HW  #71               Name:    _______________________________  Like  Terms    Directions:  Each  of  the  following  graphs  is  not  proportional.    Explain  how  you  can  tell.  1.    

                                                                                         

2.                                                                                                                                                

3.      

                                                                         

4.      

                                                                       

Chapter 4: Proportions and Expressions 399

4-37. Which of the tables below shows a proportional relationship between x and y? How can you tell? [ The table in part (a). The table in part (a) shows a multiplicative relationship between quantities; the table in part (b) does not. ]

a. b. 4-38. The following graphs show examples of relationships that are not proportional.

For each graph, explain what makes the relationship different from the proportional relationships you have studied.

a. b.

[ Does not start at origin. ]

c. d.

[ Does not start at origin. ] [ Not a straight line. ]

Jojo’s Age (yrs)

Bo

bo’s

Ag

e (y

rs)

Time (min.)

Am

oun

t o

f W

ater

(g

al.)

Side Length (in.)

Are

a (s

q in

.)

Hours After Midnight

Tem

per

atur

e (º

F)

6 12 18 24

x y 1 2 2 4 3 6 4 8

x y 1 2 2 3 3 4 4 5

[ Not a straight line and does not start at origin. ]

Chapter 4: Proportions and Expressions 399

4-37. Which of the tables below shows a proportional relationship between x and y? How can you tell? [ The table in part (a). The table in part (a) shows a multiplicative relationship between quantities; the table in part (b) does not. ]

a. b. 4-38. The following graphs show examples of relationships that are not proportional.

For each graph, explain what makes the relationship different from the proportional relationships you have studied.

a. b.

[ Does not start at origin. ]

c. d.

[ Does not start at origin. ] [ Not a straight line. ]

Jojo’s Age (yrs)

Bo

bo’s

Ag

e (y

rs)

Time (min.)

Am

oun

t o

f W

ater

(g

al.)

Side Length (in.)

Are

a (s

q in

.)

Hours After Midnight

Tem

per

atur

e (º

F)

6 12 18 24

x y 1 2 2 4 3 6 4 8

x y 1 2 2 3 3 4 4 5

[ Not a straight line and does not start at origin. ]

Chapter 4: Proportions and Expressions 399

4-37. Which of the tables below shows a proportional relationship between x and y? How can you tell? [ The table in part (a). The table in part (a) shows a multiplicative relationship between quantities; the table in part (b) does not. ]

a. b. 4-38. The following graphs show examples of relationships that are not proportional.

For each graph, explain what makes the relationship different from the proportional relationships you have studied.

a. b.

[ Does not start at origin. ]

c. d.

[ Does not start at origin. ] [ Not a straight line. ]

Jojo’s Age (yrs)

Bo

bo’s

Ag

e (y

rs)

Time (min.)

Am

oun

t o

f W

ater

(g

al.)

Side Length (in.)

Are

a (s

q in

.)

Hours After Midnight

Tem

per

atur

e (º

F)

6 12 18 24

x y 1 2 2 4 3 6 4 8

x y 1 2 2 3 3 4 4 5

[ Not a straight line and does not start at origin. ]

Chapter 4: Proportions and Expressions 399

4-37. Which of the tables below shows a proportional relationship between x and y? How can you tell? [ The table in part (a). The table in part (a) shows a multiplicative relationship between quantities; the table in part (b) does not. ]

a. b. 4-38. The following graphs show examples of relationships that are not proportional.

For each graph, explain what makes the relationship different from the proportional relationships you have studied.

a. b.

[ Does not start at origin. ]

c. d.

[ Does not start at origin. ] [ Not a straight line. ]

Jojo’s Age (yrs)

Bo

bo’s

Ag

e (y

rs)

Time (min.)

Am

oun

t o

f W

ater

(g

al.)

Side Length (in.)

Are

a (s

q in

.)

