Answer:
b = 17
∠QPS = 124°
∠SPT = 17°
∠TPR = 39°
Step-by-step explanation:
- The sum of the three angles shown is a linear angle, with a measure of 180°.
This fact can be used to write an equation:
(8b -12)° +b° +(2b+5)° = 180°
11b -7 = 180
11b = 187
b = 17
8b -12 = 8(17) -12 = 124
2b +5 = 2(17) +5 = 39
The value of b is 17.
The angle measures are ...
∠QPS = 124°
∠SPT = 17°
∠TPR = 39°
Answer:
c.
Step-by-step explanation:
That is the only answer choice that makes the most sense.
±10 = √100; in this case, they want the non-negative value, so it is 10.
Answer:
104
Step-by-step explanation:
women = 8/8
men = 5/8
all workers = 8/8 + 5/8 = 13/8
extra women workers = 8/8 - 5/8 = 3/8
so...
3/8 = 24
13/8 = x
( cross multiplication method)
3/8 x = 39
x = 104
Hence, there are 104 workers
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)
Answer:
D.
Step-by-step explanation:
The answer is D) -25n-2