The table shows the outputs y for different inputs x:
1 answer:
Part A:
For a table to be considered a function, every x-value must have one y-value.
Each x-value in this table is unique, and has only one y-value, so this table does represent a function.
Part B:
Plug in 7 for every x in the relation:
The table's output when x = 7 is 11. Compare the two outputs:
11 < 27
The relation, 2x + 13, has a greater value when x = 7.
Part C:
Set the relation to equal 75:
Subtract 13 from both sides:
Divide both sides by 2 to get x by itself:
The x value that produces an output of 75 will be 31.
For a table to be considered a function, every x-value must have one y-value.
Each x-value in this table is unique, and has only one y-value, so this table does represent a function.
Part B:
Plug in 7 for every x in the relation:
The table's output when x = 7 is 11. Compare the two outputs:
11 < 27
The relation, 2x + 13, has a greater value when x = 7.
Part C:
Set the relation to equal 75:
Subtract 13 from both sides:
Divide both sides by 2 to get x by itself:
The x value that produces an output of 75 will be 31.
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For the largest area, half the fence is used parallel to the river, and the other half is used for the two ends of the rectangular space.
The dimensions are 475 m by 237.5 m.
_____
Let x represent the length along the river. Then the area (A) is found as
.. A = x*(950 -x)/2
This equation describes a parabola with its vertex (maximum) halfway between the zeros of x=0 and x=950. That is, the maximum area is achieved when half the fence is used parallel to the river.
The dimensions are 475 m by 237.5 m.
_____
Let x represent the length along the river. Then the area (A) is found as
.. A = x*(950 -x)/2
This equation describes a parabola with its vertex (maximum) halfway between the zeros of x=0 and x=950. That is, the maximum area is achieved when half the fence is used parallel to the river.