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

2024
Views:

155

Pages:

4
Author:

Bennett Wheeler

Question 1 How do you simplify 18 18 ? Answer 1 Answer 1 18 = 3 × 3 × 2 = 9 × 2 = 3 2 18 = 3×3×2 = 9×2 =3 2 Answer 2 Prime factorize the number: 18 = 9 × 2 = 3 × 3 × 2 = 3 2 18 = 9×2 = 3×3×2 =3 2 Question 2 Use the point-slope formula and the given slope and point to find the linear equation in slope-intercept form. Given: 𝑀 = 1 M=1 and 𝑃 = ( 4 , 3 ) P=(4,3) Options: A: 𝑦 = 𝑥 − 1 y=x−1 B: 𝑦 = 𝑥 − 2 y=x−2 C: 𝑦 = 𝑥 + 2 y=x+2 D: 𝑦 = 𝑥 + 4 y=x+4 Answer 1 To find the equation of a line that passes through the point ( 4 , 3 ) (4,3) and has a slope of 1: Start with the point-slope formula: 𝑦 − 𝑦 1 = 𝑚 ( 𝑥 − 𝑥 1 ) y−y 1 =m(x−x 1 ) Substitute 𝑚 = 1 m=1, 𝑥 1 = 4 x 1 =4, and 𝑦 1 = 3 y 1 =3: 𝑦 − 3 = 1 ( 𝑥 − 4 ) y−3=1(x−4) 𝑦 − 3 = 𝑥 − 4 y−3=x−4 𝑦 = 𝑥 − 1 y=x−1 Thus, the correct answer is: A: 𝑦 = 𝑥 − 1 y=x−1 Question 3 To find the square root of a number, find its prime factors. 49 = 7 × 7 49=7×7 49 = 7 × 7 = 7 49 = 7×7 =7 (A square root can also be a negative number.) Answer 2 Explanation: A square root of a number 𝑛 n is a number 𝑥 x such that 𝑥 2 = 𝑛 x 2 =n. Note that if 𝑥 x is a real number, then 𝑥 2 ≥ 0 x 2 ≥0. The square root of a number is that number which, when multiplied by itself, will equal the original number. So, ultimate answer will be ± 7 ±7. Question 5 How do you simplify 45 𝑥 3 45x 3 ? Answer 1 Answer 1 = 3 5 𝑥 3 =3 5x 3 Explanation: 45 𝑥 3 = 45 = 3 ⋅ 3 ⋅ 5 45x 3 = 45 = 3⋅3⋅5 So, 45 𝑥 3 = 3 5 𝑥 3 45x 3 =3 5x 3