# Posts by Bosnian

Total # Posts: 2,760

1. ### geometry

1) 6 y + 3° is first angle 4 y - 13° is second angle 6 y + 3° + 4 y - 13° = 180° 10 y - 10° = 180° 10 y = 180° + 10° 10 y = 190° y = 190° / 10 y = 19° 6 y + 3° = 6 ? 19° + 3° = 114° + 3° = 117° 4 y - 13&...
2. ### Math

a = first integer a = 2 k + 1 b = second integer Becouse odd integers consecutive are consecutive: b = a + 2 = 2 k + 1 + 2 = 2 k + 3 k is some integer The square of the first, added to 3 times the second is 24 mean: a² + 3 b = 24 ( 2 k + 1 )² + 3 ? ( 2 k + 3 ) = 24...
3. ### Math

c = capital 1 = 6 / 6 1 / 2 = 3 / 6 1 / 3 = 2 / 6 c - ( 1 / 2 ) c - ( 1 / 3 ) c = ( 6 / 6 ) c - ( 3 / 6 ) c - ( 2 / 6 ) = ( 1 / 6 ) c = c / 6 c / 6 = 50 000 Multiply both sides by 6 c = 300 000
4. ### math

1 ft = 12 in 1 yd = 36 in Buildin tall: 20 ft = 12 * 20 = 240 in A tree's height: 252 in = 252 in Fagpole high: 6 yd = 6 * 36 = 216 in
5. ### Algebra

y = 1.10 ( x - 1 ) + 1.35 y = 1.10 x - 1.10 + 1.35 y = 1.10 x + 0.25
6. ### math

OR 1 h / ( 3 / 4 ) h = ( 4 / 4 ) / ( 3 / 4 ) = ( 4 ? 4 ) / ( 4 ? 3 ) = 4 / 3 ( 4 / 3 ) ? 3 1 / 2 = ( 4 / 3 ) ? ( 14 / 4 ) = 4 ? 14 / ( 4 ? 3 ) = 14 / 3 = ( 12 + 2 ) / 3 = 12 / 3 + 2 / 3 = 4 + 2 / 3 = 4 2/3 mi
7. ### math

3 1 / 2 = 3 + 1 / 2 = 3 + 2 / 4 = 12 / 4 + 2 / 4 = 14 / 4 ( 14 / 4 ) / ( 3 / 4 ) = 14 ? 4 / ( 3 ? 4 ) = 14 / 3 = ( 12 + 2 ) / 3 = 12 / 3 + 2 / 3 = 4 + 2 / 3 = 4 2/3 OR 3 1/2 / ( 3 / 4 ) = x / 1 x = 3 1/2 / ( 3 / 4 ) x = ( 14 / 4 ) / ( 3 / 4 ) = 14 ? 4 / ( 3 ? 4 ) = 14 / 3 = ( ...
8. ### math

This is the same expression becouse: - 583.33 (x) + 15,000 = - 583.33 ? x + 15,000 = - 583.33 x + 15,000 = 15,000 - 583.33 x but it is usually written - 583.33 x + 15,000 The first part of the expression with x then the number.
9. ### Math

Your number = 10 a + b a + b = 9 If 9 is subtracted from the number its digits are interchanged mean: 10 a + b - 9 = 10 b + a Now: 10 a - 9 - a = 10 b - b 9 a - 9 = 9 b Divide both sides by 9 a - 1 = b You must solve system: a + b = 9 a - 1 = b Try that. The solutions are: a...
10. ### math

In google type: gauss jordan elimination method online When you see list of results click on: Gaussian elimination calculator - OnlineMSchool When page be open type your coefficients and click option Solve the system. You will see solution step-by step. Of course in the ...
11. ### math

If f(t) = 24,500(0.84) mean f(t) =24,500 ? 0.84? then: t = present year t - 1 = last year 24,500 ? 0.84? = population in present year 24,500 ? 0.84??¹ = population in last year Rate of decreasing = 1 - ( 24,500 ? 0.84? / 24,500 ? 0.84??¹ ) = 1 - 0.84? / 0.84??¹...
12. ### Math

