope m = 2 3 m = 2 3 and y -intercept ( 0 , −1 ) ( 0 , −1 )

slope m = 1 2 m = 1 2 and y -intercept ( 0 , 3 ) ( 0 , 3 )

2 5 ; ( 0 , −1 ) 2 5 ; ( 0 , −1 )

− 4 3 ; ( 0 , 1 ) − 4 3 ; ( 0 , 1 )

− 1 4 ; ( 0 , 2 ) − 1 4 ; ( 0 , 2 )

− 3 2 ; ( 0 , 6 ) − 3 2 ; ( 0 , 6 )

ⓐ intercepts  ⓑ horizontal line  ⓒ slope–intercept  ⓓ vertical line

ⓐ vertical line  ⓑ slope–intercept  ⓒ horizontal line  ⓓ intercepts

• ⓐ 50 inches
• ⓑ 66 inches
• ⓒ The slope, 2, means that the height, h , increases by 2 inches when the shoe size, s , increases by 1. The h -intercept means that when the shoe size is 0, the height is 50 inches.
• ⓐ 40 degrees
• ⓑ 65 degrees
• ⓒ The slope, 1 4 1 4 , means that the temperature Fahrenheit ( F ) increases 1 degree when the number of chirps, n , increases by 4. The T -intercept means that when the number of chirps is 0, the temperature is 40 ° 40 ° .
• ⓒ The slope, 0.5, means that the weekly cost, C , increases by $0.50 when the number of miles driven, n, increases by 1. The C -intercept means that when the number of miles driven is 0, the weekly cost is $60
• ⓒ The slope, 1.8, means that the weekly cost, C, increases by $1.80 when the number of invitations, n , increases by 1.80. The C -intercept means that when the number of invitations is 0, the weekly cost is $35.;

not parallel; same line

perpendicular

not perpendicular

y = 2 5 x + 4 y = 2 5 x + 4

y = − x − 3 y = − x − 3

y = 3 5 x + 1 y = 3 5 x + 1

y = 4 3 x − 5 y = 4 3 x − 5

y = 5 6 x − 2 y = 5 6 x − 2

y = 2 3 x − 4 y = 2 3 x − 4

y = − 2 5 x − 1 y = − 2 5 x − 1

y = − 3 4 x − 4 y = − 3 4 x − 4

y = 8 y = 8

y = 4 y = 4

y = 5 2 x − 13 2 y = 5 2 x − 13 2

y = − 2 5 x + 22 5 y = − 2 5 x + 22 5

y = 1 3 x − 10 3 y = 1 3 x − 10 3

y = − 2 5 x − 23 5 y = − 2 5 x − 23 5

x = 5 x = 5

x = −4 x = −4

y = 3 x − 10 y = 3 x − 10

y = 1 2 x + 1 y = 1 2 x + 1

y = − 1 3 x + 10 3 y = − 1 3 x + 10 3

y = −2 x + 16 y = −2 x + 16

y = −5 y = −5

y = −1 y = −1

x = −5 x = −5

ⓐ yes  ⓑ yes  ⓒ yes  ⓓ yes  ⓔ no

ⓐ yes  ⓑ yes  ⓒ no  ⓓ no  ⓔ yes

y ≥ −2 x + 3 y ≥ −2 x + 3

y < 1 2 x − 4 y < 1 2 x − 4

x − 4 y ≤ 8 x − 4 y ≤ 8

3 x − y ≤ 6 3 x − y ≤ 6

Section 4.1 Exercises

A: ( −4 , 1 ) ( −4 , 1 )  B: ( −3 , −4 ) ( −3 , −4 )  C: ( 1 , −3 ) ( 1 , −3 )  D: ( 4 , 3 ) ( 4 , 3 )

A: ( 0 , −2 ) ( 0 , −2 )  B: ( −2 , 0 ) ( −2 , 0 )  C: ( 0 , 5 ) ( 0 , 5 )  D: ( 5 , 0 ) ( 5 , 0 )

ⓑ Age and weight are only positive.

