The most expensive car he can purchase is given by the total of all monthly payments and the down payment: $175 per month * 12 months per year * 3 years + $500 down = $6,800

Using the factor-label method we get:

approximately equals 

The units are treated like numbers and are cancelled when they are in both the  numerator and denominator.

An integer raised to an even power always yields an even integer. All of the other expressions could yield odd integers.

All four variables are positive real numbers. Each variable g, h, i, and j are multiplied by differing values to obtain the same value f. Since j is multiplied by the smallest value to obtain f it must be the greatest value. In this manner we could determine that g is necesarily the smallest value.

Use the factor-label method for conversion:

The units are considered like numbers and can be cancelled out of both the numerator and the denominator.

To find the number of different combinations, we must use the fundamental counting principal to multiply the number of options in each category together:

(3)(2)(3)(2) = 36

This question is testing the order of operations. For the equation , you must do the division problem first, then addition. .

To answer this question, we must substitute our value of  into our equation for  and follow our order of operations rules to solve for .

we first must substitute our known value into the equation. For this data:

We must now follow our order of operations to determine what we should do next. The order of operations goes as follows: parentheses, exponents, multiplication and division, and finally, addition and subtraction. So, for this equation, we must square the  because solving for exponents comes before solving multiplication.

Note that when you square a number, you are multiplying it by itself. When we multiply two negative numbers, their product is positive.

We then multiply our two integers together and solve for :

Therefore, the answer to our question is .

To solve this question, we need to understand how absolute value works within an equation.

When numbers are within an absolute value sign (the numbers will be surrounded by ), we need to use absolute value, or how far the number inside is away from zero. We must do any operations within the absolute value sign first. Therefore, the answer inside will always be positive, despite its sign, because you can't have negative distance from zero. So, for this data:

We can then just multiply our two integers in order to get our answer:

Therefore, our answer is .

To answer this question, we must substitute our given values into an equation and solve, remembering our order of operations.

First, we must take our values for each variable and substitute them into the equation given. Therefore, since we are told that , , and ,

Now that we have our values plugged in, we need to remember the order of operations in order to solve this problem. The order of operations goes as follows: parentheses, exponents, multiplication and division, and finally addition and subtraction. The first order of operations is to carry out any operations that are within parenthesis. Therefore, for this data:

We can now simply multiply these numbers together.

Our answer is .