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sasho [114]
3 years ago
5

If DE = 37 cm and EF = 16 cm, then what are the possible lengths for DF so that DE,EF, and DF can form a triangle? Explain your

reasoning.
Mathematics
2 answers:
Brut [27]3 years ago
7 0

Answer:

The length of DF must be between 21 and 53.

Step-by-step explanation:

In a triangle, the length of two sides added together must exceed the length of the 3rd side. So, since EF is the shortest of the two givens, we know that EF + DF must be greater than DE. So we can plug in these numbers to find the minimum.

EF + DF > DE

16 + DF > 37

DF > 21

Now, for the upper maximum, we know that the two given lengths must be greater than the length of DF. So again, we can solve for the maximum using the amounts.

DE + EF > DF

37 + 16 > DF

53 > DF

With these two in mind, we know that DF must be between 21 and 53

tigry1 [53]3 years ago
3 0

Answer: 21 < DF < 53 ; Triangle Inequality Theorem

<u>Step-by-step explanation:</u>

The Triangle Inequality Theorem states that the sum of any two sides is greater than the sum of the third side.

DE + EF > DF          EF + DF > DE                 DE + DF > EF

37 + 16 > DF           16 + DF > 37                  37 + DF > 16

       53 > DF                   DF > 21                           DF > -21


Now let's put together the answers.  Note that DF > -21 is irrelevant since all lengths must be greater than 0.

53 > DF  and DF > 21  means that DF is between 53 and 21

----->    21 < DF < 53


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Help please! There are 3 items in an order. They cost $8.95, $11.49, and $12.75. The sales tax for this order is 6.5%.
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Facts

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If the inspection division of a county weights and measures department wants to estimate the mean amount of
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α/2=0.025

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Solving for n using formula of margin of error.

n=(z/2ST/Me)^{2}

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By rounding off we will get 97.

Hence the sample size required will be 97.

Learn more about standard deviation at brainly.com/question/475676

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The given question is incomplete and the full question is as under:

If the inspection division of a county weights and measures department wants to estimate the mean amount of soft drink fill in 2 liters bottles to within (0.01 liter with 95% confidence and also assumes that standard deviation is 0.05 liter. What is the sample size needed?

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