Your post (" <span>f(x) = 2/3(6)x ") would be clearer and less ambiguous if you'd please format it as follows:
</span><span>f(x) = (2/3)(6)^x. The (2/3) shows that 2/3 is the coefficient of the exponential function 6^x. Please use " ^ " to indicate exponentiation.
Start by graphing </span><span>f(x) = (2/3)(6)^x. The y-intercept, obtained by setting x=0, is (0, 2/3). Can you show that the value of f(x) is (2/3)*6, or 4, at x=1, (2/3)*6^2, or 24, at x = 2, and so on? What happens if x becomes increasingly smaller? The graph approaches, but does not touch, the x-axis.
If you complete this graphing assignment, then all you'd have to do is to flip the whole graph over vertically, reflecting it in the x-axis. You'll see that the graph never touchs the x-axis. Therefore, the range of this flipped graph is (-infinity, 0).</span>
Answer:
A) Container X
Step-by-step explanation:
X=2C:6S ratio, now reduce amount but keep the same ratio
X=1C:3S
Y=4C:8S ratio, now reduce amount but keep the same ratio
Y=1C:2S
Container X has the sweeter water because it's ratio of sugar to water is higher.
First distribute the negative through the parenthesis on the left and the 2 on the right.
-5 -15y +1 = 14y -32 - y
Combine like terms on the right and left
-4 -15y = 13y -32
Now move the variables to one side and the constants to the other.
Subtract 13y from both sides
-4 -28y = -32
Add 4 to both sides
-28y = -28
Divide both sides by -28
y = 1
Miles using 4.5 gallons = 144 miles
Miles using 1 gallon
(144 miles / 4.5 gallons)
32 miles / gallon
