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Lesson 6.1.1, lesson 6.1.2, lesson 6.1.3, lesson 6.1.4, lesson 6.2.1, lesson 6.2.2, lesson 6.2.3, lesson 6.2.4, lesson 6.2.5.

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2.1 The Rectangular Coordinate Systems and Graphs

x -intercept is ( 4 , 0 ) ; ( 4 , 0 ) ; y- intercept is ( 0 , 3 ) . ( 0 , 3 ) .

125 = 5 5 125 = 5 5

( − 5 , 5 2 ) ( − 5 , 5 2 )

2.2 Linear Equations in One Variable

x = −5 x = −5

x = −3 x = −3

x = 10 3 x = 10 3

x = 1 x = 1

x = − 7 17 . x = − 7 17 . Excluded values are x = − 1 2 x = − 1 2 and x = − 1 3 . x = − 1 3 .

x = 1 3 x = 1 3

m = − 2 3 m = − 2 3

y = 4 x −3 y = 4 x −3

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

Horizontal line: y = 2 y = 2

Parallel lines: equations are written in slope-intercept form.

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

2.3 Models and Applications

C = 2.5 x + 3 , 650 C = 2.5 x + 3 , 650

L = 37 L = 37 cm, W = 18 W = 18 cm

2.4 Complex Numbers

−24 = 0 + 2 i 6 −24 = 0 + 2 i 6

( 3 −4 i ) − ( 2 + 5 i ) = 1 −9 i ( 3 −4 i ) − ( 2 + 5 i ) = 1 −9 i

5 2 − i 5 2 − i

18 + i 18 + i

−3 −4 i −3 −4 i

2.5 Quadratic Equations

( x − 6 ) ( x + 1 ) = 0 ; x = 6 , x = − 1 ( x − 6 ) ( x + 1 ) = 0 ; x = 6 , x = − 1

( x −7 ) ( x + 3 ) = 0 , ( x −7 ) ( x + 3 ) = 0 , x = 7 , x = 7 , x = −3. x = −3.

( x + 5 ) ( x −5 ) = 0 , ( x + 5 ) ( x −5 ) = 0 , x = −5 , x = −5 , x = 5. x = 5.

( 3 x + 2 ) ( 4 x + 1 ) = 0 , ( 3 x + 2 ) ( 4 x + 1 ) = 0 , x = − 2 3 , x = − 2 3 , x = − 1 4 x = − 1 4

x = 0 , x = −10 , x = −1 x = 0 , x = −10 , x = −1

x = 4 ± 5 x = 4 ± 5

x = 3 ± 22 x = 3 ± 22

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

2.6 Other Types of Equations

{ −1 } { −1 }

0 , 0 , 1 2 , 1 2 , − 1 2 − 1 2

1 ; 1 ; extraneous solution − 2 9 − 2 9

−2 ; −2 ; extraneous solution −1 −1

−1 , −1 , 3 2 3 2

−3 , 3 , − i , i −3 , 3 , − i , i

2 , 12 2 , 12

−1 , −1 , 0 0 is not a solution.

2.7 Linear Inequalities and Absolute Value Inequalities

[ −3 , 5 ] [ −3 , 5 ]

( − ∞ , −2 ) ∪ [ 3 , ∞ ) ( − ∞ , −2 ) ∪ [ 3 , ∞ )

x < 1 x < 1

x ≥ −5 x ≥ −5

( 2 , ∞ ) ( 2 , ∞ )

[ − 3 14 , ∞ ) [ − 3 14 , ∞ )

6 < x ≤ 9 ​ or ( 6 , 9 ] 6 < x ≤ 9 ​ or ( 6 , 9 ]

( − 1 8 , 1 2 ) ( − 1 8 , 1 2 )

| x −2 | ≤ 3 | x −2 | ≤ 3

k ≤ 1 k ≤ 1 or k ≥ 7 ; k ≥ 7 ; in interval notation, this would be ( − ∞ , 1 ] ∪ [ 7 , ∞ ) . ( − ∞ , 1 ] ∪ [ 7 , ∞ ) .

2.1 Section Exercises

Answers may vary. Yes. It is possible for a point to be on the x -axis or on the y -axis and therefore is considered to NOT be in one of the quadrants.

The y -intercept is the point where the graph crosses the y -axis.

The x- intercept is ( 2 , 0 ) ( 2 , 0 ) and the y -intercept is ( 0 , 6 ) . ( 0 , 6 ) .

The x- intercept is ( 2 , 0 ) ( 2 , 0 ) and the y -intercept is ( 0 , −3 ) . ( 0 , −3 ) .

