Write the decimal as a fraction or a mixed number in simplest form. 3.4
2 answers:
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Answer:
- k=27
- y=27x
Step-by-step explanation:
3 tickets to attend an Off-Broadway show cost $81,
4 tickets cost $108; and
5 tickets cost $135.
Let the price of a ticket=k
Therefore:
- 3k=81
- 4k=108
- 5k=135
Solving any of the equation above gives: x=27
We therefore have:
Let y be the total cost of x tickets
- From the above, the constant of proportionality, k=27
An equation for the relationship is therefore:
y=27x (where x is the number of tickets and y is the total costs (in $)).
Part A
A good scale for y to use would be 100, since it fits in all of the f(x)'s and the next value (243) is obviously not going to fit.
As for x, you can use 4 or 5. If you do 5, you're not going to get to it though, because f(x) will be 243.
Part B
When our input increases by 1, our output multiplies by 3.
Multiplying by 3
times can be represented as 
.
We start at 1, so we'd want to have
. However, 1 times anything doesn't change its value, so we can leave it out because it is redundant.
As for making the graph, just label your y axis 0 to 100, and your x axis 0 to 5.
Then mark out (0, 1), (1, 3), (2, 9), (3, 27), and (4, 81).
Draw a curve that includes all of these. It should hit y=100 a little after x=4, since x=5 is all the way at y=243.
A good scale for y to use would be 100, since it fits in all of the f(x)'s and the next value (243) is obviously not going to fit.
As for x, you can use 4 or 5. If you do 5, you're not going to get to it though, because f(x) will be 243.
Part B
When our input increases by 1, our output multiplies by 3.
Multiplying by 3
We start at 1, so we'd want to have
As for making the graph, just label your y axis 0 to 100, and your x axis 0 to 5.
Then mark out (0, 1), (1, 3), (2, 9), (3, 27), and (4, 81).
Draw a curve that includes all of these. It should hit y=100 a little after x=4, since x=5 is all the way at y=243.