University:
Jackson College
Course:
MAT-010 | Basic Mathematics
Academic year:

2024
Views:

251

Pages:

2
Author:

Bennett Wheeler

Question 1 Solve 𝐴 = 𝑝 + 𝑝 𝑟 𝑡 A=p+prt for 𝑡 t. Answer 1 We are given: 𝐴 = 𝑝 + 𝑝 𝑟 𝑡 A=p+prt Subtract 𝑝 p from both sides: 𝐴 − 𝑝 = 𝑝 𝑟 𝑡 A−p=prt Divide both sides by 𝑝 𝑟 pr: 𝑡 = 𝐴 − 𝑝 𝑝 𝑟 t= pr A−p Question 2 What is the explicit equation for the sequence 3 , 10 , 17 , 24 3,10,17,24? Answer 1 This sequence is an arithmetic sequence with a common difference of 7 7 between terms. The formula for an arithmetic sequence is: 𝑎 𝑛 = 𝑎 1 + ( 𝑛 − 1 ) 𝑑 a n =a 1 +(n−1)d For this sequence: First term 𝑎 1 = 3 a 1 =3 Common difference 𝑑 = 7 d=7 Using the formula: 𝑎 𝑛 = 3 + ( 𝑛 − 1 ) × 7 a n =3+(n−1)×7 Distribute the 7 7: 𝑎 𝑛 = 3 + 7 𝑛 − 7 = 7 𝑛 − 4 a n =3+7n−7=7n−4 So, the explicit formula is: 𝑎 𝑛 = 7 𝑛 − 4 a n =7n−4 Question 3 Write a two-step inequality that can be solved by first adding 4 4 to each side. Answer 1 Let 𝑥 x be the variable. If the first step is to add 4 4 to each side, then the inequality could look like: 𝑥 − 4 ≤ 6 x−4≤6 Add 4 4 to both sides: 𝑥 ≤ 10 x≤10 So, the inequality 𝑥 − 4 ≤ 6 x−4≤6 can be solved in two steps by adding 4 4 first and then isolating 𝑥 x. Question 4 Carlos has at least as many action figures as Josh. Carlos has 5 5 complete sets plus 4 4 individual figures. Josh has 3 3 complete sets plus 14 14 individual figures. Which inequality represents how many action figures can be in a complete set? Answer 1 Let 𝑥 x be the number of action figures in a complete set. Carlos has: 5 𝑥 + 4 5x+4 Josh has: 3 𝑥 + 14 3x+14 Since Carlos has at least as many action figures as Josh, we write: 5 𝑥 + 4 ≥ 3 𝑥 + 14 5x+4≥3x+14 Subtract 3 𝑥 3x from both sides: 2 𝑥 + 4 ≥ 14 2x+4≥14 Subtract 4 4 from both sides: 2 𝑥 ≥ 10 2x≥10 Divide by 2 2: 𝑥 ≥ 5 x≥5 So, the inequality that represents how many action figures can be in a complete set is: 𝑥 ≥ 5 x≥5 Question 5 Simplify the expression 4 × 3 + 4 𝑥 4×3+4x. Answer 1 Since 4 × 3 = 12 4×3=12, the expression becomes: 12 + 4 𝑥 12+4x The expression cannot be simplified further because 12 12 and 4 𝑥 4x are not like terms.