The x- intercept is ( 3 , 0 ) ( 3 , 0 ) and the y -intercept is ( 0 , 9 8 ) . ( 0 , 9 8 ) .

y = 4 − 2 x y = 4 − 2 x

y = 5 − 2 x 3 y = 5 − 2 x 3

y = 2 x − 4 5 y = 2 x − 4 5

d = 74 d = 74

d = 36 = 6 d = 36 = 6

d ≈ 62.97 d ≈ 62.97

( 3 , − 3 2 ) ( 3 , − 3 2 )

( 2 , −1 ) ( 2 , −1 )

( 0 , 0 ) ( 0 , 0 )

y = 0 y = 0

not collinear

A: ( −3 , 2 ) , B: ( 1 , 3 ) , C: ( 4 , 0 ) A: ( −3 , 2 ) , B: ( 1 , 3 ) , C: ( 4 , 0 )

d = 8.246 d = 8.246

d = 5 d = 5

( −3 , 4 ) ( −3 , 4 )

x = 0          y = −2 x = 0          y = −2

x = 0.75 y = 0 x = 0.75 y = 0

x = − 1.667 y = 0 x = − 1.667 y = 0

15 − 11.2 = 3.8 mi 15 − 11.2 = 3.8 mi shorter

6 .0 42 6 .0 42

Midpoint of each diagonal is the same point ( 2 , –2 ) ( 2 , –2 ) . Note this is a characteristic of rectangles, but not other quadrilaterals.

2.2 Section Exercises

It means they have the same slope.

The exponent of the x x variable is 1. It is called a first-degree equation.

If we insert either value into the equation, they make an expression in the equation undefined (zero in the denominator).

x = 2 x = 2

x = 2 7 x = 2 7

x = 6 x = 6

x = 3 x = 3

x = −14 x = −14

x ≠ −4 ; x ≠ −4 ; x = −3 x = −3

x ≠ 1 ; x ≠ 1 ; when we solve this we get x = 1 , x = 1 , which is excluded, therefore NO solution

x ≠ 0 ; x ≠ 0 ; x = − 5 2 x = − 5 2

y = − 4 5 x + 14 5 y = − 4 5 x + 14 5

y = − 3 4 x + 2 y = − 3 4 x + 2

y = 1 2 x + 5 2 y = 1 2 x + 5 2

y = −3 x − 5 y = −3 x − 5

y = 7 y = 7

y = −4 y = −4

8 x + 5 y = 7 8 x + 5 y = 7

Perpendicular

m = − 9 7 m = − 9 7

m = 3 2 m = 3 2

m 1 = − 1 3 ,   m 2 = 3 ;   Perpendicular . m 1 = − 1 3 ,   m 2 = 3 ;   Perpendicular .

y = 0.245 x − 45.662. y = 0.245 x − 45.662. Answers may vary. y min = −50 , y max = −40 y min = −50 , y max = −40

y = − 2.333 x + 6.667. y = − 2.333 x + 6.667. Answers may vary. y min = −10 ,   y max = 10 y min = −10 ,   y max = 10

y = − A B x + C B y = − A B x + C B

The slope for  ( −1 , 1 ) to  ( 0 , 4 ) is  3. The slope for  ( −1 , 1 ) to  ( 2 , 0 ) is  − 1 3 . The slope for  ( 2 , 0 ) to  ( 3 , 3 ) is  3. The slope for  ( 0 , 4 ) to  ( 3 , 3 ) is  − 1 3 . The slope for  ( −1 , 1 ) to  ( 0 , 4 ) is  3. The slope for  ( −1 , 1 ) to  ( 2 , 0 ) is  − 1 3 . The slope for  ( 2 , 0 ) to  ( 3 , 3 ) is  3. The slope for  ( 0 , 4 ) to  ( 3 , 3 ) is  − 1 3 .

Yes they are perpendicular.

2.3 Section Exercises

Answers may vary. Possible answers: We should define in words what our variable is representing. We should declare the variable. A heading.

2 , 000 − x 2 , 000 − x

v + 10 v + 10

Ann: 23 ; 23 ; Beth: 46 46

20 + 0.05 m 20 + 0.05 m

90 + 40 P 90 + 40 P

50 , 000 − x 50 , 000 − x

She traveled for 2 h at 20 mi/h, or 40 miles.

$5,000 at 8% and $15,000 at 12%

B = 100 + .05 x B = 100 + .05 x

R = 9 R = 9

r = 4 5 r = 4 5 or 0.8

W = P − 2 L 2 = 58 − 2 ( 15 ) 2 = 14 W = P − 2 L 2 = 58 − 2 ( 15 ) 2 = 14

f = p q p + q = 8 ( 13 ) 8 + 13 = 104 21 f = p q p + q = 8 ( 13 ) 8 + 13 = 104 21

m = − 5 4 m = − 5 4

h = 2 A b 1 + b 2 h = 2 A b 1 + b 2

length = 360 ft; width = 160 ft

A = 88 in . 2 A = 88 in . 2

h = V π r 2 h = V π r 2

r = V π h r = V π h

C = 12 π C = 12 π

2.4 Section Exercises

Add the real parts together and the imaginary parts together.

Possible answer: i i times i i equals -1, which is not imaginary.

