11/5/2022 0 Comments Word fonts![]() ![]() Both the macOS as well as the older OS X operating systems hide your own library folder. You will also notice that your personal Library folder isn't going to be present. Be sure to replace your username with your home folder's name. ![]() #Word fonts install#If you want these new downloadable fonts to only be available to you, install them in your personal Library folder at your username/Library/Fonts. How to Install Fonts Only for Your Account By closing all the open apps, you will be assured that any app you have just launched after installing the font will be able to use the new font. When you have decided to install the fonts, there will be active apps that won't be able to see the new font resources ONLY until they have been restarted. Often you'll see these fonts described as Windows fonts, but the truth is that there's an excellent chance these fonts will work just fine on your Mac especially the fonts whose filenames end in the ".ttf" (which means they're TrueType Fonts).īefore you decide to install any fonts, you should be sure to quit all open applications. Installing Fonts to Word on Macīoth the OS X and the macOS can use fonts in various formats. There are many beginner-friendly desktop publishing programs, and the more fonts along with clip art you have to choose from, the easier and the more fun you can have creating greeting cards, family newsletters, or whatever project you may be working on. #Word fonts pro#You don't have to be a graphics pro designer to need or want an extensive collection of fonts. We have found that the more there is, the harder it is to make a choice. You'd be surprised how challenging it can be to find the perfect even if you have hundreds of fonts to choose from. The web is a goldmine of free along with low-cost fonts for your Mac, and we strongly believe that you can never have too many fonts. Moreover, while the Mac did come with a nice collection of fonts, it usually is not too long before you have begun installing new fonts to your Mac as soon as you could find them. Fonts have long been one of the defining features of the Mac - ever since it was first introduced. ![]()
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11/5/2022 0 Comments Factor quadratic equation![]() \((2x – 3)\) is common to both terms, so we can write this as \((x 2)(2x – 3)\), and we have our answer. Now, lastly, step number four tells us that we should be able to see an obvious common factor, which we have. From the last two terms, we can factor out a 2, which would give us \(2(2x – 3)\). From the first two terms, we can factor out an \(x\), which would give us \(x(2x – 3)\). So, we would group together \((2x^2 – 3x) (4x-6)\), then factor. Step 3 tells us to group together the first two terms, and the last two terms, then factor them individually. Step two tells us to replace the middle of the equation with the two factors that we found. That makes our factors -3 and 4, which multiplies to give us -12 and add to give us positive 1. So, the only way that can happen is if we take the two factors 3 and 4, and throw a negative sign in front of 3. So, we need these factors to multiply to get -12, which each of them will if we through a negative sign in front of one of the factors, but we also need for it to add to get positive one. Remember, we are actually dealing with a -12, so we need to consider that when choosing which two factors work. So, obviously there is 1 and 12, then 2 and 6, and lastly 3 and 4. So, let’s go ahead and list all the possible factors of 12. So, first, we need to identify which two numbers multiply together to get \(a\times c\), which is -12, and add to get \(b\) (positive 1). #FACTOR QUADRATIC EQUATION HOW TO#Let’s look at how to factor the equation \(2x^2 x – 6\) using these four steps. The two terms, at this point, should now have an obvious common factor.Group together the first two terms and the last two terms, then factor them individually.Well, let’s look at an example of one of these equations that may be a little trickier to factor. So, it may be we don’t just know the factors off the top of our head, and guessing might not be as quick as we would hope. ![]() ![]() However, our numbers aren’t always so straightforward. In our last example, it was relatively simple to find a common factor for the two numbers 8 and 16. When we look at the graph for \(8x^2 16x = 0\), we can see that it’s zero at \(x = 0\) and \(x = -2\).Īlright, so that is kind of a side note to answer the question “why does factoring matter?”īut now, let’s look back at how to actually factor. To do that, we would set our factors equal to zero and solve. Well, factoring the quadratic equation then sets us up to be able to find out where exactly our roots are, and our roots just mean where our graph is equal to zero. Well, if you recall a quadratic equation is always a parabola (or U-shaped graph). Maybe you’re asking, why on earth do I even need to factor? Why can’t I just leave it as it is? \(x^2\) and \(x\) share a common factor of \(x\). ![]() But, we still have something that can be factored out. Now, we have \(8(x^2 2x)\) being multiplied by everything on the inside. So, we can go ahead and factor out that 8. ![]() Well, 8 and 16 share a common factor of 8. What are the common factors of \(8x^2 16x = 0\)? Say we have the equation \(8x^2 16x = 0\) The easiest way to do this is to find the common factor. Now, expanding can be pretty easy we know exactly what to do to expand them when given our factors, but figuring out how to factor our expanded version can be a little harder. So, again we have our factors \((x 2)(x 6)\) on the left, and when you multiply that you get the expanded version: \((x^2 8x 12)\). Once you multiply together you get \(x^2 8x 12\). The actual quadratic equation is the expanded, or multiplied out version, of your two factors that are being multiplied.įor example, \((x 2)\) and \((x 6)\) are my factors that are being multiplied together. In order to factor a quadratic, you just need to find what you would multiply by in order to get the quadratic. ![]() |
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