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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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Go Math! 5 Common Core, Grade: 5 Publisher: Houghton Mifflin Harcourt

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Eureka Math Grade 5 Module 2 Lesson 13 Answer Key

Engage ny eureka math 5th grade module 2 lesson 13 answer key, eureka math grade 5 module 2 lesson 13 problem set answer key.

Question 1. Solve. The first one is done for you. a. Convert weeks to days. 8 weeks = 8 × (1 week) = 8 × (7 days) = 56 days

Answer: 8 weeks = 56 days.

Explanation: In the above-given question, given that, 8 weeks = 8 x (1 week). 8 x (7 days). 1 week = 7 days. 8 x 7 = 56. 8 weeks = 56 days.

b. Convert years to days. 4 years = _____4______ × ( ____1_______ year) = ______4_____ × ( ___365________ days) = ____1460_______ days

Answer: 4 years = 1460 days.

Explanation: In the above-given question, given that, 4 years = 4 x (1 year). 4 x (365 days). 1 year = 365 days. 4 x 365 = 1460. 4 years = 1460 days.

c. Convert meters to centimeters. 9.2 m = ____9.2_______ × ( _____1______ m) = ___9.2________ × ( ____100_______ cm) = _____920______ cm

Answer: 9.2 meters = 920 cm.

Explanation: In the above-given question, given that, 9.2 meters = 9.2 x (1 meter). 9.2 x (100 cms). 1 meter = 100 cms. 9.2 x 100 = 920. 9.2 meters = 920 cm.

d. Convert yards to feet. 5.7 yards

Answer: 5.7 yards = 17.1feet.

Explanation: In the above-given question, given that, 5.7 yards = 5.7 x (1 yard). 5.7 x (3 feet). 5.7 yards =  17.1 feet. 5.7 x 7 = 17.1. 5.7 yards = 17.1 feet.

e. Convert kilograms to grams. 6.08 kg

Answer: 6.08 kg =6080 grams.

Explanation: In the above-given question, given that, 6.08 kg = 6.08 x (1 kg). 6.08 x (1000 grams). 1 kg = 1000 grams. 6.08 x 1000 = 6080 grams. 6.08 kg = 6080 grams.

f. Convert pounds to ounces. 12.5 pounds

Answer: 12.5 pounds = 200 ounces.

Explanation: In the above-given question, given that, 12.5 pounds = 12.5 x (1 pound). 12.5 x (16 ounces). 1 pound = 16 ounces. 12.5 x 16 = 200. 12.5 pounds = 200 ounces.

Question 2. After solving, write a statement to express each conversion. The first one is done for you.

a. Convert the number of hours in a day to minutes. 24 hours = 24 × (1 hour) = 24 × (60 minutes) = 1,440 minutes One day has 24 hours, which is the same as 1,440 minutes.

Answer: 24 hours = 1440 minutes.

Explanation: In the above-given question, given that, 24 hours = 24 x (1 hour). 1 x (60 minutes). 1 hour = 60 minutes. 24 x 60 = 1440. 24 hours = 1440 minutes.

b. A small female gorilla weighs 68 kilograms. How much does she weigh in grams?

Answer: 68 kg = 6800 grams.

Explanation: In the above-given question, given that, 68 kg = 68 x (1 kg). 68 x (1000 grams). 1 kg = 1000 grams. 68 x 1000 = 6800 grams. 68 kg = 6800 grams.

c. The height of a man is 1.7 meters. What is his height in centimeters?

Answer: 1.7 meters = 170 cm.

Explanation: In the above-given question, given that, 1.7 meters = 1.7 x (1 meter). 1.7 x (100 cms). 1 meter = 100 cms. 1.7 x 100 = 170. 1.7 meters = 170 cm.

d. The capacity of a syringe is 0.08 liters. Convert this to milliliters.

Answer: 0.08 liters = 80 ml.

Explanation: In the above-given question, given that, 0.08 liters = 0.08 x (1 liter). 0.08 x (1000 ml). 1 liter = 1000 ml. 0.08 x 1000 = 80 ml. 0.08 liters = 80 ml.

e. A coyote weighs 11.3 pounds. Convert the coyote’s weight to ounces.

Answer: 11.3 pounds = 180.8 ounces.

Explanation: In the above-given question, given that, 11.3 pounds = 11.3 x (1 pound). 11.3 x (16 ounces). 1 pound = 16 ounces. 11.3 x 16 = 180.8. 11.3 pounds = 180.8 ounces.

f. An alligator is 2.3 yards long. What is the length of the alligator in inches?

Answer: 2.3 yards = 6.9 feet.

Explanation: In the above-given question, given that, 2.3 yards = 2.3 x (1 yard). 2.3 x (3 feet). 2.3 yards =  6.9 feet. 2.3 x 3 = 6.9. 2.3 yards = 6.9 feet.

Eureka Math Grade 5 Module 2 Lesson 13 Exit Ticket Answer Key

Solve. a. Convert pounds to ounces. (1 pound = 16 ounces) 14 pounds = _____14____ × (1 pound) = ___14______ × ( ____16_____ ounces) = _____224____ ounces

Answer: 14 pounds = 224 ounces.