−8 + 2 i −8 + 2 i

14 + 7 i 14 + 7 i

− 23 29 + 15 29 i − 23 29 + 15 29 i

8 − i 8 − i

−11 + 4 i −11 + 4 i

2 −5 i 2 −5 i

6 + 15 i 6 + 15 i

−16 + 32 i −16 + 32 i

−4 −7 i −4 −7 i

2 − 2 3 i 2 − 2 3 i

4 − 6 i 4 − 6 i

2 5 + 11 5 i 2 5 + 11 5 i

1 + i 3 1 + i 3

( 3 2 + 1 2 i ) 6 = −1 ( 3 2 + 1 2 i ) 6 = −1

5 −5 i 5 −5 i

9 2 − 9 2 i 9 2 − 9 2 i

2.5 Section Exercises

It is a second-degree equation (the highest variable exponent is 2).

We want to take advantage of the zero property of multiplication in the fact that if a ⋅ b = 0 a ⋅ b = 0 then it must follow that each factor separately offers a solution to the product being zero: a = 0 o r b = 0. a = 0 o r b = 0.

One, when no linear term is present (no x term), such as x 2 = 16. x 2 = 16. Two, when the equation is already in the form ( a x + b ) 2 = d . ( a x + b ) 2 = d .

x = 6 , x = 6 , x = 3 x = 3

x = − 5 2 , x = − 5 2 , x = − 1 3 x = − 1 3

x = 5 , x = 5 , x = −5 x = −5

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

x = −2 , 3 x = −2 , 3

x = 0 , x = 0 , x = − 3 7 x = − 3 7

x = −6 , x = −6 , x = 6 x = 6

x = 6 , x = 6 , x = −4 x = −4

x = 1 , x = 1 , x = −2 x = −2

x = −2 , x = −2 , x = 11 x = 11

z = 2 3 , z = 2 3 , z = − 1 2 z = − 1 2

x = 3 ± 17 4 x = 3 ± 17 4

One rational

Two real; rational

x = − 1 ± 17 2 x = − 1 ± 17 2

x = 5 ± 13 6 x = 5 ± 13 6

x = − 1 ± 17 8 x = − 1 ± 17 8

x ≈ 0.131 x ≈ 0.131 and x ≈ 2.535 x ≈ 2.535

x ≈ − 6.7 x ≈ − 6.7 and x ≈ 1.7 x ≈ 1.7

a x 2 + b x + c = 0 x 2 + b a x = − c a x 2 + b a x + b 2 4 a 2 = − c a + b 4 a 2 ( x + b 2 a ) 2 = b 2 − 4 a c 4 a 2 x + b 2 a = ± b 2 − 4 a c 4 a 2 x = − b ± b 2 − 4 a c 2 a a x 2 + b x + c = 0 x 2 + b a x = − c a x 2 + b a x + b 2 4 a 2 = − c a + b 4 a 2 ( x + b 2 a ) 2 = b 2 − 4 a c 4 a 2 x + b 2 a = ± b 2 − 4 a c 4 a 2 x = − b ± b 2 − 4 a c 2 a

x ( x + 10 ) = 119 ; x ( x + 10 ) = 119 ; 7 ft. and 17 ft.

maximum at x = 70 x = 70

The quadratic equation would be ( 100 x −0.5 x 2 ) − ( 60 x + 300 ) = 300. ( 100 x −0.5 x 2 ) − ( 60 x + 300 ) = 300. The two values of x x are 20 and 60.

2.6 Section Exercises

This is not a solution to the radical equation, it is a value obtained from squaring both sides and thus changing the signs of an equation which has caused it not to be a solution in the original equation.

He or she is probably trying to enter negative 9, but taking the square root of −9 −9 is not a real number. The negative sign is in front of this, so your friend should be taking the square root of 9, cubing it, and then putting the negative sign in front, resulting in −27. −27.

A rational exponent is a fraction: the denominator of the fraction is the root or index number and the numerator is the power to which it is raised.

x = 81 x = 81

x = 17 x = 17

x = 8 ,     x = 27 x = 8 ,     x = 27

x = −2 , 1 , −1 x = −2 , 1 , −1

y = 0 ,     3 2 ,     − 3 2 y = 0 ,     3 2 ,     − 3 2

m = 1 , −1 m = 1 , −1

x = 2 5 , ±3 i x = 2 5 , ±3 i

x = 32 x = 32

t = 44 3 t = 44 3

x = −2 x = −2

x = 4 , −4 3 x = 4 , −4 3

x = − 5 4 , 7 4 x = − 5 4 , 7 4

x = 3 , −2 x = 3 , −2

x = 1 , −1 , 3 , -3 x = 1 , −1 , 3 , -3

x = 2 , −2 x = 2 , −2

x = 1 , 5 x = 1 , 5

x ≥ 0 x ≥ 0

x = 4 , 6 , −6 , −8 x = 4 , 6 , −6 , −8

2.7 Section Exercises

When we divide both sides by a negative it changes the sign of both sides so the sense of the inequality sign changes.

( − ∞ , ∞ ) ( − ∞ , ∞ )

We start by finding the x -intercept, or where the function = 0. Once we have that point, which is ( 3 , 0 ) , ( 3 , 0 ) , we graph to the right the straight line graph y = x −3 , y = x −3 , and then when we draw it to the left we plot positive y values, taking the absolute value of them.