Hours After Midnight

Tem

per

atur

e (º

F)

6 12 18 24

x y 1 2 2 4 3 6 4 8

x y 1 2 2 3 3 4 4 5

[ Not a straight line and does not start at origin. ]

     Directions:  Find  the  area  of  each  set  of  tiles.    5.               6.                                                  Directions:    What  is  the  length  of  the  marked  portion  of  each  segment?        7.             8.         9.                      Directions:    Complete  the  table  with  equivalent  fractions,  decimals,  and  percentages.    

Reduced  Fraction   Decimal   Percent  

10.      

0.23  

 

11.    1720  

   

 

424 Core Connections, Course 2

Algebra tiles help you represent unknown quantities in a concrete way. For example, in contrast to a 1� 5 tile that has a length of 5 units, like the one shown at right, an x-tile has an unknown length. Its length can be represented with a symbol or letter (like x) that represents a number, called a variable. Because its length is not considered fixed, the x-tile could be 6 units, or 5 units, or 0.37 units long.

Algebra tiles can be used to build algebraic expressions. The three main algebra tiles are shown at right. The large square has a side of length x units. Its area is x2 square units, so it is referred to as an x2 -tile.

The rectangle has length of x units and width of 1 unit. Its area is x square units, so it is called an x-tile.

The small square has a side of length 1 unit. Its area is 1 square unit, so is called a one or unit tile. Note that the unit tile in this course will not be labeled with its area.

4-75. Sketch the shape made with algebra tiles

at right on your paper. Then answer parts (a) and (b) below.

a. Find the area and perimeter of the shape. [ 2x2 + 3x square units, 6x + 6units ]

b. If the algebra tiles were rearranged into a different shape, how would the area change? [ The area would not change. ]

x

Can be any length 1 unit

ETHODS AND MEANINGS

MA

TH N

OTE

S Naming Algebra Tiles

x

x x

1

1

x2 x

1

5 units

1 unit

xx2

x2 x x

Chapter 4: Proportions and Expressions 423

4-74. The expressions that you have written to represent area and perimeter are made up of terms that are separated by addition and subtraction.

a. Write an expression for the perimeter of the figure at right. [ Answers vary: P = x + x +1 + x +1 +1 +1 + x +1 +1 ]

b. How many x lengths are represented in the expression in part (a)? How many unit lengths? [ 4 x lengths. 6 unit lengths ]

c. Combining like terms (like terms contain the same variable raised to the same power) is a way of simplifying an expression. Rewriting the perimeter of the shape above as P = 4x + 6 combines the separate x-terms as 4x and combines the units in the term 6.

If you have not already done so, combine like terms for the perimeter expressions that you wrote in problem 4-73. [ unit tile: P = 4 units, x-tile: P = 2x + 2 units, x²-tile: P = 4x units ]

x2

x

x x

Chapter 4: Proportions and Expressions 425

4-76. What is the length of the marked portion of each line segment? Copy the segment onto your paper before finding the missing length. Assume that the entire line segment is subdivided into equal sections.

a. [ 25 ] b. [ 45 ] c. [ 30 ] 4-77. Is the relationship shown in the graph at right

proportional? If so, use it to complete a Proportions Web. If not, explain why it is not. [ No. It does not contain the point (0, 0). ]

4-78. Dante is ordering wood flooring

for his bedroom, which is shaped like a trapezoid (shown at right). If the flooring materials cost $5 per square foot, how much should he expect to pay for the materials? [ Area = 130 square feet, cost = (5)(130) = $650 ]

4-79. Sammy is training for a running race. Today he ran 3 3

5miles in 33 minutes. What is

his pace in miles per hour? [ 6 6

11= 6.54 miles per hour ]

4-80. Daisy and Alexandra each have a group of algebra tiles on their desks as described

below.

Daisy has these tiles: x, x, x2 , 1, x2 , x, x2 , and x.

Alexandra has x2 , x, 1, 1, 1, x, x2 , x, and 1.

a. Sketch each girl’s tiles. [ Sketches vary. ]

b. If the girls put their tiles together, how many of each type of tile will they have? Write an expression that represents this sum. [ 5x2 + 7x + 5 ]

0 75

?

