Using the formula [tex]A=x(100-2 x)[/tex], complete the table of values given below.

[tex]
\begin{tabular}{|l|c|c|c|c|c|c|c|c|c|c|c|}\hline
X & 0 & 5 & 10 & 15 & 20 & 25 & 30 & 35 & 40 & 45 & 50 \\ \hline
(100-2 x) & 100 & & & & & & & & & & \\ \hline
A=X(100-2 x) & 0 & & & & & & & & & & \\ \hline
\end{tabular}
[/tex]

Calculate 100 − 2 x for each x value.
Calculate A = x ( 100 − 2 x ) for each x value.
Fill in the table with the calculated values.
The completed table values for A are 0 , 450 , 800 , 1050 , 1200 , 1250 , 1200 , 1050 , 800 , 450 , 0 ​ .

Explanation

Understanding the Problem We are given the formula A = x ( 100 − 2 x ) and asked to complete the table of values for different values of x . The table has three rows: the first row contains the values of x , the second row contains the values of ( 100 − 2 x ) , and the third row contains the values of A = x ( 100 − 2 x ) .

Calculations for x = 5 Let's calculate the values of ( 100 − 2 x ) and A for each given value of x .

Calculations for x = 10 When x = 5 , we have: 100 − 2 x = 100 − 2 ( 5 ) = 100 − 10 = 90 A = x ( 100 − 2 x ) = 5 ( 90 ) = 450

Calculations for x = 15 When x = 10 , we have: 100 − 2 x = 100 − 2 ( 10 ) = 100 − 20 = 80 A = x ( 100 − 2 x ) = 10 ( 80 ) = 800

Calculations for x = 20 When x = 15 , we have: 100 − 2 x = 100 − 2 ( 15 ) = 100 − 30 = 70 A = x ( 100 − 2 x ) = 15 ( 70 ) = 1050

Calculations for x = 25 When x = 20 , we have: 100 − 2 x = 100 − 2 ( 20 ) = 100 − 40 = 60 A = x ( 100 − 2 x ) = 20 ( 60 ) = 1200

Calculations for x = 30 When x = 25 , we have: 100 − 2 x = 100 − 2 ( 25 ) = 100 − 50 = 50 A = x ( 100 − 2 x ) = 25 ( 50 ) = 1250

Calculations for x = 35 When x = 30 , we have: 100 − 2 x = 100 − 2 ( 30 ) = 100 − 60 = 40 A = x ( 100 − 2 x ) = 30 ( 40 ) = 1200

Calculations for x = 40 When x = 35 , we have: 100 − 2 x = 100 − 2 ( 35 ) = 100 − 70 = 30 A = x ( 100 − 2 x ) = 35 ( 30 ) = 1050

Calculations for x = 45 When x = 40 , we have: 100 − 2 x = 100 − 2 ( 40 ) = 100 − 80 = 20 A = x ( 100 − 2 x ) = 40 ( 20 ) = 800

Calculations for x = 50 When x = 45 , we have: 100 − 2 x = 100 − 2 ( 45 ) = 100 − 90 = 10 A = x ( 100 − 2 x ) = 45 ( 10 ) = 450

Final Calculations and Table Completion When x = 50 , we have: 100 − 2 x = 100 − 2 ( 50 ) = 100 − 100 = 0 A = x ( 100 − 2 x ) = 50 ( 0 ) = 0

Completed Table So, the completed table is:





X
0
5
10
15
20
25
30
35
40
45
50



(100-2x)
100
90
80
70
60
50
40
30
20
10
0


A=X(100-2x)
0
450
800
1050
1200
1250
1200
1050
800
450
0


Examples
This formula can be used to model the area of a rectangular garden with a fixed perimeter. For example, if you have 100 meters of fencing to enclose a garden, and you want to maximize the area, you can use this formula to determine the optimal dimensions. By varying the width 'x', you can calculate the corresponding length (100-2x) and the area A. This helps in practical applications like gardening, where optimizing space is important.

Answered by GinnyAnswer | 2025-07-08

The table values for A are completed using the formula A = x ( 100 − 2 x ) . For each value of x , we calculated 100 − 2 x and then A accordingly. The completed table shows the relationship between x , ( 100 − 2 x ) , and A .
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Answered by Anonymous | 2025-08-02