MAT 136 Exam 1 With 100% Verified Solutions 2025

√2⋅9 - Cancel the common factors of 18 and 16 which would be 2 2⋅8 √9 - Rewrite 8 √9 - as √8 3 - The squareroot of 9 = 3, factor 4 out of 8 √4(2) 3 - The squareroot of 4 = 2, remove 2 from radical 2√2 ( 3 )⋅ (√2 ) - Multiply togther and simplify 2√2 √2 (3⋅√2) 2(√2)2 (3⋅√2) n x x 1 1 2 - use √a = a n to rewrite √2 as 2 2 and simplify 2(2 2 ) (3√2) 2⋅2 (3√2) 4 Ungraded Grade: 0/1.0 2/27/2023 Southern New Hampshire University - Gradebook 3/22 Question Total grade: 1.0×1/2 + 0.0×1/2 = 50% + 0% √18 = √2⋅9 Factor perfect squares from the radicand. Feedback: 16 16 = 3 √2 Simplify. 4 Q2 0/0.0 View Original Response Unfiltered Response Solve for x. 6 (x + 3) − 37 = x + 6 Enter the exact answer. x = Your response Correct response 5 5 Auto graded Grade: 1/1.0 Show your work and explain, in your own words, how you arrived at your answer. Answers with no relevant explanations may receive reduced or no credit. 2/27/2023 Southern New Hampshire University - Gradebook 4/22 Question 6 (x + 3) − 37 - Simplify the left side of the equaiton 6 x + 18 − 37 - 6*x and 6*3 6 x − 19 = x + 6 6 x − 19 − x = 6 - move x to the left side of the equation by subtracting from both sides 5 x − 19 = 6 - subtract x from 6x 5 x = 6 + 19 - Move 19 to the right side of the equation by adding 19 to both sides 5 x = 25 - Add 6+19 x = 25 - Move 5 to the right side by dividing by 5 5 x = 5 Ungraded Grade: 0/1.0 Total grade: 1.0×1/2 + 0.0×1/2 = 50% + 0% Feedback: Apply standard algebraic properties. 6 (x + 3) − 37 = x + 6 6x + 18 − 37 = x + 6 6x − 19 = x + 6 5x = 25 x = 25 5 x = 5 Apply the distributive property. Combine like terms. Place x- terms on one side and simplify. Multiply both sides by 1 , the reciprocal of 5. 5 Q3 0/0.0 View Original Response Unfiltered Response 2/27/2023 Southern New Hampshire University - Gradebook 5/22 green balls in the box. Show your work and explain, in your own words, how you arrived at your answer. Answers with no relevant explanations may receive reduced or no credit. Question Write and solve an equation to answer the question. A box contains orange balls and green balls. The number of green balls is ten more than two times the number of orange balls. If there are 55 balls altogether, then how many green balls and how many orange balls are there in the box? There are Your response Correct response 15 15 Auto graded Grade: 1/1.0 orange balls and Your response Correct response 40 40 Auto graded Grade: 1/1.0 2/27/2023 Southern New Hampshire University - Gradebook 6/22 Question Green balls = 2x+10 Orange balls = x 2 x + 10 + x = 55 - orange balls plus green balls = 55 3 x + 10 = 55 - simplify by adding 2x + x 3 x = 55 − 10 - Subtract 10 from each side 3 x = 45 x = 45 - Simplify by dividing both sides by 3 3 x = 15 - 15 orange balls 2 ⋅ 15 + 10 - put 15 back into equation for green balls 30 + 10 = 40 - 40 green balls Ungraded Grade: 0/1.0 Total grade: 1.0×1/3 + 1.0×1/3 + 0.0×1/3 = 33% + 33% + 0% Feedback: Let x be the number of orange balls in the box. The number of green balls is ten more than two times the number of orange balls, so we can write the number of green balls as 10 plus 2 times x, or 2x + 10. The total number of balls is 55. We usually interpret the word "is" as an equal sign. x + (2x + 10) = 55 3x + 10 = 55 Simplify and solve. 