Geometry: Reflections

Greetings and welcome to Mathsux! Today we are going to go over reflections, one of the many types of transformations that come up in geometry.  And thankfully, it is one of the easiest transformation types to master, especially if you’re more of a visual learner/artistic type person. So let’s get to it!

What are Reflections?

Reflections on a coordinate plane are exactly what you think! When a point, a line segment, or a shape is reflected over a line it creates a mirror image.  Think the wings of a butterfly, a page being folded in half, or anywhere else where there is perfect symmetry.

Check out the Example below:

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Practice Questions:

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Solutions:

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Still got questions?  No problem! Check out the video above or comment below! Happy calculating! 🙂

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Algebra 2: Rational Exponents

MathSux^2

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Still got questions?  Don’t hesitate to comment below for anything that still isn’t clear! 🙂

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Happy calculating! 🙂

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Algebra: Piecewise Function Review

Greetings, today’s post is for those in need of a piecewise function review!  This will cover how to graph each part of that oh so intimidating piecewise function.  There’s x’s, there are commas, there are inequalities, oh my! We’ll figure out what’s going on here and graph each part of the piecewise-function one step at a time.  Then check yourself with the practice questions at the end of this post. Happy calculating! 🙂

 

Wait, what are Piece-Wise Functions? Exactly what they sound like! A function that has multiple pieces or parts of a function.  Notice our function below has different pieces/parts to it.  There are different lines within, each with their own domain.Screen Shot 2020-07-21 at 10.01.59 AM

Now let’s look again at how to solve our example, solving step by step:

Screen Shot 2020-07-21 at 10.02.29 AM.pngScreen Shot 2020-07-21 at 10.02.41 AMScreen Shot 2020-07-21 at 10.03.06 AM.png

Translation: We are going to graph the line f(x)=x+1 for the domain where x > 0

To make sure all our x-values are greater than or equal to zero, we create a table plugging in x-values greater than or equal to zero into the first part of our function, x+1.  Then plot the coordinate points x and y on our graph.

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Translation: We are going to graph the line  f(x)=x-3 for the domain where x < 0

To make sure all our x-values are less than zero, let’s create a table plugging in negative x-values values leading up to zero into the second part of our function, x-3.  Then plot the coordinate points x and y on our graph.

Screen Shot 2020-07-21 at 10.07.33 AM.png

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Ready to try the practice problems below on your own!?

Practice Questions: Graph each piecewise function:

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Solutions:

Screen Shot 2020-07-21 at 10.09.20 AM

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Still got questions?  No problem! Check out the video above or comment below for any questions. Happy calculating! 🙂

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***Bonus! Want to test yourself with a similar NYS Regents question on piecewise functions?  Click here.

 

 

Geometry: Intersecting Secant Theorem

Ahoy! Today we’re going to cover the Intersecting Secants Theorem!  If you forgot what a secant is in the first place, don’t worry because all it is a line that goes through a circle.  Not so scary right? I was never scared of lines that go through circles before, no reason to start now.

If you have any questions about anything here, don’t hesitate to comment below and check out my video for more of an explanation. Stay positive math peeps and happy calculating! 🙂

Wait, what are Secants?

Screen Shot 2020-07-14 at 10.07.54 PM

Intersecting Secants Theorem: When secants intersect an amazing thing happens! Their line segments are in proportion, meaning we can use something called the Intersecting Secants Theorem to find missing line segments.  Check it out below: 

Screen Shot 2020-07-14 at 10.44.53 PM

Let’s now see how we can apply the intersecting Secants Theorem to find missing length.

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Ready to try the practice problems below on your own!?

Practice Questions: Find the value of the missing line segments x.

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Solutions:

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Still got questions?  No problem! Check out the video above or comment below for any questions and follow for the latest MathSux posts. Happy calculating! 🙂

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To review a similar NYS Regents question check out this post here

Algebra: Absolute Value Equations

Happy Wednesday math friends! Today, we’re going to go over how to solve absolute value equations.  Solving for absolute value equations supplies us with the magic of two potential answers since absolute value is measured by the distance from zero.  And if this sounds confusing, fear not, because everything is explained below!

