2x - 3y - 9z = -32
x + 3z = 8
-3x + y - 4z = -8
Add all the equations together.
-3y - 10z = -32
By looking at the first equation, 2x - 3y - 9z = -3y - 10z.
So 2x = -z.
By looking at the second equation, x + 3z = (-0.5z) + 3z = 8.
So 2.5z = 8, and z = 3.2.
This means that x = -1.6.
Let's substitute into our original equations!
-3.2 - 3y - 28.8 = -32
4.8 + y - 12.8 = -8
Therefore, y = 0!
Since these answers do not contradict each other, they are dependent.
The answers are x = -1.6, y = 0, z = 3.2.
Answer:
8f+4g
Step-by-step explanation:
2•4f=8f, 22g=4g, 8f+4g=8f+4g
Answer:
a) x = 69°
b) y = 69°
Step-by-step explanation:
a. Given that AB and CD are parallel lines, therefore:
x = 69° (alternate interior angles are congruent to each other)
b. y + 111° = 180° (consecutive interior angles are supplementary)
y = 180° - 111° (substraction property of equality)
y = 69°
6
18 divided by 3+6
Hope this helped :)
Answer:
-2.92178
Step-by-step explanation:
Given the function 
The average,A is calculated using the formula;
![A=\frac{1}{b-a}\int\limits^a_b F(x)\, dx \\\\A=\frac{1}{7-1}\int\limits^7_1 3x \ Sin \ x\, dx \\\\\\=\frac{3}{6}\int\limits^7_1 x \ Sin \ x\, dx \\\\\#Integration\ by\ parts, u=x, v \prime=sin(x)\\=0.5[-xcos(x)-\int-cos(x)dx]\limits^7_1\\\\=0.5[-xcos(x)-(-sin(x))]\limits^7_1\\\\=0.5[-xcos(x)+sin(x)]\limits^7_1\\\\=0.5[-6.82595--0.98240]\\\\=-2.92178](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7Bb-a%7D%5Cint%5Climits%5Ea_b%20F%28x%29%5C%2C%20dx%20%5C%5C%5C%5CA%3D%5Cfrac%7B1%7D%7B7-1%7D%5Cint%5Climits%5E7_1%203x%20%5C%20Sin%20%5C%20x%5C%2C%20dx%20%5C%5C%5C%5C%5C%5C%3D%5Cfrac%7B3%7D%7B6%7D%5Cint%5Climits%5E7_1%20x%20%5C%20Sin%20%5C%20x%5C%2C%20dx%20%5C%5C%5C%5C%5C%23Integration%5C%20%20by%5C%20%20parts%2C%20u%3Dx%2C%20v%20%5Cprime%3Dsin%28x%29%5C%5C%3D0.5%5B-xcos%28x%29-%5Cint-cos%28x%29dx%5D%5Climits%5E7_1%5C%5C%5C%5C%3D0.5%5B-xcos%28x%29-%28-sin%28x%29%29%5D%5Climits%5E7_1%5C%5C%5C%5C%3D0.5%5B-xcos%28x%29%2Bsin%28x%29%5D%5Climits%5E7_1%5C%5C%5C%5C%3D0.5%5B-6.82595--0.98240%5D%5C%5C%5C%5C%3D-2.92178)
Hence, the average of the function is -2.92178
