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Problem 19 Johns Hopkins University

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Problem 18

Some building codes require that, for indoor
stairways, the tread depth must be at least 9 inches
and the riser height must be at least 5 inches.
According to the riser-tread formula, which of the
following inequalities represents the set of all
possible values for the riser height that meets this
code requirement?
$$\begin{array}{l}{\text { A) } 0 \leq h \leq 5} \\ {\text { B) } h \geq 5} \\ {\text { C) } 5 \leq h \leq 8} \\ {\text { D) } 8 \leq h \leq 16}\end{array}$$

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SAT
SAT Practice Test # 6

## Discussion

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## Video Transcript

So for this one, it says that we want to find an inequality that represents the height. But then the information that was given is that the truck theft must be at least nine inches and the riser height must be at least five inches. So, first of all, if it the height is at least five inches, we can represent it like thiss because that means that the minimum value that it could be us five and then for the tread death when other death must be at least two nine inches. But we want to make everything in terms of the height. So we need to find a way to convert this d into the hut. Well, we have our equation over here, so we could just put that into there and see what the height value the corresponding high value would be. So if we have to age Plus, de is people twenty five and we're placing the nine. We got to H first nine twenty five From here on this of track tonight from both science, giving us to H is equal to sixteen. The finally moment Vipers heads to getting us H is equal to eight. But here's the thing. And initially we had d is greater than or equal to nine. But for that, when we converted from D to H, we actually have to flip the sign so that we get h is less than or equal to eight. Because from this equation, we know we just like this equation right here. We can see that these two are in grisly related. Which means that asked H goes up that d goes down and as d those up that HS to go down was, for example, if we had ages ten and then that makes d five. And that's equal to twenty five, but that if we made the h go down to Let's go to eight and we have sixteen. So d'You see goes up So which went down from ten to eight and then D went up from five to nine. So clearly they are inversely related, which means you have to switch the signs. So then, if we want to combine the signs that we switched this one and this one, then we have a tch. Well, that one has to be high has to be the minimum, but it has to be the maximum. So C is going to be our crack cancer