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Answer: 
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Given: 
Find: 
Solution: Since we know both a and b are positive this means that if they are multiplied against each other they would produce another positive. Therefore, this would cause the statement to be ab > 0.
The <em>correct answer</em> is:
D) If two points lie in a plane, the line containing those points lies in the same plane.
Explanation:
If two planes intersect, they intersect in a line, not a plane.
Space contains at least 4 non-coplanar points, not 3 non-collinear points.
If two lines intersect, their intersection is a point.
Only one line can be drawn through two given points.
Answer:
1000$
Step-by-step explanation:
55 = 40 hours + 15 Overtime hours
40×16 = 640$
16$×1.5 = 24$ an HR for overtime ( time and a half = 1.5)
24$ × 15 Overtime hours = 360$
640+360 = 1000$ gross
then come taxes
Write the equations in matrix,
![\left[\begin{array}{ccc}5&-1&1\\1&2&-1\\2&3&-3\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}4\\5\\5\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%26-1%261%5C%5C1%262%26-1%5C%5C2%263%26-3%5Cend%7Barray%7D%5Cright%5D%20%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%20%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%5C%5C5%5C%5C5%5Cend%7Barray%7D%5Cright%5D%20)
Using row transformation,
R₂ <---> R₃
![\left[\begin{array}{ccc}5&-1&1\\2&3&-3\\1&2&-1\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}4\\5\\5\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%26-1%261%5C%5C2%263%26-3%5C%5C1%262%26-1%5Cend%7Barray%7D%5Cright%5D%20%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%5C%5C5%5C%5C5%5Cend%7Barray%7D%5Cright%5D%20)
Using,
R₂ ---> R₂ - 2R₃
![\left[\begin{array}{ccc}5&-1&1\\0&-1&-1\\1&2&-1\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}4\\-5\\5\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%26-1%261%5C%5C0%26-1%26-1%5C%5C1%262%26-1%5Cend%7Barray%7D%5Cright%5D%20%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%20%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%5C%5C-5%5C%5C5%5Cend%7Barray%7D%5Cright%5D%20)
Using,
R₂ --- > (-1)R₂
![\left[\begin{array}{ccc}5&-1&1\\0&1&1\\1&2&-1\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}4\\5\\5\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%26-1%261%5C%5C0%261%261%5C%5C1%262%26-1%5Cend%7Barray%7D%5Cright%5D%20%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%20%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%5C%5C5%5C%5C5%5Cend%7Barray%7D%5Cright%5D%20)
Using row transformation,
R₂ <----> R₃
![\left[\begin{array}{ccc}5&-1&1\\1&2&-1\\0&1&1\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}4\\5\\5\end{array}\right]](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%26-1%261%5C%5C1%262%26-1%5C%5C0%261%261%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%7D4%5C%5C5%5C%5C5%5Cend%7Barray%7D%5Cright%5D%20)
Using,
R₂ ---> R₂ - R₁/5
![\left[\begin{array}{ccc}5&-1&1\\0&11/5&-6/5\\0&1&1\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}4\\21/5\\5\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%26-1%261%5C%5C0%2611%2F5%26-6%2F5%5C%5C0%261%261%5Cend%7Barray%7D%5Cright%5D%20%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%20%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%5C%5C21%2F5%5C%5C5%5Cend%7Barray%7D%5Cright%5D%20)
Using,
R₃ ---> R₃ - 5R₂/11
![\left[\begin{array}{ccc}5&-1&1\\0&11/5&-6/5\\0&0&17/11\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}4\\21/5\\34/11\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%26-1%261%5C%5C0%2611%2F5%26-6%2F5%5C%5C0%260%2617%2F11%5Cend%7Barray%7D%5Cright%5D%20%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%20%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%5C%5C21%2F5%5C%5C34%2F11%5Cend%7Barray%7D%5Cright%5D%20)
∴ 5x-y+z = 4 ====(i)
11y-6z = 21 === (ii)
17z=34 === (iii)
from iii,
z=2.
Plug z=2 in ii to get y,
∴y=3.
Plug y and z values in i to get x,
∴x=1
Therefore the solution to the system of equations is (1,3,2)
The value of n in given proportion is 16
<u><em>Solution:</em></u>
We have to find the value of "n" in the proportion
<em><u>Given proportion is:</u></em>
<em><u></u></em>
<em><u></u></em>
We can solve the above proportion by cross-multiplying
Multiply the numerator of the left-hand fraction by the denominator of the right-hand fraction
Multiply the numerator of the right-hand fraction by the denominator of the left-hand fraction
Set the two products equal to each other
Solve for the variable
Thus the value of n in given proportion is 16
