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Taylor S.

Using Models Use the model given to answer the questions about the object or process being modeled. A mountain climber models the temperature $T$ ( in $^{\circ} \mathrm{F}$ ) at elevation $h$ (in ft) by $$T=70-0.003 h$$ (a) Find the temperature $T$ at an elevation of 1500 $\mathrm{ft}$ . (b) If the temperature is 64$^{\circ} \mathrm{F}$, what is the elevation?

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Making Models : Write an algebraic formula that models the given quantity. 14. The average $A$ of two numbers $a$ and $b$

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Amy J.

The model $L=4 S$ gives the total number of legs that $S$ sheep have. Using this model, we find that 12 sheep have $L=$ __________ legs.

01:38

Jinseop S.

$3-12=$ Using Models Use the model given to answer the questions about the object or process being modeled. The sales tax $T$ in a certain county is modeled by the formula $T=0.06 x .$ Find the sales tax on an item whose price is $\$ 120 .$

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So in this section we're going to talk about a very brief introduction to algebra. Um, and a couple of big terms that we use a lot in Algebra are variables and expressions, and it's very important to know the difference between the two. So that's why we typically start off the year by discussing them. So the first thing is, well, what is a variable? Well, a variable. Oftentimes you'll see is used as a letter, but what it is, it's a letter that could be used to represent a value so as a simple definition for a variable. What we can say is that it's a symbol because as much as we typically see it as a letter, it's not always a letter. But I'll put in parentheses here that it's usually a letter. But essentially, it's a symbol or letter that's used to represent a number so that is used to represent a number. Like I said, it could be any variable it all, but you'll find a lot of times a math that, um, we'll use X a lot will use why a lot, but really could be any letter. So an example of a letter it could be X. It could be why, Ah, lot of times when you eventually get the trigonometry, you'll use Greek letters. So, for example, like Fada could be an example. But really, it's any type of symbol that could be used to represent the letter are sorry to represent the number. So then the next question is, Well, then what's an expression? Um, and a lot of times when you're talking about expressions using the English language, you're talking about some sort of freeze. Well, it's very similar in math, except in math. It's going to be referred to as a mathematical sentence. Okay, so in expression in math is a mathematical sentence. I know you're probably not used to hearing sentences in math, but really there we have our own language. So it's a mathematical sentence that will consist of numbers, so that consists of numbers. It could have variables in it, and the last thing it will contain is operations. So I'm gonna pay and slash or because it doesn't have to contain all of these so and or operations. And what we mean by operations is addition, subtraction, multiplication division, any of those. Okay, so let's come up with a couple of examples here. So we're gonna scroll down a little bit, hopefully not too far. So let's put a little divider here. So what we're going to come up with is some example of some expressions What they mean, So I'm gonna put their meaning and then what operation that I actually referring to on. We're really just going to talk about our four basic operations. Um, And like I said, that you're gonna we're gonna go over some of these because you'll be seeing these throughout your entire mathematical career. So an example of an expression. So let's say I wanted to multiply three by the variable X so I could rewrite this as three x. I could write this as three and then dot x, where that dot represents multiplication. Or I can use parentheses three times X. So all three of these different ways of expressing this all mean that we're going to multiply three times x, so any time, like in the first part of the example, when the number is directly touching a variable, that again means multiplication. Um, you'll notice that we don't use starting with algebra. We don't usually use expert times. Experts usually be considered the variable. If you wanted to put a some symbol in for times, you could use the DOT That would be perfectly fine for multiplication. Or you can simply put terms in parentheses and whenever to preface is air touching each other. That again also means multiplication. So these are just some examples of how we can represent multiplication. So again, for the operation, this would be multiplication. So the next thing I want to talk about is division and how it could be represented. Well, we could have. Let's use a different color here. We could say why divided by 20. Or if I was to say the same thing, we can use the division symbol Why divided by 20. But know this they mean the same thing. And what you'll find is when it comes to algebra that you typically will use a fraction to represent a division. So again, what do both of these problem means? It means that we're going to take why, and it's getting divided by divided by. There we go 20. So again, both of those expressions mean the same. So again, what operation is this. Well, this is division now. You're addition. Subtraction. Sorry. Carson got away from me. Here. Scroll Back up now. Addition. Subtraction. Like I was gonna say, they're pretty standard. So if I was to write nine plus K, this just means edition. So in terms of the meaning, it's nine plus K, and the operations is addition. And same thing for subtraction. If I was to do 11 minus m again, as I just said, this means 11 minus M. And it just means subtraction. So, really, for addition and subtraction, the way you write things and say things is pretty standard. Like you've always been using them. Maybe you'll just use variables now. Um, but there are a couple of different ways to see multiplication. Okay, So why are these important? Well, one thing that you'll find in algebra is we end up doing what's called evaluating expressions. Let me separate this. So we're going to evaluate expressions, and that word evaluate is very important. You will see that throughout your entire mathematical career. So what exactly doesn't mean to evaluate well, essentially means to find the value of something, or in this case, because we're evaluating expression is going to mean to evaluate and find the value off whatever expression you're given. So in terms of a definition, we could say that it's define the value off a given expression or of a given mathematical expression. I should say so. Like I said, the word evaluate essentially want to consider it would find the value of something. So now there's a couple of different. There's two different ways, really that you could be given in this expression, so the first could be a numerical expression. There we go. So a numerical expression. It's a mathematical sentence that doesn't use variables. You'll only see numbers and operations in here. So if I was to tell you to evaluate eight times three, that just means to find the value of this expression. And again, it's a numerical expression because we didn't use any variables. So if I was to ask you Thio to evaluate the expression eight times three well, eight times three is 24. So the value of this expression would be 24 so that's a numerical expression. Well, we could also have what is known as a variable expression, and this is theater type that you'll see a lot. So a variable expression well, kind of like how it hasn't in the name of variable expression is going to have a variable in it. So if if I was to ask you to evaluate five plus w if W is equal to seven so again our expression is five plus w. But we're trying to evaluate again mean to find the value of, and they're going to give you a value for your variable. So if I was to ask you to evaluate this expression, all we would need to dio is substitute seven and place a W and then find the value. So when I substitute seven and place a w, I would be love with five plus seven, and now I can find the value of this numerical expression. Well, five plus seven is equal to 12. So what that tells us is the value of our variable expression five plus w when W. Is equal to seven would be 12 if w was a different value then that we have a different answer to it. So this is kind of just a nice brief intro of what variables and expressions are upcoming. There will be some examples that will help you practice

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