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 22=4.
For 3 then 32=9.
For n then n2.
Therefore, the sequence is n2.
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=2m2−5 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=2m2−5 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=4x2+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)=21
f(2)=22=4
f(3)=23=8
f(4)=24=16
Therefore the next term in the sequence is, f(5)=25=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 4th 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)=20n
The 5th term is-f(5)=20⋅5=100
The function is defined by-f(n)=20n
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)=23=8
f(3)=33=27
f(4)=43=64
The function may be defined as-f(x)=x3
The 5th term may be given as,
f(5)=53=125
The function is defined by-f(x)=x3
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)=22=4
f(3)=32=9
f(4)=42=16
The function may be defined as f(x)=x2
Thus, the 5th term is, f(5)=52=25
The function is defined as f(x)=x2
The area of the frame with side length of 5 inches is 25 square inches
Graph-