0 75

?

0

?

50

Number of Books Purchased

Cos

t ($)

10 ft

16 ft

10 ft

Chapter 4: Proportions and Expressions 425

4-76. What is the length of the marked portion of each line segment? Copy the segment onto your paper before finding the missing length. Assume that the entire line segment is subdivided into equal sections.

a. [ 25 ] b. [ 45 ] c. [ 30 ] 4-77. Is the relationship shown in the graph at right

proportional? If so, use it to complete a Proportions Web. If not, explain why it is not. [ No. It does not contain the point (0, 0). ]

4-78. Dante is ordering wood flooring

for his bedroom, which is shaped like a trapezoid (shown at right). If the flooring materials cost $5 per square foot, how much should he expect to pay for the materials? [ Area = 130 square feet, cost = (5)(130) = $650 ]

4-79. Sammy is training for a running race. Today he ran 3 3

5miles in 33 minutes. What is

his pace in miles per hour? [ 6 6

11= 6.54 miles per hour ]

4-80. Daisy and Alexandra each have a group of algebra tiles on their desks as described

below.

Daisy has these tiles: x, x, x2 , 1, x2 , x, x2 , and x.

Alexandra has x2 , x, 1, 1, 1, x, x2 , x, and 1.

a. Sketch each girl’s tiles. [ Sketches vary. ]

b. If the girls put their tiles together, how many of each type of tile will they have? Write an expression that represents this sum. [ 5x2 + 7x + 5 ]

0 75

?

0 75

?

0

?

50

Number of Books Purchased

Cos

t ($)

10 ft

16 ft

10 ft

Chapter 4: Proportions and Expressions 425

4-76. What is the length of the marked portion of each line segment? Copy the segment onto your paper before finding the missing length. Assume that the entire line segment is subdivided into equal sections.

a. [ 25 ] b. [ 45 ] c. [ 30 ] 4-77. Is the relationship shown in the graph at right

proportional? If so, use it to complete a Proportions Web. If not, explain why it is not. [ No. It does not contain the point (0, 0). ]

4-78. Dante is ordering wood flooring

for his bedroom, which is shaped like a trapezoid (shown at right). If the flooring materials cost $5 per square foot, how much should he expect to pay for the materials? [ Area = 130 square feet, cost = (5)(130) = $650 ]

4-79. Sammy is training for a running race. Today he ran 3 3

5miles in 33 minutes. What is

his pace in miles per hour? [ 6 6

11= 6.54 miles per hour ]

4-80. Daisy and Alexandra each have a group of algebra tiles on their desks as described

below.

Daisy has these tiles: x, x, x2 , 1, x2 , x, x2 , and x.

Alexandra has x2 , x, 1, 1, 1, x, x2 , x, and 1.

a. Sketch each girl’s tiles. [ Sketches vary. ]

b. If the girls put their tiles together, how many of each type of tile will they have? Write an expression that represents this sum. [ 5x2 + 7x + 5 ]

0 75

?

0 75

?

0

?

50

Number of Books Purchased

Cos

t ($)

10 ft

16 ft

10 ft

Chapter 4: Proportions and Expressions 425

4-76. What is the length of the marked portion of each line segment? Copy the segment onto your paper before finding the missing length. Assume that the entire line segment is subdivided into equal sections.

a. [ 25 ] b. [ 45 ] c. [ 30 ] 4-77. Is the relationship shown in the graph at right

proportional? If so, use it to complete a Proportions Web. If not, explain why it is not. [ No. It does not contain the point (0, 0). ]

4-78. Dante is ordering wood flooring

for his bedroom, which is shaped like a trapezoid (shown at right). If the flooring materials cost $5 per square foot, how much should he expect to pay for the materials? [ Area = 130 square feet, cost = (5)(130) = $650 ]

4-79. Sammy is training for a running race. Today he ran 3 3

5miles in 33 minutes. What is

his pace in miles per hour? [ 6 6

11= 6.54 miles per hour ]

4-80. Daisy and Alexandra each have a group of algebra tiles on their desks as described

below.

