## 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!

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! 🙂

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

## Algebra: How to Graph y=mx+b

Hi everyone, welcome back to Mathsux! This week we’ll be reviewing how to graph an equation of a line in y=mx+b form. And if you have not checked out the video below, please do! Happy calculating! 🙂

Graphing an Equation of Line: An equation of a line can be represented by the formula:

Y-Intercept: This is represented by b, the stand-alone number in y=mx+b. This represents where the line hits the y-axis.  This is always the first point you want to start with when graphing at coordinate point (0,b).

Slope: This is represented by m, the number next to x in y=mx+b. Slope tells us how much we go up or down the y-axis and left or right on the x- axis in fraction form:

Now let’s check out an Example!

Graph the equation of a line .

Try the following practice questions on your own!

Practice Questions:

Want more Mathsux?  Don’t forget to check out our Youtube channel and more below! And if you have any questions, please don’t hesitate to comment below. Happy Calculating! 🙂

## Geometry: Perpendicular and Parallel Line Through a Given Point

Happy Wednesday math friends! Today we’re going to go over the difference between perpendicular and parallel lines. Then we’ll use our knowledge of equation of a line (y=mx+b) to see how to find perpendicular and parallel lines through a given point.  This is is a common question that comes up on the NYS Geometry Regents and is something we should prepare for, so let’s go!

If you need any further explanation, don’t hesitate to check out the Youtube video below that goes into detail on how to solve these types of questions one step at a time. Happy calculating! 🙂

Perpendicular lines: Lines that intersect to create a 90-degree angle and can look something like the graph below.  Their slopes are negative reciprocals of each other which means they are flipped and negated. See below for example!

Example: Find an equation of a line that passes through the point (1,3) and is perpendicular to line y=2x+1 .

Parallel lines are lines that go in the same direction and have the same slope (but have different y-intercepts). Check out the example below!

Example: Find an equation of a line that goes through the point (-5,1) and is parallel to line y=4x+2.Try the following practice questions on your own!

Practice Questions:

1) Find an equation of a line that passes through the point (2,5) and is perpendicular to line y=2x+1.

2) Find an equation of a line that goes through the point (-2,4) and is perpendicular to line

3)  Find an equation of a line that goes through the point (1,6) and is parallel to line y=3x+2.

4)  Find an equation of a line that goes through the point (-2,-2)  and is parallel to line y=2x+1.

Solutions:

Need more of an explanation? Check out the video that goes over these types of questions up on Youtube (video at top of post) and let me know if you have still any questions.

Happy Calculating! 🙂

## Algebra: 4 Ways to Factor Quadratic Equations

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

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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! 🙂

## 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!

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 detailedand practice problems. Happy calculating! 🙂

## Algebra: Completing the Square

Learn how to Complete the Square by clicking on the Youtube video and trying the practice problems below. Happy Calculating! 🙂

Click the picture below to view the Youtube video.

Practice Questions:

Solutions:

Need more of an explanation?  Check out why we complete the square in the first place here and please don’t forget to subscribe! 🙂

## Algebra 2: Solving Radical Equations

Today we’re back with Algebra 2, this time solving for radical equations!  Did you say “Radical Equations?” 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!

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## Algebra 2: Dividing Polynomials

Now 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! 🙂

Explanation:

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.Step 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.What 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:

Notice we represented the remainder by adding  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. When you’re ready, check out the solutions below:I 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! 🙂

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

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## Earth Day Fractals!

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 Fractal Examples:

(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!

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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! 🙂

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