Tag: Review

Geometry: Median of a Trapezoid Theorem

*If you haven’t done so, check out the video that goes over this exact problem, also please don’t forget to subscribe!

Medians of a Trapezoid copy

Screen Shot 2020-06-02 at 7.31.07 AMStep 1:  Let’s apply the Median of a Trapezoid Theorem to this question!  A little rusty?  No problem, check out the Theorem below.

Median of a Trapezoid Theorem: The median of a trapezoid is equal to the sum of both bases.Screen Shot 2020-06-02 at 7.32.31 AMStep 2: Now that we found the value of x , we can plug it back into the equation for Screen Shot 2020-06-02 at 7.33.44 AMmedian,  to find the value of median Screen Shot 2020-06-02 at 7.34.25 AM

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Want more practice?  Your wish is my command! Check out the practice problems below:

Practice Questions:

1.Screen Shot 2020-06-02 at 7.35.29 AMis the median of trapezoid ABCDEF, find the value of the median, given the following:Screen Shot 2020-06-02 at 7.35.47 AM2. Screen Shot 2020-06-02 at 9.01.08 AMis the median of trapezoid ACTIVE, find the value of the median, given the following:Screen Shot 2020-06-02 at 9.16.22 AM3.Screen Shot 2020-06-02 at 9.17.01 AMis the median of  trapezoid DRAGON, find the value of the median, given the following:Screen Shot 2020-06-02 at 9.22.13 AM

4. Screen Shot 2020-06-02 at 9.23.08 AMis the median of trapezoid MATRIX, find the value of the median, given the following:Screen Shot 2020-06-02 at 9.23.43 AM

Solutions:

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Need more of an explanation?  Check out the detailed video and practice problems. Happy calculating! 🙂

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Algebra 2: Dividing Polynomials

Screen Shot 2020-05-03 at 11.43.01 AMNow that everyone is home, there is no better time to go over dividing polynomials! Whether school is out or not, dividing polynomials will always come in handy… I think.

Either way at some point, you may need to know how to answer these types of questions. The cool thing about dividing polynomials is that it’s the same long division you did way back in grade school (except now with a lot of x). Ok, let’s get to it and check out the question below:

Also, if you haven’t done so, check out the video related that corresponds to this problem on Youtube! 🙂

Screen Shot 2020-05-04 at 10.21.17 PMExplanation:

How do I answer this question?

The question wants us to divide polynomials by using long division.

How do we do this?     

Step 1: First we set up a good ole’ division problem with the divisor, dividend, and quotient to solve.Screen Shot 2020-05-04 at 10.43.48 PM.pngStep 2: Now we use long division like we used to back in the day! If you have any confusion about this please check out the video in this post.Screen Shot 2020-05-04 at 10.22.52 PMScreen Shot 2020-05-04 at 10.23.27 PM.pngWhat happens when there is a remainder though!?!? When dividing polynomials with a remainder in the quotient, the answer is found and checked in a very similar way! Check it out below:
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Notice we represented the remainder by adding Screen Shot 2020-05-04 at 10.35.06 PM to our quotient! We just put the remainder over the divisor to represent this extra bit of solution.

Want more practice? Try solving these next few examples on your own. Screen Shot 2020-05-04 at 10.45.10 PM.pngWhen you’re ready, check out the solutions below:Screen Shot 2020-05-04 at 10.45.37 PMI hope everyone is finding something fun to do with all this extra time home! That can include everything from baking a cake to studying more math of course, happy calculating! 🙂 

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COVID-19: What does #FlattenTheCurve even mean?

If you are a human on Earth, then I’m sure you’ve heard about the coronavirus and are currently social distancing. Here in NYC, I’m quarantining like everyone else and listening to all the beautiful math language that has suddenly become mainstream (so, exciting)!  #FlattenTheCurve has become NY’s new catchphrase and for anyone confused about what that means, you’ve come to the right place!

The coronavirus spreads at an Exponential Rate, which means it spreads in a way that increases faster and faster every day.

What does this mean?

For Example, one person with the virus can easily spread the virus to 5 other people, those 5 people can then spread the virus to another 5 people each for a total of an extra 25 people, these 25 people can then spread it to another 5 people each for an extra 125 infected people! And the pattern continues……. See below to get a clearer picture:

Screen Shot 2020-04-12 at 1.26.39 PMScreen Shot 2020-04-12 at 1.20.22 PM.   *Note: These numbers are not based on actual coronavirus data

The Example we just went over is equal to the exponential equation Screen Shot 2020-04-12 at 1.21.48 PM, but it is only that, an Example! The exact pattern and exponential equation of the future progress of the virus is unknown! We mathematicians, can only measure what has already occurred and prepare/model for the future.  To make the virus spread less rapidly, it is our duty to stay home to slow the rate of this exponentially spreading virus as much as possible.

We want to #FlattenTheCurve a.k.a flatten the increasing exponential curve of new coronavirus cases that appear every day! Hopefully, this post brings some clarity to what’s going on in the world right now.  Even with mathematics, the true outcome of the virus may be unknown, but understanding why we are all at home in the first place and the positive impact it has is also important (and kind of cool).

Stay safe math friends and happy mathing! 🙂

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Bored and Confused?

Calling all students, teachers, and parents!  As everyone is stuck at home during a global pandemic, now is a great time we are all forced to try and understand math (and our sanity level) a little bit more.  Well, I may not be able to help you with the keeping sanity stuff, but as far as math goes, hopefully, the below websites offer some much needed mathematic support.

