(a)
To calculate: To write equations to represent the perimeter
(a)
Answer to Problem 23PPS
Function to represent the perimeter of square is
Function to represent the area of square is
Explanation of Solution
Given information: A square has a side length
Formula Used:
Perimeter of square of side length is given as
Area of square of side length is given as
Calculation:
Given a square has a side length
Function to represent the perimeter of square is given as
Function to represent the area of square is given as
Conclusion:
Hence, function to represent the perimeter of square is
Function to represent the area of square is
(b)
To calculate: To make a table showing the perimeter and area of the square for the side length
(b)
Answer to Problem 23PPS
Table is
Side Length | Perimeter | Area |
0 | 0 | 0 |
1 | 4 | 1 |
2 | 8 | 4 |
3 | 12 | 9 |
4 | 16 | 16 |
Explanation of Solution
Given information: A square has a side length
Calculation:
Given a square has a side length
Function to represent the perimeter of square is
Function to represent the area of square is
When
When
When
When
When
Thus, table showing the perimeter and area of square with different side lengths is:
Side Length | Perimeter | Area |
0 | 0 | 0 |
1 | 4 | 1 |
2 | 8 | 4 |
3 | 12 | 9 |
4 | 16 | 16 |
Conclusion:
Hence, table is created
(c)
To calculate: To graph the points whose ordered pairs are (side length, perimeter) and (side length, area) and describe the graphs
(c)
Answer to Problem 23PPS
Graph of ordered pair (side length, perimeter) is a straight line
Graph of ordered pair (side length, area) is an upward parabola
Explanation of Solution
Given information: A square has a side length
Calculation:
Given a square has a side length
Function to represent the perimeter of square is
Function to represent the area of square is
Thus, table showing the perimeter and area of square with different side lengths is:
Side Length | Perimeter | Area |
0 | 0 | 0 |
1 | 4 | 1 |
2 | 8 | 4 |
3 | 12 | 9 |
4 | 16 | 16 |
Ordered pairs (side length, perimeter) is given as
Plotting the ordered pairs (side length, perimeter) on graph:
Graph is a straight line
Ordered pairs (side length, area) is given as
Plotting the ordered pairs (side length, area) on graph:
Graph is an upward parabola
Conclusion:
Hence, graphs are sketched
Graph of ordered pair (side length, perimeter) is a straight line
Graph of ordered pair (side length, area) is an upward parabola
(d)
To calculate: To find if there are any values for
(d)
Answer to Problem 23PPS
Yes, the values of
Explanation of Solution
Given information: A square has a side length
Calculation:
Given a square has a side length
Function to represent the perimeter of square is
Function to represent the area of square is
Thus, table showing the perimeter and area of square with different side lengths is:
Side Length | Perimeter | Area |
0 | 0 | 0 |
1 | 4 | 1 |
2 | 8 | 4 |
3 | 12 | 9 |
4 | 16 | 16 |
From the table, numerical value of
Conclusion:
Hence,
Chapter 9 Solutions
Pre-Algebra Student Edition
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