3 x² + 6 - 2 x + 5 x - 4 x² + 9 = 3 x² - 4 x² - 2 x + 5 x + 6 + 9 = - x² + 3 x + 15 = - ( x² - 3 x - 15 )
13. ### math

Reiny's solution is incorrect. - ( ( x - 3 )² - 14 ) = - ( x² - 2 ? x ? 3 + 3² - 14 ) = - ( x² - 6 x + 9 - 14 ) = - ( x² - 6 x - 5 ) = - x² + 6 x + 5 but - x² + 6 x - 5 = - x² + 6 x - 9 + 4 = ( - x² + 6 x - 9 ) + 4 = - ( x²...
14. ### Math

Unknown I'm not going to do your complet homework.
15. ### Math

? rad = 180° ? / 12 = 180° / 12 = 15° 15° = 45° - 30° cos ( A - B ) = sin A ? sin B + cos A ? cos B sin 45° = cos 45° = ?2 / 2 = 1 / ?2 cos ( 45° - 30° ) = cos 15° = sin 45° ? sin 30° + cos 45° ? cos 30° = ( 1 / ?2...
16. ### Math

If your expression mean: ( sec² x - 1 ) / ( sin x ? sec x ) then: sec² x = 1 / cos² x sec² x - 1 = 1 / cos² x - 1 = 1 / cos² x - cos² x / cos² x = ( 1 - cos² x ) / cos² x = sin² x / cos² x = tan² x sin x ? sec x...
17. ### math

a1 ÷ a10 = your numbers. You can write 10th digit in form: a10 = 10 x + y Original sum: S = a1 + a2 +...+ a9 + 10 x + y If 10th digit be interchanged new number will be 10 y + x New sum wil be: S1 = a1 + a2 +...+ a9 + 10 y + x The sum of all the ten numbers increased by...
18. ### Math

In arithmetic progression; an = a1 + ( n - 1 ) ? d In this case: Initial term of arithmetic progression: a1 = - 4 Common difference: d = 6 So: a50 = a1 + ( n - 1 ) ? d = - 4 + ( 50 - 1 ) ? 6 = - 4 + 49 ? 6 = - 4 + 294 = 290
19. ### trig

cos ? = ± ? ( 1 - sin² ? ) In quadrant IV sine is negative , cosine is positive. So in quadrant IV cos ? = ? ( 1 - sin² ? ) In this case: cos ? = ? ( 1 - sin² ? ) = ? [ 1 - ( - 2 / 3 )² ] = ? ( 1 - 4 / 9 ) = ? ( 9 / 9 - 4 / 9 ) = ? ( 5 / 9 ) = ? 5...
20. ### Pre-Calculus Help?

If your expression mean: x = csc t and y = cot t then: x = csc t x = 1 / sin t sin t = 1 / x y = cot t = cos t / sin t = ± ? ( 1 - sin² t ) / sin t = ± ? ( 1 - sin² t ) ? 1 / sin t = ± ? ( 1 - sin² t ) ? csc t = ± ? [ 1 - ( 1 / x )&...
21. ### Pre-Calculus Help?

x(t) = e^-t ln x = - t t = - ln x y = 3 e ^ ( 2 t ) y = 3 e ^ [ 2 ? ( - ln x ) ] y = 3 e ^ [ - ( 2 ? ln x ) ] ______________________ Remark: e ^ [ ( 2 ? ln x ) ] = x ^ 2 e ^ [ ( - 2 ? ln x ) ] = 1 / x ^ 2 ______________________ So: y = 3 e ^ [ - ( 2 ? ln x ) ] y = 3 / x ^ 2 x...
22. ### Algebra

x = your number ( x * 2 - 8 ) / 2 + 4 = x * 2 / 2 - 8 / 2 + 4 = x - 4 + 4 = x
23. ### Math

Go on: wolframalpha.c o m When page be open in rectagle type: plot y <= x+4 and click option = after that in rectagle type: plot 2x+y <= -4 and click option =
24. ### math

