Answer: -0.71
Step-by-step explanation:
The Angle Angle Side postulate (often abbreviated as AAS) states that if two angles and the non-included side one triangle are congruent to two angles and the non-included side of another triangle, then these two triangles are congruent.
The Side Angle Side postulate (often abbreviated as SAS) states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.
SSS stands for "side, side, side" and means that we have two triangles with all three sides equal. For example: is congruent to: (See Solving SSS Triangles to find out more) If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.
ASA stands for "angle, side, angle" and means that we have two triangles where we know two angles and the included side are equal. If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.
CPCTC is an acronym for corresponding parts of congruent triangles are congruent. CPCTC is commonly used at or near the end of a proof which asks the student to show that two angles or two sides are congruent. ... Corresponding means they're in the same position in the 2 triangles.
Answer:
The slopes of line m and p will be the same: 1/25 (I think thats what that says)
Step-by-step explanation:
when two lines are parallel it means they will never touch, and so they must have the same slope. If their slopes were different (even by 1 decimal), they would touch and so would no longer be parallel.
Im pretty sure the answer is D, because if i used the right formula,
you should get this in the formula
a 2 subtracting a negative 6 makes it a positive, meaning your just adding 6 plus2, to get 8
Answer:
The solution of the system of equations is, (1,-1,2)
Step-by-step explanation:
Given system equation;
x + 5y - 3z = -10
-5x + 6y – 5z = -21
-x + 8y - 8z = -25
Matrix form is written as;
![\left[\begin{array}{ccc}1&5&-3\\-5&6&-5\\-1&8&-8\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}-10\\-21\\-25\end{array}\right] \\\\\\det. = 1\left[\begin{array}{cc}\\6&-5\\8&-8\end{array}\right] -5\left[\begin{array}{cc}\\-5&-5\\-1&-8\end{array}\right] -3\left[\begin{array}{cc}\\-5&6\\-1&8\end{array}\right] \\\\\\det. = 1(-8) -5(35)-3(-34)= -8 - 175+ 102 = -81](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%265%26-3%5C%5C-5%266%26-5%5C%5C-1%268%26-8%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-10%5C%5C-21%5C%5C-25%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5C%5Cdet.%20%3D%201%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5C%5C6%26-5%5C%5C8%26-8%5Cend%7Barray%7D%5Cright%5D%20-5%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5C%5C-5%26-5%5C%5C-1%26-8%5Cend%7Barray%7D%5Cright%5D%20-3%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5C%5C-5%266%5C%5C-1%268%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5C%5Cdet.%20%3D%201%28-8%29%20-5%2835%29-3%28-34%29%3D%20-8%20-%20175%2B%20102%20%3D%20-81)
Cofactor;
![First \ row \left[\begin{array}{cc}+\\ 6&-5\\\ 8&-8\end{array}\right \left\begin{array}{cc}-\\ -5&-5\\-1&-8\end{array}\right \left\begin{array}{cc}+\\-5&6\\-1&8\end{array}\right] = [-8 \ \ -35 \ \ -34]\\\\\\\ Second \ row \left[\begin{array}{cc}-\\ 5&-3\\\ 8&-8\end{array}\right \left\begin{array}{cc}+\\ 1&-3\\-1&-8\end{array}\right \left\begin{array}{cc}-\\1&5\\-1&8\end{array}\right] = [16\ \ -11 \ \ -13]\\\\\\](https://tex.z-dn.net/?f=First%20%5C%20row%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%2B%5C%5C%206%26-5%5C%5C%5C%208%26-8%5Cend%7Barray%7D%5Cright%20%20%5Cleft%5Cbegin%7Barray%7D%7Bcc%7D-%5C%5C%20-5%26-5%5C%5C-1%26-8%5Cend%7Barray%7D%5Cright%20%5Cleft%5Cbegin%7Barray%7D%7Bcc%7D%2B%5C%5C-5%266%5C%5C-1%268%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5B-8%20%20%5C%20%5C%20-35%20%5C%20%5C%20-34%5D%5C%5C%5C%5C%5C%5C%5C%20Second%20%5C%20row%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-%5C%5C%205%26-3%5C%5C%5C%208%26-8%5Cend%7Barray%7D%5Cright%20%20%5Cleft%5Cbegin%7Barray%7D%7Bcc%7D%2B%5C%5C%201%26-3%5C%5C-1%26-8%5Cend%7Barray%7D%5Cright%20%5Cleft%5Cbegin%7Barray%7D%7Bcc%7D-%5C%5C1%265%5C%5C-1%268%5Cend%7Barray%7D%5Cright%5D%20%20%3D%20%5B16%5C%20%5C%20-11%20%5C%20%5C%20-13%5D%5C%5C%5C%5C%5C%5C)
![Third \ row \left[\begin{array}{cc}+\\ 5&-3\\\ 6&-5\end{array}\right \left\begin{array}{cc}-\\ 1&-3\\-5&-5\end{array}\right \left\begin{array}{cc}+\\1&5\\-5&6\end{array}\right]= [-7 \ \ 20\ \ 31]](https://tex.z-dn.net/?f=Third%20%5C%20row%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%2B%5C%5C%205%26-3%5C%5C%5C%206%26-5%5Cend%7Barray%7D%5Cright%20%20%5Cleft%5Cbegin%7Barray%7D%7Bcc%7D-%5C%5C%201%26-3%5C%5C-5%26-5%5Cend%7Barray%7D%5Cright%20%5Cleft%5Cbegin%7Barray%7D%7Bcc%7D%2B%5C%5C1%265%5C%5C-5%266%5Cend%7Barray%7D%5Cright%5D%3D%20%5B-7%20%5C%20%20%5C%2020%5C%20%5C%2031%5D)
![\left[\begin{array}{ccc}-8&-35&-34\\16&-11&-13\\-7&20&31\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-8%26-35%26-34%5C%5C16%26-11%26-13%5C%5C-7%2620%2631%5Cend%7Barray%7D%5Cright%5D)
![inverse \ matrix =-\frac{1}{81} \left[\begin{array}{ccc}-8&16&-7\\-35&-11&20\\-34&-13&31\end{array}\right] \\\\\\](https://tex.z-dn.net/?f=inverse%20%5C%20matrix%20%3D-%5Cfrac%7B1%7D%7B81%7D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-8%2616%26-7%5C%5C-35%26-11%2620%5C%5C-34%26-13%2631%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5C%5C)
Solution of the matrix:
![\left[\begin{array}{c}x\\y\\z\end{array}\right] = -\frac{1}{81} \left[\begin{array}{ccc}-8&16&-7\\-35&-11&20\\-34&-13&31\end{array}\right] X \left[\begin{array}{c}-10\\-21\\-25\end{array}\right] = \left[\begin{array}{c}\frac{-8*-10 }{-81 } +\frac{16*-21 }{-81 } + \frac{-7*-25 }{-81 }\\\\\frac{-35*-10 }{-81 } +\frac{-11*-21 }{-81 }+ \frac{20*-25 }{-81 }\\\\\frac{-34*-10 }{-81 }+ \frac{-13*-21 }{-81 }+ \frac{31*-25 }{-81 }\end{array}\right] \\\\\](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%20-%5Cfrac%7B1%7D%7B81%7D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-8%2616%26-7%5C%5C-35%26-11%2620%5C%5C-34%26-13%2631%5Cend%7Barray%7D%5Cright%5D%20%20X%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-10%5C%5C-21%5C%5C-25%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D%5Cfrac%7B-8%2A-10%20%7D%7B-81%20%7D%20%2B%5Cfrac%7B16%2A-21%20%7D%7B-81%20%7D%20%2B%20%5Cfrac%7B-7%2A-25%20%7D%7B-81%20%7D%5C%5C%5C%5C%5Cfrac%7B-35%2A-10%20%7D%7B-81%20%7D%20%2B%5Cfrac%7B-11%2A-21%20%7D%7B-81%20%7D%2B%20%5Cfrac%7B20%2A-25%20%7D%7B-81%20%7D%5C%5C%5C%5C%5Cfrac%7B-34%2A-10%20%7D%7B-81%20%7D%2B%20%5Cfrac%7B-13%2A-21%20%7D%7B-81%20%7D%2B%20%5Cfrac%7B31%2A-25%20%7D%7B-81%20%7D%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5C)
![\left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}\frac{-81}{-81} \\\\\frac{81}{-81} \\\\\frac{-162}{-81} \end{array}\right] = \left[\begin{array}{c}1\\-1\\2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D%5Cfrac%7B-81%7D%7B-81%7D%20%5C%5C%5C%5C%5Cfrac%7B81%7D%7B-81%7D%20%5C%5C%5C%5C%5Cfrac%7B-162%7D%7B-81%7D%20%5Cend%7Barray%7D%5Cright%5D%20%3D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D1%5C%5C-1%5C%5C2%5Cend%7Barray%7D%5Cright%5D)
Therefore, the correct option is (1,-1,2)
