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Johns Hopkins University

University of Texas at Austin

University of California, Berkeley

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?

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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.

01:13

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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found inequality 36 is less than or equal to 11 minus five x, which is less than or equal to 66. Now here we have an example of in an inequality where both inequalities shared the same part. They both share 11 minus five x. So let's rewrite this inequality as two separate inequalities. So we'll write. 36 is less than or equal to 11 minus five X and 11 minus five. X is less than or equal to 66. So now that we have a split into two separate inequalities, we can work them out individually. So for the first one, we can subtract 11 on both sides. And when I do, I get 25 is less than or equal to negative five X. We're gonna divide by negative five on both sides. So I have negative five are signs got to change because we divided by a negative number is greater than or equal to X. Then our second one, we're gonna go ahead. We're gonna subtract 11 again. But this time from 66. So negative five x is less than or equal to 55. We're gonna divide by negative five and again because we're dividing by a negative number, our son is going to flip. So now we have X is greater than or equal to negative 11. So let's draw our number line since their negative numbers and they're all odd. We're just going to count down by our odd negative numbers. Okay, so let's start with the first one, which is negative. Five is greater than or equal toe X. Another way of writing this if I wanna flip it, which we really do. If we want a graph on the number line, it's X is less than or equal to negative five. So we have a close 0.0 negative five and her arrows going to the left because there's numbers less than name we have. X is greater than or equal to negative. 11 closed out all negative 11. Our arrows going to the right. So here we see that they're sharing the same possible solutions that come between negative 11 and negative five

Linear Equations and Functions

Linear Equations and Inequalities

Matrices and Determinants

Quadratic Equations

Applications of Trigonometric Functions

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