All jokes aside I hope everyone is staying safe and successfully social distancing.  Stay well, math friends! 🙂

Kahn Academy: The same Kahn Academy we know and love still has amazing videos and tutorials as usual, but now they also have a live “homeroom” chat on Facebook LIVE every day at 12:00pm. The chats occur daily with Kahn Academy founder Sal and at times feature famous guests such as Bill Gates. Click the link below for more:

Khan Academy Homeroom Screen Shot 2020-04-04 at 12.21.20 PM

 

Study.com: In a time when companies are being more generous, Study.com is here for us as they offer up to 1000 licenses for school districts and free lessons for teachers, students, and parents.  Check out all the education freebies here:

Study.com

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Math Planet: If you’re looking for free math resources in Pre-Algebra, Algebra, Algebra 2, and Geometry then you will find the answers you need at Math Planet.  All free all the time, find their website here:

MathPlanet 

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JMAP: For anyone who has to take the NYS Regents at some point (whenever we’re allowed to go outside again), JMAP has every old Regents exam as well as answers to boot! Did I mention each exam is free and printable?  Find their website here:

JMAP

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What is your favorite educational site?  Let me know in the comments, and stay well! 🙂

Algebra 2: Binomial Cubic Expansion

Screen Shot 2019-05-24 at 8.47.46 AM.pngScreen Shot 2019-05-24 at 8.48.17 AM.pngscreen-shot-2019-05-24-at-8.49.45-am.pngScreen Shot 2019-05-24 at 8.50.15 AM.png

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Extra Tip! Notice that we used something called FOIL to combine (a+b)(a+b).  But what does that even mean? FOIL is an acronym for multiplying the two terms together.  It’s a way to remember to distribute each term to one another.  Take a look below:

Screen Shot 2019-05-24 at 9.02.50 AM.pngScreen Shot 2019-05-24 at 9.03.23 AM.png

Add and combine all like terms together and we get Screen Shot 2019-05-24 at 9.04.45 AM.png!

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Still got questions?  Let me know in the comments and as always happy calculating!:)

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Geometry: The Voluminous “Vessel” at Hudson Yards

Calling all NYC dwellers! Have you seen the new structure at Hudson Yards?  A staircase to nowhere, this bee-hive like structure is for the true adventurists at heart; Clearly, I had to check it out!

Where does math come in here you say?  Well, during my exploration, I had to wonder (as am sure most people do) what is the volume of this structure?  What do you think the volume of the Vessel is? (Hint: feel free to approximate!)

Screen Shot 2019-04-11 at 5.38.46 PM.png

Solution: I estimated the volume by using the formula of a three-dimensional cone. (Not an exact measurement of the Vessel, but close enough!) .

Screen Shot 2019-04-11 at 5.08.42 PM Screen Shot 2019-04-12 at 1.20.08 PM.pngWe can find the radius and height based on the given information above.  Everything we need for our formula is right here!

Screen Shot 2019-04-14 at 4.49.16 PM

Now that we have our information, let’s fill in our formula and calculate! Screen Shot 2019-04-11 at 5.14.58 PM.pngScreen Shot 2019-04-11 at 5.17.30 PM.png

Screen Shot 2019-04-11 at 5.18.27 PM.png

Screen Shot 2019-04-14 at 4.51.42 PM.png

Extra Tip! Notice that we labeled the solution with feet cubed Screen Shot 2019-04-14 at 4.53.49 PM.png, which is the short-handed way to write “feet cubed.”  Why feet cubed instead of feet squared? Or just plain old feet? When we use our formula we are multiplying three numbers all measured in feet:

radius X radius X (Height/3)

All three values are measured in feet! –> Feet cubed (Screen Shot 2019-04-14 at 4.53.49 PM.png)

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Did you get the same answer? Did you use a different method or have any questions?  Let me know in the comments and happy mathing! 🙂

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Algebra: Rate of Change

Screen Shot 2018-12-28 at 8.21.26 AMScreen Shot 2018-12-28 at 8.22.23 AMScreen Shot 2018-12-28 at 8.23.21 AMScreen Shot 2018-12-28 at 8.24.00 AMScreen Shot 2018-12-28 at 8.24.30 AM.pngScreen Shot 2018-12-28 at 8.25.03 AM.png

Extra Tip! Notice that we added the labels feet/second to our answer.  Why does this make sense?? The question tells us that P(t) represents feet and that t is equal to seconds.  Another way to look at this question when applying it to the slope formula is to realize that we are finding the change of feet divided by the change of seconds.                                                          ____________________________________________________________________________________

Still got questions?  Let me know in the comments and as always happy calculating!:)

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Geometry: Intersecting Secants

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*Extra Tip! Why does this formula work in the first place!??  If we draw lines creating and proving triangle RTQ and triangle RPS are similar by AA, this leads us to know that the two triangles have proportionate sides and can follow our formula!         ___________________________________________________________________________________

Still got questions?  Let me know in the comments and remeber having questions is a  good thing!

Also, happy holidays from Mathsux! May your December break be filled with family, food, happiness, and maybe some math problems! 🙂

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Summertime Review: Factoring

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Whether you are ready to go back to school or back to sleep, I hope you found this factoring review helpful.

Still got questions?  Don’t hesitate to reach out in the comments below! Happy math-ing! 🙂

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