University:
Massachusetts Institute of Technology
Course:
18.06 | Linear Algebra
Academic year:

2024
Views:

191

Pages:

3
Author:

Mckenna Welch

Question 1 How do you simplify 2(4-3t) - (-3) + 2t? Answer 1 Step 1 You want to use distribution and addition. The equation is 2(4-3t) - (-3) + 2t If we take the 2 at the beginning of the equation and multiply it into every term in the parentheses, we get: 8-6t - (-3) + 2t Now, we take the negative sign and distribute it into the -3 to get: 8 - 6t + 3 + 2t We see that we can add the 8 and the 3 together since they are like terms (both are numbers). 11 - 6t + 2t We also see that the -6t and the 2t can be added since they are both like terms (both are a quantity of t). 11 - 4t And how it's simplified! Answer 2 Step 1 2(4-3t)-(-3)+2t Use the distributive property to multiply 2 by 4 – 3t 8-6t-(-3)+ 2t The opposite -3 is 3 8-6t+3+ 2t Add 8 and 3 to get 11. 11- 6t + 2t Combine -6t and 2t to get -4t 11- 4t Question 2 How do you identify the terms, like terms, coefficients and constants in each expression: -5x + 4 - x - 1? Answer 1 Step 1 -5x + 4 - x + 1 The given expression has 4 terms. The like terms are those which have exactly the same variables, there are two types of terms: those in x and the number terms. -5x and - x are like terms with the variable x 4 and -1 are like terms, also called constants because their value never changes. The numerical coefficient is the number at the front of the term. It would be better to simplify the expression and then give the coefficient. -5x + 4 - x - 1 = -6x + 3 The coefficient of x is -6 Answer 2 Step 1 -5x + 4 - x - 1 Combine -5x and -x to get -6x. -6x + 4 - 1 Subtract 1 from 4 to get 3. -6x + 3 Question 3 How do you define a variable and write an algebraic expression for the phrase: 10 plus the quotient of a number and 15? Answer Step 1 Plus 10 means to add 10. The quotient of a number and 15 means that the number is divided by 15. Let x represent the number. The quotient of the number and 15 can be written as x ÷ 15 or x/15 Question 4 A chef uses 4 3/4 cups of broth for 10 servings of soup. How much broth is used in one serving of soup? Let x represent the amount of broth Answer Using the equivalent ratio, we cross multiply: (4 3/4)/10 = x/1 4(3/4)(1) = 10x 4(3/4) = 10x Write the mixed number as an importer fraction: 19/4 = 10x Multiply both sides by 1/10: (19/4)(1/10) = 10x * (1/10) 19/40 = x So, there is 19/40 cup of broth per serving. 19/40 cup Question 5 How many 2-letter code words can be formed from the first 3 letters of the alphabet if no letter can be used more than once? Answer Fundamental counting principle: If the first event could occur in m ways and the second event could occur in n ways, then the number of ways that the two events could occur in sequence is m·n. We only use the first 3 letters from the alphabet: a, b, c First letter: 3 ways Second letter: 2 ways (as no letter is used more than once) By the fundamental counting principle: 3 · 2 = 6 Thus there are 6 2-letter code words that can be formed from the first three letters in the alphabet such that no letter is used more than once.