( − ∞ , 3 4 ] ( − ∞ , 3 4 ]

[ − 13 2 , ∞ ) [ − 13 2 , ∞ )

( − ∞ , 3 ) ( − ∞ , 3 )

( − ∞ , − 37 3 ] ( − ∞ , − 37 3 ]

All real numbers ( − ∞ , ∞ ) ( − ∞ , ∞ )

( − ∞ , − 10 3 ) ∪ ( 4 , ∞ ) ( − ∞ , − 10 3 ) ∪ ( 4 , ∞ )

( − ∞ , −4 ] ∪ [ 8 , + ∞ ) ( − ∞ , −4 ] ∪ [ 8 , + ∞ )

No solution

( −5 , 11 ) ( −5 , 11 )

[ 6 , 12 ] [ 6 , 12 ]

[ −10 , 12 ] [ −10 , 12 ]

x > − 6 and x > − 2 Take the intersection of two sets . x > − 2 ,   ( − 2 , + ∞ ) x > − 6 and x > − 2 Take the intersection of two sets . x > − 2 ,   ( − 2 , + ∞ )

x < − 3   or   x ≥ 1 Take the union of the two sets . ( − ∞ , − 3 ) ∪ ​ ​ [ 1 , ∞ ) x < − 3   or   x ≥ 1 Take the union of the two sets . ( − ∞ , − 3 ) ∪ ​ ​ [ 1 , ∞ )

( − ∞ , −1 ) ∪ ( 3 , ∞ ) ( − ∞ , −1 ) ∪ ( 3 , ∞ )

[ −11 , −3 ] [ −11 , −3 ]

It is never less than zero. No solution.

Where the blue line is above the orange line; point of intersection is x = − 3. x = − 3.

( − ∞ , −3 ) ( − ∞ , −3 )

Where the blue line is above the orange line; always. All real numbers.

( − ∞ , − ∞ ) ( − ∞ , − ∞ )

( −1 , 3 ) ( −1 , 3 )

( − ∞ , 4 ) ( − ∞ , 4 )

{ x | x < 6 } { x | x < 6 }

{ x | −3 ≤ x < 5 } { x | −3 ≤ x < 5 }

( −2 , 1 ] ( −2 , 1 ]

( − ∞ , 4 ] ( − ∞ , 4 ]

Where the blue is below the orange; always. All real numbers. ( − ∞ , + ∞ ) . ( − ∞ , + ∞ ) .

Where the blue is below the orange; ( 1 , 7 ) . ( 1 , 7 ) .

x = 2 , − 4 5 x = 2 , − 4 5

( −7 , 5 ] ( −7 , 5 ]

80 ≤ T ≤ 120 1 , 600 ≤ 20 T ≤ 2 , 400 80 ≤ T ≤ 120 1 , 600 ≤ 20 T ≤ 2 , 400

[ 1 , 600 , 2 , 400 ] [ 1 , 600 , 2 , 400 ]

Review Exercises

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

y = 5 3 x + 4 y = 5 3 x + 4

72 = 6 2 72 = 6 2

620.097 620.097

midpoint is ( 2 , 23 2 ) ( 2 , 23 2 )

x = 4 x = 4

x = 12 7 x = 12 7

y = 1 6 x + 4 3 y = 1 6 x + 4 3

y = 2 3 x + 6 y = 2 3 x + 6

females 17, males 56

x = − 3 4 ± i 47 4 x = − 3 4 ± i 47 4

horizontal component −2 ; −2 ; vertical component −1 −1

7 + 11 i 7 + 11 i

−16 − 30 i −16 − 30 i

−4 − i 10 −4 − i 10

x = 7 − 3 i x = 7 − 3 i

x = −1 , −5 x = −1 , −5

x = 0 , 9 7 x = 0 , 9 7

x = 10 , −2 x = 10 , −2

x = − 1 ± 5 4 x = − 1 ± 5 4

x = 2 5 , − 1 3 x = 2 5 , − 1 3

x = 5 ± 2 7 x = 5 ± 2 7

x = 0 , 256 x = 0 , 256

x = 0 , ± 2 x = 0 , ± 2

x = 11 2 , −17 2 x = 11 2 , −17 2

[ − 10 3 , 2 ] [ − 10 3 , 2 ]

( − 4 3 , 1 5 ) ( − 4 3 , 1 5 )

Where the blue is below the orange line; point of intersection is x = 3.5. x = 3.5.

( 3.5 , ∞ ) ( 3.5 , ∞ )

Practice Test

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

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

( − ∞ , 9 ] ( − ∞ , 9 ]

x = −15 x = −15

x ≠ −4 , 2 ; x ≠ −4 , 2 ; x = − 5 2 , 1 x = − 5 2 , 1

x = 3 ± 3 2 x = 3 ± 3 2

( −4 , 1 ) ( −4 , 1 )

y = −5 9 x − 2 9 y = −5 9 x − 2 9

y = 5 2 x − 4 y = 5 2 x − 4

5 13 − 14 13 i 5 13 − 14 13 i

x = 2 , − 4 3 x = 2 , − 4 3

x = 1 2 ± 2 2 x = 1 2 ± 2 2

x = 1 2 , 2 , −2 x = 1 2 , 2 , −2

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• Authors: Jay Abramson
• Publisher/website: OpenStax
• Book title: College Algebra
• Publication date: Feb 13, 2015
• Location: Houston, Texas
• Book URL: https://openstax.org/books/college-algebra/pages/1-introduction-to-prerequisites
• Section URL: https://openstax.org/books/college-algebra/pages/chapter-2

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Eureka Math Grade 2 Module 2 Lesson 7 Answer Key

Engage ny eureka math 2nd grade module 2 lesson 7 answer key, eureka math grade 2 module 2 lesson 7 sprint answer key.

Question 1. 3 – 1 = Answer: 3 – 1 = 2,

Explanation: Subtracting 1 from 3 we will get 2  .

Question 2. 13 – 1 = Answer: 13 – 1 = 12,

Explanation: Subtracting 1 from 13 we will get 12  .

Question 3. 23 – 1 = 22 Answer: 23 – 1 = 22,

Explanation: Subtracting 1 from 23 we will get 22  .

Question 4. 53 – 1 = 52 Answer: 53 – 1 = 52,

Explanation: Subtracting 1 from 53 we will get 52  .

Question 5. 4 – 2 = 2 Answer: 4 – 2 = 2,

Explanation: Subtracting 2 from 4 we will get 2  .

Question 6. 14 – 2 = 12 Answer: 14 –  2 = 12,

Explanation: Subtracting 2 from 14 we will get 12  .

Question 7. 24 – 2 = 22, Answer: 24 – 2 = 22,

Explanation: Subtracting 2 from 24 we will get 22  .

Question 8. 64 – 2 = 62, Answer: 64 – 2 = 62,

Explanation: Subtracting 2 from 64 we will get 62 .

Question 9. 4 – 3 = Answer: 4 – 3 = 1,

Explanation: Subtracting 3 from 4 we will get 1 . 

Question 10. 14 – 3 = Answer: 14 – 3 = 11,

Explanation: Subtracting 3 from 14 we will get 11.

Question 11. 24 – 3 = Answer: 24 – 3 = 21,

Explanation: Subtracting 3 from 24 we will get 21.

Question 12. 74 – 3 = Answer: 74 – 3 = 71,

Explanation: Subtracting 3 from 74 we will get 71.

Question 13. 6 – 4 = Answer: 6 – 4 = 2,

Explanation: Subtracting 4 from 6 we will get 2.

Question 14. 16 – 4 = Answer: 16 – 4 = 12,

Explanation: Subtracting 4 from 16 we will get 12.

Question 15. 26 – 4 = Answer: 26 – 4 = 22,

Explanation: Subtracting 4 from 26 we will get 22.

Question 16. 96 – 4 = Answer: 96 – 4 = 92,

Explanation: Subtracting 4 from 96 we will get 92.

Question 17. 7 – 5 = Answer: 7 – 5 = 2,

Explanation: Subtracting 5 from 7 we will get 2.

Question 18. 17 – 5 = Answer: 17 – 5 = 12,

Explanation: Subtracting 5 from 17 we will get 12.

Question 19. 27 – 5 = Answer: 27 – 5 = 22,

Explanation: Subtracting 5 from 27 we will get 22.

Question 20. 47 – 5 = Answer: 47 – 5 = 42,

Explanation: Subtracting 5 from 47 we will get 42.

Question 21. 43 – 3 = Answer: 43 – 3 = 40,

Explanation: Subtracting 3 from 43 we will get 40.

Question 22. 87 – 7 = Answer: 87 – 7 = 80,

Explaination: Subtracting 7 from 87 we will get 80.

Question 23. 8 – 7 = Answer: 8 – 7 = 1,

Explanation: Subtracting 7 from 8 we will get 1.

Question 24. 18 – 7 = Answer: 18 – 7 = 11,

Explanation: Subtracting 7 from 18 we will get 11.

Question 25. 58 – 7 = Answer: 58 – 7 = 51,

Explanation: Subtracting 7 from 58 we will get 51

Question 26. 62 – 2 = Answer: 62 – 2 = 60,

Explanation: Subtracting 2 from 62 we will get 60

Question 27. 9 – 8 = Answer: 9 – 8 = 1,

Explanation: Subtracting 8 from 9 we will get 1.

Question 28. 19 – 8 = Answer: 19 – 8 = 11,

Explanation: Subtracting 8 from 19 we will get 11.

Question 29. 29 – 8 = Answer: 29 – 8 = 21,

Explanation: Subtracting 8 from 29 we will get 21.

Question 30. 69 – 8 = Answer: 69 – 8 = 61,

Explanation: Subtracting 8 from 69 we will get 61.

Question 31. 7 – 3 = Answer: 7 – 3 = 4,

Explanation: Subtracting 3 from 7 we will get 4.

Question 32. 17 – 3 = Answer: 17 – 3 = 14,

Explanation: Subtracting 3 from 17 we will get 14.

