1. Find the midpoint and the distance between the points (8,–6) and (13, 4).
1. (4, –3), 10 units
2.
3.
4. (10, –1), 9 units
2. Find the vertex and the focus of the parabola with the equation 4y = x2 – 12x + 52.
1. V(6, 4), F(6, 5)
2. V(6, 4), F(7, 4)
3. V(4, 6), F(4, 7)
4. V(4, 6), F(5, 6)
3. Find the center and radius of a circle whose equation is x2 + y2 + 88 = 8y – 22x.
1.
2.
3. C(11, –4), r = 7
4. C(–11, 4), r = 7
4. Find the center and foci of the ellipse with the following equation.
1.
2.
3.
4.
5. Find the slopes of the asymptotes of the hyperbola with the equation 36 = 9x2 – 4y2.
1. 3/2, –3/2
2. –4/9, –4/9
3. 1/4, 1/9
4. 1/36, 1/13
6. Identify the type of equation 0 = 3x2 + y2 – 12x – 30y + 181.
1. parabola
2. circle
3. ellipse
4. hyperbola
7. Solve the following system of equations.
x2 + y2 = 9
x2 – 3y = 9
1. (–3, 9)
2. (–3, 9), (–3, 0)
3. (–3, 0), (0, –3), (3, 0)
4. (–3, 0), (3, 0), (–3, 9), (3, 9)
8. Identify the number of possible real zeros of the function f(x) = x4 – 6x2 + 6.
1. 1
2. 2
3. 3
4. 4
9. Given the function f(x) = x3 – 7x + 6 and one of its factors (x – 1), find all remaining factors.
1. (x – 1)(x – 2)(x + 3)
2. (x – 1)(x – 7)(x + 6)
3. (x – 1)(x + 1)(x – 6)
4. (x – 1)(x – 7)(x + 6)
10. Identify all rational zeros of the polynomial function f(x) = 3x4 – 5x3 – 29x2 + 45x + 18.
1. –6, –2/3, 6, 18
2. –3, –1/3, 2, 3
3. –2, 6
4. 1/3, 2/3
11. Find f(g(2)) if f(x) = x2 + 3x and g(x) = 3 – x2.
1. –2
2. –7
3. –97
4. 103
12. If f(x) = x2 + 2, find f –1(3).
1. 11
2. 3
3.
4.
13. Find the equations of the vertical and horizontal asymptotes for the graph of the rational function with the following equation.
1. y = 0, x = 3, x = –2
2. x = –2, y = 6
3. x = –3, y = 0, x = 2
4. y = 0, x = 6, x = 2
14. If y varies jointly as x and z, and y = 28 when x = 14 and z = 1, find the value of y when x = 7 and z = 4.
1. 7/4
2. 8
3. 14
4. 56
15. Simplify the following expression.
1. 1
2.
3.
4.
16. Solve the following equation.
1. –2, 5
2. 5, 3
3. 3, –2
4. Ø, no solution
17. Two pickup trucks have towing capacities in a ratio 5 to 4. The larger pickup truck can tow 800 lbs more than the smaller truck. What is the towing capacity of the larger truck?
1. 1,000 lbs
2. 2,400 lbs
3. 3,200 lbs
4. 4,000 lbs
18. Solve the equation 92x + 1 = 3x – 3.
1. –4
2. –5/3
3. 2/3
4. 3
19. Solve the equation log3 (3x + 4) = 1/3 log3 8.
1. –2/3
2. –4/9
3. 4/3
4. 2/3
20. Find antilog 1.2, round your answer to the nearest hundredth.
1. 0.08
2. 0.18
3. 3.32
4. 15.85
21. Solve the equation ln (x + 2) = 3. Round your answer to the nearest hundredth.
1. 1.00
2. 18.09
3. 22.09
4. 998.00
22. Solve the equation 47x – 2 = 17x + 1. Round your answer to the nearest thousandth.
1. 0.489
2. 0.816
3. 1.386
4. 2.833
23. Find the 4 arithmetic means between the numbers 45 and 80.
1. 50, 55, 60, 65
2. 52, 57, 62, 67
3. 50, 57, 64, 71
4. 52, 59, 66, 73
24. Find the sum of the following arithmetic series.
1. 120
2. 120 ½
3. 124
4. 124 ½
25. Identify the twelfth term in the geometric sequence in which a1 = 10, r = 2.
1. 110
2. 1,280
3. 20,480
4. 5,242,940
26. Find the sum of the following geometric series.
1. 55,986
2. 19,530
3. 9,330
4. 3,905
27. Find the sum of the infinite geometric series 100 + 90 + 81 + 72.9 + 65.61 . . .
1. 750
2. 12.456
3. 1000
4. 1245.0435
28. Identify the binomial expansion of (x + 4y)4.
1. x4 + 256y4
2. x4 + 8x2y2 + 16y4
3. x4 + 12x3y + 96xy3 + 256y4
4. x4 + 16x3y + 96x2y2 + 256xy3 + 256y4
29. Find the number of 7-digit phone numbers that can be formed if the first three digits come from the numbers 1 to 3 and the last four digits come from the numbers 1 to 9.
