Answer:
Step-by-step explanation:
Answer-116
The point (-2, 5) is not included in the solution area
<h3>The graph of the inequalities</h3>
The system of inequalities is given as:
y > 5x + 5
y > -2x+1
See attachment for the graph.
Since the inequalities use the greater than symbol, then the lines of the inequalities would be a dotted line and the upper part would be shaded
<h3>The solution area</h3>
The point is given as:
(-2, 5)
The point (-2, 5) is not in the shaded area of the system of inequalities
Hence, the point is not included in the solution area
Mathematically, we have:
5 > 5 * -2 + 5 ⇒ 5 > -5 --- true
5 > -2 * -2 +1 ⇒ 5 > 5 --- false
Since both inequalities are not true, then the point is justified
Read more about system of inequalities at:
brainly.com/question/19526736
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They both have the same slope which is 2/3
Since they have the same slope and different y intersects, they are parallel, so the two lines will never cross. Meaning there are No solutions
Answer:
575 cm
Step-by-step explanation:
5 * 100 = 500
15*5=75
500+75 = 575
Answer:
- D = -87
- Dx = 174
- Dy = -435
- Dz = 0
- (x, y, z) = (-2, 5, 0)
Step-by-step explanation:
The determinant of the coefficient matrix is ...
![D=\left|\begin{array}{ccc}2&5&3\\4&-1&-4\\-5&-2&6\end{array}\right|\\\\=2(-1)(6)+5(-4)(-5)+3(4)(-2)-2(-4)(-2)-5(4)(6)-3(-1)(-5)\\\\=-12+100-24-16-120-15=\boxed{-87}](https://tex.z-dn.net/?f=D%3D%5Cleft%7C%5Cbegin%7Barray%7D%7Bccc%7D2%265%263%5C%5C4%26-1%26-4%5C%5C-5%26-2%266%5Cend%7Barray%7D%5Cright%7C%5C%5C%5C%5C%3D2%28-1%29%286%29%2B5%28-4%29%28-5%29%2B3%284%29%28-2%29-2%28-4%29%28-2%29-5%284%29%286%29-3%28-1%29%28-5%29%5C%5C%5C%5C%3D-12%2B100-24-16-120-15%3D%5Cboxed%7B-87%7D)
The other determinants are found in similar fashion after substituting the constants on the right for each of the above matrix columns, in turn.
Those determinants are ...
![D_x=\left|\begin{array}{ccc}21&5&3\\-13&-1&-4\\0&-2&6\end{array}\right|=174](https://tex.z-dn.net/?f=D_x%3D%5Cleft%7C%5Cbegin%7Barray%7D%7Bccc%7D21%265%263%5C%5C-13%26-1%26-4%5C%5C0%26-2%266%5Cend%7Barray%7D%5Cright%7C%3D174)
![D_y=\left|\begin{array}{ccc}2&21&3\\4&-13&-4\\-5&0&6\end{array}\right|=-435](https://tex.z-dn.net/?f=D_y%3D%5Cleft%7C%5Cbegin%7Barray%7D%7Bccc%7D2%2621%263%5C%5C4%26-13%26-4%5C%5C-5%260%266%5Cend%7Barray%7D%5Cright%7C%3D-435)
![D_z=\left|\begin{array}{ccc}2&5&21\\4&-1&-13\\-5&-2&0\end{array}\right|=0](https://tex.z-dn.net/?f=D_z%3D%5Cleft%7C%5Cbegin%7Barray%7D%7Bccc%7D2%265%2621%5C%5C4%26-1%26-13%5C%5C-5%26-2%260%5Cend%7Barray%7D%5Cright%7C%3D0)
The solutions are ...
x = 174/-87 = -2
y = -435/-87 = 5
z = 0
That is, (x, y, z) = (-2, 5, 0).