Answer:
a) see the plots below
b) f(x) is exponential; g(x) is linear (see below for explanation)
c) the function values are never equal
Step-by-step explanation:
a) a graph of the two function values is attached
__
b) Adjacent values of f(x) have a common ratio of 3, so f(x) is exponential (with a base of 3). Adjacent values of g(x) have a common difference of 2, so g(x) is linear (with a slope of 2).
__
c) At x ≥ 1, the slope of f(x) is greater than the slope of g(x), and the value of f(x) is greater than the value of g(x), so the curves can never cross for x > 1. Similarly, for x ≤ 0, the slope of f(x) is less than the slope of g(x). Once again, f(0) is greater than g(0), so the curves can never cross.
In the region between x=0 and x=1, f(x) remains greater than g(x). The smallest difference is about 0.73, near x = 0.545, where the slopes of the two functions are equal.
Step-by-step explanation:
x²/(x²-9) + 1/(x-3) = 1/(4x-12)
4x² + 4(x+3) = 1
4x² + 4x + 11 = 0
Since the discriminant is negative, there are no real solutions.
1/3 is greater. Picture a pie with nothing cut into it. Then, you cut 3 equal pieces out of it, leaving no pie remaining. So, if you take 1 piece, you have 2 pieces that you didn't take. So if you do the exact same thing, but you cut <em>8 </em>pieces out of the pie and you take 1 piece, there are still 7 pieces remaining. So 1/8 is a smaller part of the pie than the 1/3, since you are cutting the pie into 8 identical pieces while with 1/3 you are cutting the same sized pie into 3 pieces. Sorry if I was confusing, just ask me if you want an easier-to-understand explanation. Also, if you pick a "brainliest" answer, it actually <em>gives </em>you points.
Answer:
I do not know how it wants the answer, but it is -4.1 repeating.
I am guessing you meant solve for z too? If there are multiple choice I can help choose the right one.
Step-by-step explanation:
-32>5+9z
subtract 5 from both sides
-37>+9z
then divide 9 from both sides
-4.1111 repeating > z
The simplify answer is 550.