Section 4.2 Exercises

ⓐ yes; no  ⓑ no; no  ⓒ yes; yes  ⓓ yes; yes

ⓐ yes; yes  ⓑ yes; yes  ⓒ yes; yes  ⓓ no; no

$722, $850, $978

Section 4.3 Exercises

( 3 , 0 ) , ( 0 , 3 ) ( 3 , 0 ) , ( 0 , 3 )

( 5 , 0 ) , ( 0 , −5 ) ( 5 , 0 ) , ( 0 , −5 )

( −2 , 0 ) , ( 0 , −2 ) ( −2 , 0 ) , ( 0 , −2 )

( −1 , 0 ) , ( 0 , 1 ) ( −1 , 0 ) , ( 0 , 1 )

( 6 , 0 ) , ( 0 , 3 ) ( 6 , 0 ) , ( 0 , 3 )

( 0 , 0 ) ( 0 , 0 )

( 4 , 0 ) , ( 0 , 4 ) ( 4 , 0 ) , ( 0 , 4 )

( −3 , 0 ) , ( 0 , 3 ) ( −3 , 0 ) , ( 0 , 3 )

( 8 , 0 ) , ( 0 , 4 ) ( 8 , 0 ) , ( 0 , 4 )

( 2 , 0 ) , ( 0 , 6 ) ( 2 , 0 ) , ( 0 , 6 )

( 12 , 0 ) , ( 0 , −4 ) ( 12 , 0 ) , ( 0 , −4 )

( 2 , 0 ) , ( 0 , −8 ) ( 2 , 0 ) , ( 0 , −8 )

( 5 , 0 ) , ( 0 , 2 ) ( 5 , 0 ) , ( 0 , 2 )

( 4 , 0 ) , ( 0 , −6 ) ( 4 , 0 ) , ( 0 , −6 )

( 3 , 0 ) , ( 0 , 1 ) ( 3 , 0 ) , ( 0 , 1 )

( −10 , 0 ) , ( 0 , 2 ) ( −10 , 0 ) , ( 0 , 2 )

ⓐ ( 0 , 1000 ) , ( 15 , 0 ) ( 0 , 1000 ) , ( 15 , 0 ) ⓑ At ( 0 , 1000 ) ( 0 , 1000 ) , he has been gone 0 hours and has 1000 miles left. At ( 15 , 0 ) ( 15 , 0 ) , he has been gone 15 hours and has 0 miles left to go.

Section 4.4 Exercises

−3 2 = − 3 2 −3 2 = − 3 2

− 1 3 − 1 3

− 3 4 − 3 4

− 5 2 − 5 2

− 8 7 − 8 7

ⓐ 1 3 1 3   ⓑ 4 12 pitch or 4-in-12 pitch

3 50 3 50 ; rise = 3, run = 50

ⓐ 288 inches (24 feet)  ⓑ Models will vary.

When the slope is a positive number the line goes up from left to right. When the slope is a negative number the line goes down from left to right.

A vertical line has 0 run and since division by 0 is undefined the slope is undefined.

Section 4.5 Exercises

slope m = 4 m = 4 and y -intercept ( 0 , −2 ) ( 0 , −2 )

slope m = −3 m = −3 and y -intercept ( 0 , 1 ) ( 0 , 1 )

slope m = − 2 5 m = − 2 5 and y -intercept ( 0 , 3 ) ( 0 , 3 )

−9 ; ( 0 , 7 ) −9 ; ( 0 , 7 )

4 ; ( 0 , −10 ) 4 ; ( 0 , −10 )

−4 ; ( 0 , 8 ) −4 ; ( 0 , 8 )

− 8 3 ; ( 0 , 4 ) − 8 3 ; ( 0 , 4 )

7 3 ; ( 0 , −3 ) 7 3 ; ( 0 , −3 )

horizontal line

vertical line

slope–intercept

• ⓒ The slope, 2.54, means that Randy’s payment, P , increases by $2.54 when the number of units of water he used, w, increases by 1. The P –intercept means that if the number units of water Randy used was 0, the payment would be $28.
• ⓒ The slope, 0.32, means that the cost, C , increases by $0.32 when the number of miles driven, m, increases by 1. The C -intercept means that if Janelle drives 0 miles one day, the cost would be $15.
• ⓒ The slope, 0.09, means that Patel’s salary, S , increases by $0.09 for every $1 increase in his sales. The S -intercept means that when his sales are $0, his salary is $750.
• ⓒ The slope, 42, means that the cost, C , increases by $42 for when the number of guests increases by 1. The C -intercept means that when the number of guests is 0, the cost would be $750.

not parallel

• ⓐ For every increase of one degree Fahrenheit, the number of chirps increases by four.
• ⓑ There would be −160 −160 chirps when the Fahrenheit temperature is 0 ° 0 ° . (Notice that this does not make sense; this model cannot be used for all possible temperatures.)

