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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?

02:33

Taylor S.

Using Models Use the model given to answer the questions about the object or process being modeled. The power $P$ measured in horsepower (hp) needed to drive a certain ship at a speed of $s$ knots is modeled by $$P=0.06 s^{3}$$ (a) Find the power needed to drive the ship at 12 knots. (b) At what speed will a 7.5 -hp engine drive the ship?

0:00

Kelli P.

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

03:34

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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So in this direction in this section, we're going to talk about exponents and powers. So powers basically are when we're taking a number and we're doing repeated multiplication. So an example of this would be if I had the expression to raised to the third power. So what does this really mean? Because it doesn't look like any sort of multiplication. Well, the exponents is this number that's written up here kinda as a superscript. This part is going to be referred to as your exponents and the number down here. Typically, it's also written larger, just as it is here is called your base. So what you're exponents does is it tells us how many times we need to multiply our base by itself. So, for example, to raise to the third power means we need to multiply two by itself three times. So we would need to do to times two times two. And that's essentially what powers mean. So again, your base is the fact that that's getting multiplied, and the exponents tells us how many times it needs to get multiplied. So, another example. Let's say I had X getting raised to the fifth Power Well, that would mean I have to take my factor of X. That's my base and multiply it by itself five times so I would have x times, x times, X times X time sex, And it also makes life going easier for us if we go the opposite way. So, for example, if I had three times, three times three times three, sometimes it's a lot easier to not have it written out that many times. So if I was connecting to write this multiplication now using exponents, my base is the number that's getting repeated. Multiplication, which in this case is three so are based would be three, and our exponents is how many times it's getting multiplied well, 1234 times. So our exponents would be four. So again, this just makes our life a little bit easier in terms of writing it. So now one thing sorry that could be helpful is we have some specific terms that we typically used for these. So just a couple of terms for us to know. So let's say I had the expression for with exponents, too. So now the question is, Well, how would I read this expression. Well, we can say it in one of two ways. One of the most common is to say, your base, which in this case is for, is getting raised to the second power. So we'll say four raised to the second power. Or you can simply just say four to the second power. Now, when we have exponents of two, there's another term that we can use. So that way we don't have to write it as, uh, right out that long sentence. We use the word square, so we could also say the expression for squared. So the squared something means to multiply it by itself twice. So those were just a couple of ways to say an expression that has an expletive, too. Well, what could we do if its exponents was three? So, for example, let's say we had seven getting raised to the third power. Well, you could go back to our basic sentence just like we did in the first one. We could say that this is seven raised to the third Power. This would be a completely fine way of reading the sentence. However, we do also have a shortcut when our explanations. Three. What we can say is the word cube. So for this, I could sure than this and just say seven cubed so that we're cubed means to multiply the seven by itself three times now. I wish I could say that there was a lot more shortcuts for expletive four or five or so forth. But there isn't so, for example, if I had eight getting raised to the six power, there is no shortcut. I would just say eight. Raised to the six power and the next couple of videos. We'll go over some examples of how we can actually use thes how we can evaluate them and use them in different examples.

Linear Functions

Solve Linear Inequalities

Functions

Systems of Equations and Inequalities

Graph Linear Functions

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