Explanation: In the above-given question, given that, 14 pounds = 14 x (1 pound). 14 x (16 ounces). 1 pound = 16 ounces. 14 x 16 = 224. 14 pounds = 224 ounces.

b. Convert kilograms to grams. 18.2 kilograms = ____18.2_____ × ( ____1 kg_____ ) = ____18.2_____ × ( _1000________ ) = ___18,200______ grams

Answer: 18.2 kg = 18200 grams.

Explanation: In the above-given question, given that, 18.2 kg = 18200 x (1 kg). 18.2 x (1000 grams). 1 kg = 1000 grams. 18.2 x 1000 = 18200 grams. 18.2 kg = 18200 grams.

Eureka Math Grade 5 Module 2 Lesson 13 Homework Answer Key

Question 1. Solve. The first one is done for you. a. Convert weeks to days. 6 weeks = 6 × (1 week) = 6 × (7 days) = 42 days

Answer: 6 weeks = 42 days.

Explanation: In the above-given question, given that, 6 weeks = 6 x (1 week). 6 x (7 days). 1 week = 7 days. 6 x 7 = 42. 6 weeks = 42 days.

b. Convert years to days. 7 years = ____7_______ × ( ____1_______ year) = ______7_____ × ( ____365_______ days) = _____2555______ days

Answer: 7 years = 2555 days.

Explanation: In the above-given question, given that, 7 years = 7 x (1 year). 7 x (365 days). 1 year = 365 days. 7 x 365 = 2555. 7 years = 2555 days.

c. Convert meters to centimeters. 4.5 m = ____4.5_______ × ( ____1_______ m) = ____4.5_______ × ( ____100_______ cm) = _____450______ cm

Answer: 4.5 meters = 450 cm.

Explanation: In the above-given question, given that, 4.5 meters = 4.5 x (1 meter). 4.5 x (100 cms). 1 meter = 100 cms. 4.5 x 100 = 450. 4.5 meters = 450 cm.

d. Convert pounds to ounces. 12.6 pounds

Answer: 12.6 pounds = 201.6 ounces.

Explanation: In the above-given question, given that, 12.6 pounds = 12.6 x (1 pound). 12.6 x (16 ounces). 1 pound = 16 ounces. 12.6 x 16 = 201.6. 12.6 pounds = 201.6 ounces.

e. Convert kilograms to grams. 3.09 kg

Answer: 3.09 kg = 3090 grams.

Explanation: In the above-given question, given that, 3.09 kg = 3.09 x (1 kg). 3.09 x (1000 grams). 1 kg = 1000 grams. 3.09 x 1000 = 3090 grams. 3.09 kg = 3090 grams.

f. Convert yards to inches. 245 yd

Answer: 245 yards = 8820 inches.

Explanation: In the above-given question, given that, 245 yards = 245 x (1 yard). 245 x (36 inches). 245 yards =  8820. 245 x 36 = 8820. 245 yards = 8820 inches.

Question 2. After solving, write a statement to express each conversion. The first one is done for you. a. Convert the number of hours in a day to minutes. 24 hours = 24 × (1 hour) = 24 × (60 minutes) = 1,440 minutes One day has 24 hours, which is the same as 1,440 minutes.

b. A newborn giraffe weighs about 65 kilograms. How much does it weigh in grams?

Answer: 65 kg = 6500 grams.

Explanation: In the above-given question, given that, 65 kg = 3.09 x (1 kg). 65 x (1000 grams). 1 kg = 1000 grams. 65 x 1000 = 6500 grams. 65 kg = 6500 grams.

c. The average height of a female giraffe is 4.6 meters. What is her height in centimeters?

Answer: 4.6 meters = 460 cm.

Explanation: In the above-given question, given that, 4.6 meters = 4.6 x (1 meter). 4.6 x (100 cms). 1 meter = 100 cms. 4.6 x 100 = 460. 4.6 meters = 460 cm.

d. The capacity of a beaker is 0.1 liter. Convert this to milliliters.

Answer: 0.1 liters = 100 ml.

Explanation: In the above-given question, given that, 0.1 liters = 0.1 x (1 liter). 0.1 x (1000 ml). 1 liter = 1000 ml. 0.1 x 1000 = 100 ml. 0.1 liters = 100 ml.

e. A pig weighs 9.8 pounds. Convert the pig’s weight to ounces.

Answer: 9.8 pounds = 156.8 ounces.

Explanation: In the above-given question, given that, 9.8 pounds = 9.8 x (1 pound). 9.8 x (16 ounces). 1 pound = 16 ounces. 9.8 x 16 = 156.8. 9.8 pounds = 156.8 ounces.

f. A marker is 0.13 meters long. What is the length in millimeters?

Answer: 0.13 meters = 130 mm.

Explanation: In the above-given question, given that, 0.13 meters = 0.13 x (1 meter). 0.13 x (1000 mm). 1 meter = 1000 mm. 0.13 x 1000 = 130. 0.13 meters = 130 mm.

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Home > CC2 > Chapter 3 > Lesson 3.2.5

Lesson 3.1.1, lesson 3.1.2, lesson 3.2.1, lesson 3.2.2, lesson 3.2.3, lesson 3.2.4, lesson 3.2.5, lesson 3.3.1, lesson 3.3.2, lesson 3.3.3.

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