tenmarks+note+for+Simplifying+Algebraic+Expressions

1 Question: Enrique is baking muffins and bread. He wants to bake a total of 10 batches. Each batch of muffins bakes for 30 minutes, and each batch of bread bakes for 50 minutes. Let m represent the number of batches of muffins. Write and simplify an expression for the total time required to bake a combination of muffins and bread if each batch is baked separately.

Correct Answer: m represents the number of batches of muffins. So, 10 - m represents the number of batches of bread. Total time required = Time required to bake muffins + Time required to bake bread Time required to bake muffins = 30m Time required to bake bread = 50(10 - m) The expression for the total time required to bake a combination of muffins and bread if each batch is baked separately is: 30m + 50(10 - m) = 30m + 500 - 50m [Distribute 50]
 * = 500 - 20m** [Combine like terms]

2 Question:

Identify which expressions are equivalent for the given value of x. (x + 3)2, (x2 + 9), (x2 + 6x + 9); x = 2 Correct Answer: Substitute x = 2 in each expression. (x + 3)2 = (2 + 3)2 = (5)2 = 25

(x2 + 9) = (2)2 + 9 = 4 + 9 = 13

(x2 + 6x + 9) = (2)2 + 6(2) + 9 = 4 + 12 + 9 = 25

Which expression is greatest when s = 10? Correct Answer: Find the value of each expression for s = 10 and then compare. Number of inches in s feet 1 foot = 12 inches s feet = 12s inches 10 feet = 12 x 10 = 120 inches Number of days in s weeks 1 week = 7 days s weeks = 7s days 10 weeks = 7 x 10 = 70 days Number of minutes in s hours 1 hour = 60 minutes s hours = 60s minutes 10 hours = 60 x 10 = 600 minutes Number of inches in s yards 1 yard = 36 inches s yards = 36s inches 10 yards = 36 x 10 = 360 inches Out of 120, 70, 600, and 360, the greatest is 600. So, for s = 10, the expression **‘number of minutes in s hours’** is the greatest.
 * For x = 2, the expressions (x + 3)2 and (x2 + 6x + 9) have the same value (25), so they are equivalent.**
 * 3** Question: