# Posts by Reiny

Total # Posts: 40,197

1. ### Algebra

number correct --- x number wrong ---- 30-x 9x - 5(30-x) = 18 solve for x
2. ### Calculus

look at the graph http://www.wolframalpha.com/input/?i=y+%3D+x%5E2+-+1+and+y+%3D+cos(x) and notice the symmetry. So we need the intersection cosx = x^2 - 1 which you found correctly as ± 1.177 correct to 3 decimals area = 2[integral] (cosx - (x^2 -1)) dx from 0 to 1.177...
3. ### Math

original: boys: 80 girls : 95 now: boys = 1.15(80) = ... girls = .8(95) = ... add them up to get the new total. take the difference, percent change = difference/175 , interpret the positive vs negative answer.
4. ### Math

solve for x , the price of the car .15x = 247.50
5. ### Math

or, you could do it using decimals .... 2 1/5 subtract 1 1/5 = 2.2 - 1.2 = 1
6. ### Algebra 1

let the part invested at 10% be x let the part invested at 14% be 10000-x solve for x .1x + .14(10000-x) = 1280 let me know what you get, so I can check it
7. ### Math

Are you solving 3tanA.tanA-4?3TanA+3=0 ? What does the . in 3tanA.tanA mean? Is it multiplication? I have no clue what TanA=n,3n.n-4?3n+3=0 in the second part of your post means.
8. ### Algebra

You need 2 numbers which have a sum or difference of 3, c will be their product e.g. 1,2 , product = 2 , c = 2 ----- (x+1)(x+2) = x^2 + 3x + 2 5, -2, product = -10 , c = -10 ----- (x+5)(x-2) = x^2 + 3x - 10 7, -4 , product = -28 , c = -28 ----- (x+7)(x-4) = x^2 + 3x - 28 -1, 4...
9. ### maths

number at the beginning ----- x Paul took (1/3)x - 4 number left after Paul's turn = x - (x/3 - 4) = 2x/3 + 4 after Sarah ate 6, number left = 2x/3 + 4 - 6 = 2x/3 - 2 took 1/4 of that, so remaining = (3/4)(2x/3 - 2) = x/2 - 3/2 Kate took 1/3 of that plus 4 = (1/3)(x/2 - 3/...
10. ### Trigonometry

you can't show graphs in this format
11. ### Math

Just did that
12. ### MATH

max - min = 1 - (-7) = 8 so a = 4 , could be any of the first 3 from 3? to ? = 2? , so the period is 4? 2?/k = 4? 4?k = 2? k = 1/2 so we should see either sin(x/2) or cos(x/2) so it has to be either a) or b) test a) if x = ? , y = 4cos(?/2) - 3 = 4(0) - 3 = -3 ? 1 , that is ...
13. ### Trigonometry

If R is the resultant vector, then R = (24cos42,24sin42) + (9cos312,9sin312) = (17.8355, 16.059) + (6.02218, -6.6883) = (23.85766, 9.3707) magnitude = ?(23.85766^2 + (9.3707)^2) = appr 25.63 km/h direction: Ø = tan^-1(9.3707/23.85766) = appr 21.44° or make a sketch ...
14. ### math

number of school days ----- x walking to school = (3/5)x = 3x/5 getting ride = (7/8)(2x/5) = 7x/20 walking plus riding = 3x/5 + 7x/20 = 19x/20 staying home --- 1 day 3x/5 + 7x/20 + 1 = x 19x/20 + 1 = x times 20 19x + 20 = 20x x = 20
15. ### Math

Recall what I just said in the previous post? This time I will reverse that idea to avoid fractions, start with the largest. Also I noticed that the LCD for 1/3 and 3/4 is 12, so .... let Mary's amount be 12x then Sally has (1/3)(12x) or 4x and Jane has (3/4)(4x) or 3x 12x...
16. ### MATH!!!!

Start with the smallest amount, usually that avoids fractions ... Let Ryan's amount be x then David has 3x , and Henry has 4(3x) or 12x now it is easy: x + 3x + 12x = 128 etc
17. ### precalc

here is one version https://socratic.org/questions/how-do-you-solve-the-identity-cos3x-4cos-3x-3cosx
18. ### algebra 2

f(x)= (x^2-2x-8)/(x+6) to have a point discontinuity, (x+6) should have been a factor of the numerator and cancelled out. e.g. if g(x) = (x^2 - x - 12)/(x-4) g(x) = (x-4)(x+3)/(x-4) = x+3, x ? 4 There would have been a discontinuity at the point (4,7) So in your question , we ...
19. ### Math

y = rsinØ, x = rcosØ y^2 - 8x - 16 = 0 r^2 sin^2 Ø - 8rcosØ - 16 = 0
20. ### Math

Make a sketch of the right-angled triangle with angle 45° and hypotenuse of 4 sin45 = y/4, cos45 = x/4 y = 4(?2/2) , x = 4?2/2 new point = B(2?2 , -2?2)
21. ### geometry

areas ... the areas of similar figures are proportional to the square of their corresponding sides. so 4^2 : 3^2 or 16 : 9
22. ### Math

let the third side be x , where x > 0 then x+15 > 27 ---> x > 12 and x+27> 15 ---> x > -12 so far we have x > 12 and 12+27 > x x < 39 so : 12 < x < 39

Even though you don't say, I will assume the time was 1 year. so look at this way: you started with 8750 and at the end of the year you had 10,000+ 1,000 or 11,000 8750(1+r) = 11000 1+r = 1.25714.. r = .25714 or 25.71%
24. ### GEOMETRY helpppp

arc length = ? r Ø where r is the radius, and Ø is the central angle measured in radians You have all the data.

I agree
26. ### math

x+y = 30 or y = 30-x let S = 2x^2 + 5y^2 = 2x^2 + 5(30-x)^2 = 2x^2 + 4500 - 300x + 5x^2 = 7x^2 - 300x + 4500 dS/dx = 14x - 300 = 0 for a max/min x = 300/14 , sub into y = 30-x
27. ### Maths

sin²_cos²/2sin2cosx1/tan² re-enter in proper form e.g. sin = 12/13 is meaningless, "sin" is an operator and needs an operand did you mean : sinØ = 12/13 or sinx = 12/13 ?? that is like saying ? = 3 , or log = 1.3
28. ### Geometry

change your 604 ft to inches, then set up the ratio
29. ### Precalculus

Only B is correct in your choices. What are your resources for this major topic if you don't have a textbook ?
30. ### Precalculus

The correct relations are listed in your textbook or in your notes. They are easy to look up Let me know which ones you think do apply.
31. ### Geometry

In a ratio, you need the same units. Change your 5 ft to inches, and set up the ratio.
32. ### Math

total number of outfits = 12 total number of outfits with blue skirt = 3x1x2 = 6 prob of outfit with blue skirt = 6/12 = 12 prob of outfit without blue skirt = 1 - 1/2 = 1/2
33. ### maths

speed of rocket = (2.99x10^8 m/s)/5 = 5.98 x 10^7 Wow, somebody has been watching Startrek.
34. ### Probability

prob(yellow, then red) = (2/5)(3/4) = 3/10 prob(red, then yellow) = 3/5(2/4) = 3/10 so prob(your event) = 6/10 = 3/5
35. ### Geometry

vector PQ = (2-(-6), 4-0) = (8,4) magnitude = ?(64+16) = ?80 = appr 8.9 , ruling out c. angle = tan^-1 (4/8) = 26.57° from the x-axis what angle description describes that ?

correct
37. ### Maths

Since they right-bisect each other, you will have 4 congruent right-angled triangles, with legs of 5 and 12. Perhaps you recognize the 5-12-13 right-angled triangle, if not use Pythagoras to find the hypotenuse to be 13 So the perimeter is ......
38. ### algebra 2

did you mean? 4 ^(3?(3x-3)^2)+2=38 or 4^3(?(3x-3)^2 + 2 = 38 ??
39. ### Trigonometry

drift angle is clearly 12° Make a sketch to have a triangle with sides 500 and 580 with 12° as the contained angle. Using cosine law, let the third side be R (the wind speed) R^2 = 500^2 + 580^2 - 2(500(580)cos12° R = .... then use the Sine Law to find one of the ...
40. ### @ Scott - Math