Also, if you have any questions about anything here, don’t hesitate to comment. Happy calculating! 🙂

Absolute Value measures the “absolute value” or absolute distance from zero.  For example, the absolute value of 4 is 4 and the absolute value of -4 is also 4.  Take a look at the number line below for a clearer picture:

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Now let’s see how we can apply our knowledge of absolute value equations when there is a missing variable!Screen Shot 2020-07-08 at 2.03.07 PMScreen Shot 2020-07-08 at 2.03.46 PM.pngScreen Shot 2020-07-08 at 2.04.00 PMScreen Shot 2020-07-08 at 2.04.26 PM.pngScreen Shot 2020-07-08 at 2.04.56 PM

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Screen Shot 2020-07-08 at 2.05.39 PMNow let’s look at a slightly different example:

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Practice Questions: Given the following right triangles, find the missing lengths and side angles rounding to the nearest whole number.

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Solutions:

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Still got questions?  No problem! Check out the video the same examples outlined above. Happy calculating! 🙂

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Geometry: How to use SOH CAH TOA

Welcome back to Mathsux! This week, we’re going to go over how to find missing angles and side lengths of right triangles by using trigonometric ratios (sine, cosine, and tangent).  Woo hoo! These are the basics of right triangle trigonometry, and provides the basis for mastering so many more interesting things in trig! So, let’s get to it!

Also, if you have any questions about anything here, don’t hesitate to comment below. Happy calculating! 🙂

Trigonometric Ratios (more commonly known as Sine, Cosine, and Tangent) are ratios that naturally exist within a right triangle.  This means that the sides and angles of a right triangle are in proportion within itself.  It also means that if we are missing a side or an angle, based on what we’re given, we can probably find it!

Let’s take a look at what Sine, Cosine, and Tangent are all about!

Screen Shot 2020-07-04 at 5.03.29 PM.pngNow let’s see how we can apply trig ratios when there is a missing side or angle in a right triangle!Screen Shot 2020-07-04 at 5.04.02 PM

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Now for another type of question; using trig functions to find missing angles, let’s take a look:Screen Shot 2020-07-04 at 5.05.01 PM.pngScreen Shot 2020-07-04 at 5.19.13 PMScreen Shot 2020-07-04 at 5.19.30 PM.png

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Try the following Practice Questions on your own!

Screen Shot 2020-07-04 at 5.05.55 PMSolutions:

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Still got questions?  No problem! Check out the video the same examples outlined above and happy calculating! 🙂

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Algebra 2: How to Solve Log Equations

Welcome to Mathsux! Today, we’re going to go over how to solve logarithmic equations, yay! But before we get into finding x, though, we need to go over what logarithms are and why we use them in the first place…..just in case you were curious!

Also, if you have any questions about anything here, don’t hesitate to comment below or shoot me an email.  Happy calculating! 🙂

Logarithms are the inverses of exponential functions.  This means that when graphed, they are symmetrical along the line y=x.  Check it out below!

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When on the same set of axis, notice how the functions are symmetrical over the line y=x:

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We use logarithms to find the unknown values of exponents, such as the x value in the equation, Screen Shot 2020-06-24 at 9.30.55 PM.png.  This is a simple example, where we know the value of x is equal to 2,(Screen Shot 2020-06-24 at 9.32.30 PM.png). But what if it were to get more complicated?  That’s where logs come in!

Logarithms follow a swooping pattern that allows us to write it in exponential form, let’s take a look at some Examples below:Screen Shot 2020-06-24 at 9.34.16 PM.pngBut wait there’s more! Logs have a certain set of Rules that makes working with them easier! Check it out below:

Screen Shot 2020-06-24 at 9.35.10 PMWe can use these rules to help us algebraically solve logarithmic equations, let’s look at an example that applies the Product Rule.

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Try the following practice questions on your own!

Practice Questions:

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Solutions:

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Still got questions?  No problem! Check out the video that goes over the same example outlined above.  And for more info. on logarithms check out this post that goes over a NYS Regent’s question here.  Happy calculating! 🙂

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****Check out this Bonus Video on How to Change Log Bases****

 

 

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

Screen Shot 2020-06-02 at 7.34.48 AM

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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