Answer:
10q - 1
Step-by-step explanation:
Sum/difference:
Let
This means that
Now, assume that 
is rational. The sum/difference of two rational numbers is still rational (so 5-x is rational), and the division by 3 doesn't change this. So, you have that the square root of 8 equals a rational number, which is false. The mistake must have been supposing that was rational, which proves that the sum/difference of the two given terms was irrational
Multiplication/division:
The logic is actually the same: if we multiply the two terms we get
if again we assume x to be rational, we have
But if x is rational, so is -x/15, and again we come to a contradiction: we have the square root of 8 on one side, which is irrational, and -x/15 on the other, which is rational. So, again, x must have been irrational. You can prove the same claim for the division in a totally similar fashion.
If a is the number of events, then a = 1. Plugging in 1 for a in the equation
, you get
.
Total cost is $9.
So,first step is to write ![(fog)(-4)) =f[g(-4)] \\](https://tex.z-dn.net/?f=%20%28fog%29%28-4%29%29%20%3Df%5Bg%28-4%29%5D%20%5C%5C%20)
Now we start from inner paranthesis
,we need to first find value of
![g(-4) =\frac{\sqrt{12-(-4)}}{3}\\ =\frac{\sqrt{12+4}}{3}\\ =\frac{\sqrt{16}}{3}\\ =\frac{4}{3}\\ (fog)(-4)) =f[g(-4)] =f(\frac{4}{3}) =9(4/3)^{2} =9*(16/9) =144/9 =16](https://tex.z-dn.net/?f=%20g%28-4%29%20%3D%5Cfrac%7B%5Csqrt%7B12-%28-4%29%7D%7D%7B3%7D%5C%5C%20%3D%5Cfrac%7B%5Csqrt%7B12%2B4%7D%7D%7B3%7D%5C%5C%0A%3D%5Cfrac%7B%5Csqrt%7B16%7D%7D%7B3%7D%5C%5C%0A%3D%5Cfrac%7B4%7D%7B3%7D%5C%5C%0A%28fog%29%28-4%29%29%20%3Df%5Bg%28-4%29%5D%20%3Df%28%5Cfrac%7B4%7D%7B3%7D%29%20%3D9%284%2F3%29%5E%7B2%7D%20%3D9%2A%2816%2F9%29%20%3D144%2F9%20%3D16%20)
Answer:
f(x) = |x|, f(x) = [x] + 6
Step-by-step explanation:
Almost all of these are absolute values equations, which means the y doesn't change if x is positive or negative. The first one is the parent form, which is the simplest equation of the absolute equation, so it's symmetric with respect to the y-axis. The second equation is translated 3 units to the left, and the third is translated 31 to the left. The forth is translated 6 up, so it's still symmetric with respect to the y-axis. The fifth is translated 61 units left, and the last one is simply a line, which isn't symmetric.