Question 33. 77 – 3 = Answer: 77 – 3 = 74,

Explanation: Subtracting 3 from 77 we will get 74.

Question 34. 59 – 9 = Answer: 59 – 9 = 50,

Explanation: Subtracting 9 from 59 we will get 50.

Question 35. 9 – 7 = Answer: 9 – 7 = 2,

Explanation: Subtracting 7 from 9 we will get 2.

Question 36. 19 – 7 = Answer: 19 – 7 = 12,

Explanation: Subtracting 7 from 19 we will get 12.

Question 37. 89 – 7 = Answer: 89  – 7 = 82,

Explanation: Subtracting 7 from 89 we will get 82.

Question 38. 99 – 5 = Answer: 99 – 5 = 94,

Explanation: Subtracting 5 from 99 we will get 94.

Question 39. 78 – 6 = Answer: 78 – 6 = 72,

Explanation: Subtracting 6 from 78 we will get 72.

Question 40. 58 – 5 = Answer: 58 – 5 = 53,

Explanation: Subtracting 5 from 58 we will get 53.

Question 41. 39 – 7 = Answer: 39 – 7 = 32,

Explanation: Subtracting 7 from 39 we will get 32

Question 42. 28 – 6 = Answer: 28 – 6 = 22,

Explanation: Subtracting 6 from 28 we will get 22

Question 43. 49 – 4 = Answer: 49 – 4 = 45,

Explanation: Subtracting 4 from 49 we will get 45.

Question 44. 67 – 4 = Answer: 67 – 4 = 63,

Explanation: Subtracting 4 from 67 we will get 63.

Question 1. 2 – 1 = 1 Answer: 2 – 1 = 1,

Explanation: Subtracting 1 from 2 we will get 1.

Question 2. 12 – 1 = 11 Answer: 12 – 1 = 11,

Explanation: Subtracting 1 from 12 we will get 11.

Question 3. 22 – 1 = Answer: 22 – 1 = 21,

Explanation: Subtracting 1 from 22 we will get 21.

Question 4. 52 – 1 = 51 Answer: 52 – 1 = 51,

Explanation: Subtracting 1 from 52 we will get 51.

Question 5. 5 – 2 = 3 Answer: 5 – 2 = 3,

Explanation: Subtracting 2 from 5 we will get 3.

Question 6. 15 – 2 = 13 Answer: 15 – 2 = 13,

Explanation: Subtracting 2 from 15 we will get 13.

Question 7. 25 – 2 = 13 Answer: 25 – 2 = 23,

Explanation: Subtracting 2 from 25 we will get 23.

Question 8. 65 – 2 = 63 Answer: 65 – 2 = 63,

Explanation: Subtracting 2 from 65 we will get 63.

Question 9. 4 – 3 = 1 Answer: 4 – 3 = 1,

Explanation: Subtracting 3 from 4 we will get 1.

Question 10. 14 – 3 = 11 Answer: 14 – 3 = 11,

Question 11. 24 – 3 = 21 Answer: 24 – 3 = 21,

Question 12. 84 – 3 = 81 Answer: 84 – 3 = 81,

Explanation: Subtracting 3 from 84 we will get 81.

Question 13. 7 – 4 = 3 Answer: 7 – 4 = 3,

Explanation: Subtracting 4 from 7 we will get 3.

Question 14. 17 – 4 = 13 Answer: 17 – 4 = 13,

Explanation: Subtracting 4 from 17 we will get 13.

Question 15. 27 – 4 = 23 Answer: 27 – 4 = 23,

Explanation: Subtracting 4 from 27 we will get 23.

Question 16. 97 – 4 = 93 Answer: 97 – 4 = 93,

Explanation: Subtracting 4 from 97 we will get 93.

Question 17. 6 – 5 = 1 Answer: 6 – 5 = 1,

Explanation: Subtracting 5 from 6 we will get 1.

Question 18. 16 – 5 = 11 Answer: 16 – 5 = 11,

Explanation: Subtracting 5 from 16 we will get 11.

Question 19. 26 – 5 = 21 Answer: 26 – 5 = 21,

Explanation: Subtracting 5 from 26 we will get 21.

Question 20. 46 – 5 = 41 Answer: 46 – 5 = 41,

Explanation: Subtracting 5 from 46 we will get 41.

Question 21. 23 – 3 = 20 Answer: 23 – 3 = 20,

Explanation: Subtracting 3 from 23 we will get 20.

Question 22. 67 – 7 = 60 Answer: 67 – 7 = 60,

Explanation: Subtracting 7 from 67 we will get 60.

Question 23. 8 – 7 = 1 Answer: 8 – 7 = 1,

Question 24. 18 – 7 = 11 Answer: 18 –  7 = 11,

Explanation: Subtracting 18 from 7 we will get 11.

Question 25. 68 – 7 = 61 Answer: 68 – 7 = 61,

Explanation: Subtracting 7 from 68 we will get 61.

Question 26. 32 – 2 = 30 Answer: 32 – 2 = 30,

Explanation: Subtracting 2 from 32 we will get 30.

