Evaluating Expressions and Heart Rate

This video tutorial covers evaluating algebraic expressions using substitution and order of operations. It includes examples of evaluating expressions like a² - b² and -a² - (b - c) with specific values, emphasizing the importance of parentheses. The tutorial also solves a word problem involving calculating the recommended maximum heart rate using a given formula. Each example is verified using a graphing calculator to ensure accuracy.

Why is it important to use parentheses when substituting negative values in algebraic expressions?

• To ensure the correct order of operations

• To make the expression look neat

• To avoid confusion with positive values

• To ensure the base remains negative

What is the result of evaluating a^2 - b^2 when a = -5 and b = -3?

• 16

• 25

• 9

• 0

When evaluating a^2 - b^2, what is the value of b^2 if b = -3?

• -9

• 9

• -3

• 3

In the expression -a^2 - (b - c), what is the first step according to the order of operations?

• Add the constants

• Multiply the terms

• Evaluate the expression inside the parentheses

• Simplify the exponent

What is the result of evaluating -a^2 - (b - c) when a = -5, b = 4, and c = -2?

• 25

• 31

• -31

• -25

What is the equivalent expression for 4 - (-2)?

• -4 - 2

• 4 - 2

• -4 + 2

• 4 + 2

What is the formula used to calculate the recommended maximum heart rate?

• m = 0.8 * (a - 220)

• m = 220 - 0.8 * a

• m = a - 0.8 * 220

• m = 0.8 * (220 - a)

For a 40-year-old, what is the recommended maximum heart rate according to the formula?

• 80 beats per minute

• 220 beats per minute

• 180 beats per minute

• 144 beats per minute

What is the purpose of checking the solution in the heart rate problem?

• To change the formula

• To find a different solution

• To ensure the calculation is reasonable

• To verify the age

What is the value of m when a = 40 in the heart rate formula?

• 144

• 40

• 180

• 220