# Posts by Reiny

Total # Posts: 40,239

1. ### math

term(1) = a term(n) = a + (n-1)d = a + (n-1)(4a) = 37a (n-1)(4a) = 36a n-1 = 9 n = 10
2. ### math

term(1) = a = 6.1 term(14) = a + 13d = 7.1 6.1 + 13d = 7.1 13d = 1 d = 1/13
3. ### Math

so female = (3/8)(5000) = 1875 then male = 3125 total admitted= .4(5000) = 2000 so half were male, half were female male admitted = 1000 female admitted = 1000 percentage of females admitted = 1000/1875 = 53.3% percentage of males admitted = 1000/3125 = 32%
4. ### Math

(k+ 1/k)^2 = k^2 + 2(K)(1/k) + (1/k) = 36 k^2 + (1/k)^2 + 2 = 36 so k^2 + (1/k)^2 = 34 you are correct
5. ### Math

each equation can be solved indivually to get two answers. I suppose you want the value of x which satisfies both equations. so .... x^2 + 5x+6 = x^2 - x - 6 6x = -12 x = -2 or: x^2 - x - 6 (x-3)(x+2) = 0 so x = 3 or x = -2 x^2 + 5x+6 = 0 (x+2)(x+3) = 0 x = -2 or x = -3 so the...
6. ### Calculus

Since you want the average velocity, you don't even need the derivative when t = 1, s = 6(1) + 2(1) = 8 when t = 4, s = 6(16) + 2(4) = 104 average speed = total distance/total time = (104-8)/(4-1) = 32 mph
7. ### Algebra

Since distance = time x rate number of miles = 66h
8. ### Algebra

Meg---- m Jill ---- m-2 Beth ---- m/2 or Meg ---- 2x Jill ----- 2x - 2 Beth ---- x or Jill ---- x Meg --- x+2 Beth ---- (x+2)/2 or Meg ---- 10x Jill ----- 10x-2 Beth ---- 5x or .....
9. ### statistics

-1.00 ? z is the same as z ? -1 or 1 - P(z ? -1.00) ----> .8413 I don't know how old your tables are or what they look like, but for most of them ... here is a typical one: http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf find -1.0 in the horizontal under the 00 ...
10. ### math

What is a square qt ??
11. ### Algebra

You must know the basic formulas for a geometric sequence. term(n) = a r^(n-1), where a is the first term, r is the common ratio and n is the term number for yours: ar = 9 and ar^3 = 81 divide one equation by the other: ar^3/(ar) = 81/9 r^2 = 9 r = ± 3 then ar = 9 So if...
12. ### math

Why do you have a double division sign? Did you mean (d+g)/h ?? the way you typed it: d+g/h = 15 + 27/7 = 132/7 , not one of the choices if you meant: (d+g)/h = (15+27)/7 = 42/7 = 6 Now, tell me why you could not have done this yourself?
13. ### math 5th

original: Beena ---- x Alisha --- x+114 after give-away: Beena ---- x+96 Alisha ---- x+114 - 96 = x + 18 x+96 = 2(x+18) solve for x
14. ### correction - mathh

in the line near the end: x = ? - .60136... = 2.5102 it should be x = ? - .60136... = 2.5402>/b>
15. ### mathh

I am sure bobpursly had already answered this for you, but I could not find the post. I recall he took you as far as the quadratic. Why did you not finish it ?? 2sec^2x -3tanx =5 for [0,2pi) make use of your identities sec^2 A = 1 + tan^2 A 2(1 + tan^2 x) - 3tanx - 5 = 0 2 + ...
16. ### calc

Because it is customary, and it often makes it easier, if the coefficient of the square term is positive. So I switched all the signs, you must have known that this would not change the solution to the equation.
17. ### calc

Final word: http://www.wolframalpha.com/input/?i=solve+2cos(2x)%3D-sinx look at the graph, let your mouse hover over the red intersection points.
18. ### calc

Nope, my equation is correct, I should not have skipped that one step: 2cos2x=-sinx 2cos2x + sinx = 0 2(1 - 2sin^2 x) + sinx = 0 2 - 4sin^2 x + sinx = 0 times -1 -2 + 4sin^2 x - sinx = 0 4sin^2 x - sinx - 2 = 0 checking one of your answers in the original equation: let x = 2....
19. ### calc

2cos2x=-sinx 2cos 2x + sinx = 0 2( 1 - 2sin^2 x) + sinx = 0 4sin^2 x - sinx - 2 = 0 sinx = (1 ± ?1 - 4(4)(-2)) /8 = (1 ± ?33)/8 = appr .84307.... or appr -.59307... If sinx = .84307 x is in quads I or II, and x = appr 1.002967 or appr. 2.1386 if sinx = -.59307.. ...
20. ### Maths

How does this question and its solution tie in with your problem? /display.cgi?id=1447959082
21. ### Maths

"sum of circumferences of two circles wirh radii r1 & r2" = 2?r1 + 2?r2 "the circumference of a circle of radius r" = 2?r they are equal .... 2?r1 + 2?r2 = 2?r 2?(r1 + r2) = 2?r divide both sides by 2?

