Since ABCD is a parallelogram, the opposite sides will be parallel and equal,
![\begin{gathered} AB=CD \\ BC=AD \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20AB%3DCD%20%5C%5C%20BC%3DAD%20%5Cend%7Bgathered%7D)
Consider that AC acts as a transversal to the parallel lines AB and CD, so we can write,
![\begin{gathered} \angle CAD=\angle ACB\text{ (Alternate Interior Angles)} \\ BC=AD\text{ (Opposite sides of parallelogram)} \\ \angle ADB=\angle CBD\text{ (Alternate Interior Angles)} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cangle%20CAD%3D%5Cangle%20ACB%5Ctext%7B%20%28Alternate%20Interior%20Angles%29%7D%20%5C%5C%20BC%3DAD%5Ctext%7B%20%28Opposite%20sides%20of%20parallelogram%29%7D%20%5C%5C%20%5Cangle%20ADB%3D%5Cangle%20CBD%5Ctext%7B%20%28Alternate%20Interior%20Angles%29%7D%20%5Cend%7Bgathered%7D)
So by the ASA criteria, the triangle AED is congruent to the triangle CEB,
Then the corresponding parts of the triangles will be equal,
![\begin{gathered} AE=CE \\ BE=DE \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20AE%3DCE%20%5C%5C%20BE%3DDE%20%5Cend%7Bgathered%7D)
Hence Proved.
Answer: Second option.
Step-by-step explanation:
Given the functions f(x) and g(x):
![f(x)=12x^2-4x-8\\\\g(x)=11x-6](https://tex.z-dn.net/?f=f%28x%29%3D12x%5E2-4x-8%5C%5C%5C%5Cg%28x%29%3D11x-6)
You need to divide them in order to find
asked in the exercise. Then:
![(\frac{f}{g})(x) =\frac{12x^2-4x-8}{11x-6}](https://tex.z-dn.net/?f=%28%5Cfrac%7Bf%7D%7Bg%7D%29%28x%29%20%3D%5Cfrac%7B12x%5E2-4x-8%7D%7B11x-6%7D)
Now, it is important to remember that, by definition, the division by zero is not defined. Therefore, the denominator of the function cannot be zero.
Let's find the value of "x" for which the denominator of the function would be zero:
1. You need to make the denominator equal to zero:
![11x-6=0](https://tex.z-dn.net/?f=11x-6%3D0)
2. Finally, you must solve for "x":
![11x=6\\\\x=\frac{6}{11}](https://tex.z-dn.net/?f=11x%3D6%5C%5C%5C%5Cx%3D%5Cfrac%7B6%7D%7B11%7D)
Therefore, as you can see, the answer is:
, ![x=\frac{6}{11}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B6%7D%7B11%7D)
Answer:
the answer is 128.4
Step-by-step explanation:
To round up a number to the nearest tenth if the hundredth is more than or 5 you add 1 to the tenth but if it less than 5 you remove the other numbers and leave the number like that which will give you 128.4.
Answer:20000200
Step-by-step explanation: