Answer:
Option (1)
Step-by-step explanation:
By the property of alternate segment theorem,
"Angle formed between the tangent and the chord in a circle measures the half of the measure of the intercepted arc"
m(∠EFG) = 
× m(minor arc FG)
minor arc FG = 2m(∠EFG)
= 2(76°)
= 152°
Therefore, Option (1) will be the correct option.
Answer: Length = 11
Width = 9
Step-by-step explanation:
Let x represent the unknown length.
Let x - 2 represent the unknown width.
The perimeter is equal to 2 times x + (x -2)
Equation:
2 (x + (x - 2)) = 40
x + (x - 2) = 40/2
x + x - 2 = 20
2x - 2 = 20
2x -2 + 2 = 20 + 2
The length is: 2x = 22 -> x = 22/2 -> x = 11
The width is: x - 2 = 9
To be parallel with that line the equation has to have the same slope as the equation given, like y = 10x + 3.
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