If your expression mean h = - 16 t² + 40 t + 6 then: Vertex of this quadratic function have coordinates: t = - b / 2a , h = c - b² / 4a In this case: a = - 16 , b = 40 , c = 6 So: t = - b / 2a = - 40 / [ 2 ? ( - 16 ) ] = - 40 / - 32 = ( - 8 ) ? 5 / ( - 8 ) ? 4 = 5 / ...
25. ### math

7 / ( 2 a ) ? 5 / a² = 7 ? 5 / ( 2 a ? a² ) = 35 / 2 a³
26. ### math

( 12 t? - 8 t? ) / 2 t³ = 12 t?/ 2 t³ - 8 t?/ 2 t³ = ( 12 / 2 ) t?/ t³ - ( 8 / 2 ) t?/ t³ = 6 t³ - 4 t?= 2 t³ ( 3 - 2 t² )

28. ### Math

14 % = 0.14 31 % = 0,31 Total volume of containers: 72 ml + 64 ml = 136 ml Volume of acid in first container: 72 ml * 0.14 = 10.08 ml Volume of acid in second container: 64 ml * 0.31 = 19.84 ml Volume of alcohol in the mixture : 10.08 ml + 19.84 ml = 29.92 ml Percentage ...
29. ### Math

1 h = 60 min 41 min = 41 / 60 h 4 h 41 min = 4 + 41 / 60 = 4 ? 60 / 60 + 41 / 60 = 240 / 60 + 41 / 60 = 281 / 60 h average speed = 281 mi / 4 h 41 min = 281 / ( 281 / 60 ) = ( 281 / 1 ) / ( 281 / 60 ) = 281 ? 60 / 1 ? 281 = 60 / 1 = 60 mi / h
30. ### Math

In quadrant I the x coordinate and the y coordinate are positive. In quadrant II the x coordinate is negative , y coordinate are positive. In quadrant III the x coordinate and the y coordinate are negative. In quadrant IV the x coordinate is positive , y coordinate are ...
31. ### Algebra

Recent coordinates: x = 4 , y = 2 After reflection: ( x , y ) ---> ( x + 1 , y - 5 ) New coordinates: ( x + 1 , y - 5 ) ( 4 + 1 , 2 - 5 ) ( 5 , - 3 ) a) ( 4 , 2 ) is in the first quadrant b) ( 5 , - 3 ) is in fourth quadrant c) reflection across y axis: change sign of x , ...
32. ### math

Solve e + 5 = 3 e – 11 to find the value of e j = j e + 5 = 3 e – 11 5 + 11 = 3 e - e 16 = 2 e e = 8 j = e + 5 = 8 + 5 = 13
33. ### math algebra 1

A = Area w = width l = length A = w ? l Divide both sides by l A / l = w w = A / l Find the value of A by substituting the given information: w = 60 yd l = 75 yd A = w ? l = 60 ? 75 A = 4500 yd² Substitute l = 72 yd to find the width of the second field: w = A / l w = ...
34. ### Algebra

4 ? ?6 / ? 30 = 4 ? ?6 / ? ( 6 ? 5 ) = 4 ? ?6 / ?6 ? ?5 = 4 / ?5 By the way 4 ?5 / 5 is the same as 4 / ?5 becouse: 4 ?5 / 5 = 4 ?5 / ?5 ? ?5 = 4 / ?5
35. ### Math

9 m = 900 cm 80 * 12 cm = 960 cm You do not have enough ribbon to make 80 ribbons 12cm long.
36. ### math

o = orange marbles y = yellow marbles There are 97 marbles in the bag mean: o + y = 97 There are 25 more yellow marbles than orange marbles mean: y = o + 25 Now: o + y = 97 Replace y with o + 25 o + o + 25 = 97 2 o + 25 = 97 2 o = 97 - 25 2 o = 72 o = 72 / 2 = 36 y = o + 25 = ...
37. ### Math

