Answer:
50 degrees
Step-by-step explanation:
The angles of a triangle add up to 180 degrees. We would set up the equation like this:
2x+18 + 4x+11 + 55 = 180
Combine like terms:
6x + 84 = 180
Solve for x:
6x = 96
x = 16
We substitute 16 back in for x and see the measure of the smallest angle.
2(16)+18 = 50
4(16)+11 = 75
55
The smallest angle here in 50 degrees.
F(x) = 2÷(x² - 2x - 3)
1)
Domain:
The domain is all the values for x that will produce a real number for y
Factor the denominator to find where y is not defined:
f(x) = 2÷(x² - 2x - 3)
f(x) = 2 ÷ (x-3)(x+1)
The domain is all real numbers except x=3 and x=-1
Range:
The range for y is all the values that y can take, given the domain.
The range is all real numbers, because y approaches both positive and negative infinite at different points on the graph.
The y-intercept is where x=0
y= 2 ÷ (0² - 2(0) -3)
y= 2 ÷ -3 = -2/3
The x-intercept are the points at which y=0.
Let's use the factored form again:
f(x) = 2 ÷ (x-3)(x+1)
This function has no x-intercepts. All values of X either produce a real number, or are undefined in the case of x=3 and x=-1
Horizontal Asymptotes
As X approaches inifinite, how does y behave?
f(x) = 2÷(x² - 2x - 3)
As x approaches both positive and negative infinite, the dominate term in the denominator, x², is vastly greater than 2, and thus y approaches zero.
The horizontal asymptote is zero, in both the positive and negative direction.
Again, let's consult the factored form:
2 ÷ (x-3)(x+1)
There are vertical asymptotes at both x=3 and x=-1. As x approaches these numbers, depending on whether x is a little bigger or smaller than either one, y approaches positive and negative infinite, since the denominator of the function approaches zero.
Therefore, there are both positive and negative vertical asymptotes at both x=3 and x=-1
As for the graph, we'll leave that to you and the many applications that can aid in such a task!
Answer:
26.9
Step-by-step explanation:
Right now we have '8' in the tenths place. That '6' following the '8' requires us to round up. Thus, 26.86 to the nearest tenth is 26.9.
The area would be .4 cubic feet. The perimeter would be 2.1