Question 27. 9 – 8 = 1 Answer: 9 – 8 = 1,

Explanation: Subtracting 9 from 8 we will get 1.

Question 28. 19 – 8 = 11 Answer: 19 – 8 = 11,

Explanation: Subtracting 19 from 8 we will get 11.

Question 29. 29 – 8 = 21 Answer: 29 – 8 = 21,

Question 30. 79 – 8 = Answer: 79 – 8 = 71,

Explanation: Subtracting 8 from 79 we will get 71.

Question 31. 8 – 4 = 4 Answer: 8 – 4 = 4,

Explanation: Subtracting 4 from 8 we will get 4.

Question 32. 18 – 4 = 14 Answer: 18 – 4 = 14,

Explanation: Subtracting 4 from 18 we will get 14.

Question 33. 78 – 4 = 74 Answer: 78 – 4 = 74,

Explanation: Subtracting 4 from 78 we will get 74.

Question 34. 89 – 9 = 80 Answer: 89 – 9 = 80,

Explanation: Subtracting 9 from 89 we will get 80.

Question 36. 19 – 7 = 12 Answer: 19 – 7 = 12,

Question 37. 79 – 7 = 72 Answer: 79 – 7 = 72,

Explanation: Subtracting 7 from 79 we will get 72.

Question 38. 89 – 5 = 84 Answer: 89 – 5 = 84,

Explanation: Subtracting 5 from 89 we will get 84.

Question 39. 68 – 6 = 62 Answer: 68 – 6 = 62,

Explanation: Subtracting 6 from 68 we will get 62.

Question 40. 48 – 5 = 43 Answer: 48 – 5 = 43,

Explanation: Subtracting 5 from 48 we will get 43.

Question 41. 29 – 7 = 22 Answer: 29 – 7 = 22,

Explanation: Subtracting 7 from 29 we will get 22.

Question 42. 38 – 6 = 32 Answer: 38 – 6 = 32,

Explanation: Subtracting 6 from 32 we will get 32.

Question 43. 59 – 4 = 55 Answer: 59 – 4 = 55,

Explanation: Subtracting 4 from 59 we will get 55.

Question 44. 77 – 4 = 73 Answer: 77 – 4 = 73,

Explanation: Subtracting 4 from 77 we will get 73.

Eureka Math Grade 2 Module 2 Lesson 7 Problem Set Answer Key

Measure each set of lines with one small paper clip, using mark and move forward. Measure each set of lines in centimeters using a ruler.

Question 1. Line A ____________________ Line B ____________________ a. Line A ___3__ paper   clips ___9__ cm Answer: 3 paper clips, 9 cm,

Explanation: Line A has 3 paper clips and measures 9 cm.

b. Line B __2___ paper                 clips __6_ cm Answer: 2 paper clips, 6 cm,

Explanation: Line B has 2 paper clips and measures 6 cm.

c. Line B is about __1___ paper clips shorter than Line A. Answer: Line B is about 1 paper clips shorter than Line A,

Explanation: As Line A is 3 paper clips, Line B is 2 paper clips, So Line B is about 3 – 2 = 1 paper clips shorter than Line A.

d. Line A is about __3__ cm longer than Line B. Answer: Line A is about 3 cm longer than Line B,

Explanation: As Line A is 9 cm and Line B is 6 cm, So Line A is about 9- 6 = 3 cm longer than Line B.

Question 2. ____________________ Line L ______________ Line M a. Line L __3___ paper  clips __9___ cm Answer: 3 paper clips, 9 cm,

Explanation: Line L has 3 paper clips and measures 9 cm.

b. Line M __1__ paper  clips __3___ cm Answer: 1 paper clips, 3 cm,

Explanation: Line M has 1 paper clip and measures 3 cm.

c. Line L is about __2___ paper clips longer than Line M. Answer: Line L is about 2 paper clips longer than Line M,

Explanation: As Line L is 3 paper clips and Line M is 1 paper clips, Line L is about 3 – 1 = 2 paper clips longer than Line M.

d. Line M doubled is about __3___ cm shorter than Line L. Answer: Line M doubled is about 3 cm shorter than Line L,

Explanation: As Line M is 3 cm and Line L is 9 cm and Line M is doubled so it is 6 cm now Line M doubled is about 9 – 6 = 3 cm shorter than Line L.

a. Line C                                 Line D __2___ paper clips                 ___5__ paper clips Answer: Line C is 2 paper clips, Line D is 5 paper clips,

Explanation: As shown Line C is 2 paper clips and Line D is 5 paper clips.

b. Line D is about __9___ cm longer than Line C. Answer: Line D is about 9 cm longer than Line C,

Explanation: As Line C is 6 cm and Line D is 15 cm, So Line D is about 15 – 6 = 9 cm longer than Line C.

c. Line C is about __3___ paper clips shorter than Line D. Answer: Line C is about 3 paper clips shorter than Line D,

Explanation: As Line C is 2 paper clips and Line D is 5 paper clips, So Line C is about 3 paper clips shorter than Line D.

d. Lines C and D together are about __7__ paper clips long. Answer: Lines C and D together are about 7 paper clips long,

Explanation: As Line C is 2 paper clips and Line D is 5 paper clips, Lines C and D together are about 2 + 5 = 7 paper clips long.

e. Lines C and D together are about __21___ centimeters long. Answer: Lines C and D together are about 21 centimeters long,

Explanation: As Line C is 6 cm and Line D is 15 cm, So Lines C and D together are about 21 centimeters long.

