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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.

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?

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?

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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compound inequalities. Now, when we look at the word compound, you may think of something like a compound sentence. And really and truly, it is the same thing and a compound sentence. We have two sentences that come together to make one. When a compound inequality, we have to inequalities that make one. So it's the same concept as a compound sentence. So when we're looking at compound inequalities, we look at two types we look at. Our statements are and statements, so let's look at some examples. So let's look at the first one as in plus, one is less than or equal to three or negative four in is less than negative eight. Here we have two competent to inequalities that air connected with the word or now remember the word or means it can be one or the other. For example, if I go to the movies and I buy a Coke or but box of popcorn, I can only buy one or the other. I'm not gonna purchase both. So because of that, that is the difference with the word or so let's look at thes. So in order to do this, we're gonna solve these individually. So let's go ahead and solve the first inequality. And the first inequality is in. Plus one is less than or equal to three. So I would start off by subtracting one on both sides. So for my first inequality, I would have in is less than or equal to negative four. We also had the inequality negative four n is less than negative eight. Well, for this one, I don't have anything to add or subtract. So I'm gonna go ahead and divide by negative four so in and because we divided by negative four is going to be greater than positive, too. Now I'm gonna show you why this is or so Let's say I drew a number line. I'm gonna go with my number line. I'm just gonna count by four me toos. So for this number one, let's start with in is less center equal to four. Well, because it's equal to we're gonna have a close circle and it's going to go to the left so it could be any number less than or equal to negative four. Well in is greater than our in. Could be greater than two. Well, because it's just greater than we know. It can't be, too, but it can be any number greater than two. Notice that my arrows air going in the opposite direction away from each other because they're moving away from each other. They don't have any shared numbers. So this is where our or statement comes in. Sometimes we have inequalities that are connected by the word, and so an example of this could be negative. 10 minus two V is less than six and six V plus 12 is less than negative six. Now this is an example because we're using the word, and this is an example of where both of them have to be true. So go back to the movie. Example. If I go to the movies and buy a Coke and a box of popcorn, you should expect me toe walk with both of those items in and means both. So for this one, both have to be true for this toe workout, just like with the or we're gonna work thes individually. So let's start with the first one so we would start off by adding 10 to both sides. So negative to be is less than 16 we're gonna divide by two. Negative too. Which means our inequality signs gonna change. So we have V is greater than negative eight. For our second one we have we're going to subtract 12 from both sides. So we have six day is less than negative 18. We're gonna divide by six. Now, this time the six is positive. So we are not going to change our inequality, son. Instead, we're gonna have V is less than negative three. And we're gonna bring down our and but we're gonna look at a number line to show why this example is Aunt. So let's look at a number line really quick. Okay, So we have the is greater than negative eight and the is less than negative three. So if I drew this as a number one, we're gonna let count by ones. But we're just gonna do our negative numbers since both of these air negative. So we'll have negative one. Negative to negative three Negative four Negative five Negative. Six. Negative. Seven. Negative. Eight and negative. Not so. Let's start with V is greater than negative eight. So it's an open circle, and my arrow could be any number is greater than negative eight. Then we have V is less than through negative three, so it's eating numbers in three. So notice what happens is my arrows are going opposite direction, but they're going towards each other, which means that they share all possible solutions. So all the numbers between negative eight and negative three are possible solutions to the compound inequality. Let's look at another example of an and let's look at negative 33 is less than or equal to negative seven in modest 12, which is less than negative 26. Now this is also an example of an and inequality. But the difference is is they didn't write the word because what's happened is both inequalities share one part of it, and in this case, they're gonna share this middle part, which is negative seven in minus 12. So, really, another way of writing these inequalities would be negative. 33 is less than or equal to negative. Seven n minus 12 A and negative seven in minus 12 is less than negative. 26. Both inequality share the negative seven minus 12, but toe work it out. We're actually gonna work these out separately, So we're gonna work them out just like this, right here. Split up into two different inequalities. So let's work the first one. So let's add 12 to both shots. So negative 33 plus 12 is negative 21 and then we would divide by negative seven. So we're gonna have positive three. We're gonna change. Our son is greater than or equal to Ian. And for a second one, we're gonna add 12 again. Negative seven in is less than negative. 14. We're going to vie by negative seven. Again, our side is gonna change We live in is greater than to So now we have another and statement. So let's create a number line to show why these are in an statement. So, Marie writer answer. So we have three is greater than or equal Thio end and Ian is greater than two. So we're gonna draw our number line, and I'm just gonna do positive numbers for this one's of zero one to three, four and five. So we have three is greater than or equal to end. Another way of writing this one is actually going to be. Ian is less than or equal to three. This is why it's a good idea to always have your inequality first. So we're gonna really close dot and my arrow is going to go to the left because it's gonna be number smaller. I'm not gonna finish my arrow yet, and then in is greater than two. So that's an open dot, and it's going to go to the right. So again, once I work these out, both are sharing the same solutions right here. These could be any solution that falls between two and three for that inequality. Let's look at one more example, and this is another or statement. So let's look at K over four is greater than or equal to one or que over three is less than or equal to negative one. Now this is an or statement. So when I draw my number line, we should see our arrows going opposite directions away from each other. But let's go ahead and work these out, so we've got a fraction. So to get rid of our fraction, we're gonna multiply both sides by the denominator. So that's going to cancel out our denominator and leave me with K is greater than or equal to four. Or for this one, we're gonna multiply both sides by the denominator again, which will be three. So that leads me with K is less than or equal to negative three. So now let's do our number one mind to three four. They wanted our negative numbers. All right, So okay is greater than or equal to four. So it's gonna close dot and my arrow is going to go to the right. Que is less than or equal to negative three. Ah, close dot Going to the left. And again you see that the arrows, they're going opposite directions away from each other. So they do not share any solution, so it has to be one or the other.

Linear Equations and Functions

Linear Equations and Inequalities

Matrices and Determinants

Quadratic Equations

Applications of Trigonometric Functions

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