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01:04

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.

01:11

Ruirui L.

Making Models : Write an algebraic formula that models the given quantity. 13. The number $N$ of cents in $q$ quarters

03:07

Taylor S.

Using Models Use the model given to answer the questions about the object or process being modeled. Arizonans use an average of 40 gal of water per person each day. The number of gallons $W$ of water used by $x$ Arizonans each day is modeled by $W=40 x$ . (a) Make a table that gives the number of gallons of water used for each $1000-$ person change in population, from 0 to $5000 .$ (b) If the pressure is $30 \mathrm{lb} / \mathrm{in}^{2},$ what is the depth? (b) What is the population of an Arizona town whose water usage is $120,000$ gal per day?

0:00

Kyle I.

Using Models Use the model given to answer the questions about the object or process being modeled. The distance $d$ (in mi) driven by a car traveling at a speed of $v$ miles per hour for $t$ hours is given by $$d=v t$$ If the car is driven at 70 milh for 3.5 $\mathrm{h}$ , how far has it traveled?

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we're gonna look right now at how to simplify out to break expressions. Algebraic expressions are simply expressions that have at least one variable. An example could be the expression Just X X is a variable by itself, so it could just be a single term. It could be even something similar to two X Plus five. We have two terms, and one of our terms has a variable in it. It could even be something a little bit more complicated as, for example, three times V plus Y plus four, we have at least one variable. Now, when we're trying to simplify an algebraic expression, we want to minimize the expression to a few terms as possible. Now all the examples I just gave you are all examples of algebraic expressions that have already been simplified. But sometimes they're not. So there's two things we commonly look for when we're trying to simplify an algebraic expression. The first thing we look for is to see if we can get rid of any parentheses by using the distributive property. Now, when we learned the order of operations, we learned that the first thing we always want to workout is whatever in the parentheses, but sometimes you can't work out what's in the parentheses. Instead, you have to use distributive property. Distributive property says that if I multiply a times in the parentheses, B Times C, this is equivalent as to going a Times B plus a Times C using our example from above. We have three times V plus why we can multiply three V and we could multiply three y. But that's a Sfar as we can go, and those are examples of simplified algebraic expressions. The other thing we always want to look for when simplifying algebraic expressions is to see if we can combine any like terms. Now, when we do talk about combining like terms we are talking about in reference to adding or subtracting, you're not gonna do any multiplying or dividing in this point. So combining like terms now in order to combine like terms, the terms must have the same variable, and they must have the same exponents. Now it's really important to know that when I say the same exponents, we're actually just looking at the variable. We wanna make sure the variable has the same exponents. The coefficient does not matter So, for example, we could have X plus. Why? Well, both of these were just variables, but they're not the same variable ones and x one. So why? So I can't combine them. I could have two x plus x. Well, both of these terms have x as a variable. So I'm gonna add my coefficient. So two plus one is three X. We could have negative tin y squared monos wa When this case, I cannot combine them because my wife has an exponents of two in the first term and there's not an exponents in the second term, but I could have four b squared minus six B square. In this case, I can combine because both terms have be square. So I would just simply, in this case of track my coefficient so negative to and bring my b squared over. And in our examples, we're gonna see when you have to use both distributive property and combining like terms

Linear Equations and Functions

Linear Equations and Inequalities

Matrices and Determinants

Quadratic Equations

Applications of Trigonometric Functions

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