PSAT Math Practice Test - Medium Level - 65 Questions
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Question 1 of 65
1. Question
1 pointsA plane ascends at a constant rate. Ten minutes after takeoff, it is 1,225 feet above sea level. Twenty-five minutes after takeoff, it is 15,570 feet above sea level. What is the rate of ascent per minute?
Correct
Explanation: Height increase = 15,570 – 1,225 = 14,345 ft over 25-10=15 minutes → Rate = 14,345 ÷ 15 ≈ 956.33 ft/min.
Incorrect
Explanation: Subtract initial height from final height and divide by the time difference.
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Question 2 of 65
2. Question
1 pointsAmanda pays $50/month, plus $1 per minute and $0.50 per text. Betty pays $25/month, plus $2 per minute and $0.75 per text. If both use 100 minutes and 200 texts per month, how much more will Betty spend than Amanda in a year?
Correct
Explanation: Monthly cost: Amanda = 50 + 100×1 + 200×0.5 = 200 → Annual = 200×12 = 2,400; Betty = 25 + 100×2 + 200×0.75 = 275 → Annual = 3,300 → Difference = 900. Wait, let’s check: Amanda = 50+100+100=250 → Annual = 3,000; Betty = 25+200+150=375 → Annual = 4,500 → Difference = 1,500. Correct.
Incorrect
Explanation: Calculate monthly cost first, then multiply by 12.
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Question 3 of 65
3. Question
1 pointsThe function f(x) = 2x^2 – 3x + 5. What is f(3)?
Correct
Explanation: f(3)=2(3)^2-3(3)+5=18-9+5=14.
Incorrect
Explanation: Substitute x=3 into the function and simplify step by step.
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Question 4 of 65
4. Question
1 pointsA rectangle has a length 3 times its width. If perimeter is 64, what is the width?
Correct
Explanation: Let width = w → length = 3w. Perimeter = 2(w+3w)=8w=64 → w=8.
Incorrect
Explanation: Use formula P=2(l+w), solve for w.
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Question 5 of 65
5. Question
1 pointsIf 5x – 7 = 3x + 9, what is x?
Correct
Explanation: 5x – 3x = 9 + 7 → 2x = 16 → x = 8.
Incorrect
Explanation: Combine like terms and solve for x.
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Question 6 of 65
6. Question
1 pointsIf 3/4 of a number is 18, what is the number?
Correct
Explanation: Let x be the number. 3/4 x = 18 → x = 18 × 4/3 = 24.
Incorrect
Explanation: Multiply both sides by 4/3 to isolate x.
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Question 7 of 65
7. Question
1 pointsThe sum of the first 5 positive even numbers is?
Correct
Explanation: First 5 even numbers: 2,4,6,8,10 → sum = 2+4+6+8+10=30.
Incorrect
Explanation: List first 5 even numbers and add.
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Question 8 of 65
8. Question
1 pointsA triangle has angles in the ratio 2:3:4. Find the largest angle.
Correct
Explanation: Let angles be 2x,3x,4x → 2x+3x+4x=180 → 9x=180 → x=20 → largest = 4x=80°.
Incorrect
Explanation: Sum of angles in triangle = 180. Use ratio to find each angle.
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Question 9 of 65
9. Question
1 pointsIf y = 2x + 5 and y = 13, what is x?
Correct
Explanation: 13 = 2x + 5 → 2x = 8 → x = 4.
Incorrect
Explanation: Solve for x by isolating it on one side of the equation.
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Question 10 of 65
10. Question
1 pointsA store sells pencils at 3 for $1. How many pencils can you buy with $10?
Correct
Explanation: $10 ÷ $1 = 10 sets → 10×3 pencils = 30 pencils.
Incorrect
Explanation: Find how many sets of 3 pencils fit into $10, then multiply by 3.
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Question 11 of 65
11. Question
1 pointsThe sum of three consecutive integers is 51. What is the largest integer?
Correct
Explanation: Let integers be x, x+1, x+2 → sum = 3x+3 = 51 → 3x=48 → x=16 → largest = 18.
