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

2024
Views:

325

Pages:

3
Author:

Mckenna Welch

Question 1 Reduce the rational expression to the lowest terms: (x² + 36) / (6x + 36) State any real numbers that should be excluded from the domain. Answer (x² + 36) / (6x + 36) = (x² + 36) / 6(x + 6) The real number that should be excluded from the domain is -6. Question 2 Solve (2/3)(4x - 5) = 8 by using the division property of equality Answer (2/3)(4x - 5) = 8 (3/2) * (2/3)(4x - 5) = 8 * (3/2) 4x - 5 = 24 / 2 = 12 4x = 12 + 5 = 17 x = 17 / 4 x = 4.25 x = 4 1/4 Question 3 Two games went on for a total of 32 minutes. One game took 12 minutes longer than the other. How long did it take to complete each game? Answer Let's assume: x = 1st game y = 2nd game x + y = 32 (total of 32 mins) x - y = 12 (one game is 12 mins longer than the other) Let's combine the two equations now 2x = 44 x = 22 y = x - 12 = 22 - 12 = 10 Two games were 22 mins and 10 mins Question 4 Identify, whether x - 7 > -2 and x > 5 are equivalent inequalities or not equivalent? Answer x - 7 > -2 x - 7 + 7 > -2 + 7 x > 5 So, the inequalities are equivalent. Question 5 The total cost C (in dollars) to participate in a ski club is given by the literal equation C = 85x + 60, where x is the number of ski trips you take. How many ski trips do you take if you spend a total of $315? Answer 1 To solve a literal equation for a variable, isolate that variable by performing operations on both sides of the equation. To identify the number of ski trips, substitute the dollars spent in the equation above: For C=315: x = (C - 60) / 85 Substitute: x = (315 - 60) / 85 Simplify: x = 255 / 85 Simplify: x = 3 ski trips Answer 2 Result: 3 Solution: We have the equation C = 85x + 60 and we know that C = 315. Substituting this value into the equation, we get: 315 = 85x + 60 To isolate x, we can subtract 60 from both sides of the equation: 315 - 60 = 85x Simplifying the left side: 255 = 85x To solve for x, we divide both sides of the equation by 85: 255 / 85 = 85x / 85 Simplifying: 3 = x Therefore, the number of ski trips, x, is equal to 3. Answer 3 Given: C = 315 Substituting this value into the equation, we have: 315 = 85x + 60 To isolate x, we subtract 60 from both sides of the equation: 315 - 60 = 85x + 60 - 60 Simplifying the equation, we get: 255 = 85x To solve for x, we divide both sides of the equation by 85: 255 / 85 = 85x / 85 Simplifying further, we have: x = 3 Therefore, if the total cost is 315, you would take 3 ski trips.