3x = 45 x = 15 If there are 15 orange balls, then there are 2 (15) + 10 = 40 green balls. We can check that 15 + 40 = 55. 2/27/2023 Southern New Hampshire University - Gradebook 7/22 0/0.0 Show your work and explain, in your own words, how you arrived at your answer. Answers with no relevant explanations may receive reduced or no credit. m ⋅ m2 + m (3 m) + m ⋅ −4 − 3 ⋅ m2 − 3 (3 m) − 3 ⋅ −4 - expand by multiplying each term in the first expression by each term in the second m3 + m (3 m) + m ⋅ −4 − 3 m2 − 3 (3 m) − 3 ⋅ −4 - raise first m to power of 1 and add using power rule to combine exponents m3 + 2 m ⋅ m + m ⋅ −4 − 3 m2 − 3 (3 m) − 3 ⋅ −4 - rewrite using cummutative property of multiplication m3 + 3 m2 + m ⋅ −4 − 3 m2 − 3 (3 m) − 3 ⋅ −4 - Move m and multiply m*m m3 + 3 m2 − 4 m − 3 m2 − 9 m + 12 - multiply 3*-3 and 3*-4 m3 − 13 m + 12 - simplify by adding terms(m^3, m^2 and m) Question Q4 View Original Response Unfiltered Response Auto graded Grade: 1/1.0 Ungraded Grade: 0/1.0 Perform the given operation and simplify. (m − 3)(m2 + 3m − 4) Your response Correct response m3 − 13 m + 12 m^3-13*m+12 2/27/2023 Southern New Hampshire University - Gradebook 8/22 Question Total grade: 1.0×1/2 + 0.0×1/2 = 50% + 0% Feedback: m (m2 + 3m − 4) − 3 (m2 + 3m − 4) Use the distributive property. m3 + 3m2 − 4m − 3m2 − 3 ⋅ 3m + 3 ⋅ 4 Multiply. m3 − (4 + 9)m + 12 Combine like terms. m3 − 13m + 12 Simplify. Q5 0/0.0 View Original Response Unfiltered Response Auto graded Grade: 1/1.0 miles. Show your work and explain, in your own words, how you arrived at your answer. Answers with no relevant explanations may receive reduced or no credit. Write and solve an equation to answer the question. A truck rental is $25 plus $. 45/mi. Find out how many miles Ken traveled if his bill was $60.10. Ken traveled Your response Correct response 78 78 2/27/2023 Southern New Hampshire University - Gradebook 9/22 Question 25 + .45 x = 60.10 - write equation to find x .45 x = 60.10 − 25 - subtract 25 from each side .45 x = 35.1 - simplify x = 35.1 - divide both sides by .45 .45 x=78 miles Ungraded Grade: 0/1.0 Total grade: 1.0×1/2 + 0.0×1/2 = 50% + 0% Feedback: Let x be the number of miles Ken traveled. Then, as the bill is $25 plus $. 45/mi, we can write the cost of his trip in dollars as 0.45x + 25. Ken's bill was $60.10. We usually interpret the word is as an equal sign. 0.45x + 25 = 60.10 0.45x = 35.10 Collect like terms. x = 78 Divide both sides by 0.45. Thus, Ken traveled 78 miles during his trip. Q6 0/0.0 View Original Response Unfiltered Response 2/27/2023 Southern New Hampshire University - Gradebook 10/22 Question Simplify the expression. 9y2−64 9y2−48y+64 Enclose numerators and denominators in parentheses. For example, (a − b)/ (1 + n). Your response (3 y+8) (3 y−8) Auto graded Grade: 1/1.0 Correct response (3*y+8)/(3*y-8) Show your work and explain, in your own words, how you arrived at your answer. Answers with no relevant explanations may receive reduced or no credit.