Incorrect
Explanation: Use x, x+1, x+2 as consecutive integers and solve for x.
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Question 12 of 65
12. Question
1 pointsIf f(x) = 2x + 3, what is f(5)?
Correct
Explanation: f(5) = 2*5 + 3 = 10 + 3 = 13.
Incorrect
Explanation: Substitute x=5 into the function and simplify.
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Question 13 of 65
13. Question
1 pointsA rectangle has length 8 and width 5. What is its diagonal length?
Correct
Explanation: Diagonal = √(8² + 5²) = √(64+25)=√89.
Incorrect
Explanation: Use Pythagoras theorem: diagonal² = length² + width².
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Question 14 of 65
14. Question
1 pointsIf 5x – 7 = 3x + 9, what is x?
Correct
Explanation: 5x – 7 = 3x + 9 → 2x = 16 → x = 8.
Incorrect
Explanation: Move 3x to left and -7 to right, then solve for x.
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Question 15 of 65
15. Question
1 pointsA store sells 4 notebooks for $3. How much would 10 notebooks cost?
Correct
Explanation: Price per notebook = 3/4 → 10 notebooks = 10*(3/4)=7.5 dollars.
Incorrect
Explanation: Find unit price first, then multiply by number of notebooks.
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Question 16 of 65
16. Question
1 pointsIf 3(x – 2) = 2x + 4, what is the value of x?
Correct
Explanation: 3x – 6 = 2x + 4 → x = 10.
Incorrect
Explanation: Expand and simplify the equation to solve for x.
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Question 17 of 65
17. Question
1 pointsA circle has a radius of 7. What is its area in terms of π?
Correct
Explanation: Area = πr² = π*7² = 49π.
Incorrect
Explanation: Use formula area = π*r^2.
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Question 18 of 65
18. Question
1 pointsThe sum of the first n positive integers is 55. What is n?
Correct
Explanation: Sum formula: n(n+1)/2=55 → n(n+1)=110 → n=10.
Incorrect
Explanation: Solve n(n+1)/2=55 for n.
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Question 19 of 65
19. Question
1 pointsIf y/4 + 3 = 7, what is y?
Correct
Explanation: y/4 = 4 → y = 16.
Incorrect
Explanation: Subtract 3 then multiply by 4 to solve for y.
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Question 20 of 65
20. Question
1 pointsA train travels 60 miles in 1.5 hours. What is its average speed in miles per hour?
Correct
Explanation: Speed = distance/time = 60/1.5 = 40 mph.
Incorrect
Explanation: Divide total distance by total time to find speed.
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Question 21 of 65
21. Question
1 pointsIf 5x – 3 = 2x + 12, what is x?
Correct
Explanation: 5x – 3 = 2x + 12 → 3x = 15 → x = 5.
Incorrect
Explanation: Subtract 2x and add 3 to isolate x.
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Question 22 of 65
22. Question
1 pointsA rectangle has a length of 12 and a width of 5. What is its perimeter?
Correct
Explanation: Perimeter = 2*(length+width) = 2*(12+5) = 34.
Incorrect
Explanation: Use formula P = 2(l + w).
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Question 23 of 65
23. Question
1 pointsIf 3x + 7 = 16, what is x?
Correct
Explanation: 3x = 9 → x = 3.
Incorrect
Explanation: Subtract 7 then divide by 3.
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Question 24 of 65
24. Question
1 pointsThe sum of two consecutive integers is 35. What are the integers?
Correct
Explanation: Let integers be n and n+1 → n + (n+1) = 35 → 2n+1=35 → 2n=34 → n=17. Integers: 17, 18.
Incorrect
Explanation: Solve using n and n+1 for consecutive integers.
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Question 25 of 65
25. Question
1 pointsA car rental company charges $25 per day plus $0.20 per mile. If a customer rents the car for 3 days and drives 150 miles, what is the total cost?
Correct
Explanation: 3*25 + 150*0.20 = 75 + 30 = 105.
Incorrect
Explanation: Multiply daily rate by days and per-mile rate by miles, then sum.
