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dmitriy555 [2]
3 years ago
13

The sumof the angle measures of any triangle is 180 degrees. Suppose that one angle in a triangle has a degree for 6x-9 and anot

her has a degree measures 9x+1. Write an expression for the degree measure of the third angle in the triangle.
Mathematics
1 answer:
vovikov84 [41]3 years ago
6 0
Remark
No matter what kind of triangle it is, the angles must add up to 180, just as you said.

Suppose we say 
A = 6x - 9
B = 9x + 1
C = y          We need an expression for C or y.

A + B + C = 180
6x - 9 + 9x + 1 + y = 180   Collect the like terms on the left.
6x + 9x + 1 - 9 + y = 180
15x - 8 + y = 180               Add 8 to both sides.
15x + y = 180 + 8
15x + y = 188                    Subtract 15x from both sides.
y = 188 - 15x <<<<<<<<< Answer
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Find the area of a triangle whose vertices are located at (-2,5), (-4, -3), and (3,1). Evaluate the determinant using diagonals.
myrzilka [38]

Answer:

The area of the triangle is 48 unit²

Step-by-step explanation:

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(-2, 5), (-4, -3), and (3, 1)

The formula for finding the area of a triangle with given coordinates of the vertices is as follows;

\Delta  = \dfrac{1}{2}\times \begin{vmatrix}x_1 & y_1 & 1\\ x_2 & y_2 & 1\\ x_3 & y_3 & 1\end{vmatrix} = \dfrac{1}{2}\times \left | x_1\cdot y_2 - x_2\cdot y_1 + x_2\cdot y_3 - x_3\cdot y_2 + x_3\cdot y_1 - x_1\cdot y_3\right |

Substituting gives;

\Delta  = \dfrac{1}{2}\times \begin{vmatrix}-2& 5 & 1\\ -4 & -3 & 1\\ 3 & 1 & 1\end{vmatrix} \\\Delta  = \dfrac{1}{2}\times \left | (-2)\times (-3) - ((-4)\times 5) + (-4)\times 1 - 3\times (-3) + 3 \times 5 - (-2)\times 1\right | \\\Delta  = \dfrac{1}{2}\times \left | 6 +20 -4 +9 + 15+2\right |  = 48

The area of the triangle = 48 unit².

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3 years ago
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