lesson 14 homework 4.7 answer key

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

• Authors: Lynn Marecek, MaryAnne Anthony-Smith
• Publisher/website: OpenStax
• Book title: Elementary Algebra
• Publication date: Feb 22, 2017
• Location: Houston, Texas
• Book URL: https://openstax.org/books/elementary-algebra/pages/1-introduction
• Section URL: https://openstax.org/books/elementary-algebra/pages/chapter-4

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Eureka Math Grade 5 Module 4 Lesson 7 Answer Key

Engage ny eureka math 5th grade module 4 lesson 7 answer key, eureka math grade 5 module 4 lesson 7 problem set answer key.

Solve using a tape diagram. a. \(\frac{1}{3}\) of 18 Answer: 6

b. \(\frac{1}{3}\) of 36 Answer: 11

c. \(\frac{3}{4}\) × 24 Answer: 18

d. \(\frac{3}{8}\) × 24 Answer: 9

e. \(\frac{4}{5}\) × 25 Answer: 20

f. \(\frac{1}{7}\) × 140 Answer: 20

g. \(\frac{1}{4}\) × 9 Answer: 2 1/4

h. \(\frac{2}{5}\) × 12

i. \(\frac{2}{3}\) of a number is 10. What’s the number?

j. \(\frac{3}{4}\) of a number is 24. What’s the number?

Question 2. Solve using tape diagrams. a. There are 48 students going on a field trip. One-fourth are girls. How many boys are going on the trip? Answer: 36 boys are going on the field trip.

Explanation: As 48 students are going on a field trip in this \(\frac{1}{4}\) are girls. Hence 36 boys are going on the field trip. \(\frac{1}{4}\) × 48 = \(\frac{48}{4}\) = 12 12 × 3 = 36

Explanation: The smallest angle given is \(\frac{3}{8}\) and the largest angle is 160°. 160 × \(\frac{3}{8}\) = \(\frac{480}{8}\) = 60 160 + 60 = 220 360-220= 140 Hence the value of angle a is 140°

c. Abbie spent \(\frac{5}{8}\) of her money and saved the rest. If she spent $45, how much money did she have at first? Answer: Abbie had $72.

Explanation: 45 ÷ \(\frac{5}{8}\) = 45 × \(\frac{8}{5}\) = \(\frac{360}{5}\) =72

d. Mrs. Harrison used 16 ounces of dark chocolate while baking. She used \(\frac{2}{5}\) of the chocolate to make some frosting and used the rest to make brownies. How much more chocolate did Mrs. Harrison use in the brownies than in the frosting? Answer: Mrs. Harrison use 3 × \(\frac{1}{5}\) chocolate for the brownie

Explanation: Harrison used 16 ounces of dark chocolate. She used \(\frac{2}{5}\) of the chocolate to make some frosting and the remaining to make brownies. 16 × \(\frac{1}{5}\) = \(\frac{16}{5}\) = 3 × \(\frac{1}{5}\) Hence, Mrs. Harrison use 3 × \(\frac{1}{5}\) chocolate for the brownie.

Eureka Math Grade 5 Module 4 Lesson 7 Exit Ticket Answer Key

Solve using a tape diagram.

a. \(\frac{3}{5}\) of 30

b. \(\frac{3}{5}\) of a number is 30. What’s the number?

c. Mrs. Johnson baked 2 dozen cookies. Two-thirds of the cookies were oatmeal. How many oatmeal cookies did Mrs. Johnson bake?

Eureka Math Grade 5 Module 4 Lesson 7 Homework Answer Key

Question 1. Solve using a tape diagram. a. \(\frac{1}{4}\) of 24

b. \(\frac{1}{4}\) of 48

c. \(\frac{2}{3}\) × 18

d. \(\frac{2}{6}\) × 18

e. \(\frac{3}{7}\) × 49

f. \(\frac{3}{10}\) × 120

g. \(\frac{1}{3}\) × 31

h. \(\frac{2}{5}\) × 20

i. \(\frac{1}{4}\) × 25

j. \(\frac{3}{4}\) × 25

k. \(\frac{3}{4}\) of a number is 27. What’s the number?

i. \(\frac{2}{5}\) of a number is 14. What’s the number?

Question 2. Solve using tape diagrams. a. A skating rink sold 66 tickets. Of these, \(\frac{2}{3}\) were children’s tickets, and the rest were adult tickets. What total number of adult tickets were sold?

c. Annabel and Eric made 17 ounces of pizza dough. They used \(\frac{5}{8}\) of the dough to make a pizza and used the rest to make calzones. What is the difference between the amount of dough they used to make pizza and the amount of dough they used to make calzones?

d. The New York Rangers hockey team won \(\frac{3}{4}\) of their games last season. If they lost 21 games, how many games did they play in the entire season?

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