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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?

00:50

Taylor S.

Making Models : Write an algebraic formula that models the given quantity. 14. The average $A$ of two numbers $a$ and $b$

02:33

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?

00:55

Using Models Use the model given to answer the questions about the object or process being modeled. The volume $V$ of a cylindrical can is modeled by the formula $$V=\pi r^{2} h$$ where $r$ is the radius and $h$ is the height of the can. Find the volume of a can with radius 3 in. and height 5 in.

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we're being asked to determine if seven is a solution to each inequality. So remember to see if a values a solution. We're going to take it and substitute in place of our variable and see if we get a true or false statement. Now, if you look at the problems for number one and two, they look very similar. Except take a look at their in the quality sides. For number one, we have a greater than number two. We have greater than or equal to, so let's see if that makes a difference. So let's start with number one to see if it's a solution. We're going to take seven and substituted in place of X, so we're gonna have to times seven plus nine and we're going to determine is it greater than 23? So we're gonna follow the order of operations? Well, two times seven is 14, so we're gonna have 14 plus nine and we need to figure out Is it greater than 23? Well, 14 plus nine is 23 so we have 23 is greater than 23. Well, is 23 greater than 23? No, it's not. It's equal to it, but it's not bigger than it. So that means that this is a false statement. So because it's a false statement, that means seven is not a solution. So seven is not a solution. All right, now, let's go toe number two. And you might quickly think, Oh, well, then maybe this won't work because it looks the similar. Well, again, we're going to solve it the same way we're going to substitute seven in place of X. So we're gonna have to times seven plus nine. And we have to figure out, Is it greater than equal to 23? Well, we've already evaluated left hand side. We already said two times seven is 14, so we had 14 plus nine is greater than or equal to 23 and we already mentioned 14 plus nine is 23. So we have 23 is greater than or equal to 23. Well, that or equal to part makes a big difference because 23 is greater than or equal to 23 because it's equal. Which means that this is a true statement, which means that seven is a solution for our second inequality, so seven is now a solution, so it's very important that you're paying attention to if there's an inequality or the equal sign underneath, because if that equal signs there, that means it can be the same as that value. However, if that or equal to is not part of the year inequality sign, then it must strictly be even greater than less than depending on the inequality side.

Linear Functions

Solve Linear Inequalities

Functions

Systems of Equations and Inequalities

Graph Linear Functions

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