Section 1.7 Using Variables and Formulas
Dec 27, 2015
1.7 Lecture Guide: Using Variables and Formulas
Objective 1: Evaluate an algebraic expression for specific values of the variables.
Evaluate for each value of x. (Hint: See Technology Perspective 1.7.1 for using a calculator or a spreadsheet to check your work.)
2 4 5x x
1. 2. 3.3x 5x 2x
Algebraic formulas are used in nearly all areas of mathematics, business, and the sciences. A formula describes a relationship between specific variables. For example, the
area A of a triangle is given by the formula , where b
represents the length of the base of the triangle and h represents the height of the triangle. This relationship holds true for all triangles.
12
A b h
Objective 2: Use algebraic formulas.
Find the area of each triangle. Remember, this area is given in square units.
A = ______9. 4 cm
7 cm
A = ______10.
3 in
8 in
Find the area of each triangle. Remember, this area is given in square units.
The formula for Fahrenheit temperature is given by 11. 9
325
F C . Find the Fahrenheit temperature if the
Celsius temperature C is . 55
12. The formula for the amount in a bank account paying a simple interest rate R for T years is given by ,A P PRT
where P is the principal or initial amount. Find the amount in a bank account after 1 year if there was an initial deposit of $5,000 and the account earned 5% simple interest.
13. The formula for the perimeter of a rectangle is given by 2 2P l w . Find the perimeter P of a rectangle if the
length l is 20 meters and the width w is 35 meters.
One common usage of subscript notation is the slope
formula, , which will be developed in
Chapter 3. This formula is used to calculate m, the slope of a line that passes through the points and .
2 1
2 1
y ym
x x
1 1,x y 2 2,x y
Objective 3: Use subscript notation.
1 1, 3,5x y 2 2, 7,8x y and .
14.Use this formula to calculate the value of m for the line through the points
1 1, 1,4x y 2 2, 2, 3x y and .
15.Use this formula to calculate the value of m for the line through the points
A sequence is an ordered set of numbers with a first number, a second number, a third number, etc. Subscript notation often is used to denote the terms of a sequence: These terms are read a sub one, a sub two, and a sub n, respectively. If a sequence follows a predictable pattern, then we may be able to describe this pattern with a formula for . Consider the sequence 5, 4, 3, 2. Here
1 2, and .na a a
1 25, 4,a a 3 43, and 2.a a na
Use each formula to calculate the first three terms of each sequence.
1 2 3( , ,and )a a a
16. 2 5na n
Use each formula to calculate the first three terms of each sequence.
1 2 3( , ,and )a a a
17. 5 8na n
Objective 4: Check a possible solution of an equation.
A solution of an equation is a value for the variable that satisfies the equation. This means that when the value is substituted for the variable, the expressions on each side of the equation will have the ____________ value.
Check whether each indicated value of x is a solution of the given equation.
18.
(a) Check
(b) Check
1 2 4x x 3x
5x
Check whether each indicated value of x is a solution of the given equation.
19.
(a) Check
(b) Check
2 3 10 0x x 3x
5x
20.
(a) Check
(b) Check
Check whether each indicated value of x is a solution of the given equation.
3 2 24 3
xx
4x
2x