We have (1,4) + (-1,-4) = (0,0), because 1 + (-1) = 1 - 1 = 0 and 4 + (-4) = 4 - 4 = 0.
Hey there!
Let's think of both of these functions as two different slope-intercept equations (y=mx+b). Don't let all of the fs and gs confuse you; those are just showing that they are two different functions!
Our function f has an equation of y=x, which is a diagonal line that passes through the origin and goes across each small grid on the graph diagonally.
Our function g has an equation of y=-1/3x+2, which means that it will intersect with the y-axis at two units above the origin and for every three whole steps it goes to the right, it will have gradually gone down one whole step as well.
Attached to my answer is what a graph of it would kind of look like. Sorry if the lines don't look too much like a line it's a bit difficult to draw with a mouse haha!
I hope that this helps! Have a wonderful day!
Answer:
It should be -5/2 for the points (-6,8) (-16,33)
Step-by-step explanation:
Input is the same as the x-term and output is the same as the y-term.
For example, take a look at the image provided with thee table.
Looking at the first box of our table, notice that if we subtract 5 from 1, we get -4 and if we subtract 5 from 2 we get -3 and if we subtract 5 from 3, we get -2. Notice that in each case, we're subtracting 5 from the input to get the output.
I attached a table so you can practice if you'd like to. All you have to do is subtract 5 from each input and you will end up with the output. The first few are done for you. I also provided an answer key in the next image so you can check your work.
The last one might be a little trick. In the input, we have n which is a variable that represents any number. If we want to find the nth term, we simply subtract 5. So we have n - 5.
First image is practice if you'd like and the second is the key.
If you don't want to do it, no worries.
Answer:
45
Step-by-step explanation:
If a(1) = 5, then a(2) = a(1)*3, or 5*3, or 15.
If a(2) = 15, then a(3) = a(2)*3, or a(3) = 15*3 = 45
This is a geometric sequence with first term a(1) = 5 and common ratio 3. We can immediately write the explicit formula
a(n) = 5*3^(n - 1), which correctly predicts that a(3) = 5*3^(3 - 1) = 5*9 = 45