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Harvey Mudd College
University of Michigan - Ann Arbor
Idaho State University
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.
Making Models : Write an algebraic formula that models the given quantity.
15. The cost $C$ of purchasing $x$ gallons of gas at $\$ 3.50$ a gallon
Suppose gas costs $\$ 3.50$ a gallon. We make a model for the cost $C$ of buying $x$ gallons of gas by writing the formula $C=$ _________.
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and this example, we're being asked to simplify the following expressions by combining like terms. Remember, like terms have the same variables. Raced to the same exponents, so to combine, like terms What we're gonna do first is group are like terms together. So let's start with number one. So we have eight x squared minus five x plus two X squared plus x So let's first identify are like terms. Our first term. Eight X squared has a light term of positive two X squared. So what we can dio using the computer and associative properties is weaken. Group those together so we can have eight x squared plus two. Expert. Now let's look at our next term being negative five x Well, it has a like term, a positive X so we can group these together as well. So we'll have negative five x plus x. So now to combine like terms, what we're going to do is combine the coefficients and we're gonna bring down the variable with their exponents. Almost want to think about it as, uh, if you were to do inventory at the store and you're combining apples and oranges, you would Onley add the apples all together, and then add or subtract the apples all together and then add and subtract all the oranges or bananas together. You wouldn't actually combine them. So essentially, if we need to combine eight x squared with positive two X Square in this case, we're gonna add the coefficients. Well, eight plus two is 10, so that means we have 10 X Square. Now let's combine our second parallel terms. We have negative five X plus X. So again we're supposed to combine the coefficients now for that last term positive ax. Remember, we don't see a coefficient is really and imagine everyone there. Well, now let's go ahead and combine them. Well, negative five plus one is negative four, which means we have negative for X now. We can't simplify any fervor because 10 X squared and negative forex are not like terms, so this will be our final answer. All right, let's go ahead and try Number two. We have three x y plus two x squared Y minus seven x squared y. So the first thing we need to do is group are like terms together. Well, let's take a look at our first term. We have three x Y, and it doesn't have a like term because even though the other two terms have X's and Y's in it, they're not both raised to the same exponents. So all we're going to do with this first term is just bring it down and it won't end up combining with anything. Now let's take a look at our next term. We have two X squared Y Well, that has a late term of negative X squared y. And because there, over the next to each other, we can go ahead and combine them. Remember, we're just going to combine the coefficients, so we have two minus seven, which is negative. Five, which means we have negative five X squared. Why so notice? When you combine like terms, the variables and their exponents never change just to coefficient of the term changes. Now, because three x Y and negative five X squared wire not like terms, we cannot simplify any fervor. So three x y minus five X squared y will be our final answer
Solve Linear Inequalities
Systems of Equations and Inequalities
Graph Linear Functions