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Reptile [31]
2 years ago
14

An acute triangle has sides measuring 10 cm and 16 cm. The length of the third side is unknown.

Mathematics
1 answer:
saveliy_v [14]2 years ago
6 0

Answer: Choice B

12.5 < x < 18.9

================================================

Explanation:

We have a triangle with these side lengths:

  • a = 10
  • b = 16
  • c = x = unknown

Let's assume that b = 16 is the largest side of this triangle.

By the converse of the pythagorean theorem, we need b^2 < a^2+c^2 to be true in order for an acute triangle to happen.

So,

b^2 < a^2 + c^2\\\\c^2 > b^2 - a^2\\\\c > \sqrt{b^2-a^2}\\\\x > \sqrt{16^2-10^2}\\\\x > \sqrt{156}\\\\x > 12.4899959967968 \ \text{(approximate)}\\\\x > 12.5

Now let's consider the possibility that the missing side x is actually the longest side.

Using the same theorem as before, we would say,

c^2 < a^2 + b^2\\\\c < \sqrt{a^2 + b^2}\\\\x < \sqrt{10^2 + 16^2}\\\\x < \sqrt{356}\\\\x < 18.8679622641132 \ \text{(approximate)}\\\\x < 18.9\\\\

We found that x > 12.5 and x < 18.9

This is the same as saying 12.5 < x and x < 18.9

Put together, they form the approximate answer of 12.5 < x < 18.9

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A manager wishes to determine the relationship between the number of miles (in hundreds of miles) the manager's sales representa
Aleksandr [31]

Answer:

y=3.529 x +37.91

We can predict the sales representative travelled 8 miles replacing x =8 and we got:

y(8) = 3.529*8 + 37.91= 66.142

And we can predict the sales representative travelled 11 miles replacing x =11 and we got:

y(11) = 3.529*11 + 37.91= 76.729

Step-by-step explanation:

For this case we have the following data:

Miles Traveled x: 2,3,10,7,8,15,3,1,11

Sales y :31,33,78,62,65,61,48,55,120

For this case we need to calculate the slope with the following formula:

m=\frac{S_{xy}}{S_{xx}}

Where:

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}

So we can find the sums like this:

\sum_{i=1}^n x_i =60

\sum_{i=1}^n y_i =553

\sum_{i=1}^n x^2_i =582

\sum_{i=1}^n y^2_i =39653

\sum_{i=1}^n x_i y_i =4329

With these we can find the sums:

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=582-\frac{60^2}{9}=182

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}=4329-\frac{60*553}{9}=642.33

And the slope would be:

m=\frac{642.33}{182}=3.529

Nowe we can find the means for x and y like this:

\bar x= \frac{\sum x_i}{n}=\frac{60}{9}=6.67

\bar y= \frac{\sum y_i}{n}=\frac{553}{9}=61.44

And we can find the intercept using this:

b=\bar y -m \bar x=61.44-(3.529*6.67)=37.91

So the line would be given by:

y=3.529 x +37.91

We can predict the sales representative travelled 8 miles replacing x =8 and we got:

y(8) = 3.529*8 + 37.91= 66.142

And we can predict the sales representative travelled 11 miles replacing x =11 and we got:

y(11) = 3.529*11 + 37.91= 76.729

4 0
3 years ago
13501 rounded to the nearest 10000
tino4ka555 [31]
13,501 rounded to the nearest 10,000 is 10,000.
8 0
3 years ago
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