Lorena and Julio purchased a home for $205,950. Their loan amount was $164,760, and the assessed value is now $200,500. Their ta
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We are given points 
and 
.
We first find the midpoint M, of AB, which divides the segment AB into 2 equal parts,
then we find the midpoint N of AM, and midpoint K of MB.
Thus each of the half parts is divided into 2 equal parts. The whole segment is divided into 4 equal parts.
The coordinates of M, N and K are found as follows:
the coordinates of M are:
the coordinates of N are:
similarly, the coordinates of k are:
We first find the midpoint M, of AB, which divides the segment AB into 2 equal parts,
then we find the midpoint N of AM, and midpoint K of MB.
Thus each of the half parts is divided into 2 equal parts. The whole segment is divided into 4 equal parts.
The coordinates of M, N and K are found as follows:
the coordinates of M are:
the coordinates of N are:
similarly, the coordinates of k are:
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.
Answer:
Ryan would like to eat <em>more than</em> 50 carbs per day, but <em>no more than</em> 150 carbs per day.
So, Ryan's total carb intake must be <em>between </em>50 and 150 carbs.
Step-by-step explanation:
So he wants to keep his consumption of carbs between the inequalities:
So, let's solve both inequalities.
1)
Subtract 10 from both sides:
Divide both sides by 2:
2)
Subtract 10 from both sides:
Divide both sides by 2:
So, our inequality is now:
Since we solved the equations:
Written as a compound inequality, this is:
In other words, Ryan would like to eat <em>more than</em> 50 carbs per day, but <em>no more than</em> 150 carbs per day.
So, Ryan's total carb intake must be <em>between </em>50 and 150 carbs.