Answer:
B. move forward 7, left 6, and down 5
Step-by-step explanation:
By the <u>convention of 3D geometr</u>y, the coordinates of a point (x,y,z) represent how far the point is from the origin forward-backward , right/left , up-down respectively with prior one for the positive coordinate and latter for the negative coordinate.
so we need to move forward 7 for x=7 then to left 6 for y=-6 and then down 5 for z=-5.
Answer:
104.6 deg, 75.4 deg
Step-by-step explanation:
One angle measures x.
The other angle measures 29.2 deg less than x, so it measures x - 29.2.
They are supplementary angles, so the sum of their measures is 180 deg.
x + x - 29.2 = 180
2x - 29.2 = 180
2x = 209.2
x = 104.6
x - 29.2 = 75.4
Answer: 104.6 deg, 75.4 deg
Answer:
1) The solution of the system is

2) The solution of the system is

Step-by-step explanation:
1) To solve the system of equations

using the row reduction method you must:
Step 1: Write the augmented matrix of the system
![\left[ \begin{array}{ccc|c} 0 & 3 & -5 & 89 \\\\ 6 & 0 & 1 & 17 \\\\ 1 & -1 & 8 & -107 \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7Cc%7D%200%20%26%203%20%26%20-5%20%26%2089%20%5C%5C%5C%5C%206%20%26%200%20%26%201%20%26%2017%20%5C%5C%5C%5C%201%20%26%20-1%20%26%208%20%26%20-107%20%5Cend%7Barray%7D%20%5Cright%5D)
Step 2: Swap rows 1 and 2
![\left[ \begin{array}{ccc|c} 6 & 0 & 1 & 17 \\\\ 0 & 3 & -5 & 89 \\\\ 1 & -1 & 8 & -107 \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7Cc%7D%206%20%26%200%20%26%201%20%26%2017%20%5C%5C%5C%5C%200%20%26%203%20%26%20-5%20%26%2089%20%5C%5C%5C%5C%201%20%26%20-1%20%26%208%20%26%20-107%20%5Cend%7Barray%7D%20%5Cright%5D)
Step 3: 
![\left[ \begin{array}{ccc|c} 1 & 0 & \frac{1}{6} & \frac{17}{6} \\\\ 0 & 3 & -5 & 89 \\\\ 1 & -1 & 8 & -107 \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7Cc%7D%201%20%26%200%20%26%20%5Cfrac%7B1%7D%7B6%7D%20%26%20%5Cfrac%7B17%7D%7B6%7D%20%5C%5C%5C%5C%200%20%26%203%20%26%20-5%20%26%2089%20%5C%5C%5C%5C%201%20%26%20-1%20%26%208%20%26%20-107%20%5Cend%7Barray%7D%20%5Cright%5D)
Step 4: 
![\left[ \begin{array}{ccc|c} 1 & 0 & \frac{1}{6} & \frac{17}{6} \\\\ 0 & 3 & -5 & 89 \\\\ 0 & -1 & \frac{47}{6} & - \frac{659}{6} \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7Cc%7D%201%20%26%200%20%26%20%5Cfrac%7B1%7D%7B6%7D%20%26%20%5Cfrac%7B17%7D%7B6%7D%20%5C%5C%5C%5C%200%20%26%203%20%26%20-5%20%26%2089%20%5C%5C%5C%5C%200%20%26%20-1%20%26%20%5Cfrac%7B47%7D%7B6%7D%20%26%20-%20%5Cfrac%7B659%7D%7B6%7D%20%5Cend%7Barray%7D%20%5Cright%5D)
Step 5: 