1. 5,040
2. 177,147
3. 362,886
4. 823,543
30. Find the number of ways eight people can be seated in an eight-passenger van.
1. 8
2. 216
3. 40,320
4. 16,777,216
31. Find the number of ways 4 bikes can be placed on a bike rack with 12 spots.
1. 24
2. 495
3. 11,880
4. 479,001,600
32. A meal at a certain restaurant consists of 3 entrées chosen from group of 15 possible entrées. Find the number of possible meal combinations.
1. 6
2. 455
3. 2,730
4. 217,945,728,000
33. Find the probability of rolling a die three times and rolling a ’2’ each time.
1. 34/100
2. 139/2500
3. 1/216
4. 1667/1000
34. If the Independent Party has lost 10 of the last 15 elections, find the odds against an Independent victory in the next election.
1. 1 to 2
2. 2 to 1
3. 1 to 3
4. 3 to 1
35. Suppose that you are drawing cards from a set of 6 cards, the colors of which are red, blue, orange, yellow, pink, and green. What is the probability of drawing a red card followed by a blue card without replacement?
1. 1/3
2. 1/15
3. 1/30
4. 1/36
36. Find the probability of drawing a spade or a face card from a standard deck of cards.
1. 11/26
2. 25/56
3. 22/56
4. 15/56
For questions 37–39, use the data in the stem-and-leaf plot.
37. Determine which of following best describes 64.
1. 64 is the range of the data
2. 64 is the mode of the data
3. 64 is the mean of the data
4. 64 is the median of the data
38. Find the quartiles of the data.
1. 61, 67, 78
2. 39, 64, 74.71
3. 12, 67, 93
4. 28, 65.45
39. How many outliers do the data have?
1. 1
2. 2
3. 3
4. none
40. Find cot A, sec A, and csc A.
1. cot A = 4/3, sec A = 3/5, csc A = 4/5
2. cot A = 3/4, sec A = 5/4, csc A = 5/3
3. cot A = 3/4, sec A = 5/3, csc A = 5/4
4. cot A = 4/3, sec A = 4/5, csc A = 3/5
41. Which trigonometric function should be used to solve for x?
1. sine
2. cosine
3. tangent
4. cosecant
42. Find the values of side c and angle B. Round to the nearest hundredth.
1. c = 5.60, B = 45°
2. c = 11.95, B = 49°
3. c = 10.87, B = 195°
4. c = 13.24, B = 65°
43. The pilot of a hot air balloon approaching a mountain peak measures that its altitude above sea level is 10,000 ft. If the mountain peak is 5 mi (26,400 ft) away and is 5,000 ft above sea level, what is the angle of depression from the balloon to the mountain peak? Round to the nearest hundredth degree.
1. 8.34°
2. 10.72°
3. 11.31°
4. 79.08°
44. Find the measure of angles B and C using the law of sines. Round to the nearest hundredth.
1. B = 100.27°, C = 42.73°
2. B = 27.89°, C = 115.11°
3. B = 84.88°, C = 58.12°
4. B = 45.76°, C = 97.24°
45. Using the law of cosines, find the angle measures of triangle with sides 55, 75, and 80. Round to the nearest degree.
1. 74°, 64°, 41°
2. 59°, 95°, 25°
3. 70°, 74°, 35°
4. 24°, 65°, 91°
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@ryan stop making up lies ;-;
To answer these questions, we will go through each question and explain the steps to find the answer.
1. Find the midpoint and the distance between the points (8,–6) and (13, 4).
To find the midpoint, you can use the midpoint formula, which states that the coordinates of the midpoint between two points (x1, y1) and (x2, y2) is given by:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
Substituting the values from the given points, we get:
Midpoint = ((8 + 13)/2, (-6 + 4)/2)
Midpoint = (21/2, -2/2)
Midpoint = (10.5, -1)
So, the midpoint is (10.5, -1).
To find the distance between two points, you can use the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is given by:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Substituting the values from the given points, we get:
Distance = √((13 - 8)^2 + (4 - (-6))^2)
Distance = √(5^2 + 10^2)
Distance = √(25 + 100)
Distance = √125
Distance = 11.18
So, the distance between the points is 11.18 units.
Therefore, the answer is 1. (10.5, -1), 11.18 units.