For x = 3 and y = 4 4 x - 5 = 4 ? 3 - 5 = 12 - 5 = 7 3 < 7 y < 4 x - 5 For x = 2 and y = 1 4 x - 5 = 4 ? 2 - 5 = 8 - 5 = 3 1 < 3 y < 4 x - 5 For x = 3 and y = 0 4 x - 5 = 4 ? 3 - 5 = 12 - 5 = 7 0 < 7 y < 4 x - 5 For x = 1 and y = 1 4 x - 5 = 4 ? 1 - 5 = 4 - 5...
38. ### precalculus

tan 60° = ?3 Use trigonometric identity: tan ( 180° + x ) = tan x In this case x = 60° tan ( 180° + 60° ) = tan 60° tan 240° = tan 60° tan 240° = ?3 so ? = 240°
39. ### calculus

Correction: C?10? = 3500 - 2500?e?¹??²¹??¹²? = 2600
40. ### calculus

A rate directly proportional to 3500 - C(t) mean: your answer should contain constant k. dC / dt = k ? ( 3500 - C?t? ) dC = k ? ( 3500 - C?t? ) ? dt dC / ( 3500 - C?t? ) = k ? dt ? dC / ( 3500 - C?t? ) = k ? ? dt ? ln | 3500 - C?t? | = k?t + h h = constant of integration ...
41. ### math

12a³ + 10a² - 8a = 2a ( 6a² + 5a - 4 ) = 2a ( 6a² - 3a + 8a - 4 ) = 2a [ ( 6a² - 3a ) + ( 8a - 4 ) ] = 2a [ 3a ( 2a - 1 ) + 4 ( 2a - 1 ) ] = 2a [ ( 2a - 1 ) ( 3a + 4 ) ] = 2a ( 2a - 1 ) ( 3a + 4 ) 12 a³ + 10 a² - 8 a = 2a ( 2a - 1 ) ( 3a + 4 )
42. ### Algebra

Volume of cylinder = ( 2 x ) ² ? ? ? 9 x = 4 x² ? ? ? 9 x = 36 x³ ? ? Volume of a sphere with radius r = ( 4 / 3 ) ? ? ? r³ Volume of cylinder = Volume of a sphere 36 x³ ? ? = ( 4 / 3 ) ? ? ? r³ Divide both sides by ? 36 x³ = ( 4 / 3 ) ? r&...
43. ### Maths

g = goats c = chickenes The 45 heads mean : Number of goat heads plus the number of chicken heads = 45 g + c = 45 150 legs mean: 4 g (number of goat legs) + 2 c (number of chicken legs) = 150 4 g + 2 c = 150 Now you must solve system of equations: g + c = 45 4 g + 2 c = 150 ...
44. ### Calculus

Draw a square 10 by10 in. Cut the squares x by x in each corner. Notice the new dimension for the length and width of the base ( 10 - 2 x ) The area of the base = ( 10 - 2 x )² To find the volume of a rectangular prism (your box), you must multiply the area of the base ...
45. ### Math

20% = 20 / 100 = 0.2 You will save: 0.2 ? ( \$2.50 + \$4.95 + \$6.00 ) = 0.2 ? \$13.45 = \$2.69
46. ### Algebra

Your function: y = 4 - x x = - 2 , y = 4 - ( - 2 ) = 4 + 2 = 6 x = - 1 , y = 4 - ( - 1 ) = 4 + 1 = 5 x = 0 , y = 4 - 0 = 4 x = 1 , y = 4 - 1 = 3 x = 2 , y = 4 - 2 = 2 x = 3 , y = 4 - 3 = 1
47. ### Math

3 / 81 = 3 / 3 ? 27 = 1 / 27 ( 1 / 9 ) / 3 = 1 / 27 Answer B. The sequence is geometric because it decreases by a factor of 1 / 27
48. ### Math (Updated)

You're welcome.
49. ### Math (Updated)

f (x) - g (x) = 9 x³ + 2 x² - 5 x + 4 - ( 5 x³ - 7 x + 4 ) = 9 x³ + 2 x² - 5 x + 4 - 5 x³ + 7 x - 4 = 9 x³ - 5 x³ + 2 x² - 5 x + 7 x + 4 - 4 = 4 x³ + 2 x² + 2 x = 2 x ? ( 2 x² + x + 1 )
50. ### math

No it's not. sin ( 90° - ? ) = cos ? cos ( 90° - ? ) = sin ? tan ( 90° - ? ) = sin ( 90° - ? ) / cos ( 90° - ? ) = cos ? / sin ? = cot ? tan ( 90° - ? ) = cot ?
51. ### algebra

9 x + 5 y = 35 - 2 x + 5 y = 0 __________ 9 x - 2 x + 5 y - 5 y = 35 - 0 7 x = 35 x = 35 / 7 x = 5 Sustitute this in 9 x + 5 y = 35 9 ? 5 + 5 y = 35 45 + 5 y = 35 5 y = 35 - 45 5 y = - 10 y = - 10 / 5 y = - 2
52. ### Math

1 / 3 ( x + 3 ) - 1 > 1 / 5 ( x + 6 ) Multiply both sides by 15 1 / 3 ( x + 3 ) ? 15 - 1 ? 15 > 1 / 5 ( x + 6 ) ? 15 5 ( x + 3 ) - 15 > 3 ( x + 6 ) 5 x + 15 - 15 > 3 x + 18 5 x > 3 x + 18 5 x - 3 x > 18 2 x > 18 x > 18 / 2 x > 9
53. ### Math

A cubic polynomial has the form: P(x) = a x³ + b x² + c x + d P(1) mean value of a polynomial when x = 1 P(2) mean value of a polynomial when x = 2 P(3) mean value of a polynomial when x = 3 P(4) mean value of a polynomial when x = 4 P(6) mean value of a polynomial ...
54. ### Algebra

If your question mean: Given that a? = x, evaluate the following: a??² then: a??? = a? ? a? In this case: a??² = a? ? a² = x ? a²
55. ### Algebra

a­­^b = x a^b + 2 = x + 2
56. ### maths

In guadratic equation a x² + b x + c = 0 Product of roots = c / a If your expression mean: x² - ( 5 / 2 ) x + k = 0 then In this equqation: a = 1 , b = - 5 / 2 , c = k In quadratic eguation product of roots = c / a = k / 1 = k Given that the roots are reciprocals of ...
57. ### Math

The terms n-th term of a geometric sequence: an = a1 ? r??¹ where: a1 = first term r = common ratio In this case: a1 = 3 a2 = x a3 = y a4 = 18 a4 = a1 ? r ??¹ = a1 ? r³ 18 = 3 ? r³ r³ = 18 / 3 = 6 r = ?6 a2 = a1 ? r x = 3 ? r x = 3 ? ?6 a3 = a1 ? r&...
58. ### maths

Sorry. My mistake. t = d / s t = 8 / 15 t = 0.5333...h t = 32 min
59. ### maths

s = speed d = distance t = time s = d / t t = d / s t = 15 / 8 h t = 1.875 h t = 1 h 52 min 30 sec
60. ### ALGEBRA 1!!!! PLS HELP!!!!

My typo: 2 a1 = 56 a1 = 56 / 2 = 28
61. ### ALGEBRA 1!!!! PLS HELP!!!!

a1 = first even integers a2 = second even integers = a1 + 2 a3 = third even integers = a1 + 4 a4 = fourth even integers = a1 + 6 The sum of the first and third is multiplied by 3 the result is 44 more than 4 times fourth mean: ( a1 + a3 ) ? 3 = 4 ? a4 + 44 ( a1 + a1 + 4 ) ? 3...
62. ### maths

x = distance y = speed t = time t = x / y Had he moved 3 kmph faster, he would have taken 40 minutes mean: x / y - x / ( y + 3 ) = 40 / 60 = 20 ? 2 / 20 ? 3 = 2 / 3 x / y - x / ( y + 3 ) = 2 / 3 If he had moved 2 kmph slower, he would have taken 40 minutes more mean: x / ( y...
63. ### Math

Exponential function: f(x) =a b? f(3) = a b³ = 1 / 4 f(-1) = a b?¹ = 4 a b³ = 1 / 4 ÷ a b?¹ = 4 __________ b? = 1 / 16 b = ?1/16 b = 1 / 2 Substitute that into: a b³ = 1 / 4 a ( 1 / 2 )³ = 1 / 4 a ? ( 1 / 8 ) = 1 / 4 Divide both sides by 1...
64. ### Pre-Algebra

360° ? 218 / 245 = 360° ? 0,88979596 = 320.3265456° = 320° 19´ 36´´
65. ### MATH

Graphic solutions: Use the graph. a) y = 4x²-6x+3 has its mimum value at : xmin = 3 / 4 ymin = 3 / 4 b) A vertical translation by 3 - ( - 3 ) = 3 + 3 = 6 units Subtract 6 to each value of y. The roots of the equation 4x²-6x-3=0 approx. x = - 0.4 and x = 1.9 c) y = 4x...
66. ### Math

y = - ( 5 x + 1 ) x = - 2 y = - [ 5 * ( - 2 ) + 1 ] = - ( - 10 + 1 ) = - ( - 9 ) = 9 x = - 1 y = - [ 5 * ( - 1 ) + 1 ] = - ( - 5 + 1 ) = - ( - 4 ) = 4 x = 0 y = - ( 5 * 0 + 1 ) = - ( 0 + 1 ) = - 1 x = 1 y = - ( 5 * 1 + 1 ) = - ( 5 + 1 ) = - 6 x = 2 y = - ( 5 * 2 + 1 ) = - ( 10...
67. ### algebra 2

My typo: - 0.0081 = - 81 / 10,000 ?- 0.0081 = ?- 81 / ?10,000 = ? [ 81 * ( - 1 ) ] / ?10,000 = ? 81 * ? ( - 1 ) / 100 = 9 * i / 100 = 0.09
68. ### algebra 2

a.) 0.0064 = 64 / 10,000 ?0.0064 = ? 64 / ?10,000 = 8 / 100 = 0.08 b.) - 0.0081 = - 81 / 10,000 ?- 0.0081 = ?- 81 / ?10,000 = ? [ 81 * ( - 1 ) ] / ?10,000 = ? 81 * ? ( - 1 ) / ?100 = 9 * i / ?100 = 0.09 i
69. ### algebra 2

32 = 2 ^ 5 32 ^ ( 3 / 5 ) = ( 2 ^ 5 ) ^ ( 3 / 5 ) = 2 ^ ( 5 * 3 / 5 ) = 2 ^ 3 = 8
70. ### Math

23 Becouse: 15 = 3 ? 5 45 = 3 ? 3 ? 5 51 = 3 ? 17
71. ### Maths

x? - x² ? y - 6 ? y² = x² ? x² - x² ? y - 6 ? y² = x² ? x² - 3 x² ? y + 2 x² ? y - 2 ? y² ? 3 = x² ? x² - 3 x² ? y + 2 y ? x² - 2 ? y ? y ? 3 = x² ? ( x² - 3 y ) + 2 y ? ( x² - y ? 3 ) = ...
72. ### algebra

You probably make typing error. If your fifth pair is (5,32768) then: y = 8^n n = 1 , y = 8^1 = 8 n = 2 , y = 8^2 = 64 n = 3 , y = 8^3 = 512 n = 4 , y = 8^4 = 4096 n = 5 , y = 8^5 = 32768
73. ### Math

Your function: y = - x³ - x³ isn't an exponential functionis. - x³ is a power function.
74. ### Math

f(x) - g(x ) = 9 x^3 + 2 x^2 - 5 x + 4 - ( 5 x^3 - 7 x + 4 ) = 9 x^3 + 2 x^2 - 5 x + 4 - 5 x^3 - ( - 7 x ) - 4 = 9 x^3 + 2 x^2 - 5 x + 4 - 5 x^3 + 7 x - 4 = 9 x^3 - 5 x^3 + 2 x^2 - 5 x + 7 x + 4 - 4 = 4 x^3 + 2 x^2 + 2 x = 2 x * 2 x^2 + 2 x * x + 2 x * 1 = 2 x * ( 2 x^2 + x + ...
75. ### Calculus (increasing/decreasing)

f'(x) = ( - x² - 5 ) / x² = - 1 - 5 / x² = - ( 1 + 5 / x² ) function is increasing on the interval, where f?(x) > 0 function is decreasing on the interval, where f?(x) < 0 In this case: f'(x) = - ( 1 + 5 / x² ) is always < 0 becouse: ...
76. ### Maths

