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**Evaluating Formulas By Substitution**: At a Glance

- Topics At a Glance
- Variables
- Variables as Unknown Quantities
- Variable Notations
- Constants
- Expressions and Equations
- Rearranging Expressions
- Commutative Properties
- Associative Properties
- Distributive Properties
- Factoring (Distributive Property in Reverse)
- Combining Like Terms
- Eliminating Parentheses
- Simplifying
- Equations, Functions, and Formulas
- Equations
- Functions
- Independent and Dependent Variables
- Formulas
**Applications to Toolbox**- Evaluating Expressions by Substitution
**Evaluating Formulas by Substitution**- Geometric Formulas
- Four-Sided Shapes
- Three-Sided Shapes
- Circles
- Unit Conversion
- Temperatures
- Weights
- Distances and Speeds
- Money
- In the Real World
- I Like Abstract Stuff; Why Should I Care?
- How to Solve a Math Problem

As we mentioned, a formula has a dependent variable on one side and an expression involving the independent variable(s) on the other side. To evaluate a formula, we evaluate the expression containing the independent variable(s). The result is the value of the dependent variable. Ready, Miss Independent? Let's make you Miss Dependent.

Consider the formula *C* = 5*xy*. Find *C* if *x* = 2 and *y* = 3.

*C* is the dependent variable, and that will be our result. Now, how do we find its value? We evaluate the expression on the other side of the equals sign, 5*xy*, for *x* = 2 and *y* = 3. This step gives us *C* = 5(2)(3) = 30. We now know *C*'s value is 30. However, we don't know if that is in dollars or pesos—no getting excited just yet.

We can use geometric formulas to answer all sorts of questions. Like, "Why is the sky blue?" or "What makes birds sing?" or "Why does Julia Stiles have a career?" Still, more practically, it can help us solve something like the below...

Find the area of a square with side length 4 cm.

The area of a square is given by the formula *A* = *s*^{2}, where *A* is the area of the square and* s* is the length of a side. In this case, the length of a side is 4, and we substitute 4 for *s* and evaluate the area formula: *A* = (4)^{2} = 16 cm^{2}. We will now let r represent rock star, which is what we are for finding the area of this square.

Example 1

Sara has a clock with a circular face. She wants to glue a ribbon around the outer edge of the face of the clock. Heaven knows why she thinks this will look good. It would be enough to make Martha Stewart have a conniption fit. Ah, well. To each her own. If the face of the clock has a radius of 5 inches, how much ribbon will Sara need to complete her aesthetic disaster? |

Exercise 1

Zach has a rectangular living room that measures 10 feet wide by 20 feet long. He has thought about bringing in some furniture, but he doesn't want to spoil the perfect rectangularness of it. In order to cover the floor of his living room with carpet, how many square feet of carpet does Zach need?

Exercise 2

Zach has a rectangular living room that measures 10 feet wide by 20 feet long. He has thought about bringing in some furniture, but he doesn't want to spoil the perfect rectangularness of it. How much trim will Zach need if he is to put trim all around the edge of the floor?

Exercise 3

What is the area of the triangle shown below? No fair guessing. We know what a lucky guesser you are.