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The two functions should never intersect.
Since y = y, we can equate the other side of both equations together.
x^2 + 2x + 1 = x^2 + 2x - 2
Rearrange the equation to bring all the terms to one side.
0 = x^2 - x^2 + 2x - 2x - 2 - 1
0 = -3
You can see that does not make sense, so we can conclude that there are no points of intersection between the two functions.
I also graphed the functions. In the first pic you can see that the red is between the blue and they don't intersect. In the second pic I zoomed in so you can see the right side of the graph going up to y = 600 and the red is still between the blue.
Answer:
OPTION B: 57x - 3
Step-by-step explanation:
Total tires produced is the sum of number of over-sized tires and the number of compact tires.
So, we have when x = 1, tires, y = 23 + 31 = 54
When x = 2, total tires y = 48 + 63 = 111
When x = 3, total tires y = 73 + 95 = 168
When x = 4, total tires y = 98 + 127 = 225
We can substitute the options to check which one will be the correct representation.
Option A: 55x - 1
When x = 1, y = 55(1) - 1 = 54
When x = 2, y = 55(2) - 1 = 109 111
So, this option is eliminated.
Option B: 57x - 1
When x = 1, y = 57(1) - 3 = 54
When x = 2, y = 57(2) - 3 = 111
When x = 3, y = 57(3) - 3 = 168
When x = 4, y = 57(4) - 3 = 225
These values exactly match with the values from the table. So, Option B is the right answer.
Option C: 110x - 2
When x = 1, y = 110(1) - 2 = 108 54
Hence, this option is incorrect.
Option D: 114x - 6
When x = 1, y = 114(1) - 6 54
Hence, this option is also eliminated.
Option B is the required answer.