Explanation: Christiana is wrong because even though line f is only 6 quaters long size of quater is bigger than pennies. So Christiana is wrong.

Eureka Math Grade 2 Module 2 Lesson 7 Exit Ticket Answer Key

Measure the lines with small paper clips and then with a centimeter ruler. Then, answer the questions below.

Line 1 ______________________________ Line 2 ______________________________ Line 3 ______________________________

a. Line 1 ___5__ paper clips __15___ cm Answer: Line 1 is 5 paper clips 15 cm,

Explanation: As shown in the picture Line 1 is 5 paper clips 15 cm long.

b. Line 2 __3__ paper clips __9___ cm Answer: Line 2 is 3 paper clips 9 cm,

Explanation: As shown in the picture Line 2 is 3 paper clips 9 cm long.

c. Line 3 __4__ paper clips __12___ cm Answer: Line 3 is 4 paper clips 12 cm,

Explanation: As shown in the picture Line 3 is 4 paper clips 12 cm long.

Explain why each measurement required more centimeters than paper clips. _____________________________________________________________ _____________________________________________________________ _____________________________________________________________ Answer: Paper clips are already 3 cm long,

Explanation: Each measurement requires more centimeters than paper clips because paper clips are already 3 cm long.

Eureka Math Grade 2 Module 2 Lesson 7 Homework Answer Key

Question 1. _________________________ Line Z a. Line Z ___4__ paper clips __12___ cm Answer: Line Z is 4 paper clips 12 cm,

Explanation: As shown above Line Z is 4 paper clips and 12 cm long.

b. Line Z doubled would measure about __8__ paper clips or about __24___ cm long. Answer: Line Z doubled would measure about 8 paper clips or about 24 cm long,

Explanation: If Line Z  is doubled then it would measure about 4 + 4 = 8 paper clips and about 12 + 12 = 24 cm long.

Question 2. _________________________ Line A _______________ Line B a. Line A __5___ paper clips __15___ cm Answer: Line A is 5 paper clips, 15 cm,

Explanation: As shown above Line A has 5 paper clips and 15 cm long.

b. Line B __3___ paper clips __9___ cm Answer: Line B is 3 paper clips, 9 cm,

Explanation: As shown above Line B has 3 paper clips and 9 cm long.

c. Line A is about ___2__ paper clips longer than Line B. Answer: Line A is about 2 paper clips longer than Line B,

Explanation: Line A is 5 paper clips and Line B is 3 paper clips, Line A is about 5 – 3 = 2 paper clips longer than Line B.

d. Line B doubled is about __3___ cm shorter than Line A. Answer: Line B doubled is about 3 cm shorter than Line A,

Explanation: As Line A is 15 cm and Line B is 9 cm, Line B doubled is about 18 – 15 = 3 cm shorter than Line A.

Explanation: As shown above Line F is 3 paper clips and Line G is 4 paper clips.

b. Line G is about __3___ cm longer than Line F. Answer: Line G is about 3 cm longer than Line F,

Explanation: As Line F is 9 cm and Line G is 12 cm, So Line G is about 12 – 9 = 3 cm longer than Line F.

c. Line F is about __1___ paper clips shorter than Line G. Answer: Line F is about 1 paper clips shorter than Line G,

Explanation: As Line F is 3 paper clips and Line G is 4 paper clips, So Line F is about 4 – 3 = 1 paper clips shorter than Line G.

d. Lines F and G are about __7___ paper clips long. Answer: Lines F and G are about 7 paper clips long,

Explanation: As Line F is 3 paper clips and Line G is 4 paper clips, Lines F and G are about 3 + 4 = 7 paper clips long.

e. Lines F and G are about __21___ centimeters long. Answer: Lines F and G are about 21 centimeters long,

Explanation: As Line F is 9 cm and Line G is 12 cm, Lines F and G are about 9 + 12 = 21 centimeters long.

Explanation: As shown in the picture if we see there are about 4 larger paper clips did Jordan used.

b. About how many small paper clips did his friend use? __6___ small paper clips Answer: About 6 small paper clips did his friend used,

Explanation: As shown in the picture if we see there are about 6 small paper clips did Jordan’s friend used.

c. Why did Jordan’s friend need more paper clips to measure the same line as Jordan? ________________________________________________________ ________________________________________________________ Answer: Jordan’s friend need more paper clips due to smaller size,

Explanation: Jordan’s friend need more paper clips to measure the same line as Jordan because Jordan’s friend has used smaller clips than Jordan thats why Jordan’s freind need more clips and Jordan has used larger clips to measure the same.

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