Julio bought a total of 20 medium and large pumkins if he spent 53$ and bought 6 more large pumkins as medium pumkins how many l
1 answer:
You might be interested in
Two figures are similar if one is the scaled version of the other.
This is always the case for circles, because their geometry is fixed, and you can't modify it in anyway, otherwise it wouldn't be a circle anymore.
To be more precise, you only need two steps to prove that every two circles are similar:
- Translate one of the two circles so that they have the same center
- Scale the inner circle (for example) unit it has the same radius of the outer one. You can obviously shrink the outer one as well
Now the two circles have the same center and the same radius, and thus they are the same. We just proved that any two circles can be reduced to be the same circle using only translations and scaling, which generate similar shapes.
Recapping, we have:
- Start with circle X and radius r
- Translate it so that it has the same center as circle Y. This new circle, say X', is similar to the first one, because you only translated it.
- Scale the radius of circle X' until it becomes
. This new circle, say X'', is similar to X' because you only scaled it
So, we passed from X to X' to X'', and they are all similar to each other, and in the end we have X''=Y, which ends the proof.
To determine the maximum value of a quadratic function opening downwards, we are going to find the vertex; then the y-value of the vertex will be our maximum.
To find the vertex (h,k) (where h=x-coordinate and k=y-coordinate) of a quadratic function of the form
we'll use the vertex formula: 
, and then we are going to replace that value in our original function to find k.
So, in our function
, 
and 
.
Lets replace those values in our vertex formula:
Now that we know the x-coordinate of our vertex, lets replace it in the original function, to get the y-coordinate:
We just prove that the vertex of
is (2,1), and for the graph we can tell that the vertex of 
is (-2,4). The only thing left is compare their y-coordinates to determine w<span>hich one has the greater maximum value. Since 4>1, we can conclude that </span> has the greater maximum.
To find the vertex (h,k) (where h=x-coordinate and k=y-coordinate) of a quadratic function of the form
So, in our function
Lets replace those values in our vertex formula:
Now that we know the x-coordinate of our vertex, lets replace it in the original function, to get the y-coordinate:
We just prove that the vertex of