Thanks, why didn't I see that ?
41. ### Math

I hope you weren't trying to expand all of this. let's look at the last part first, by looking at a some patterns (1+x)^2 = 1 + 2x + x^2 , 3 terms, coefficients run 1,2,1 (1+x+x^2) = 1 + 2x + 3x^2 + 2x^3 + x^4, 5 terms, coefficients run 1,2,3,2,1 (1+x+x^2+x^3)^2 = 1 + ...
42. ### Math

Now: daughter ---- x mother ------ 2x 2 years ago: daughter = x-2 mother = 2x-2 x-2 + 2x-2 = 56 solve for x
43. ### math urgent

I saw this question when you posted it yesterday. I did not answer it since it wasn't quite clearly stated. Is the 30 million split into 25 equal annual payments?? I will assume that. In that case we are simply finding the present value of those payments payment = 30 ...

Method1 Since the basic formulas for annuity assume payments at the end of a period, a slight adjustment is needed. PV = 9400 +9400(1 - 1.034^-9)/.034 = 81243.05 method 2. look at the geometric series 9400 + 9400(1.034^-1) + 9400(1.034^-2) + ... + 9400(1.034^-9) here a = 9400...
46. ### Math

25a^2+ ? + .25 b^2 You know it must look something like: (5a ± .5b)^2 , expand to see the middle term take your pick
47. ### Math

35 minutes is 35/60 of a ration, so the central angle of the sector covered = (35/60)(2?) radians = 7?/6 radians arc length = radius * angle , where the angle is in radians or circumference = 2?r = 2?(6) = 12? so the hand covered 35/60 of that, so .....
48. ### Math

polynomials have factors, not factories .... we could write the factors of p(x) as 2*2*3*(x-5)*(x+4) any combination of these will also be a factor. How about 2*3*(x-5)(x+4) expand it and see what you get 2) correct 3) x^2 - x = .24 x^2 - x -.24 = 0 solve for x using the ...
49. ### Math

the sides would be ?3x and 2x , then (?3x)^2 + (2x)^2 = 10^2 3x^2 + 4x^2 = 100 solve for x and you have the two sides. area = (1/2)(side1)(side2) = ....
50. ### Math

16 men and 12 women A - you want 4 from 28 , so C(28,4) B - 3 men, must be 1 woman, so C(16,3)*C(12,1) C - at least 2 men ---> 2men-2women , 3men1woman, 4men , add up the 3 cases D - your turn
51. ### Math

nope, not what I got show me your steps to catch the error
52. ### Math

steph;s wage = x/10 eve;a wage = y/29 but you said: x/10=y/29 10y=29x y = 29x/10 sub that into x+y=60 and solve 2. area of large circle = ?(r+3)^2 area of small circle = ?r^2 ?(r+3)^2 - ?r^2 = 21? divide by ?(the r^2 drops out) 3. make a sketch and really think about it Hint: ...
53. ### Pre-Calc

you have one complex root, but they always come as conjugate pairs The other must be 2-2?2i You also know that one factor is (x+2) the sum of the complex roots = 2+2?2i + 2-2?2i = 4 product of the complex roots = (2+2?2i)(2-2?2i) = 4 + 8 = 12 So the quadratic factor is x^2 - ...
54. ### Math

original fraction -- n/d new fraction formed = (n+d)/2d you want: (n+d)/2d = 4(n/d) 8nd = nd + d^2 7nd = d^2 7n = d it looks like we can find an infinite number of cases like that. e.g. let n = 1, then d = 7 then the original fraction was 1/7 and the fraction formed by your ...
55. ### algebra

If arithmetic, you know that d=6 and a=6 a+(n-1)d = term(n) 6+(n-1)(6) = 1536 6 + 6n - 6 = 1536 6n = 1536 n = 256 If GP,then a=6, r=2 In the same way, use the definition of term(n) to solve the second part
56. ### Mathematics

