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miss Akunina [59]
3 years ago
7

What is the area of a triangle with vertices (3,0) (9,0) (7,6)

Mathematics
1 answer:
Nezavi [6.7K]3 years ago
5 0

Answer:

The area of the triangle is of 21 units of area.

Step-by-step explanation:

The area of a triangle with three vertices (x_1,y_1),(x_2,y_2),(x_3,y_3) is given by the determinant of the following matrix:

A = \pm 0.5 \left|\begin{array}{ccc}x_1&y_1&1\\x_2&y_2&1\\1_3&y_3&1\end{array}\right|

In this question:

Vertices (3,0) (9,0) (7,6). So

A = \pm 0.5 \left|\begin{array}{ccc}3&0&1\\9&0&1\\7&7&1\end{array}\right|

A = \pm 0.5(3*0*1+0*1*7+1*9*7-0*7*1-0*9*1-3*1*7)

A = \pm 0.5*(63-21)

A = \pm 0.5*42 = 21

The area of the triangle is of 21 units of area.

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3 years ago
A student wanted to construct a 95% confidence interval for the average age of students in her statistics class. She randomly se
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Answer: (17.42, 20.78)

Step-by-step explanation:

As per given , we have

Sample size : n= 9

\overline{x}=19.1 years

Population standard deviation is not given , so it follows t-distribution.

Sample standard deviation : s= 1.5 years

Confidence level : 99% or 0.99

Significance level : \alpha= 1-0.99=0.01

Degree of freedom : df= 8  (∵df =n-1)

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19.1\pm (3.355)\dfrac{1.5}{\sqrt{ 9}}\\\\=19.1\pm1.6775\\\\=(19.1-1.6775,\ 19.1+1.6775)\\\\=(17.4225,\ 20.7775)\approx(17.42,\ 20.78)

Hence, the 99% confidence interval for the population mean is (17.42, 20.78) .

7 0
3 years ago
1) 12 <br><br> 2) 10<br><br> 3) 8<br><br> 4) 6
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3 years ago
(w-2) (w+5) <br> I need help I don't understand ...
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<h3>Answer: w^2 + 3w - 10</h3>

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

Work Shown:

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w(x) + 5(x)

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w(x) + 5(x)

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w*w + w*(-2) + 5*w + 5*(-2)

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6 0
3 years ago
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