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Missouri State University

Campbell University

07:20

Alix S.

Using Models Use the model given to answer the questions about the object or process being modeled. The gas mileage $M($ in milgal) of a car is modeled by $M=N / G,$ where $N$ is the number of miles driven and $G$ is the number of gallons of gas used. (a) Find the gas mileage $M$ for a car that drove 240 mi on 8 gal of gas. (b) $A$ car with a gas mileage $M=25$ mi/gal is driven 175 mi. How many gallons of gas are used?

02:13

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?

07:29

James C.

Using Models Use the model given to answer the questions about the object or process being modeled. An ocean diver models the pressure $P$ ( in $\mathrm{lb} / \mathrm{in}^{2} )$ ) at depth $d$ (in ft) by $$P=14.7+0.45 d$$ (a) Make a table that gives the pressure for each 10 -ft change in depth, from a depth of 0 ft to 60 $\mathrm{ft}$ . (b) If the pressure is $30 \mathrm{lb} / \mathrm{in}^{2},$ what is the depth?

00:50

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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So in this section, we're gonna be talking about adding, subtracting rational numbers, Remember a rational number. Those are all the types of numbers you've been talking about throughout your entire mathematical career So far, you could talk about whole numbers. Um, negative numbers, decimals, fractions, all of these. But essentially, we're gonna be dealing with what happens when numbers have the same sign. Different signs, etcetera. So the couple of general rules to remember is that when you're adding two numbers that have the same side, what you want to do is add their absolute values and keep the sign of the larger number. So you're gonna add their absolute values and we'll go over this in some examples. So we'll add their absolute values and keep the sign meaning If both numbers were positive, your answer will be positive. If both numbers were negative, then you'll keep your answer negative. Okay, so that's what happens when they're the same sign you're gonna add their absolute values and keep the sign. Well, then what are you going to dio when they're different signs? Well, the opposite of adding would be subtract. So we're going to subtract their absolute values So that's gonna be the first thing is we're going to subtract their absolute values. Absolute. Let's make that letter a little eligible here. There we go. So we're going to subtract their absolute values now, in regards to the sign, we're going to keep the sign of the larger absolute value number so and keep keep to sign of the bigger number and keep the sign of the bigger number. And like I said, we'll do a couple of examples together. All right, so that's how we add Thio rational numbers when they have the same sign you're gonna add when they have different signs should probably put signs in here. We'll put insert that. So now the question is, Well, then, what's the rule when you're subtracting? Well, what we're gonna end up doing is we're gonna end up turning it into an addition problem? So what you're gonna do when you're subtracting, you're gonna add the opposite and again, we're going to do showing some examples here, So add the opposite. Okay, so let's do a couple of quick examples here, so separate this. So some examples. So first thing, let's say we have eight plus five So in terms of the absolute value, the absolute value of eight is a the absolute value. Five is five. So these two numbers both have the same sign. They're both positive. Therefore, we're gonna add the absolute values. Will eight plus five is equal to 13 and because both of their signs are positive, our answer will be positive. 13. Now, let's say I was to take negative eight plus negative five. So again, both of these numbers have the same sign. They're both negative. So in order to add these, what we're going to dio is we're gonna add their absolute values. Well meaning absolute value. Remember, makes them positive. See absolute value. Negative eight is eight. The absolute value negative five is five and eight plus five is 13 Now, remember, because both signs were the same, we have to keep design, so our answer will be negative. 13. All right, let's show another example. So, in this case, let's say we had negative eight plus five. Well, this is an example of when they have different signs because the eight is negative and the five is positive. So what do we do when we have different signs we're going to subtract their absolute values. So the absolute value of eight is eight, and then we're going to do eight minus five, which is three. But remember, we're going to keep the sign of the larger number. So in this case, the absolute value of negativity is eight, which is larger than five. So we're going to keep this as a negative answer. So the answer to negative eight plus five is negative three. And lastly, the upper case scenario we could have here is, let's say we had eight plus negative five again. Both of these numbers have different signs because they ate is positive and the fives negative. So what we're gonna do is we're going to subtract their absolute values well again. The absolute value of eight is eight. The absolute value negative five is five and eight, minus five is three. But remember, we're going to keep the larger of the two signs and because the absolute value of eight is bigger than the absolute value negative five, our answer is going to stay positive. So eight plus negative five is equal to positive three. So now the question is, well, what happens when we start subtracting. So let's say we had eight minus five. Now, this might be one of those examples were like, Oh, I've seen this problem before. I know the answers. Three, But in terms of what we're doing here, if we wanted to change this into addition problem, we would rewrite this as eight plus negative five. What we do is we take the opposite off our second number. And as you can see, this problem is just let the exact same is number four on. We already found that eight plus negative five is positive. Three. So let's say we had a problem like negative eight minus five. So again, we have a subtraction problem because we're taking negative eight and remind missing five. So what we want to do is rewrite it as an addition problem. So the first number stays the same. Negative eight, and then we're gonna add the opposite. So we're gonna add the opposite of positive five, which is negative. Five. So now we have negative eight plus negative five. And as you can see, this is the exact same problem is number two. So what we found is that our answer will be negative. 13. Well, let's do another scenario. Let's say we had eight minus negative five. So again, we have subtraction, So we're gonna add the opposite. So we're gonna bring down the first number eight, and we're gonna add the opposite of negative five, which is positive. Five. So, really, this just becomes a plus five, which is the exact same problem is number one. So a plus five is positive. 13. And now for our last example that we could have, let's say we had negative eight minus negative five. So again, we have a subtraction problem. So we're gonna bring down our first number negativity, and then we're gonna add the opposite of negative five, which is positive. Five. So, really, this problem is the same as negative eight plus five. And this is problem is the exact same is number three. And what we found is that negative eight plus five is negative three. So these are all the different scenarios that you could potentially see now, just as a couple of reminders. The first thing is just a quick review when you're adding decimals, adding or subtracting decimals, I should say So you're going to say, follow the same rules as above, but the one thing you have to remember and again just going to do. A brief review here is that when you add and subtract decimals, you need toe line up the decimal values. So just to remember, tow line up the decimals. So whenever you and it's a checked, always make sure you line up two decimals. The second thing I wanted to remind you off is, Well, what about when you're adding, subtracting fractions? Because fractions air also rational numbers. So the biggest thing to remember that when you're adding, subtracting fractions, you need to have a common denominator. So you must have a common denominator in order to add or subtract two fractions. So despite what their science might be, they could be positive. They could be negative. But no matter what, make sure that they have a common denominator. So that's the key thing here. And as you go in through the next couple examples, I will do some examples with adding subtracting decimals and adding subtracting fractions to remind you how to do both of these

Linear Functions

Solve Linear Inequalities

Functions

Systems of Equations and Inequalities

Graph Linear Functions

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