The answers is 14 if you follow the equation i just did it on a calculator (attached)
Answer:
k =4
Step-by-step explanation:
5k-2k=12
Combine like terms
3k = 12
Divide each side by 3
3k/3 = 12/3
k = 4
This graph has a horizontal asymptote so it is an exponential graph. It also passes through two points (0,-2) and (1,3). The horizontal asymptote is at y=-3.
The unchanged exponential equation is y=a(b)^x +k
For exponential equations, k is always equal to the horizontal asymptote, so k=-3.
You can check this with the ordered pair (0,-2). After that plug in the other ordered pair, (1,3).
This gives you 3=a(b)^1 or 3=ab. If you know the base the answer is simple as you just solve for a.
If you don't know the base at this point you have to sort of guess. For example, let's say both a and b are whole numbers. In that case b would have to be 3, as it can't be 1 since then the answer never changes, and a is 1. Then choose an x-value and not exact corresponding y-value. In this case x=-1 and y= a bit less than -2.75. Plug in the values to your "final" equation of y=(3)^x -3.
So -2.75=(3^-1)-3.
3^-1 is 1/3, 1/3-3 is -8/3 or -2.6667 which is pretty close to -2.75. So we can say the final equation is y=3^x -3.
Hope this helps! It's a lot easier to solve problems like these given either more points which you can use system of equations with, or with a given base or slope.
We have the equation
Let's complete the square, to do it let's add and subtract 25 on the right side
Now we can have y in function of x
Now we can already identify the vertex because it's in the vertex form:
Where the vertex is
As we can see, h = 5 and k = -2, then the vertex is
Now we can continue and find the focus, the focus is
We have a = 1/20, therefore
The focus is
And the last one, the directrix, it's
Then
Hence the correct answer is: vertex (5, -2); focus (5, 3); directrix y = -7
Answer:
Step-by-step explanation:
Ivan and 3 others were evenly matched.
1+3=4
So there were 4 grandmas on the other team. :)