In an arithmetic progression; a1 a2 = a1 + d a3 = a1 + 2d a4 = a1 + 3d In this case: a1 = -12 a2 = P a3 = Q a4 = 18 a4 - a1 = a1 + 3d - a1 a4 - a1 = 3 d 18 - ( - 12 ) = 3 d 18 + 12 = 3 d 30 = 3 d 3 d = 30 Divide both sides by 3 d = 10 a2 = P = a1 + d = - 12 + 10 = - 2 a3 = Q...
77. ### Science

My typo. sin ( A - B ) = sin ( A ) cos ( B ) - cos ( A ) sin ( B )
78. ### Science

375°= 360° + 15° sin ( 360° + ? ) = sin ? sin 375° = sin ( 360° + 15° ) = sin 15° 15° = 60° - 45° sin ( A + B ) = sin ( A ) cos ( B ) - cos ( A ) sin ( B ) sin 15° = sin ( 60° - 45° ) = sin ( 60° ) cos ( 45° ) - ...
79. ### Algebra

? < u < 3 ? / 2 180° < u < 270° u lies in Quadrant III csc ( u ) = 1 / sin ( u ) = - 5 / 3 sin ( u ) = - 3 / 5 cos ( u ) = ±? ( 1 - sin² u ) cos ( u ) = ±? [ 1 - ( - 3 / 5 )² ] cos ( u ) = ±? ( 1 - 9 / 25 ) cos ( u ) = ±...
80. ### Algebra

33 This is an arithmetic progression with common difference of 9
81. ### MATH

Are you kidding? 1.04 ( cos A )² + 0.2 ( cos A ) - 0.75 = 0 Divide both sides by 1.04 1.04 ( cos A )² / 1.04 + 0.2 ( cos A ) / 1.04 - 0.75 / 1.04 = 0 / 1.04 ( 1.04 / 1.04 ) ? ( cos A )² + ( 0.2 / 1.04 ) ? ( cos A ) - 0.75 / 1.04 = 0 1 ? ( cos A )² + ( 0.2...
82. ### Math

5 + 4.2 -( - 3 )= 5 + 4.2 + 3 5 -( -4.2 ) + 3 = 5 + 4.2 + 3
83. ### algebra

9 - a? + 2 a³ b³ - b? = - a? + 2 a³ b³ - b? + 9 = - ( a? - 2 a³ b³ + b? - 9 ) ____________ Substitution: u = a³ v = b³ ____________ - ( a? - 2 a³ b³ + b? - 9 ) = - ( u² - 2 u v + v² - 9 ) = _____________________ ...
84. ### Prealgebra

a = smallest number b = middle number = a + 2 c = largest number = b + 2 = a + 2 + 2 = a + 4 50 times the smallest is 88 less than 46 times the largest, mean: 50 a = 46 c - 88 Now: 50 a = 46 ( a + 4 ) - 88 50 a = 46 ? a + 46 ? 4 - 88 50 a = 46 a + 184 - 88 50 a = 46 a + 96 ...
85. ### Math

1 / 2 % = 0.5 % = 0.5 / 100 = 0.005 1 / 2 % of 18 = 0.005 ? 18 = 0.09
86. ### AlgebrA

5.4 + 0.2 x = - 1.4 x + 8.6 Subtract 0.2 x to both sides 5.4 + 0.2 x - 0.2 x = - 1.4 x + 8.6 - 0.2 x 5.4 = - 1.6 x + 8.6 Subtract 8.6 to both sides 5.4 - 8.6 = - 1.6 x + 8.6 - 8.6 - 3.2 = - 1.6 x - 1.6 x = - 3.2 Divide both sides by -1.6 - 1.6 x / - 1.6 = - 3.2 / - 1.6 x = 2
87. ### Math