Section 4.6 Exercises

y = 4 x + 1 y = 4 x + 1

y = 8 x − 6 y = 8 x − 6

y = − x + 7 y = − x + 7

y = −3 x − 1 y = −3 x − 1

y = 1 5 x − 5 y = 1 5 x − 5

y = − 2 3 x − 3 y = − 2 3 x − 3

y = 2 y = 2

y = −4 x y = −4 x

y = −2 x + 4 y = −2 x + 4

y = 3 4 x + 2 y = 3 4 x + 2

y = − 3 2 x − 1 y = − 3 2 x − 1

y = 6 y = 6

y = 3 8 x − 1 y = 3 8 x − 1

y = 5 6 x + 2 y = 5 6 x + 2

y = − 3 5 x + 1 y = − 3 5 x + 1

y = − 1 3 x − 11 y = − 1 3 x − 11

y = −7 y = −7

y = − 5 2 x − 22 y = − 5 2 x − 22

y = −4 x − 11 y = −4 x − 11

y = −8 y = −8

y = −4 x + 13 y = −4 x + 13

y = x + 5 y = x + 5

y = − 1 3 x − 14 3 y = − 1 3 x − 14 3

y = 7 x + 22 y = 7 x + 22

y = − 6 7 x + 4 7 y = − 6 7 x + 4 7

y = 1 5 x − 2 y = 1 5 x − 2

x = 4 x = 4

x = −2 x = −2

y = −3 y = −3

y = 4 x y = 4 x

y = 1 2 x + 3 2 y = 1 2 x + 3 2

y = 5 y = 5

y = 3 x − 1 y = 3 x − 1

y = −3 x + 3 y = −3 x + 3

y = 2 x − 6 y = 2 x − 6

y = − 2 3 x + 5 y = − 2 3 x + 5

x = −3 x = −3

y = −4 y = −4

y = x y = x

y = − 3 4 x − 1 4 y = − 3 4 x − 1 4

y = 5 4 x y = 5 4 x

y = 1 y = 1

y = x + 2 y = x + 2

y = 3 4 x y = 3 4 x

y = 1.2 x + 5.2 y = 1.2 x + 5.2

Section 4.7 Exercises

ⓐ yes  ⓑ no  ⓒ no  ⓓ yes  ⓔ no

ⓐ yes  ⓑ no  ⓒ no  ⓓ yes  ⓔ yes

ⓐ no  ⓑ no  ⓒ no  ⓓ yes  ⓔ yes

y < 2 x − 4 y < 2 x − 4

y ≤ − 1 3 x − 2 y ≤ − 1 3 x − 2

x + y ≥ 3 x + y ≥ 3

x + 2 y ≥ −2 x + 2 y ≥ −2

2 x − y < 4 2 x − y < 4

4 x − 3 y > 12 4 x − 3 y > 12

• ⓑ Answers will vary.

Review Exercises

ⓐ ( 2 , 0 ) ( 2 , 0 )   ⓑ ( 0 , −5 ) ( 0 , −5 )   ⓒ ( −4.0 ) ( −4.0 )   ⓓ ( 0 , 3 ) ( 0 , 3 )

ⓐ yes; yes  ⓑ yes; no

( 6 , 0 ) , ( 0 , 4 ) ( 6 , 0 ) , ( 0 , 4 )

− 1 2 − 1 2

slope m = − 2 3 m = − 2 3 and y -intercept ( 0 , 4 ) ( 0 , 4 )

5 3 ; ( 0 , −6 ) 5 3 ; ( 0 , −6 )

