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:

Practice Questions:

Solutions:

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

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?

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:

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

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

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

Solutions:

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! 🙂

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:

Now let’s see how we can apply our knowledge of absolute value equations when there is a missing variable!

Now let’s look at a slightly different example:

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

Solutions:

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

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!

Now let’s see how we can apply trig ratios when there is a missing side or angle in a right triangle!

Now for another type of question; using trig functions to find missing angles, let’s take a look:

Try the following Practice Questions on your own!

Solutions:

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

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!

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

We use logarithms to find the unknown values of exponents, such as the x value in the equation, . This is a simple example, where we know the value of x is equal to 2,(). 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:But wait there’s more! Logs have a certain set of Rules that makes working with them easier! Check it out below:

We can use these rules to help us algebraically solve logarithmic equations, let’s look at an example that applies the Product Rule.

Try the following practice questions on your own!

Practice Questions:

Solutions:

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! 🙂

____________________________________________________________________ Choose the factoring method that works best for you and try the practice problems on your own below!

Practice Questions:

Solutions:

Want a review of all the different factoring methods out there? Check out the ones left out here (DOTS and GCF) and happy calculating! 🙂

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

Step 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.Step 2: Now that we found the value of x , we can plug it back into the equation for median, to find the value of median

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

Practice Questions:

1.is the median of trapezoid ABCDEF, find the value of the median, given the following:2. is the median of trapezoid ACTIVE, find the value of the median, given the following:3.is the median of trapezoid DRAGON, find the value of the median, given the following:

4. is the median of trapezoid MATRIX, find the value of the median, given the following:

Solutions:

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

Today we’re back with Algebra 2, this time solving for radical equations! Did you say “RadicalEquations?” As in wild and crazy equations? No, not exactly, radicals in math are used to take the square root, cubed root, or whatever root of a number.

Radicals are actually pretty cool because we can write them a couple of different ways and they all mean the same thing! Check it out below:Still not sure of their coolness? Let’s see what they look like with actual numbers: Example: Solve the following algebraic equation below for the missing variable (aka, solve for x).Explanation:

How do I answer this question?

The question wants us to solve for x using our knowledge of radicals and algebra. You can also check out how to solve this question on Youtube here!

How do we do this?

Step 1: We start solving this radical equation like any other algebraic problem: by getting x alone. We can do this easily by subtracting 7 and then dividing out 5.Step 2: Now, to get rid of that pesky radical, we need to square the entire radical. Remember, whatever we do to one side of the equation, we must also do to the other side of the equation, therefore, we also square 14 on the other side of the equal sign.

*This gets rid of our radical and allows us to solve for x algebraically as normal!What happens when there is a cubed root though!?!?When dividing polynomials with different value roots, raise the entire radical to that same power of root to cancel it out:Remember, we know radicals can also be written as fractions: Therefore we also know that if we raise the entire radical expression to the same power of the root, the two exponents will cancel each other out:Want more practice? Try solving these next few examples on your own. When you’re ready, check out the below:

Did I miss anything? Don’t let any questions go unchecked and let me know in the comments! Happy calculating! 🙂

Don’t forget to check out the latest with Mathsux and subscribe!

In honor of Earth Day last week, I thought we’d take a look at some math that appears magically in nature. Math? In nature? For those of you who think math is unnatural or just terrible in general, this is a great time to be proven otherwise!

The key that links math to nature is all about PATTERNS. All math is based on is patterns. This includes all types of math, from sequences to finding x, each mathematical procedure follows some type of pattern. Meanwhile back in the nearest forest, patterns are occurring everywhere in nature.

The rock star of all patterns would have to be FRACTALS. A Fractal is a repeating pattern that is ongoing and has different sizes of the exact same thing! And the amazing thing is that we can actually find fractals in our neighbor’s local garden.

Let’s look at some FractalExamples:

(1) Romanesco Broccoli: Check out those repeating shapes, that have the same repeating shapes on those shapes and the same repeating shapes on even smaller shapes and…. my brain hurts!

(2) Fern Leaves: The largest part of this fractal is the entire fern leaf itself. The next smaller and identical part is each individual “leaf” along the stem. If you look closely, the pattern continues!

(3) Leaves: If you’ve ever gotten up real close to any type of leaf, you may have noticed the forever repeating pattern that gets smaller and smaller. Behold the power and fractal pattern of this mighty leaf below!

.

Just in case fractals are still a bit hard to grasp, check out the most famous Fractal below, otherwise known as Sierpinski’s Triangle. This example might not be found in your local back yard, but it’s the best way to see what a fractal truly is up close and infinite and stuff.

Looking for more math in nature? Check out this post on the Golden Ratio and happy calculating! 🙂