Answer:
50
Step-by-step explanation:
ABCD is quadrilateral. Sum of all the angles in a quadrilateral is 360. This means angle ADC will be 130.
ADE is a straight line. Angle ADC and angle CDE should sum up to 180. From here we can infer that angle CDE=x is 50
Answer:
![(4^{-2})^5=\dfrac{1}{4^{10}}](https://tex.z-dn.net/?f=%284%5E%7B-2%7D%29%5E5%3D%5Cdfrac%7B1%7D%7B4%5E%7B10%7D%7D)
Step-by-step explanation:
The given expression is : ![(4^{-2})^5](https://tex.z-dn.net/?f=%284%5E%7B-2%7D%29%5E5)
We need to simplify the above expression.
We know that, ![x^{-a}=\dfrac{1}{x^a}](https://tex.z-dn.net/?f=x%5E%7B-a%7D%3D%5Cdfrac%7B1%7D%7Bx%5Ea%7D)
or
![(4^{-2})^5=(\dfrac{1}{4^2})^5\\\\=\dfrac{1^5}{(4^2)^5}\\\\\because (x^b)^c=x^{b\times c}\\\\=\dfrac{1}{4^{10}}](https://tex.z-dn.net/?f=%284%5E%7B-2%7D%29%5E5%3D%28%5Cdfrac%7B1%7D%7B4%5E2%7D%29%5E5%5C%5C%5C%5C%3D%5Cdfrac%7B1%5E5%7D%7B%284%5E2%29%5E5%7D%5C%5C%5C%5C%5Cbecause%20%28x%5Eb%29%5Ec%3Dx%5E%7Bb%5Ctimes%20c%7D%5C%5C%5C%5C%3D%5Cdfrac%7B1%7D%7B4%5E%7B10%7D%7D)
So, the simplified form of the given expression is
. Hence, the correct option is (A).
Answer:
Option 3 - 4 miles
Step-by-step explanation:
Given : In a city, the distance between the library and the police station is 3 miles less than twice the distance between the police station and the fire station. The distance between the library and the police station is 5 miles.
To find : How far apart are the police station and the fire station?
Solution :
Let the distance between police station and fire station be 'x'.
The distance between the library and the police station is 3 miles less than twice the distance between the police station and the fire station.
i.e. ![2x-3](https://tex.z-dn.net/?f=2x-3)
The distance between the library and the police station is 5 miles.
i.e. ![2x-3=5](https://tex.z-dn.net/?f=2x-3%3D5)
![2x=5+3](https://tex.z-dn.net/?f=2x%3D5%2B3)
![2x=8](https://tex.z-dn.net/?f=2x%3D8)
![x=4](https://tex.z-dn.net/?f=x%3D4)
Therefore, The police and fire stations is 4 miles apart.
So, Option 3 is correct.
The first thing you should do in this case is to write the expression correctly:
- (1/9) y + (1/3)
Now, we take out common factor (1/9) obtaining:
1/9 (-y + 3)
Let's check:
1/9 (-y + 3)
-1/9y + 3/9
-1/9y + 1/3
OK
Answer:
An expression equivalent is:
1/9 (-y + 3)