With only three ages in play here, your best bet is likely to use the given information to calculate each age and then select the middle one as the median. You're given that:

1. Andrea is 24

2. Andrea is 2 years older than Rory

So you can calculate that Rory is 24 - 2 = 22 years old.

1. Rory is 3 years older than Joe, so Joe is 22 - 3 = 19 years old.

With ages of 19, 22, and 24, the median age is 22.

Function questions tend to derive most of their difficulty from the abstract function notation itself. So being comfortable with approaching function notation is most of the battle. When you see function notation such as , keep in mind that is the "input" (whatever they tell you is, put that into the equation), and that is the "output" (once you've put your input through the equation, the result is the value of ).

So when you're given , what the problem is really saying is that "whatever we put in the parentheses of , plug that value in wherever you see an in . Which means you'll take the input value, square it, subtract the product of the input value and two, add one to that, and then take the square root of the whole thing. With 9, that looks like:

You can then simplify the math underneath the radical to get:

And since you know that you have your answer.

When you're given the definition of a function as you are here, , your job to calculate a function is to take the value in parentheses and plug that in for wherever it appears in the definition. Here, qualitatively, you're being told "whatever is, square it and then subtract from that square." That means that:

So:

And for you'd have:

So:

This means that , so the correct answer is .

To simplify, remove parentheses and combine like terms:

Simplify each of the expressions to determine which satisfies the condition of the problem:

You should see on this problem that the numbers used, 2, 4, and 8, are all powers of 2. So to get the exponents in a way to be able to be used together, you can factor each base into a base of 2. That gives you:

Then you can apply the rule that when you take one exponent to another, you multiply the exponents. This then simplifies your equation to:

And now on the left hand side of the equation you can apply another exponent rule, that when you multiply two exponents of the same base, you add the exponents together:

Since the bases here are all the same, you can set the exponents equal. This gives you:

All of the exponent rules deal with multiplying, rather than adding, bases. In order to turn this into a multiplication question, we count apples (or chickens, or s, or whatever). How many ’s are there here? Three. This expression can be rewritten as . Now the exponent rules will apply; . The answer is .

We can quickly visualize this line to draw conclusions.

In order to do so, plug in 0 for x to find a point on the line:

3(0)+2y=6

y=3

Thus, (0,3) is a point on the line.

Plug in 0 for y to find a second point on the line:

3x+2(0)=6

x=2

(2,0) is another point on the line.

Now we know that the line passes through the points (2,0) and (0,3).

A quick sketch of the two points reveals that the line passes through all but the third quadrant.

*note - a line with a positive slope will always pass through quadrants I and III, while a line with a negative slope will always pass through quadrants II and IV.*

Whenever you're facing a unit conversion problem it is a good idea to use dimensional analysis to help you structure the math - whether you should multiply or divide by the provided conversion ratio - properly. That means that you'll set up the math such that the units you don't want in your answer cancel, leaving you with the units you do want. Here you're given quarts but asked to convert to pints, so you'll set up the math so that quarts are in the denominator and cancel, leaving you with pints:

This means that quarts cancel leaving you with pints, and tells you that you have to multiply 12 by 2. The correct answer is 24.

We can use dimensional analysis to solve this problem. We will create ratios from the conversions given.

Since Joaquin cannot trade for part of a shiny rock, the most he can get is shiny rocks.