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Question 26 of 65
26. Question
1 pointsIf 2(x – 3) + 5 = 15, what is x?
Correct
Explanation: 2(x-3)+5=15 → 2(x-3)=10 → x-3=5 → x=8.
Incorrect
Explanation: Solve step by step: subtract 5, divide by 2, then add 3.
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Question 27 of 65
27. Question
1 pointsA triangle has sides of length 5, 12, and 13. What is the area of the triangle?
Correct
Explanation: This is a right triangle (5^2+12^2=13^2). Area = (1/2)*base*height = (1/2)*5*12 = 30.
Incorrect
Explanation: Check if the triangle is right, then use area formula 1/2*base*height.
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Question 28 of 65
28. Question
1 pointsIf 4x + 7 = 3x + 15, what is x?
Correct
Explanation: 4x – 3x = 15 – 7 → x = 8.
Incorrect
Explanation: Subtract 3x and 7 from both sides to isolate x.
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Question 29 of 65
29. Question
1 pointsA store offers a 20% discount on a jacket that originally costs $60. What is the sale price?
Correct
Explanation: Discount = 20% of 60 = 12 → Sale price = 60 – 12 = 48.
Incorrect
Explanation: Multiply 60 by 0.2 to find discount, then subtract from original price.
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Question 30 of 65
30. Question
1 pointsIf x/3 + 5 = 9, what is x?
Correct
Explanation: x/3 = 4 → x = 12.
Incorrect
Explanation: Subtract 5 then multiply both sides by 3.
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Question 31 of 65
31. Question
1 pointsIf 3x – 4 = 2x + 5, what is x?
Correct
Explanation: 3x – 2x = 5 + 4 → x = 9.
Incorrect
Explanation: Subtract 2x and add 4 to both sides to isolate x.
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Question 32 of 65
32. Question
1 pointsA rectangle has a length of 10 and width of 7. What is the length of its diagonal?
Correct
Explanation: Diagonal d = √(10^2 + 7^2) = √149.
Incorrect
Explanation: Use Pythagoras theorem: d = √(length^2 + width^2).
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Question 33 of 65
33. Question
1 pointsIf 5x + 3 = 2x + 18, what is x?
Correct
Explanation: 5x – 2x = 18 – 3 → 3x = 15 → x = 5.
Incorrect
Explanation: Subtract 2x and 3 from both sides, then divide by 3.
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Question 34 of 65
34. Question
1 pointsThe sum of three consecutive integers is 72. What is the largest integer?
Correct
Explanation: Let integers be n, n+1, n+2 → n+n+1+n+2=3n+3=72 → 3n=69 → n=23. Largest = n+2=25.
Incorrect
Explanation: Use variable n for smallest integer, sum them, solve for n.
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Question 35 of 65
35. Question
1 pointsA notebook costs $2.50, and a pen costs $1.20. If you buy 4 notebooks and 3 pens, what is the total cost?
Correct
Explanation: 4*2.50 + 3*1.20 = 10 + 3.6 = 13.6 → $13.60.
Incorrect
Explanation: Multiply quantities by unit prices, then sum.
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Question 36 of 65
36. Question
1 pointsIf 2(x – 3) + 5 = 15, what is x?
Correct
Explanation: 2(x-3) = 10 → x-3=5 → x=8.
Incorrect
Explanation: Subtract 5, divide by 2, then add 3 to solve for x.
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Question 37 of 65
37. Question
1 pointsA car travels 60 miles in 1.5 hours. What is the average speed in miles per hour?
Correct
Explanation: speed = distance/time = 60 / 1.5 = 40 mph.
Incorrect
Explanation: Divide total miles by total hours to get speed.
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Question 38 of 65
38. Question
1 pointsA triangle has sides 5, 12, and 13. What type of triangle is it?
Correct
Explanation: 5^2 + 12^2 = 25 + 144 = 169 = 13^2, so it’s a right triangle.
Incorrect
Explanation: Check if the Pythagorean theorem holds to identify a right triangle.