Let the radius of the base be r and the height be h (1/3)? r2 h = 5 ?r^2 h = 15 The new cone will be similar to the original cone, the new height i h/3 and the new radius is r/3 volume of top cone = (1/3)?(r^2/9)(h/3) = (1/9)?r^2 h = 15/9 = 5/3 the bottom fulcrum will be 15 - ...
57. ### math

yes, you want: |k-21| = 48 so, k-21 = 48 OR -k+21 = 48 k = 69 or k = -27 think of a number line and place a dot at 21 now count 48 places to the right ---> 69 and count 48 places to the left -----> -27
58. ### Math

Not silver ----> gold coin you have 123 golds out of a total of 323 prob(not silver) = 123/323
59. ### MATH

I don't have the foggiest idea. my calculator says: (2360448/(2?))² = 1.4113318 x 10^11 , (notice the change in the division by 2?) don't know how the R³/3.98x10^14 fits in
60. ### Math

20 < T < 80 , where T is temperature in Fahrenheit Since C = (5/9)(F - 32) , I will let you do the conversion

correct
62. ### math

number passed ---- x number failed ------ 36-x sum of scores of passers = 78x sum of scores of failures = 60(36-x) 78x + 60(36-x) = 71(36) solve for x
63. ### math

48/x - x = 2 multiply each term by x to get the quadratic 48 - x^2 = 2x x^2 + 2x - 48 = 0 (x - 6)(x + 8) = 0 x = 6 or x = -8 btw, What she was told to do should have been: (48-x)/x if x = 6, (48-x)/x = (48-6)/6 = 7 if x = -8, (48-x)/x = (48 + 8)/-8 = -7
64. ### math

What she was told to do: (x-48)/x what she did: 48/x - x = 2 solve for x, then plug into "what she was told to do" btw, there are two values of x.
65. ### math

My money is definitely on Damon ! Annabelle just tossed some number salad.
66. ### Math

You just told me that Maya was m years old. Why are you asking how old Maya is ?
67. ### Math

3(3/7)^-2 + 2/3 = 3(7/3)^2 + 2/3 = 3(49/9) + 2/3 = 49/3 + 2/3 = 51/3 = 17
68. ### Math

By definition: 2? radians <-----> 360°

correct
70. ### Math

The easy part is to find the areas of the 3 rectangles, they are: 2x7, 3x7, and 4x7. The hard part is to find the area of the triangular base. Since it is not right-angled, 2^2 + 3^2 ? 4^2, we need more complex methods. method one: Heron's formula area = ?(s(s-a)(s-b)(s-c...
71. ### Calculus

a = -32 ft/sec^2 v = -32t + c when t = 0 , v = 64 64 = 0 + c , so c = 64, and v = -32t + 64 d = -16t^2 + 64t + k, but when t=0 , d = 0 0 = 0 + 0 + k k = 0 d = -16t^2 + 64t The vertex of this parabola will tell you the maximum height, and the t when that max occurs. I assume ...
72. ### Math

1/12(cos8t-3sin8t) = 0 cos8t-3sin8t = 0 3sin8t = cos8t sin8t/cos8t = 1/3 tan 8t = 1/3 8t = .32175 or 8t = ?+.32175 t = .0402 or t = .4329
73. ### Alegbra 1

Easiest way: An equation perpendicular to 2x - 5y = 3 must have the form 5x + 2y = c plug in our given point on this line: 5(-2) + 2(7) = c = 4 5x + 2y = 4
74. ### math

distance straight across = 120 m distance half-way around the circumference = 60? = .. compare them.
75. ### Math

average is 84, so the total is 20(84) or 1680 points points of 6 students at 100 = 600 points of 4 students at 50 = 200 remaining points = 1680 - 600 - 200 = 880 average of those 10 students = 880/10 = 88
76. ### math

5 machines 5 minutes to make 5 widgets 100 machines 5 minutes to make 100 widgets - you have 20 times as many machines, so 20 times as many products in the same time of 5 minutes
77. ### MATH HELP ASAP

change all numbers to decimals and it will be easy to tell
78. ### Pre- Algebra

(218/245)*360° will be the angle of the larger part.
79. ### Algebra

larger angle --- x smaller angle --- x/4 x + x/4 = 180 solve for x, and sub in my definitions. or smaller angle ---- y larger angle ---- 4y y+4y = 180 solve for y, y will be the smaller angle, since I defined it as such
80. ### Algebra

contributions in 2002 ---- contributions in 2003 ---- 1.15x contributions in 2004 ---- (1.1)(1.15x) (1.1)(1.15x) = 8855 solve for x
81. ### Maths

take the derivative of the ellipse equation using implicit differentiation. The slope of 3x+2y - 5 = 0 is -3/2 so the slope of the perpendicular will be +2/3 set your derivative of the ellipse equal to 2/3 . You will get a linear equation in x and y Solve that with the ...
82. ### Math (Word Problems)

Just set up a simple ratio x/9 = (3/4) / 6 6x = 9(3/4) 6x = 27/4 x = 27/24 = 9/8 or 1 1/8 cups of sugar
83. ### extended mathematics

You can't post diagrams in this forum
84. ### Math

Arora, nicely done, impressive!
85. ### Maths

In these kind of questions, when they state that 30% workers are BTeach holders, we don't assume that it is 30% exclusively. e.g. When I say, that 8% of boys play football, that doesn't mean that they can't play some other sport as well. In a Venn diagram for this ...
86. ### Maths

I disagree .. number(BT or MBA) = 30%+25% - 20% = 35% (we can't count the 20% twice ) so 65% are without degrees .65x= 325 x = 500
87. ### geometry

by basic geometry: CP:PD = 30:48 = 5:8 let CP=5x, and PD = 8x let the height between AB and CD = h so area of BCP + area of ADP = 5xh +8xh = 13xh = 78 area of ABC = 13xh = 78 area of whole thing = 78+30+48 = 156
88. ### algebra

Scientific notation consists of a number between 1 and 10, multiplied by a power of 10. I see only one that fits this.
89. ### Maths

I am sure DrBob meant: 600 = r*4 + 2r*3
90. ### Maths

Guessing that the question is to find the sides. x^2 + (3x-1)^2 = (3x+1)^2 x^2 + 9x^2 - 6x + 1 = 9x^2 + 6x + 1 x^2 - 12x = 0 Use your favourite method to solve this quadratic, remember that x > 0
91. ### Maths

from 4x – 3 = 3x + y y = x - 3 ** plug ** into 3x + y = 2y + 5x – 12 3x + x-3 = 2(x-3) + 5x - 12 4x - 3 = 2x - 6 + 5x - 12 4x-3 = 7x - 18 -3x = -15 x = 5 then y = 5-3 = 2
92. ### Math

I really don't understand what part of my analysis you don't get. Volume is (base area) x (width) So if you consider the sideview as the base, you have rectangle = 44(3) = 132 ft^2 triangle = (1/2)(44)(6) = 132 ft^2 total area of sideview = 264 ft^2 volume = that total...
93. ### Math

The top view is a rectangle It is the side view that illustrates the shape of the pool, it will be the trapezoid. Do you know what a trapezoid looks like ?
94. ### Math

Draw a side-view of the pool to see the trapezoid, the two vertical ends are your parallel sides. draw a horizontal from the short vertical to meet the longer vertical. You now have a rectangle and a right-angled triangle. The rectangle is 44 by 3 and the triangle is 44 by 6 ...
95. ### Pri 5 maths

3s = 2b s = 2b/3 5b + 6s = 108 5b + 6(2b/3) = 108 5b + 4b = 108 b = 12 then s = 8 6 skirts = 48
96. ### pre algebra

amount of pretzels ---- x lbs amount of cereal ----- 12-x lbs 1.5x + 3(12-x) = 2(12) continue
97. ### math

You just asked the same question 5 minutes ago!
98. ### math

The volume of a pyramid = (1/3)(area of base)(height) test them, I see two of them
99. ### math

since it is parallel, it will differ only in the constant, so new equation is x - 4y + c = 0 plug in the given point to find c.
100. ### Math

No, it can't be W=15, since 15/36 ? 5/18 but 10/36 = 5/18
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