4 5 ; ( 0 , − 8 5 ) 4 5 ; ( 0 , − 8 5 )

plotting points

ⓐ −$250  ⓑ $450  ⓒ The slope, 35, means that Marjorie’s weekly profit, P , increases by $35 for each additional student lesson she teaches. The P –intercept means that when the number of lessons is 0, Marjorie loses $250.  ⓓ

y = −5 x − 3 y = −5 x − 3

y = −2 x y = −2 x

y = −3 x + 5 y = −3 x + 5

y = 3 5 x y = 3 5 x

y = −2 x − 5 y = −2 x − 5

y = 1 2 x − 5 2 y = 1 2 x − 5 2

y = − 2 5 x + 8 y = − 2 5 x + 8

y = 3 y = 3

y = − 3 2 x − 6 y = − 3 2 x − 6

ⓐ yes  ⓑ no  ⓒ yes  ⓓ yes  ⓔ no

y > 2 3 x − 3 y > 2 3 x − 3

x − 2 y ≥ 6 x − 2 y ≥ 6

Practice Test

ⓐ yes  ⓑ yes  ⓒ no

( 3 , 0 ) , ( 0 , −4 ) ( 3 , 0 ) , ( 0 , −4 )

y = − 3 4 x − 2 y = − 3 4 x − 2

y = 1 2 x − 4 y = 1 2 x − 4

y = − 4 5 x − 5 y = − 4 5 x − 5

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• Book title: Elementary Algebra
• Publication date: Feb 22, 2017
• Location: Houston, Texas
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Eureka Math Grade 4 Module 6 Lesson 9 Answer Key

Engage ny eureka math 4th grade module 6 lesson 9 answer key, eureka math grade 4 module 6 lesson 9 problem set answer key.

Answer: 0.27 m.

Explanation: In the above-given question, given that, \(\frac{2}{10}\)m + \(\frac{7}{100}\)m = \(\frac{27}{100}\)m = 0.27m 2/10 = 0.2. 7/100 = 0.07. 0.2 + 0.07 = 0.27 m

Answer: 0.35 m.

Explanation: In the above-given question, given that, \(\frac{3}{10}\)m + \(\frac{5}{100}\)m = \(\frac{35}{100}\)m = 0.35m 3/10 = 0.3. 5/100 = 0.05. 0.3 + 0.05 = 0.35 m

Answer: c. 0.27, 0.3, 0.35, 0.4. 0.4, 0.35, 0.3, 0.27.

Explanation: In the above-given figures, given that, the 1-meter stick. least to greatest = 0.27, 0.3, 0.35, 0.4. greatest to least = 0.4, 0.3, 0.35, 0.4.

Answer: a. Avocado = 0.2 kg. Apple = 0.12 kg. Banana = 0.6 kg. grapes = 0.61 kg.

b. Express the mass of each item on the place value chart.

Mass of Fruit (kilograms)

c. Complete the statements below using the words heavier than or lighter than in your statements. The avocado is ____geater_____ the apple. The bunch of bananas is ___less than_____ the bunch of grapes.

Answer: The avocado is greater than the apple. the bunch of bananas is less than the bunch of grapes.

Explanation: In the above-given question, given that, The avocado is greater than the apple. the bunch of bananas is less than the bunch of grapes. avocado = 0.2 kg. bananas = 0.6 kg. grapes = 0.61 kg. apple – 0.12 kg.

Volume of Water (liters)

Compare the values using >, <, or =. a. 0.9 L __>___ 0.6 L b. 0.48 L ___<____ 0.6 L c. 0.3 L __>___ 0.19 L d. Write the volume of water in each graduated cylinder in order from least to greatest.

Answer: The volume of water in cylinder  A = 0.6 liters. The volume of water in cylinder  B = 0.3 liters. The volume of water in cylinder  C = 0.9 liters. The volume of water in cylinder  D = 0.97 liters. The volume of water in cylinder  E = 0.19 liters. The volume of water in cylinder  F = 0.48 liters.

Explanation: In the above-given question, given that, The volume of water in cylinder  A = 0.6 liters. The volume of water in cylinder  B = 0.3 liters. The volume of water in cylinder  C = 0.9 liters. The volume of water in cylinder  D = 0.97 liters. The volume of water in cylinder  E = 0.19 liters. The volume of water in cylinder  F = 0.48 liters. least to greatest in cylinders. 0.19, 0.3, 0.48, 0.6, 0.9, 0.97.