L = the length W = the width A = the area L = W + 5 A = L ? W 66 = ( W + 5 ) ? W 66 = W² + 5 W Subtract 66 to both sides 66 - 66 = W² + 5 W - 66 0 = W² + 5 W - 66 W² + 5 W - 66 = 0 The solutions are: W = - 11 and W = 6 The width can't be negative, so W...
88. ### Inflection and concavity

first derivation = 2 - 3 / x² second derivation = 6 / x³ Second derivation is undefined when: 6 / x³ ?? 6 / x³ ?? when x = 0 f''(x) is undefined at x = 0 The graph of a function is concave up on interval where f "(x) > 0 The graph of a ...
89. ### engineering

? = density ? = 7800 kg /m³ 1 m = 1000 mm 1 m³ = ( 1000 )³ = ( 10³ )³ = 10? mm³ ? = 7800 / 10? = 7.8 ? 10³ / 10? = 7.8 / 10? kg / mm³ A = Area A = d² ? ? / 4 V = Volume V = w ? A V = w ? d² ? ? / 4 m = ? ? V m = ? ? w ? d²...

1) 50:10 = 5 ? 10 / 10 = 5 = 5:1 2) r / 5 = 9 / 21 r / 5 = 3 ? 3 / 3 ? 7 r / 5 = 3 / 7 cross multiply 7 ? r = 5 ? 3 7 r = 15 r = 15 / 7
91. ### Geometry

( x + 18 )² + ( y + 7 )² = 12² ( x + 18 )² + ( y + 7 )² = 144
92. ### Trigonometry

My typo. cot²x = 1 / sin² x - sin² x / sin² x
93. ### Trigonometry

ctg x = cos x / sin x cot²x = cos² x / sin² x cot²x = ( 1 - sin² x ) / sin² x cot²x = 1 / sin² x - sin x / sin² x cot²x = csc² x - 1 Add 1 to both sides cot²x + 1 = csc² x - 1 + 1 cot²x + 1 = csc² x csc...
94. ### Math / Algebra

8 a b - 16 a c + 12 a = 4 ? a ? 2 ? b - 4 a ? 4 ? c + 4 ? a ? 3 = 4 a ( 2 b - 4 c + 3 )
95. ### Maths

Find the first number in thist interval that is divisible by 8 In this case: 200 / 8 = 25 Find the last number in thist interval that is divisible by 8 In this case: 496 / 8 = 62 Numbers 200 and 496 assume arithmetic progression, where first member a1 = 200 and last member a62...
96. ### Math

y² = 4 x 4 x = y² Divide both sides by 4 x = y² / 4 Use the vertex form: x = a ( y - k )² + h to determine the values of a, h and k. a = 1 / 4 , k = 0 , h = 0 Since the value of a is positive, the parabola opens right. Axis of symmetry: x = 0 Since ...
97. ### Math

100% - 7 % = 93% = 93 / 100 = 0.93 0.93 ? \$364,000 = \$338,520
98. ### Algebra II

( x + 2 )² + 2 = 0 Subtract 2 to both sides ( x + 2 )² + 2 - 2 = 0 - 2 ( x + 2 )²= - 2 Take square root of both sides x + 2 = ± ?( - 2 ) x + 2 = ± ?( - 1 ? 2 ) x + 2 = ±?( - 1 ) ? ?2 x + 2 = ± i ?2 Subtract 2 to both sides x + 2 - 2...
99. ### maths

a = first digit b = second digit Two digit number is formed when ten's digit which is multiplied by 10 and add to unit place digit is multiplied by 1. In this case your number is 10 a + b The number obtained by interchanging the digits is 10 b - a The sum of digits is 11 ...
100. ### geometry

Point-slope form of a linear equation: y ? y1 = m ( x ? x1 ) ( x1 , y1 ) is a point the line passes through m = slope In this case: x1 = 4 y1 = 1 m = - 4 y ? y1 = m ( x ? x1 ) y ? 1 = ( - 4 ) ? ( x ? 4 ) y ? 1 = ( - 4 ) ? x ? 4 ? ( ? 4 ) y ? 1 = - 4 x + 16
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