To get  by itself, divide each side by  to get .  Then add  to both sides to get .

The absolute value of a nonnegative number is the number itself; the absolute value of a negative number is its positive opposite.

By substitution, 10.5 can be seen to be a solution of each of the equations in the five choices. For example:

 - a true statement.

That 10.5 is a solution of the other four equations can be proved similarly. Therefore, the question is essentially to choose the equation with  as its other solution. Again, we can do this using substitution in each equations. We see that  is correct as follows:

 - a true statement.

Similar substitution in the other four statements shows that  is not a solution of any of them; for example, in :

 - a false statement.

Convert  to the Celsius scale by setting  in the conversion formula and solving for :

The question is therefore asking for the number of days that the temperature topped . Examine the graph below:

The high temperature was greater than  on Tuesday, Friday, and Saturday - three different days.

Tommy's current age is represented by t, and Sara's is represented by s. In five years, both Tommy's and Sara's ages will be increased by five. Thus, in five years, we can represent Tommy's age as and Sara's as .

The problem tells us that Tommy's age in five years will be twice as great as Sara's in five years. Thus, we can write an algebraic expression to represent the problem as follows:

In order to solve for t, first simplify the right side by distributing the 2.

Then subtract 5 from both sides.

The answer is .

In order to solve this, we need to set up an equation. , where  is time. All we need to do is divide by  on each side.

First we need to create equations that represent the path's of the Rocket's.

For Rocket , the equation is

For Rocket , the equation is

In order to solve for the time the Rocket's cross, we need to set the equations equal to each other.

Now solve for 

In order to solve for the slope, we need to recall how to find the slope of a line. , where  are points on the line.

So we will pick , and .

The first step is to find the common ratio amongst the data. 

We can that the common ratio is .

Now we need to set up an equation that will give an answer for any time.

We can set up an exponential decay model, the general equation is,

, where  is the starting amount,  is the common ratio and  is time.

After plugging our numbers in, we get

The break-even point is where the costs equal the revenues.

Let  = # of frames sold

Costs: 

Revenues: 

Thus,

So 14 picture frames must be sold each month to break-even.

In order to solve for the unknown number, you must write an equation and solve for a variable. 8 is 3 greater than the square root of an unknown number translates to

To solve for a you must subtract 3 from both sides, and then square both sides.

As you can see,

 and

So, the value of the unknown number is 25.