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Algebra and Functions Videos 52 videos

SAT Math 7.3 Algebra and Functions
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SAT Math 7.3 Algebra and Functions

SAT Math 1.5 Algebra and Functions
218 Views

SAT Math 1.5 Algebra and Functions. If f (x) = x2 - 16 and g(x) = x4 - 256, what is f of x divided by g of x?

SAT Math 3.5 Algebra and Functions
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SAT Math 3.5 Algebra and Functions

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SAT Math 3.3 Algebra and Functions 182 Views


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Description:

SAT Math 3.3 Algebra and Functions

Language:
English Language

Transcript

00:02

And here's your shmoop du jour...

00:04

Justin rode his bike to school, pedaling at an average speed of 12 miles/hour.

00:08

When he rode his bike back home at a leisurely pace of 10 miles/hour, it took him an extra 15 min.

00:14

How far is his school from his home?

00:17

And here are the potential answers...

00:20

OK, we want to find the distance between Justin's home and his school.

00:24

We know that he biked to school at 12 miles per hour, but we don't know how long it

00:28

took him to get there. We'll call the time it takes him to bike there, x.

00:33

Next, we know that when coming home, he biked at only 10 miles per hour.

00:38

And it took him 15 minutes longer than before.

00:43

We can take the old time, add 15 minutes to it, and get the new time.

00:48

But wait.

00:48

His velocity is given in miles per hour, and the extra time is in minutes.

00:54

The units don't match up.

00:55

Remember that 60 minutes are in an hour, and 15 minutes is .25, or a quarter of an hour.

01:01

Now, we can set up equations that help us solve this problem.

01:04

We'll start with biking to school.

01:06

We know that velocity is equal to the distance Justin travels divided by

01:09

the time it takes him to travel that distance. His velocity is 12 miles per hour.

01:14

We get the equation 12 = d (distance) / x (time).

01:18

Okay, now biking home.

01:20

We get 10 = d over the quantity x + .25.

01:26

We have two equations, and two variables.

01:28

Sounds a little like we have to solve a system of equations.

01:32

By isolating x in the first equation, we get x = d/12.

01:35

We can then plug x into our second equation, like this.

01:39

We multiply both sides by d/12 + .25, and we get 10 times d/12 + .25 = d.

01:47

Distributing in the 10 we get 10/12 d + 2.5 is equal to d.

01:54

We then subtract 10/12d from both sides to get 2/12 d,

01:59

which we can simplify to 1/6 d is equal to 2.5.

02:03

Finally, multiplying both sides by 6, and we get that d is equal to 15 miles.

02:08

So our answer is (E).

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