Answer :
We start with the equation
[tex]$$
w = 112 + 8t.
$$[/tex]
Step 1. Find the input [tex]$t$[/tex] that results in an output [tex]$w = 176$[/tex].
Set up the equation:
[tex]$$
112 + 8t = 176.
$$[/tex]
Subtract [tex]$112$[/tex] from both sides:
[tex]$$
8t = 176 - 112 = 64.
$$[/tex]
Divide both sides by [tex]$8$[/tex]:
[tex]$$
t = \frac{64}{8} = 8.
$$[/tex]
So, the input that produces an output of [tex]$176$[/tex] is [tex]$t=8$[/tex].
Step 2. Determine the output in the ordered pair [tex]$(4,144)$[/tex].
For the ordered pair [tex]$(4,144)$[/tex], the input value is [tex]$t = 4$[/tex]. Substitute [tex]$4$[/tex] into the equation:
[tex]$$
w = 112 + 8(4) = 112 + 32 = 144.
$$[/tex]
This shows that when [tex]$t = 4$[/tex], the output is [tex]$144$[/tex].
Final Answers:
- The input [tex]$t=8$[/tex] results in an output of [tex]$176$[/tex].
- The ordered pair [tex]$(4,144)$[/tex] indicates that the output for [tex]$t=4$[/tex] is [tex]$144$[/tex].
[tex]$$
w = 112 + 8t.
$$[/tex]
Step 1. Find the input [tex]$t$[/tex] that results in an output [tex]$w = 176$[/tex].
Set up the equation:
[tex]$$
112 + 8t = 176.
$$[/tex]
Subtract [tex]$112$[/tex] from both sides:
[tex]$$
8t = 176 - 112 = 64.
$$[/tex]
Divide both sides by [tex]$8$[/tex]:
[tex]$$
t = \frac{64}{8} = 8.
$$[/tex]
So, the input that produces an output of [tex]$176$[/tex] is [tex]$t=8$[/tex].
Step 2. Determine the output in the ordered pair [tex]$(4,144)$[/tex].
For the ordered pair [tex]$(4,144)$[/tex], the input value is [tex]$t = 4$[/tex]. Substitute [tex]$4$[/tex] into the equation:
[tex]$$
w = 112 + 8(4) = 112 + 32 = 144.
$$[/tex]
This shows that when [tex]$t = 4$[/tex], the output is [tex]$144$[/tex].
Final Answers:
- The input [tex]$t=8$[/tex] results in an output of [tex]$176$[/tex].
- The ordered pair [tex]$(4,144)$[/tex] indicates that the output for [tex]$t=4$[/tex] is [tex]$144$[/tex].