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Question 39 of 65
39. Question
1 pointsIf 4/5 of a number is 32, what is the number?
Correct
Explanation: number = 32 ÷ (4/5) = 32 * 5/4 = 40.
Incorrect
Explanation: Divide by the fraction to find the original number.
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Question 40 of 65
40. Question
1 pointsA rectangle has a perimeter of 36 and a length of 11. What is the width?
Correct
Explanation: 2(l + w) = 36 → 11 + w = 18 → w = 7.
Incorrect
Explanation: Use formula P = 2(l+w) and solve for w.
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Question 41 of 65
41. Question
1 pointsIf f(x) = 3x + 2, what is f(5)?
Correct
Explanation: f(5) = 3*5 + 2 = 15 + 2 = 17.
Incorrect
Explanation: Substitute 5 for x in the function and simplify.
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Question 42 of 65
42. Question
1 pointsA bookstore sells 3 notebooks for $5. How much would 12 notebooks cost?
Correct
Explanation: $5 ÷ 3 = $1.6667 per notebook → 12*1.6667 ≈ $20.
Incorrect
Explanation: Calculate unit price and multiply by 12 notebooks.
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Question 43 of 65
43. Question
1 pointsSimplify: 2(3x + 4) – x
Correct
Explanation: 2*3x + 2*4 – x = 6x + 8 – x = 5x + 8.
Incorrect
Explanation: Distribute 2 and then combine like terms.
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Question 44 of 65
44. Question
1 pointsIf a circle has a radius of 6, what is its area? Use π ≈ 3.14
Correct
Explanation: Area = πr^2 ≈ 3.14*6^2 = 3.14*36 ≈ 113.04.
Incorrect
Explanation: Use formula A = πr² and substitute r=6.
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Question 45 of 65
45. Question
1 pointsIf 3x – 7 = 11, what is x?
Correct
Explanation: 3x = 18 → x = 6.
Incorrect
Explanation: Add 7 to both sides, then divide by 3.
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Question 46 of 65
46. Question
1 pointsThe sum of three consecutive integers is 72. What is the largest integer?
Correct
Explanation: Let integers be x, x+1, x+2. Sum = 3x + 3 = 72 → 3x = 69 → x = 23 → largest = 25.
Incorrect
Explanation: Set up equation with consecutive integers and solve for x.
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Question 47 of 65
47. Question
1 pointsIf y = 2x + 5 and y = 11, what is x?
Correct
Explanation: 11 = 2x + 5 → 2x = 6 → x = 3.
Incorrect
Explanation: Substitute y = 11 into equation and solve for x.
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Question 48 of 65
48. Question
1 pointsA rectangle has a length of 8 and width of 3. If both dimensions are doubled, what is the new area?
Correct
Explanation: Original area = 8*3 = 24. Double: length = 16, width = 6 → new area = 16*6 = 96.
Incorrect
Explanation: Multiply new length and width after doubling.
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Question 49 of 65
49. Question
1 pointsFactor completely: x^2 + 5x + 6
Correct
Explanation: x^2 + 5x + 6 = (x + 2)(x + 3).
Incorrect
Explanation: Find two numbers that multiply to 6 and add to 5.
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Question 50 of 65
50. Question
1 pointsThe sum of the interior angles of a polygon is 900°. How many sides does the polygon have?
Correct
Explanation: Sum = (n-2)*180 → 900 = (n-2)*180 → n-2 = 5 → n = 7.
Incorrect
Explanation: Use formula for sum of interior angles: (n-2)*180°.
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Question 51 of 65
51. Question
1 pointsIf 3x – 7 = 11, what is the value of x?
Correct
Explanation: 3x – 7 = 11 → 3x = 18 → x = 6.
Incorrect
Explanation: Add 7 to both sides, then divide by 3.
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Question 52 of 65
52. Question
1 pointsA store sells pencils at 3 for $1.50. How much would 10 pencils cost?
Correct
Explanation: 3 pencils = $1.50 → 1 pencil = $0.50 → 10 pencils = $5.00.
Incorrect
Explanation: Find price per pencil, then multiply by 10.
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Question 53 of 65
53. Question
1 pointsIf f(x) = x^2 – 4, what is f(3)?
Correct
Explanation: f(3) = 3^2 – 4 = 9 – 4 = 5.
Incorrect
Explanation: Substitute x = 3 into the function and simplify.
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Question 54 of 65
54. Question
1 pointsA triangle has angles in the ratio 2:3:4. What is the measure of the largest angle?
Correct
Explanation: 2x + 3x + 4x = 180 → 9x = 180 → x = 20 → largest = 4x = 80°.
Incorrect
Explanation: Set up proportion, sum = 180, solve for x.
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Question 55 of 65
55. Question
1 pointsSimplify: 4(2x + 3) – 5x
Correct
Explanation: 4*2x + 4*3 – 5x = 8x + 12 – 5x = 3x + 12.
Incorrect
Explanation: Apply distributive property, combine like terms.
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Question 56 of 65
56. Question
1 pointsThe sum of three consecutive integers is 72. What is the middle integer?
Correct
Explanation: Let integers be x-1, x, x+1 → sum = 3x = 72 → x = 24.
Incorrect
Explanation: Set up consecutive integer equation and solve for x.
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Question 57 of 65
57. Question
1 pointsIf 5x + 3 = 2x + 18, what is x?
Correct
Explanation: 5x – 2x = 18 – 3 → 3x = 15 → x = 5.
Incorrect
Explanation: Subtract 2x and 3 from both sides to solve for x.
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Question 58 of 65
58. Question
1 pointsA rectangle has a length of 8 cm and a width of 5 cm. If both are increased by the same amount x to make the area 96 cm², what is x?
Correct
Explanation: (8 + x)(5 + x) = 96 → 40 + 13x + x² = 96 → x² + 13x – 56 = 0 → x = 4 (positive solution).
Incorrect
Explanation: Set up new area equation and solve quadratic for x.
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Question 59 of 65
59. Question
1 pointsSimplify: 2(3x – 4) + 5(x + 1)
Correct
Explanation: 2*3x – 8 + 5x + 5 = 6x – 8 + 5x + 5 = 11x – 3.
Incorrect
Explanation: Apply distributive property, then combine like terms.
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Question 60 of 65
60. Question
1 pointsA box contains 3 red balls, 4 blue balls, and 5 green balls. If one ball is picked at random, what is the probability it is blue?
Correct
Explanation: Total balls = 3 + 4 + 5 = 12 → P(blue) = 4/12 = 1/3.
Incorrect
Explanation: Divide the number of blue balls by total balls.
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Question 61 of 65
61. Question
1 pointsIf 2(x + 3) = 4x – 2, what is x?
Correct
Explanation: 2x + 6 = 4x – 2 → 6 + 2 = 4x – 2x → 8 = 2x → x = 4.
Incorrect
Explanation: Apply distributive property, then isolate x.
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Question 62 of 65
62. Question
1 pointsThe perimeter of a square is 48 cm. What is the length of one side?
Correct
Explanation: Perimeter = 4 × side → 4s = 48 → s = 12 cm.
Incorrect
Explanation: Divide the perimeter by 4 to get the side length.
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Question 63 of 65
63. Question
1 pointsIf y/3 + 5 = 12, what is y?
Correct
Explanation: y/3 = 12 – 5 → y/3 = 7 → y = 21.
Incorrect
Explanation: Subtract 5 then multiply both sides by 3.
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Question 64 of 65
64. Question
1 pointsA car travels 150 miles in 3 hours. What is its average speed in miles per hour?
Correct
Explanation: Speed = distance/time → 150/3 = 50 mph.
Incorrect
Explanation: Divide total miles by total hours to get average speed.
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Question 65 of 65
65. Question
1 pointsSimplify: 4(2x – 3) – 3(x + 5)
Correct
Explanation: 8x – 12 – 3x – 15 = 5x – 27.
Incorrect
Explanation: Apply distributive property then combine like terms.