Exponents and radicals #22 - Q&A | Answer Key

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

2024
Views:

265

Pages:

2
Author:

Bennett Wheeler

Question 1 Evaluate 𝑦 = 4 𝑥 − 3 y=4x−3 for 𝑥 = 1 , 2 , 3 , 4 , 5 , 6 x=1,2,3,4,5,6. Answer 1 Using the given equation, replace 𝑥 x with the given values and evaluate 𝑦 y: When 𝑥 = 1 x=1: 𝑦 = 4 ( 1 ) − 3 = 4 − 3 = 1 y=4(1)−3=4−3=1 When 𝑥 = 2 x=2: 𝑦 = 4 ( 2 ) − 3 = 8 − 3 = 5 y=4(2)−3=8−3=5 When 𝑥 = 3 x=3: 𝑦 = 4 ( 3 ) − 3 = 12 − 3 = 9 y=4(3)−3=12−3=9 When 𝑥 = 4 x=4: 𝑦 = 4 ( 4 ) − 3 = 16 − 3 = 13 y=4(4)−3=16−3=13 When 𝑥 = 5 x=5: 𝑦 = 4 ( 5 ) − 3 = 20 − 3 = 17 y=4(5)−3=20−3=17 When 𝑥 = 6 x=6: 𝑦 = 4 ( 6 ) − 3 = 24 − 3 = 21 y=4(6)−3=24−3=21 Question 2 Express "10 less than the product of a number and 3." Answer 1 Let 𝑥 x be the number. The expression means that we subtract 10 from the product of 𝑥 x and 3. Hence, we write: 3 𝑥 − 10 3x−10 Question 3 How many gallons of 20% antifreeze solution and 10% antifreeze solution must be mixed to obtain 40 gallons of a 16% antifreeze solution? Answer 1 Let 𝑥 x be the number of gallons of 20% antifreeze solution, so 40 − 𝑥 40−x is the number of gallons of 10% antifreeze solution. Using the concentration formula: 0.20 𝑥 + 0.10 ( 40 − 𝑥 ) = 0.16 ( 40 ) 0.20x+0.10(40−x)=0.16(40) Solving for 𝑥 x: 0.20 𝑥 + 4 − 0.10 𝑥 = 6.4 0.20x+4−0.10x=6.4 0.10 𝑥 = 2.4 0.10x=2.4 𝑥 = 2.4 0.10 = 24 x= 0.10 2.4 =24 So, you need to mix 24 gallons of 20% antifreeze solution and 16 gallons of 10% antifreeze solution. Question 4 Solve the system: 𝑦 = 1 2 𝑥 − 2 y= 2 1 x−2 6 𝑥 + 2 𝑦 = 10 6x+2y=10 Answer 1 Substitute 𝑦 = 1 2 𝑥 − 2 y= 2 1 x−2 into the second equation: 6 𝑥 + 2 ( 1 2 𝑥 − 2 ) = 10 6x+2( 2 1 x−2)=10 6 𝑥 + 𝑥 − 4 = 10 6x+x−4=10 7 𝑥 = 14 7x=14 𝑥 = 2 x=2 Substitute 𝑥 = 2 x=2 into 𝑦 = 1 2 𝑥 − 2 y= 2 1 x−2: 𝑦 = 1 2 ( 2 ) − 2 = 1 − 2 = − 1 y= 2 1 (2)−2=1−2=−1 The solution is 𝑥 = 2 x=2 and 𝑦 = − 1 y=−1. Question 5 Write each number in standard form: 3 × 1 + ( 3 × 1 10 ) + ( 9 × 1 1000 ) 3×1+(3× 10 1 )+(9× 1000 1 ). Answer 1 3 × 1 = 3 3×1=3 3 × 1 10 = 0.3 3× 10 1 =0.3 9 × 1 1000 = 0.009 9× 1000 1 =0.009 Adding these together: 3 + 0.3 + 0.009 = 3.309 3+0.3+0.009=3.309 Standard form: 3.309 3.309