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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?

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?

00:57

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.

02:33

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?

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So in this example, we're being asked to find each product and notice we're given more than just one number. We're gonna try and see if there's some type of pattern. So let's start with part A. We have negative two times negative three times negative. Four. So we go from left to right. So first we multiply Negative two times. Negative three. Well, two times three or six. And because both sides are negative, are result will be positive. That will bring down the negative four. So now we need to multiply six times. Negative four. Well, six times four is 24. And because both numbers have different signs, the result will be negative. So know this here that our final answer is going to be a negative value. And I want you to notice how many negative numbers were in our original problem. We had 123 values that were negative. Keep that in mind as we go along now for part B. So we're going to multiply in order from left to right. So we're gonna start with negative two times negative three Well, two times three or six. And because both numbers have the same sign. Our result will be positive and I'll bring down the negative two and the negative five. So next will multiply six times negative, too. Well, six times two is 12, but both numbers air different signs. We have one positive one negative silver result will be negative and I will bring down the negative five. So lastly, we need to multiply negative 12 by negative five. Well, 12 times five is 60 and negative times a negative is going to be a positive, so a result will be a positive value. So notice here we have four negative values. So when we have three negative values, it was negative. Four is positive. Let's see about part C. So first we have three times negative, too. Well, three times to a six. And because both signs were different, that means the result should be a negative value. Then we'll bring down the negative four. So then we have negative six times negative four while six times four is 24. And because both numbers have the same sign, our result will be positive. So take a look. What we had when we have an odd number and negatives are answer is odd, just like in part A. But when we have an even number of negatives just like an example, B and C are answer is going to be positive. And that's always going to be true. So that might be a little shortcut for you. When you have an odd number of negative factors, your answer will be negative on. When you have a even number and negative factors, your answer will be positive. Or you could always go through step by step, just like we did, and you'll still get the same result.

Linear Functions

Solve Linear Inequalities

Functions

Systems of Equations and Inequalities

Graph Linear Functions

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