Eureka Math Grade 4 Module 6 Lesson 9 Exit Ticket Answer Key

Answer: String 1 = 0.54 cm. string 2 = 0.5 cm. string 3 = 0.47 cm.

Explanation: In the above-given question, given that, the length of the string in meter. String 1 = 0.54 cm. string 2 = 0.5 cm. string 3 = 0.47 cm.

b. List the lengths of the strings in order from greatest to least.

Answer: The strings in order from greatest to least = string 1, string 2, string 3.

Explanation: In the above-given question, given that, the length of the string in the meter. String 1 = 0.54 cm. string 2 = 0.5 cm. string 3 = 0.47 cm. The strings in order from greatest to least = string 1, string 2, string 3.

Question 2. Compare the values below using >, <, or =. a. 0.8 kg ___>___ 0.6 kg b. 0.36 kg __<___ 0.5 kg c. 0.4 kg ___<___ 0.47 kg

Answer: 0.8 kg > 0.6 kg. 0.36 kg < 0.5 kg. 0.4 kg < 0.47 kg.

Explanation: In the above-given question, given that, 0.8 kg > 0.6 kg. 0.36 kg < 0.5 kg. 0.4 kg < 0.47 kg.

Eureka Math Grade 4 Module 6 Lesson 9 Homework Answer Key

Answer: a. 1. 6.8 cm. a. 2. 7 cm. b. 1. 5 cm. b. 2. 4.4 cm.

Explanation: In the above-given question, given that, the lengths of the meter sticks. a. 1. 6.8 cm. a. 2. 7 cm. b. 1. 5 cm. b. 2. 4.4 cm.

c. List all four lengths from least to greatest.

Answer: The four lengths from least to greatest = 4.4, 5, 6.8, 7cm.

Explanation: In the above-given question, given that, the lengths of the meter sticks. a. 1. 6.8 cm. a. 2. 7 cm. b. 1. 5 cm. b. 2. 4.4 cm. The four lengths from least to greatest = 4.4, 5, 6.8, 7cm.

Answer: a. baseball = 0.15 kg. volleyball= 0.62 kg. basketball = 0.43 kg. soccer ball = 0.25 kg.

Explanation: In the above-given question, given that, the items that are heavier than volleyball are no items. a. baseball = 0.15 kg. volleyball= 0.62 kg. basketball = 0.43 kg. soccer ball = 0.25 kg.

Mass of Sport Balls (kilograms)

c. Complete the statements below using the words heavier than or lighter than in your statements. The soccer ball is _________heavier than______ the baseball. The volleyball is _____heavier than_________ the basketball.

Answer: The soccer ball is heavier than the baseball. The volleyball is heavier than the basketball.

Explanation: In the above-given question, given that, a. baseball = 0.15 kg. volleyball= 0.62 kg. basketball = 0.43 kg. soccer ball = 0.25 kg. The soccer ball is heavier than the baseball. The volleyball is heavier than the basketball.

Compare the values using >, <, or =. a. 0.4 L ___>__ 0.2 L b. 0.62 L _<____ 0.7 L c. 0.2 L ___<___ 0.28 L d. Write the volume of water in each graduated cylinder in order from least to greatest.

Answer: The volume of water in cylinder  A = 0.7 liters. The volume of water in cylinder  B = 0.62 liters. The volume of water in cylinder  C = 0.28 liters. The volume of water in cylinder  D = 0.4 liters. The volume of water in cylinder  E = 0.85 liters. The volume of water in cylinder  F = 0.2 liters.

Explanation: In the above-given question, given that, The volume of water in cylinder  A = 0.7 liters. The volume of water in cylinder  B = 0.62 liters. The volume of water in cylinder  C = 0.28 liters. The volume of water in cylinder  D = 0.4 liters. The volume of water in cylinder  E = 0.85 liters. The volume of water in cylinder  F = 0.2 liters. least to greatest in cylinders. 0.2, 0.28, 0.4, 0.62, 0.7, 0.85.

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