For this case we have the following equation:
![\frac {5} {6} (2x + 12) -8 = 4- (x + 1)](https://tex.z-dn.net/?f=%5Cfrac%20%7B5%7D%20%7B6%7D%20%282x%20%2B%2012%29%20-8%20%3D%204-%20%28x%20%2B%201%29)
We apply distributive property on the left side of the equation:
![\frac {5 * 2} {6} x + \frac {5 * 12} {6} -8 = 4- (x + 1)\\\frac {10} {6} x + \frac {60} {6} -8 = 4- (x + 1)](https://tex.z-dn.net/?f=%5Cfrac%20%7B5%20%2A%202%7D%20%7B6%7D%20x%20%2B%20%5Cfrac%20%7B5%20%2A%2012%7D%20%7B6%7D%20-8%20%3D%204-%20%28x%20%2B%201%29%5C%5C%5Cfrac%20%7B10%7D%20%7B6%7D%20x%20%2B%20%5Cfrac%20%7B60%7D%20%7B6%7D%20-8%20%3D%204-%20%28x%20%2B%201%29)
We simplify the left side of the equation:
![\frac {5} {3} x + 10-8 = 4- (x + 1)](https://tex.z-dn.net/?f=%5Cfrac%20%7B5%7D%20%7B3%7D%20x%20%2B%2010-8%20%3D%204-%20%28x%20%2B%201%29)
Different signs are subtracted and the major sign is placed.
![\frac {5} {3} x + 2 = 4- (x + 1)](https://tex.z-dn.net/?f=%5Cfrac%20%7B5%7D%20%7B3%7D%20x%20%2B%202%20%3D%204-%20%28x%20%2B%201%29)
On the right side we must take into account that:
![- * + = -](https://tex.z-dn.net/?f=-%20%2A%20%2B%20%3D%20-)
So:
![\frac {5} {3} x + 2 = 4-x-1\\\frac {5} {3} x + 2 = 3-x](https://tex.z-dn.net/?f=%5Cfrac%20%7B5%7D%20%7B3%7D%20x%20%2B%202%20%3D%204-x-1%5C%5C%5Cfrac%20%7B5%7D%20%7B3%7D%20x%20%2B%202%20%3D%203-x)
We add x to both sides of the equation:
![\frac {5} {3} x + x + 2 = 3\\\frac {5 * 1 + 3 * 1} {3} x + 2 = 3\\\frac {5 + 3} {3} x + 2 = 3\\\frac {8} {3} x + 2 = 3](https://tex.z-dn.net/?f=%5Cfrac%20%7B5%7D%20%7B3%7D%20x%20%2B%20x%20%2B%202%20%3D%203%5C%5C%5Cfrac%20%7B5%20%2A%201%20%2B%203%20%2A%201%7D%20%7B3%7D%20x%20%2B%202%20%3D%203%5C%5C%5Cfrac%20%7B5%20%2B%203%7D%20%7B3%7D%20x%20%2B%202%20%3D%203%5C%5C%5Cfrac%20%7B8%7D%20%7B3%7D%20x%20%2B%202%20%3D%203)
We subtract 2 from both sides of the equation:
![\frac {8} {3} x = 3-2\\\frac {8} {3} x = 1](https://tex.z-dn.net/?f=%5Cfrac%20%7B8%7D%20%7B3%7D%20x%20%3D%203-2%5C%5C%5Cfrac%20%7B8%7D%20%7B3%7D%20x%20%3D%201)
We multiply by 3 on both sides of the equation:
![8x = 3](https://tex.z-dn.net/?f=8x%20%3D%203)
We divide by 8 on both sides of the equation:
![x = \frac {3} {8}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%20%7B3%7D%20%7B8%7D)
Thus, the solution of the equation is:
![x = \frac {3} {8}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%20%7B3%7D%20%7B8%7D)
Answer:
![x = \frac {3} {8}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%20%7B3%7D%20%7B8%7D)
Answer:
The radius is 2 units, and the graph is symmetric about the line Theta = StartFraction pi Over 2 EndFraction. Its answer A
Step-by-step explanation:
9514 1404 393
Answer:
8 : 125
Step-by-step explanation:
The volume is proportional to the cube of the side lengths. Hence, the ratio of volumes is proportional to the cube of the ratio of side lengths.
v1 : v2 = (2 : 5)^3 = 2^3 : 5^3 = 8 : 125
Answer:5/2 times 1/3
Step-by-step explanation:
were goated if you asner
G ( x ) = 2 - ( x - 7 )²
g ( x ) = 2 - ( x² - 14 x + 49 )
g ( x ) = 2 - x² + 14 x - 49
g ( x ) = - x² + 14 x - 47
The maximum of the function is at:
x= - b / 2 a
x = - 14 / ( - 2 ) = 7
Therefore the function is increasing form x ∈ ( - ∞, 7 ) and decreasing for x ∈ ( 7, +∞ ).
Answer:
C. increasing, x < 7; decreasing x > 7.