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

2024
Views:

67

Pages:

2
Author:

Bennett Wheeler

Question 1 Find the simplest radical form of 306 306 . Answer 1 Factor 306 306 into a product of a perfect square and another factor: 306 = 9 × 34 = 9 × 34 = 3 34 306 = 9×34 = 9 × 34 =3 34 So, the simplest radical form of 306 306 is 3 34 3 34 . Question 2 Solve 5 𝑥 + 3 𝑦 = 15 5x+3y=15 for 𝑦 y when 𝑥 = 0 x=0. Answer 1 Substitute 𝑥 = 0 x=0 into the equation: 5 ( 0 ) + 3 𝑦 = 15 5(0)+3y=15 0 + 3 𝑦 = 15 0+3y=15 3 𝑦 = 15 3y=15 Divide both sides by 3: 𝑦 = 5 y=5 So, when 𝑥 = 0 x=0, 𝑦 = 5 y=5. Question 3 Solve the equation 5 𝑥 + 5 𝑦 = 0 5x+5y=0. Answer 1 Factor out the common factor of 5: 5 ( 𝑥 + 𝑦 ) = 0 5(x+y)=0 Divide both sides by 5: 𝑥 + 𝑦 = 0 x+y=0 Rearrange to solve for 𝑦 y: 𝑦 = − 𝑥 y=−x So, the solution is 𝑦 = − 𝑥 y=−x, which indicates there are infinitely many solutions along the line 𝑦 = − 𝑥 y=−x. Question 4 Solve the equation: 2 2 𝑤 − 3 = 𝑤 − 2 3 𝑤 − 7 2w−3 2 = 3w−7 w−2 Answer 1 Cross-multiply to eliminate the fractions: 2 ( 3 𝑤 − 7 ) = ( 𝑤 − 2 ) ( 2 𝑤 − 3 ) 2(3w−7)=(w−2)(2w−3) Expand both sides: 6 𝑤 − 14 = 2 𝑤 2 − 3 𝑤 − 4 𝑤 + 6 6w−14=2w 2 −3w−4w+6 6 𝑤 − 14 = 2 𝑤 2 − 7 𝑤 + 6 6w−14=2w 2 −7w+6 Move all terms to one side to set the equation to 0: 0 = 2 𝑤 2 − 13 𝑤 + 20 0=2w 2 −13w+20 Solve the quadratic equation 2 𝑤 2 − 13 𝑤 + 20 = 0 2w 2 −13w+20=0 using the quadratic formula: 𝑤 = − ( − 13 ) ± ( − 13 ) 2 − 4 ⋅ 2 ⋅ 20 2 ⋅ 2 w= 2⋅2 −(−13)± (−13) 2 −4⋅2⋅20 𝑤 = 13 ± 169 − 160 4 w= 4 13± 169−160 𝑤 = 13 ± 9 4 w= 4 13± 9 𝑤 = 13 ± 3 4 w= 4 13±3 Calculate the two solutions: 𝑤 = 16 4 = 4 and 𝑤 = 10 4 = 5 2 w= 4 16 =4andw= 4 10 = 2 5 So, the solutions are 𝑤 = 4 w=4 and 𝑤 = 5 2 w= 2 5 . Question 5 Suppose that you’re running some errands for your boss, and she says, "I imagine you’ll need to spend at least 30 bucks on cab fare. Don’t spend more than 50, though." Write an inequality that matches these conditions. Answer 1 "At least 30" means ≥ 30 ≥30. "No more than 50" means ≤ 50 ≤50. So, if 𝑥 x is the cab fare, the inequality that matches these conditions is: 30 ≤ 𝑥 ≤ 50 30≤x≤50