![\left[ \begin{array}{ccc|c} 1 & 0 & \frac{1}{6} & \frac{17}{6} \\\\ 0 & 1 & - \frac{5}{3} & \frac{89}{3} \\\\ 0 & -1 & \frac{47}{6} & - \frac{659}{6} \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7Cc%7D%201%20%26%200%20%26%20%5Cfrac%7B1%7D%7B6%7D%20%26%20%5Cfrac%7B17%7D%7B6%7D%20%5C%5C%5C%5C%200%20%26%201%20%26%20-%20%5Cfrac%7B5%7D%7B3%7D%20%26%20%5Cfrac%7B89%7D%7B3%7D%20%5C%5C%5C%5C%200%20%26%20-1%20%26%20%5Cfrac%7B47%7D%7B6%7D%20%26%20-%20%5Cfrac%7B659%7D%7B6%7D%20%5Cend%7Barray%7D%20%5Cright%5D)
Step 6: 
![\left[ \begin{array}{ccc|c} 1 & 0 & \frac{1}{6} & \frac{17}{6} \\\\ 0 & 1 & - \frac{5}{3} & \frac{89}{3} \\\\ 0 & 0 & \frac{37}{6} & - \frac{481}{6} \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7Cc%7D%201%20%26%200%20%26%20%5Cfrac%7B1%7D%7B6%7D%20%26%20%5Cfrac%7B17%7D%7B6%7D%20%5C%5C%5C%5C%200%20%26%201%20%26%20-%20%5Cfrac%7B5%7D%7B3%7D%20%26%20%5Cfrac%7B89%7D%7B3%7D%20%5C%5C%5C%5C%200%20%26%200%20%26%20%5Cfrac%7B37%7D%7B6%7D%20%26%20-%20%5Cfrac%7B481%7D%7B6%7D%20%5Cend%7Barray%7D%20%5Cright%5D)
Step 7: 
![\left[ \begin{array}{ccc|c} 1 & 0 & \frac{1}{6} & \frac{17}{6} \\\\ 0 & 1 & - \frac{5}{3} & \frac{89}{3} \\\\ 0 & 0 & 1 & -13 \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7Cc%7D%201%20%26%200%20%26%20%5Cfrac%7B1%7D%7B6%7D%20%26%20%5Cfrac%7B17%7D%7B6%7D%20%5C%5C%5C%5C%200%20%26%201%20%26%20-%20%5Cfrac%7B5%7D%7B3%7D%20%26%20%5Cfrac%7B89%7D%7B3%7D%20%5C%5C%5C%5C%200%20%26%200%20%26%201%20%26%20-13%20%5Cend%7Barray%7D%20%5Cright%5D)
Step 8: 
![\left[ \begin{array}{ccc|c} 1 & 0 & 0 & 5 \\\\ 0 & 1 & - \frac{5}{3} & \frac{89}{3} \\\\ 0 & 0 & 1 & -13 \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7Cc%7D%201%20%26%200%20%26%200%20%26%205%20%5C%5C%5C%5C%200%20%26%201%20%26%20-%20%5Cfrac%7B5%7D%7B3%7D%20%26%20%5Cfrac%7B89%7D%7B3%7D%20%5C%5C%5C%5C%200%20%26%200%20%26%201%20%26%20-13%20%5Cend%7Barray%7D%20%5Cright%5D)
Step 9: 
![\left[ \begin{array}{ccc|c} 1 & 0 & 0 & 5 \\\\ 0 & 1 & 0 & 8 \\\\ 0 & 0 & 1 & -13 \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7Cc%7D%201%20%26%200%20%26%200%20%26%205%20%5C%5C%5C%5C%200%20%26%201%20%26%200%20%26%208%20%5C%5C%5C%5C%200%20%26%200%20%26%201%20%26%20-13%20%5Cend%7Barray%7D%20%5Cright%5D)
Step 10: Rewrite the system using the row reduced matrix:
![\left[ \begin{array}{ccc|c} 1 & 0 & 0 & 5 \\\\ 0 & 1 & 0 & 8 \\\\ 0 & 0 & 1 & -13 \end{array} \right] \rightarrow \left\begin{array}{ccc}x_1&=&5\\x_2&=&8\\x_3&=&-13\end{array}\right](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7Cc%7D%201%20%26%200%20%26%200%20%26%205%20%5C%5C%5C%5C%200%20%26%201%20%26%200%20%26%208%20%5C%5C%5C%5C%200%20%26%200%20%26%201%20%26%20-13%20%5Cend%7Barray%7D%20%5Cright%5D%20%5Crightarrow%20%5Cleft%5Cbegin%7Barray%7D%7Bccc%7Dx_1%26%3D%265%5C%5Cx_2%26%3D%268%5C%5Cx_3%26%3D%26-13%5Cend%7Barray%7D%5Cright)
2) To solve the system of equations

using the row reduction method you must:
Step 1:
![\left[ \begin{array}{ccc|c} 4 & -1 & 3 & 12 \\\\ 2 & 0 & 9 & -5 \\\\ 1 & 4 & 6 & -32 \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7Cc%7D%204%20%26%20-1%20%26%203%20%26%2012%20%5C%5C%5C%5C%202%20%26%200%20%26%209%20%26%20-5%20%5C%5C%5C%5C%201%20%26%204%20%26%206%20%26%20-32%20%5Cend%7Barray%7D%20%5Cright%5D)
Step 2: 
![\left[ \begin{array}{ccc|c} 1 & - \frac{1}{4} & \frac{3}{4} & 3 \\\\ 2 & 0 & 9 & -5 \\\\ 1 & 4 & 6 & -32 \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7Cc%7D%201%20%26%20-%20%5Cfrac%7B1%7D%7B4%7D%20%26%20%5Cfrac%7B3%7D%7B4%7D%20%26%203%20%5C%5C%5C%5C%202%20%26%200%20%26%209%20%26%20-5%20%5C%5C%5C%5C%201%20%26%204%20%26%206%20%26%20-32%20%5Cend%7Barray%7D%20%5Cright%5D)
Step 3: 
![\left[ \begin{array}{ccc|c} 1 & - \frac{1}{4} & \frac{3}{4} & 3 \\\\ 0 & \frac{1}{2} & \frac{15}{2} & -11 \\\\ 1 & 4 & 6 & -32 \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7Cc%7D%201%20%26%20-%20%5Cfrac%7B1%7D%7B4%7D%20%26%20%5Cfrac%7B3%7D%7B4%7D%20%26%203%20%5C%5C%5C%5C%200%20%26%20%5Cfrac%7B1%7D%7B2%7D%20%26%20%5Cfrac%7B15%7D%7B2%7D%20%26%20-11%20%5C%5C%5C%5C%201%20%26%204%20%26%206%20%26%20-32%20%5Cend%7Barray%7D%20%5Cright%5D)
Step 4: 
![\left[ \begin{array}{ccc|c} 1 & - \frac{1}{4} & \frac{3}{4} & 3 \\\\ 0 & \frac{1}{2} & \frac{15}{2} & -11 \\\\ 0 & \frac{17}{4} & \frac{21}{4} & -35 \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7Cc%7D%201%20%26%20-%20%5Cfrac%7B1%7D%7B4%7D%20%26%20%5Cfrac%7B3%7D%7B4%7D%20%26%203%20%5C%5C%5C%5C%200%20%26%20%5Cfrac%7B1%7D%7B2%7D%20%26%20%5Cfrac%7B15%7D%7B2%7D%20%26%20-11%20%5C%5C%5C%5C%200%20%26%20%5Cfrac%7B17%7D%7B4%7D%20%26%20%5Cfrac%7B21%7D%7B4%7D%20%26%20-35%20%5Cend%7Barray%7D%20%5Cright%5D)
Step 5: 
![\left[ \begin{array}{ccc|c} 1 & - \frac{1}{4} & \frac{3}{4} & 3 \\\\ 0 & 1 & 15 & -22 \\\\ 0 & \frac{17}{4} & \frac{21}{4} & -35 \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7Cc%7D%201%20%26%20-%20%5Cfrac%7B1%7D%7B4%7D%20%26%20%5Cfrac%7B3%7D%7B4%7D%20%26%203%20%5C%5C%5C%5C%200%20%26%201%20%26%2015%20%26%20-22%20%5C%5C%5C%5C%200%20%26%20%5Cfrac%7B17%7D%7B4%7D%20%26%20%5Cfrac%7B21%7D%7B4%7D%20%26%20-35%20%5Cend%7Barray%7D%20%5Cright%5D)
Step 6: 
![\left[ \begin{array}{cccc} 1 & 0 & \frac{9}{2} & - \frac{5}{2} \\\\ 0 & 1 & 15 & -22 \\\\ 0 & \frac{17}{4} & \frac{21}{4} & -35 \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bcccc%7D%201%20%26%200%20%26%20%5Cfrac%7B9%7D%7B2%7D%20%26%20-%20%5Cfrac%7B5%7D%7B2%7D%20%5C%5C%5C%5C%200%20%26%201%20%26%2015%20%26%20-22%20%5C%5C%5C%5C%200%20%26%20%5Cfrac%7B17%7D%7B4%7D%20%26%20%5Cfrac%7B21%7D%7B4%7D%20%26%20-35%20%5Cend%7Barray%7D%20%5Cright%5D)
Step 7: 
![\left[ \begin{array}{ccc|c} 1 & 0 & \frac{9}{2} & - \frac{5}{2} \\\\ 0 & 1 & 15 & -22 \\\\ 0 & 0 & - \frac{117}{2} & \frac{117}{2} \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7Cc%7D%201%20%26%200%20%26%20%5Cfrac%7B9%7D%7B2%7D%20%26%20-%20%5Cfrac%7B5%7D%7B2%7D%20%5C%5C%5C%5C%200%20%26%201%20%26%2015%20%26%20-22%20%5C%5C%5C%5C%200%20%26%200%20%26%20-%20%5Cfrac%7B117%7D%7B2%7D%20%26%20%5Cfrac%7B117%7D%7B2%7D%20%5Cend%7Barray%7D%20%5Cright%5D)
Step 8: 
![\left[ \begin{array}{cccc} 1 & 0 & \frac{9}{2} & - \frac{5}{2} \\\\ 0 & 1 & 15 & -22 \\\\ 0 & 0 & 1 & -1 \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bcccc%7D%201%20%26%200%20%26%20%5Cfrac%7B9%7D%7B2%7D%20%26%20-%20%5Cfrac%7B5%7D%7B2%7D%20%5C%5C%5C%5C%200%20%26%201%20%26%2015%20%26%20-22%20%5C%5C%5C%5C%200%20%26%200%20%26%201%20%26%20-1%20%5Cend%7Barray%7D%20%5Cright%5D)
Step 9: 
![\left[ \begin{array}{cccc} 1 & 0 & 0 & 2 \\\\ 0 & 1 & 15 & -22 \\\\ 0 & 0 & 1 & -1 \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bcccc%7D%201%20%26%200%20%26%200%20%26%202%20%5C%5C%5C%5C%200%20%26%201%20%26%2015%20%26%20-22%20%5C%5C%5C%5C%200%20%26%200%20%26%201%20%26%20-1%20%5Cend%7Barray%7D%20%5Cright%5D)
Step 10: 
![\left[ \begin{array}{cccc} 1 & 0 & 0 & 2 \\\\ 0 & 1 & 0 & -7 \\\\ 0 & 0 & 1 & -1 \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bcccc%7D%201%20%26%200%20%26%200%20%26%202%20%5C%5C%5C%5C%200%20%26%201%20%26%200%20%26%20-7%20%5C%5C%5C%5C%200%20%26%200%20%26%201%20%26%20-1%20%5Cend%7Barray%7D%20%5Cright%5D)
Step 11:
![\left[ \begin{array}{ccc|c} 1 & 0 & 0 & 2 \\\\ 0 & 1 & 0 & -7 \\\\ 0 & 0 & 1 & -1 \end{array} \right]\rightarrow \left\begin{array}{ccc}x_1&=&2\\x_2&=&-7\\x_3&=&-1\end{array}\right](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7Cc%7D%201%20%26%200%20%26%200%20%26%202%20%5C%5C%5C%5C%200%20%26%201%20%26%200%20%26%20-7%20%5C%5C%5C%5C%200%20%26%200%20%26%201%20%26%20-1%20%5Cend%7Barray%7D%20%5Cright%5D%5Crightarrow%20%5Cleft%5Cbegin%7Barray%7D%7Bccc%7Dx_1%26%3D%262%5C%5Cx_2%26%3D%26-7%5C%5Cx_3%26%3D%26-1%5Cend%7Barray%7D%5Cright)
To Prove: ΔEFI ~ Δ GFH
Proof:
When two triangles are similar, their corresponding sides are Proportional and their corresponding interior angles are equal.
Two Triangles can be proven similar by following Similarity Criterion.
1. AA
2.SSS
3.SAS
→∠EFI=∠GFH-------[Vertically Opposite angles]
The Other statement which is needed to prove that triangles EFI and GFH are similar is
Option C:→ ∠E ≅ ∠G
So, Two triangles ΔEFI and Δ GFH are Similar by Angle-Angle(AA) Criterion.
-7+(9)=2
you can do the opposite of what is given (9-7)