Which set(s) of points show x in DIRECT PROPORTION to y?
2 answers:
Answer: OPTION D.
Step-by-step explanation:
For this exercise it is important to remember that:
1. Direct proportion equations have the following form:
Where "k" is the constant of proportionality.
2. The graph of Direct proportions is an straight line that passes through the origin.
Observe the picture attached.
If you join the points G, C and A, you get a straight line that passes through the origin,
If you join the points F, G and H, you also get a straight line that passes through the origin,
Therefore, the sets of points show "x" in Direct proportion to "y", are:
and
You might be interested in
Answer:
B) 20
Step-by-step explanation:
Don't think to hard about the answer, all the numbers and text can be distracting.
Look at only the length of both Rachel 12 and Amos 16
Now use the Pythagorean theorem to find the unknown side in this right triangle.
Answer:
The equation for the curve is:
Step-by-step explanation:
We know that for a curve defined as:
y = f(x)
The slope of the curve at the point x is:
y = f'(x)
where f'(x) = df(x)/dx
Here we know that we have a function that passes through the point (0, 7)
We also know that the slope of the curve at every point is twice the value of the y-coordinate. (remember that the y-coordinate is given by f(x))
Then we have two equations:
f(0) = 7
f'(x) = 2*f(x)
From the shape of the equation, we can assume than this is an exponential equation like:
Replacing that in the second equation, we get:
From that equation, we can conclude that k = 2
Then:
Now we can use the first equation:
f(0) = 7
With this, we can find the value of A.
Then we can conclude that the equation for the curve is: