Since g(6)=6, and both functions are continuous, we have:
![\lim_{x \to 6} [3f(x)+f(x)g(x)] = 45\\\\\lim_{x \to 6} [3f(x)+6f(x)] = 45\\\\lim_{x \to 6} [9f(x)] = 45\\\\9\cdot lim_{x \to 6} f(x) = 45\\\\lim_{x \to 6} f(x)=5](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%206%7D%20%5B3f%28x%29%2Bf%28x%29g%28x%29%5D%20%3D%2045%5C%5C%5C%5C%5Clim_%7Bx%20%5Cto%206%7D%20%5B3f%28x%29%2B6f%28x%29%5D%20%3D%2045%5C%5C%5C%5Clim_%7Bx%20%5Cto%206%7D%20%5B9f%28x%29%5D%20%3D%2045%5C%5C%5C%5C9%5Ccdot%20lim_%7Bx%20%5Cto%206%7D%20f%28x%29%20%3D%2045%5C%5C%5C%5Clim_%7Bx%20%5Cto%206%7D%20f%28x%29%3D5)
if a function is continuous at a point c, then
,
that is, in a c ∈ a continuous interval, f(c) and the limit of f as x approaches c are the same.
Thus, since
, f(6) = 5
Answer: 5
Answer:
x= 4, -1
Step-by-step explanation:
-2x - 2 + x^2 + x + 180 - 2x - 2 = 180
add like terms and put in descending order
x^2 - 3x + 176 = 180
subtract 180 from both sides
x^2 - 3x - 4 = 0
factor out the equation
(x-4)(x+1)=0
solve for x
x-4=0 x+1=0
x=4 x=-1
Answer:
Width 
units
Length 
units
Step-by-step explanation:
The rectangle has an area of 
The width of the rectangle is equal to the greatest common monomial factor of 
and 
Find this monomial factor:
Hence, the width of the rectangle is units.
The area of the rectangle can be rewritten as
The area of the rectangle is the product of its width by its length, then the length of the rectangle is units.
Which number line represents the solution set for the inequality 2x – 6 ≥ 6(x – 2) + 8?
So, you know that there were 5 people there, Kara and 4 friends. To divide equally, just divide 42.30 by 5=
42.30/5 = 8.46
Each person played $8.46.
Hope this helps!!
~Kiwi