really ??
23. ### math

sum(21) = 28 (21/2)(2a + 20d) = 28 2a+20d = 56/21 sum(28) = 21 (28/2)(2a + 27d) = 21 2a+27d = 42/28 = 3/2 subtract the two equations: 7d = 3/2 - 56/21 = -7/6 d = -1/6 in 2a + 20d = 56/21 2a - 20/6 = 56/21 2a = 6 a = 3 so we need: a + (n-1)d = 0 3 + (n-1)(-1/6) = 0 3 - (-1/6)n...
24. ### Math

1/4 square inches = 5 ft <---- makes little sense or 1/4 square inches = 5 square ft ?? is this a continuation of your previous "scale factor" question? if so, the scale was 1 : 24?5 then model : 46950 = 1 : 24?5 model = 874.86 I sure some author did not embarrass...
25. ### math

let the sum be x x(1.05)^2 - x - x(.05)(2) = 205 x(1.05^2 - 1 - .05(2) ) = 205 .... let me know what you got
26. ### Math

1/4 square inches -----> 5 square ft 1/2 inch -----> ?5 ft 1 inch -----> 2?5 ft 1 inch ----- 2?5(12) = 24?5 inches scale : 1 : 24?5 or appr 1 : 53.67 , just like Arora had.
27. ### Maths

let the areas of the flats be 5x , 6x, and 8x for a, b, c respectively Now use your given data: "the difference in the area of flat c and flat a is 270 square metres" ----> 8x - 5x = 720 solve for x, and sub into my definitions
28. ### Math

Use your definitions 2nd term : ar = 1 5th term : ar^4 = 1 divide: r^3 = 1 r = 1 the ar = 1 a(1) = 1 a = 1 your GP is 1,1,1,.... (not a very exciting sequence, some authors would exclude r = 1 in a GP)
29. ### calculus 1-chemistry

It will reach a max when R '(T) = 0 R'(T) = .1(-.15T^2 + 8T) = 0 .15t^2 - 8t = 0 t(.15t - 8) = 0 t = 0 , (at the beginning) or t = 8/.15 sec = 160/3 sec find R(160/3) to get that maximum
30. ### continued - Algebra and Geometry

take a line segment of length 1 , and divide it into a larger and a smaller segment , so that the ratio of the whole line to the larger = the ratio of the larger segment to the smaller. Let the larger segment be x then the smaller is 1 - x 1/x = x/(1-x) x^2 = 1 - x x^2 + x - 1...
31. ### continued - Algebra and Geometry

list the first 20 or so Fibonacci numbers. From left to right, divide one number by the number before it, noting the result. What do you notice about the answers ??
32. ### continued - Algebra and Geometry

after you find the golden ratio, take its reciprocal on your calculator. Notice the decimal sequence does not change. No other number has that property
33. ### Algebra and Geometry

One of my favourite websites: http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fib.html It would take you weeks to follow all the links and side-interests of this wonderful webpage It starts with the Fibonacci numbers, which are very closely linked with the Golden ...
34. ### algebra math, 8th grade

Or, to illustrate Scott's concept, just plot the given points.
35. ### Math

R = mE + b case1: R = 530, E = 16000 530 = 16000m + b ** case2: R = 730, E = 3600 730 = 3600m + b *** subtract *** from ** -200 = 12400m m = -1/62 back in *** 3600(-1/62) + b = 730 b = 24430/31 R = (-1/62)E + 24430/31 so when E = 1300 R = (-1/62) + 24230/31 = 23780/31 or appr 767
36. ### Math

well, if 1 inch ---> 15 ft then 8 inches ---> 8(15) ft or 120 ft and 12 inches ........
37. ### Algebra

in 3 - 3/x , x cannot be zero ! did you mean x ? 0 ?? 3- 3/x = x+7 times x 3x - 3 = x^2 + 7x x^2 + 4x + 3 = 0 (x+3)(x+1) = 0 x = -3 or x = -1 what do you think?
38. ### AP Calculus 12

I will assume you mean lim (1 - cosx)/sinx , as x ---> 0 = lim (1 - cosx)/sinx * (1+cosx)/(1+cosx) = lim (1 - cos^2 x)/(sinx(1+cosx) = lim sin^2 x/(sinx(1+cosx) , as x ---> 0 = lim sinx/(1+cosx) , as x ---> 0 = 0/2 = 0
39. ### algebra

what is 6 + 5(-2) ? = 6 - 10 = -4
40. ### algebra

just replace n with 6 a(6) = 6 + (5)(-2) = -4 2nd question: correct let x = -8, y = -3(-8)+7 = 31 let x = -6, y = -3(-6)+7 = 25 ... let x = 2, y = -3(2)+7 = 1 so the range is {31, 25, ... ,1}
41. ### algebra 1

from mailroom at floor x : x + 4 - 7 + 9 - 6 + 2 - 8 = 1 x = ....
42. ### Math

in your repertoire of factoring techniques and formulas, you should have: x^3 + y^3 = (x+y)(x^2 - xy + y^2) and x^3 - y^3 = (x-y)(x^2 + xy + y^2) so .... x^3 + 125 = x^3 + (5)^3 = (x+5)(.....) let me know what you get
43. ### Algebra

the domain of the inverse of f(x) is the range of f(x) if f^-1 (x) = x^2 - 4/5 the inverse of that is x = y^2 - 4/5 5x = 5y^2 - 4 (5x+4)/5 = y^2 f(x) = y = ±?((5x+4)/5) <----- the range of that is any real number
44. ### Math

after first discount: cost = .8(149.99) = 119.99 so yes, you qualify for the second discount. cost after second discount = .9(119.99) = 107.99 total savings = 149.99 - 107.99 = \$42.00 none of the choices are correct, unless you have a typo in a)

