Answer:
3x+75=180
3x=180-75
3x=105
x=105/3
x=35
Answer:
A) Not mutually exclusive
Step-by-step explanation:
Given
Required
Determine if they are mutually exclusive or not
Mutually exclusive are defined by:
So, we have:
Take LCM
By comparing:
---- Calculated
---- Given
We can conclude that A and B are not mutually exclusive because:
To calculate minimum value, do -b/2a to get the x-value, and plug it in to get the y-value:
-6/8 = -3/4
So the minimum value of g(x) is -81/4
This shows that g(x) has a lesser minimum value than f(x)
Answer:
a.) a² + b² + c ² + 2ab + 2ac + 2bc
b.) a² + b² + c² - 2ab - 2 ac + 2bc
c ) a² + b² + c² + 2ab - 2ac - 2bc
d.) a² + b² + c² - 2ab + 2ac - 2bc
Step-by-step explanation:
- Use ( a + b + c )² = a² + b² + c² + 2 × ab + 2 × ac + 2 × bc to expand all these expression
a) ( a + b + c )²
= a² + b² + c² + 2 × ab + 2 × ac + 2 × bc
= a² + b² + c ² + 2ab + 2ac + 2bc
b.) ( a - b - c )
= a² + ( - b )² + ( - c)² + 2a ( -b ) + 2a(-c) + 2(-b)(-c)
= a² + b² + c² - 2ab - 2 ac + 2bc
c.) ( a + b - c )²
= a² + b² + ( -c)² + 2ab + 2a ( - c) + 2 b( -c)
= a² + b² + c² + 2ab - 2ac - 2bc
d.) (a - b + c ) ²
= a² + ( -b)² + c² + 2a(-b) + 2ac + 2c( -b)
= a² + b² + c² - 2ab + 2ac - 2bc