Answer:
Area of the lawn = 62493π m^2
Step-by-step explanation:
Answer:
Name: Circle A
Chords: Chord DP, Chord HC
Tangent: EFG
Step-by-step explanation:
Name a circle by the center, in this case it's A.
Chord: A chord is a line only in the circle, not outside of it, and its endpoints are right on the circle.
Tangent of a circle: "Tangent" means touching, and this is a line, in terms of a circle, that touches the circle but is not INSIDE of the circle.
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)
Step-by-step explanation:
<h3><u>G</u><u>i</u><u>v</u><u>e</u><u>n</u><u> </u><u>Inform</u><u>ation</u><u> </u><u>:</u></h3>
- Ryan spent 1/3 of his monthly salary for rent and 1/7 of his monthly salary for his utility bill.
- Remaining money = $759
<h3><u>T</u><u>o</u><u> </u><u>calculate</u><u> </u><u>:</u></h3>
<h3><u>C</u><u>a</u><u>l</u><u>c</u><u>u</u><u>l</u><u>a</u><u>t</u><u>i</u><u>o</u><u>n</u><u> </u><u>:</u></h3>
Let us assume his monthly salary as x. According to the question,
➝ Money spent on rent + Money spent for utility bill + Remaining money = His salary








<u>Therefore,</u><u> </u><u>his</u><u> </u><u>monthly</u><u> </u><u>income</u><u> </u><u>is</u><u> </u><u>$</u><u>1</u><u>4</u><u>4</u><u>9</u><u>.</u>
<span>C12H22O11(s)+12O2(g) =12CO2(g)+11H2O(g)</span>