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Missouri State University

McMaster University

Harvey Mudd College

University of Michigan - Ann Arbor

01:04

Taylor S.

Using Models Use the model given to answer the questions about the object or process being modeled. Mintonville School District residents pay a wage tax $T$ that is modeled by the formula $T=0.005 x .$ Find the wage tax paid by a resident who earns $\$ 62,000$ per year.

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?

06:25

Daniel P.

Using Models Use the model given to answer the questions about the object or process being modeled. The portion of a floating iceberg that is below the water sur- face is much larger than the portion above the surface. The total volume $V$ of an iceberg is modeled by $$V=9.5 S$$ where $S$ is the volume showing above the surface. (a) Find the total volume of an iceberg if the volume show- ing above the surface is 4 $\mathrm{km}^{3}$ . (b) Find the volume showing above the surface for an ice- berg with total volume 19 $\mathrm{km}^{3}$ .

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.

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This next section is on evaluating algebraic expressions. Now, at the beginning, we talked about algebraic expressions. Um, they can even be a numerical or variable expressions. Remember, numerical expressions don't have any variables and variable expressions. Well, they do have variables now, typically in algebra. When we're evaluating, algebraic expressions were evaluating variable expressions. So you might be thinking, How is this different from before? Well, before when we had our variable expressions, they're typically was only one operation. Now there's going to be multiple, well, to solve them. You just want to follow the same order of operations that we have that. So just as a little reminder for you, just in case you didn't have your, um, notes with you, there's four steps when evaluating algebraic expressions. And here they are. I remember the first thing you wanna look for our grouping symbols we want evaluate inside the grouping, symbols and member. Even if there's multiple steps inside the grouping symbols, you still want to follow the same order of operations step to evaluate your exponents. Step three. Multiply and divide from left to right and step four. You're going to also add a subtract for going in order from left to right, so it's going to be very much like order operations. The only difference is you might be given an expression like this. Let's say you are given three X minus two and then you want to evaluate. So that's our expression on what they're going to say is you want to evaluate this expression. If X is equal to and they will give you some number, they want you to evaluate it for so example, they might give you the value of seven. So all you would need to do first is substitute seven in place of X. My recommendation. It's any time you substitute values into your expression, you should always use parentheses. So here's how I would write this. I would say three. And then in place of X, we're gonna put seven notice how he put in parentheses minus two. And now from here, you just follow the order of operations. Well, do we have grouping symbols? Yes, but it's just to indicate multiplication. Step two exponents, we dio, But I'm sorry we don't have any exponents. Step three. Multiply and divide Well, we dio we have three times seven which is 21. So we're gonna have 21 minus two, and then we just have one. Operation 21 minus two is 19. So what we found is the value of our original expression to re X minus two is equal to 19. When X is equal to seven. It would have a different value of X was different value. But again, we were on Lee looking for its value when X is seven.

Linear Functions

Solve Linear Inequalities

Functions

Systems of Equations and Inequalities

Graph Linear Functions

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