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

2024
Views:

323

Pages:

3
Author:

Mckenna Welch

Question 1 Evaluate the expression. P(8, 3) Answer P(n,r) = n! / (n-r)! P(8,3) = 8! / (8-3)! = 8! / 5! = 876*5! / 5! = 8 * 7 * 6 = 336 Answer is P(8,3)=336 Question 2 Which expression below is equivalent to (9x - 4) + 13(3x - 2)? (A) 9x + 26 (B) 48x - 30 (C) 39 - 26 (D) 48x + 30 Answer (9x - 4) + 13(3x - 2) = (9x - 4) + (13 * 3x + 13 * -2) = (9x + 39x) + (-4 + -26) = 48x - 30 answer is (B). 48x - 30 Question 3 Solve the following system of equations and show all work. y = 2x² y = -3x-1 Answer Step 1 Solve the system of equation Step 2 y = 2x² (1) y = -3x - 1 (2) Substitute y = 2x² in (2), we have 2x² = -3x - 1 2x² + 3x + 1 = 0 2x² + 2x + x + 1 = 0 2x(x + 1) + 1(x + 1) = 0 (2x + 1)(x + 1) = 0 2x + 1 = 0 ⇒ x = -1/2 x + 1 = 0 ⇒ x = -1 At x = -1/2 y = 2x² = 2(-1/2)² = 2 * 1/4 = 1/2 At x = -1 y = 2x² = 2(-1)² = 2 Question 4 Write an algebraic expression of the verbal expression. 20 divided by t to the fifth power. Answer 1 The phrase, "t to the fifth power", indicates that the variable, "t", is raised to an exponent of "5". The expression is then represented : t^5 The phrase, "divided by", indicates a division operation, which can be represented by the "fraction line" symbol. Therefore, we can express the entire verbal expression as the algebraic expression: 20 / t^5 Thus, answer: 20 / t^5 Answer 2 "divided by" implies division 20 / "to the power" implies exponents t^5 Answer: 20 ÷ t^5 Question 5 Write an algebraic expression for each word phrase. 4 more than p Answer 1 Given word phrase: 4 more than. More indicate the symbol plus. So the resultant expression is 4 + p Answer 2 The word "more" indicates addition, and the phrase "4 more than p" implies that we need to add 4 to the value of p. Therefore, the expression can be written as: p + 4 In this expression, p represents the unknown value, and we are adding 4 to it. The addition is denoted by the plus sign (+), and the result of the addition is p + 4. Alternatively, if you prefer to write the expression as "p plus 4," you can use the symbol to represent addition, like this: p + 4 In this expression, the plus sign represents the addition operation between p and 4. Therefore, the algebraic expression for the word phrase "4 more than p" is p + 4. Answer 3 To write an algebraic expression for the word phrase "4 more than p," we can start by identifying the variable represented by the word "p." In this case, "p" represents the unknown value. The phrase "4 more than p" implies that we need to add 4 to the value of p. To express this algebraically, we can use the addition operation. Therefore, the algebraic expression for "4 more than p" can be written as: p + 4 In this expression, the variable p represents the unknown value, and we add 4 to it to indicate "4 more than p."