## Carnegie Learning Algebra II Student Skills Practice 1st Edition Chapter 1 Skills Practice

**Page 257 Problem 1 Answer**

Given the table.

The aim is to find the relation.

For 1 then 1.

For 2 then 2^{2}=4.

For 3 then 3^{2}=9.

For n then n^{2}.

Therefore, the sequence is n^{2}.

**Page 257 Problem 2 Answer**

Given:

To find: Complete each table, then graph the function.

Table

Side length | Volume |

1 | 1 |

2 | 8 |

3 | 27 |

4 | 64 |

5 | 125 |

Required graph is

The graphical representation of Volume= (side length )^{3} is as shown below

**Page 258 Problem 3 Answer**

Given:

To find: Complete each table, then graph the function.

Table

Number of Seeds planted | Number of plants that grow |

5 | 1 |

10 | 6 |

15 | 11 |

20 | 16 |

25 | 21 |

Required graph is

The graphical representation of the equation y=x−4

**Page 258 Problem 4 Answer**

Given:

To find: Complete each table, then graph the function

Table

Number of quizzes | Total time spent (hours) |

3 | 5 |

6 | 8 |

3 | 5 |

4 | 6 |

5 | 7 |

Required graph is

The graphical representaion of the expression : Total time = time for quiz (3hr)+ time for project (2hr)

**Page 258 Problem 5 Answer**

y=2m^{2}−5 is a quadratic equation which when plotted on a graph gives a parabolic curve.

Table

Time since start of Year (months) | Total number of photos published |

2 | 3 |

3 | 13 |

4 | 27 |

5 | 45 |

6 | 67 |

The graphical representation of the equation y=2m^{2}−5 is as shown below

**Page 259 Problem 6 Answer**

Given:

To find: Complete each table, then graph the function.

Table:

Time since start of year (months) | Total number of words per article |

1 | 54 |

2 | 66 |

3 | 86 |

4 | 114 |

Required graph is

The graphical representation of the equation y=4x^{2}+50 is as shown below

**Page 260 Problem 7 Answer**

Given the table.

The aim is to find the relation.

For 1 then 620.

For 2 then 620−40.

For 3 then 620−40−40.

The general formula is 620−40n.

Therefore, the n term is, 620−4n.

**Page 260 Problem 8 Answer**

Define the function and graph it. Analyse the pattern and predict the next term, of the following –

By observing the table, we can see that each term n is the 2n of the term,

1 | 2 | |

2 | 4 | |

3 | 8 | |

4 | 16 | |

5 |

e.g

f(1)=2^{1}

f(2)=2^{2}=4

f(3)=2^{3}=8

f(4)=2^{4}=16

Therefore the next term in the sequence is, f(5)=2^{5}=32

Final Answer The function is defined as

On the day, employees are sick.

Graph-

**Page 261 Problem 9 Answer**

Define a function and graph it to answer the question given.

Analyze the pattern and predict the 4th term-

1 | 189 | |

2 | 369 | |

3 | 549 | |

4 | ||

5 | 909 |

By looking and analysing the sequence, we see that each term the number of passengers increases by 180

f(1)=180+9

f(2)=2⋅(180)+9=369

f(3)=3⋅(180)+9=549

f(5)=5⋅(180)+9=909

Thus the function may be defined as-f(x)=180x+9

The 4thterm is-f(4)=4⋅(180)+9=729

The function may be defined as-f(x)=180x+9

The 4^{th} term is-729

Graph-

**Page 261 Problem 10 Answer**

Define a function and graph it to answer the question given. Analyze the pattern and predict the 5th term-

1 | 20 | |

2 | 40 | |

3 | 60 | |

4 | 80 | |

5 |

Analyzing the pattern, we can see that the nth is the 20 times n, i.e

f(1)=20

f(2)=2⋅20=40

f(3)=3⋅20=60

f(4)=4⋅20=80

Thus the function is defined as-f(n)=20^{n}

The 5^{th} term is-f(5)=20⋅5=100

The function is defined by-f(n)=20^{n}

For 5 appetizers, Garry need 100 minutes to prepare.

Graph-

**Page 262 Problem 11 Answer**

Define a function and graph it to answer the question given. Analyze the pattern and predict the 5th term-

1 | 1 | |

2 | 8 | |

3 | 27 | |

4 | 64 | |

5 |

By analyzing the terms, we can see that each term is the cube of the given term, i.e

f(1)=1

f(2)=2^{3}=8

f(3)=3^{3}=27

f(4)=4^{3}=64

The function may be defined as-f(x)=x^{3}

The 5^{th} term may be given as,

f(5)=5^{3}=125

The function is defined by-f(x)=x^{3}

The volume of the box with side length5 feet is 125 cubic feet.

Graph-

**Page 262 Problem 12 Answer**

Define a function and graph it to answer the question given. Analyze the pattern and predict the 5th

1 | 1 | |

2 | 4 | |

3 | 9 | |

4 | 16 | |

5 |

By looking and analyzing at the pattern, we can see that each term’s value is the square of the term i.e

f(1)=1

f(2)=2^{2}=4

f(3)=3^{2}=9

f(4)=4^{2}=16

The function may be defined as f(x)=x^{2}

Thus, the 5th term is, f(5)=5^{2}=25

The function is defined as f(x)=x^{2}

The area of the frame with side length of 5 inches is 25 square inches

Graph-