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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

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?

03:07

Taylor S.

Using Models Use the model given to answer the questions about the object or process being modeled. Arizonans use an average of 40 gal of water per person each day. The number of gallons $W$ of water used by $x$ Arizonans each day is modeled by $W=40 x$ . (a) Make a table that gives the number of gallons of water used for each $1000-$ person change in population, from 0 to $5000 .$ (b) If the pressure is $30 \mathrm{lb} / \mathrm{in}^{2},$ what is the depth? (b) What is the population of an Arizona town whose water usage is $120,000$ gal per day?

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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linear inequalities. Now solving linear inequalities is very similar to solving an equation you want to solve for the variable and get it isolated. So, for an example, let's look at the problem. Six X plus two plus six X is less than or equal to 14, so begin before I can begin solving for X. I need to simplify one side of the inequality, so I need to combine my life terms. I have a six X and a six x so I can combine and make those 12 X plus two is less than or equal to 14, so I need to start from here. I need to go ahead and subtract two on both sides, so 12 X is less than or equal to 14. Minus two is 12. We would divide by 12, and so X would be less than or equal toe. One. Now notice that when I divided by 12, I divided by a positive 12 and my inequality sign stayed the same. What happens if I divided by a negative number? Well, let's look at one. Let's look at the problem. Three is less than negative. Five in plus two year. Well, when I simplify the right side. I'm giving three. It's less than negative. Three. Ian. From here. I don't have anything to add or subtract, so I can go ahead and divide, and I'm going to divide by a negative number. Now here is the one of the major differences when it comes to inequalities. When you divide by a negative number, you're inequality. Son changes. So what will happen is where it says less than it's now going to change to greater than because we're dividing by negative number. So we'll just change it. Thio greater than now. This Onley happens when you divide by negative number. Whatever you add or subtract by does not change our sign. So three over negative three is negative one, and that's gonna lead me with Ian. Now it is a good habit and rule to go ahead and flip. You're inequalities toe where your variable for it comes first, so I'm gonna rearrange this one to In is less than negative one. They're actually the same thing. I just wanna really put my variable first. It's a good practice toe always have with inequalities, so let's try one more example. Let's do negative p minus four p is greater than negative. 10 negative P minus four p is negative. Five p is greater than negative. 10. So we're going to divide by negative five. And because we're dividing by negative five, my son is going to change. So instead of greater than it's now gonna be less than and negative Tin Toms Negative five are divided by negative. Five is positive, too. Now it's really important to know it's the number you divide by. So even though this tennis negative, I really just wanna look at what's on the bottom, that denominator that I divided by, we'll see some more as we do some practice problems.

Linear Equations and Functions

Linear Equations and Inequalities

Matrices and Determinants

Quadratic Equations

Applications of Trigonometric Functions

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