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

2024
Views:

10

Pages:

4
Author:

Bennett Wheeler

Question 1 Which expression is equivalent to the following complex fraction? − 2 𝑥 + 5 𝑦 ÷ 3 𝑦 − 2 𝑥 − x 2 + y 5 ÷ y 3 − x 2 Answer 1 Given: − 2 𝑥 + ( 5 𝑦 ÷ 3 𝑦 ) − 2 𝑥 − x 2 +( y 5 ÷ y 3 )− x 2 Simplify 5 𝑦 ÷ 3 𝑦 y 5 ÷ y 3 by multiplying by the reciprocal of 3 𝑦 y 3 : 5 𝑦 × 𝑦 3 = 5 3 y 5 × 3 y = 3 5 Substitute back: − 2 𝑥 + 5 3 − 2 𝑥 − x 2 + 3 5 − x 2 Combine terms: − 4 𝑥 + 5 3 − x 4 + 3 5 So, the expression simplifies to − 4 𝑥 + 5 3 − x 4 + 3 5 . Question 2 Express the radical expression 75 81 81 75 in simplest radical form. Answer 1 75 81 = 75 81 81 75 = 81 75 Simplify each square root: 75 = 5 3 and 81 = 9 75 =5 3 and 81 =9 Substitute back: 5 3 9 9 5 3 So, the simplest form is 5 3 9 9 5 3 . Question 3 When the length ( 𝑙 l) and width ( 𝑤 w) of a rectangle are known, the formula 𝑃 = 2 𝑙 + 2 𝑤 P=2l+2w can be used to determine its perimeter ( 𝑃 P). For the width, solve this literal equation. Answer 1 Starting with: 𝑃 = 2 𝑙 + 2 𝑤 P=2l+2w Subtract 2 𝑙 2l from both sides: 𝑃 − 2 𝑙 = 2 𝑤 P−2l=2w Divide both sides by 2 to solve for 𝑤 w: 𝑤 = 𝑃 − 2 𝑙 2 w= 2 P−2l So, the solution for 𝑤 w is 𝑃 − 2 𝑙 2 2 P−2l . Question 4 Solve the system of equations: 3 𝑦 − 4 𝑥 = 26 3y−4x=26 𝑥 = 2 𝑦 − 14 x=2y−14 Answer 1 Substitute 𝑥 = 2 𝑦 − 14 x=2y−14 into the first equation: 3 𝑦 − 4 ( 2 𝑦 − 14 ) = 26 3y−4(2y−14)=26 Expand and simplify: 3 𝑦 − 8 𝑦 + 56 = 26 3y−8y+56=26 − 5 𝑦 = − 30 −5y=−30 𝑦 = 6 y=6 Substitute 𝑦 = 6 y=6 back into 𝑥 = 2 𝑦 − 14 x=2y−14: 𝑥 = 2 ( 6 ) − 14 = 12 − 14 = − 2 x=2(6)−14=12−14=−2 So, the solution is 𝑥 = − 2 x=−2, 𝑦 = 6 y=6. Question 5 Solve for 𝑔 g in the formula 𝑠 = 1 2 𝑔 𝑡 2 s= 2 1 gt 2 . Answer 1 Starting with: 𝑠 = 1 2 𝑔 𝑡 2 s= 2 1 gt 2 Multiply both sides by 2: 2 𝑠 = 𝑔 𝑡 2 2s=gt 2 Divide both sides by 𝑡 2 t 2 to solve for 𝑔 g: 𝑔 = 2 𝑠 𝑡 2 g= t 2 2s So, 𝑔 = 2 𝑠 𝑡 2 g= t 2 2s .