Daisy has these tiles: x, x, x2 , 1, x2 , x, x2 , and x.

Alexandra has x2 , x, 1, 1, 1, x, x2 , x, and 1.

a. Sketch each girl’s tiles. [ Sketches vary. ]

b. If the girls put their tiles together, how many of each type of tile will they have? Write an expression that represents this sum. [ 5x2 + 7x + 5 ]

0 75

?

0 75

?

0

?

50

Number of Books Purchased

Cos

t ($)

10 ft

16 ft

10 ft

Chapter 4: Proportions and Expressions 425

4-76. What is the length of the marked portion of each line segment? Copy the segment onto your paper before finding the missing length. Assume that the entire line segment is subdivided into equal sections.

a. [ 25 ] b. [ 45 ] c. [ 30 ] 4-77. Is the relationship shown in the graph at right

proportional? If so, use it to complete a Proportions Web. If not, explain why it is not. [ No. It does not contain the point (0, 0). ]

4-78. Dante is ordering wood flooring

for his bedroom, which is shaped like a trapezoid (shown at right). If the flooring materials cost $5 per square foot, how much should he expect to pay for the materials? [ Area = 130 square feet, cost = (5)(130) = $650 ]

4-79. Sammy is training for a running race. Today he ran 3 3

5miles in 33 minutes. What is

his pace in miles per hour? [ 6 6

11= 6.54 miles per hour ]

4-80. Daisy and Alexandra each have a group of algebra tiles on their desks as described

below.

Daisy has these tiles: x, x, x2 , 1, x2 , x, x2 , and x.

Alexandra has x2 , x, 1, 1, 1, x, x2 , x, and 1.

a. Sketch each girl’s tiles. [ Sketches vary. ]

b. If the girls put their tiles together, how many of each type of tile will they have? Write an expression that represents this sum. [ 5x2 + 7x + 5 ]

0 75

?

0 75

?

0

?

50

Number of Books Purchased

Cos

t ($)

10 ft

16 ft

10 ft

Chapter 4: Proportions and Expressions 425

4-76. What is the length of the marked portion of each line segment? Copy the segment onto your paper before finding the missing length. Assume that the entire line segment is subdivided into equal sections.

a. [ 25 ] b. [ 45 ] c. [ 30 ] 4-77. Is the relationship shown in the graph at right

proportional? If so, use it to complete a Proportions Web. If not, explain why it is not. [ No. It does not contain the point (0, 0). ]

4-78. Dante is ordering wood flooring

for his bedroom, which is shaped like a trapezoid (shown at right). If the flooring materials cost $5 per square foot, how much should he expect to pay for the materials? [ Area = 130 square feet, cost = (5)(130) = $650 ]

4-79. Sammy is training for a running race. Today he ran 3 3

5miles in 33 minutes. What is

his pace in miles per hour? [ 6 6

11= 6.54 miles per hour ]

4-80. Daisy and Alexandra each have a group of algebra tiles on their desks as described

below.

Daisy has these tiles: x, x, x2 , 1, x2 , x, x2 , and x.

Alexandra has x2 , x, 1, 1, 1, x, x2 , x, and 1.

a. Sketch each girl’s tiles. [ Sketches vary. ]

b. If the girls put their tiles together, how many of each type of tile will they have? Write an expression that represents this sum. [ 5x2 + 7x + 5 ]

0 75

?

0 75

?

0

?

50

Number of Books Purchased

Cos

t ($)

10 ft

16 ft

10 ft

Chapter 4: Proportions and Expressions 425

4-76. What is the length of the marked portion of each line segment? Copy the segment onto your paper before finding the missing length. Assume that the entire line segment is subdivided into equal sections.

a. [ 25 ] b. [ 45 ] c. [ 30 ] 4-77. Is the relationship shown in the graph at right

proportional? If so, use it to complete a Proportions Web. If not, explain why it is not. [ No. It does not contain the point (0, 0). ]

4-78. Dante is ordering wood flooring

for his bedroom, which is shaped like a trapezoid (shown at right). If the flooring materials cost $5 per square foot, how much should he expect to pay for the materials? [ Area = 130 square feet, cost = (5)(130) = $650 ]

4-79. Sammy is training for a running race. Today he ran 3 3

5miles in 33 minutes. What is

his pace in miles per hour? [ 6 6

11= 6.54 miles per hour ]

4-80. Daisy and Alexandra each have a group of algebra tiles on their desks as described

below.

Daisy has these tiles: x, x, x2 , 1, x2 , x, x2 , and x.

Alexandra has x2 , x, 1, 1, 1, x, x2 , x, and 1.

a. Sketch each girl’s tiles. [ Sketches vary. ]

b. If the girls put their tiles together, how many of each type of tile will they have? Write an expression that represents this sum. [ 5x2 + 7x + 5 ]

0 75

?

0 75

?

0

?

50

Number of Books Purchased

Cos

t ($)

10 ft

16 ft

10 ft

Chapter 4: Proportions and Expressions 425

4-76. What is the length of the marked portion of each line segment? Copy the segment onto your paper before finding the missing length. Assume that the entire line segment is subdivided into equal sections.

a. [ 25 ] b. [ 45 ] c. [ 30 ] 4-77. Is the relationship shown in the graph at right

proportional? If so, use it to complete a Proportions Web. If not, explain why it is not. [ No. It does not contain the point (0, 0). ]

4-78. Dante is ordering wood flooring

for his bedroom, which is shaped like a trapezoid (shown at right). If the flooring materials cost $5 per square foot, how much should he expect to pay for the materials? [ Area = 130 square feet, cost = (5)(130) = $650 ]

4-79. Sammy is training for a running race. Today he ran 3 3

5miles in 33 minutes. What is

his pace in miles per hour? [ 6 6

11= 6.54 miles per hour ]

4-80. Daisy and Alexandra each have a group of algebra tiles on their desks as described

below.

Daisy has these tiles: x, x, x2 , 1, x2 , x, x2 , and x.

Alexandra has x2 , x, 1, 1, 1, x, x2 , x, and 1.

a. Sketch each girl’s tiles. [ Sketches vary. ]

b. If the girls put their tiles together, how many of each type of tile will they have? Write an expression that represents this sum. [ 5x2 + 7x + 5 ]

0 75

?

0 75

?

0

?

50

Number of Books Purchased

Cos

t ($)

10 ft

16 ft

10 ft

Chapter 4: Proportions and Expressions 425

4-76. What is the length of the marked portion of each line segment? Copy the segment onto your paper before finding the missing length. Assume that the entire line segment is subdivided into equal sections.

a. [ 25 ] b. [ 45 ] c. [ 30 ] 4-77. Is the relationship shown in the graph at right

proportional? If so, use it to complete a Proportions Web. If not, explain why it is not. [ No. It does not contain the point (0, 0). ]

4-78. Dante is ordering wood flooring

for his bedroom, which is shaped like a trapezoid (shown at right). If the flooring materials cost $5 per square foot, how much should he expect to pay for the materials? [ Area = 130 square feet, cost = (5)(130) = $650 ]

4-79. Sammy is training for a running race. Today he ran 3 3

5miles in 33 minutes. What is

his pace in miles per hour? [ 6 6

11= 6.54 miles per hour ]

4-80. Daisy and Alexandra each have a group of algebra tiles on their desks as described

below.

Daisy has these tiles: x, x, x2 , 1, x2 , x, x2 , and x.

Alexandra has x2 , x, 1, 1, 1, x, x2 , x, and 1.

a. Sketch each girl’s tiles. [ Sketches vary. ]

b. If the girls put their tiles together, how many of each type of tile will they have? Write an expression that represents this sum. [ 5x2 + 7x + 5 ]

0 75

?

0 75

?

0

?

50

Number of Books Purchased

Cos

t ($)

10 ft

16 ft

10 ft