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3 years ago

For the arithmetic sequence , determine the related function. Then determine if its proportional or nonproportional. explain.

1 answer:

4 0

It is adding 4, because -4+4=0 and 0+4 =4. I also think it is proportional, hope this helps a bit if not sorry. <span />

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Step-by-step explanation:

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3 years ago

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which of the three sets could not be the lengths of the sides of a triangle {6,10,12} {5,7,10} {4,4,9} {2,3,3}

Phoenix [80]

So for this, we will be applying the Triangle Inequality Theorem, which states that the sum of 2 sides must be greater than the third side for it to be a triangle. If any inequality turns out to be false, then the set cannot be a triangle.

$A+B>C\\A+C>B\\B+C>A$

<h2>First Option: {6, 10, 12}</h2>

Let A = 6, B = 10, and C = 12:

$6+10>12\\16>12\ \textsf{true}\\\\6+12>10\\18>10\ \textsf{true}\\\\12+10>6\\22>6\ \textsf{true}$

<h2>Second Option: {5, 7, 10}</h2>

Let A = 5, B = 7, and C = 10

$5+7>10\\12>10\ \textsf{true}\\\\5+10>7\\15>7\ \textsf{true}\\\\10+7>5\\17>5\ \textsf{true}$

<h2>Third Option: {4, 4, 9}</h2>

Let A = 4, B = 4, and C = 9

$4+4>9\\8>9\ \textsf{false}\\\\4+9>4\\13>4\ \textsf{true}\\\\4+9>4\\13>4\ \textsf{true}$

<h2>Fourth Option: {2, 3, 3}</h2>

Let A = 2, B = 3, and C = 3

$2+3>3\\5>3\ \textsf{true}\\\\2+3>3\\5>3\ \textsf{true}\\\\3+3>2\\6>2\ \textsf{true}$

<h2>Conclusion:</h2>

Since the third option had an inequality that was false, <u>the third option cannot be a triangle.</u>

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