Yes
46. ### Math Algebra 1

Cost A = 125 + 50t Cost B = 200 + 25t You really should have been able to do this.
47. ### Math

I am sure you meant: f(x) = (x+1)/(x-1) or y = (x+1)/(x-1) f(y) = ( (x+1)/(x-1) + 1) / ( (x+1)/(x-1) - 1) multiply top and bottom by x-1 f(y) = ( x+1 + x-1) / ( x+1 - (x-1) ) = 2x/2 = x
48. ### math

If I recall those old non-metric units ... 1 gallon = 4 quarts, so 3 gallons = 12 quarts 2 cups juice : 3 quarts punch = x cups juice : 12 quarts punch 2/3 = x/12 x = 12(2/3) = 8
49. ### math

yes, of course, hit the wrong key
50. ### math

The areas of two similar figures are proportional to the square of their corresponding sides so 225 : 81 = side1^2 : side2^2 then ?225 : ?81 = side1 : side2 side1 : side2 = 15 : 8
51. ### Math

A) 1 cm : 5 m = 1 cm : 500 cm = 1 : 500 B) ... C) 5 cm : 10 m = 5 cm : 1000 cm = 5 : 1000 = 1 : 200 D) ... you work out the other two, then decide

correct
53. ### Algebra 1

I would choose elimination: first one times 2 ---> 6x + 4y = -20 2nd times 3 -------> 6x - 15y = 9 subtract them: 19y = -29 y = -29/19 back into the original first: 3x - 58/19 = -10 3x = 58/19-10 = -132/19 x = -44/19
54. ### Math

Was there a question? What are those decimals in your second post ?
55. ### Math

Start with y = | x | you should be able to graph this if not, look at Wolfram: http://www.wolframalpha.com/input/?i=y+%3D+%7Cx%7C a big V with nothing below the x-axis consider: y = |x| - 2 , we just moved the entire graph down 2 units. http://www.wolframalpha.com/input/?i=y+%...
56. ### Math

you stated correctly, that the depth depends on the time? - so doesn't the depth depend on time, making time the independent variable, and depth the dependent one ?? Usually the independent variable goes on the vertical axis, (the y-axis), and the independent variable ...
57. ### @ Candi

Candi, do not put a new question as an answer to somebody else's. It may not be looked at , since we might think the first question has been answered. '2/3 of a given number is 40' --- (2/3)x = 40 x = 40(3/2) = 60 now 2/5 of that is (2/5)(60) = 24 Where did the 200...
58. ### Math

No, did you notice that the y values are all powers with base 5 ? (1,5) ---> (1, 5^1) (2, 25) ---> (2, 5^2) ... (5, 3125) ---> (5, 5^5) So y = 5^x , which I don't see as one of the options, unless you have typo in either B or C
59. ### Math

2(18) + 2(1.5) + soda = 10 + 30.25 solve for 'soda'
60. ### math

Draw your sketch and find the intersection of the two straight lines. The y of that intersection point is the height of your triangle. In your head, you can see that the x-intercept of x+y=24 is (24,0) and the x-intercept of 3x - 2y = 12 is (4,0) so you know the base length of...
61. ### math geometry

Find the volume of the first cone. You know r = 5 and h = 18 You MUST know the formula for the second cone you know r = 7.5 and you have to find h sub in r = 7.5 and h in the formula and set it equal to the volume of the first cone. Solve for h let me know what you get.
62. ### Algebra

john's rate = 5 cups/2 min = 2.5 cups/min sam's rate = 6 cups/2.5 min = 2.4 cups/min combined rate = 4.9 cups/min so time to make 245 cups = 245/4.9 = 50 minutes check: in 50 minutes, john can make 50(5/2) = 125 cups in 50 minutes , sam can make 50(6/2.5) = 120 cups ...
63. ### Math

Again, what formula are you using ??
64. ### Math

That's what I used to call mathemagics - unfortunately you are wrong! "I just added in the numbers to the formula and 59 just appeared" ---- nonsense! What formula? Show me if you want help
65. ### Math

no show me your work so I can tell you where you went wrong.
66. ### Math

correct, if you use all the digits that you can hold in your calculator's memory, you will get it exactly to the cent.
67. ### Math

i = .05/12 = .0041666.. (keep it in your calculator, don't round off) n = 60 paym( 1 - (1.04166...)^-60)/ ..041666... = 2000 solve for paym let me know what you got.
68. ### math

original: number of math books -- 5x number of geogr books -- 7x number of science books - 8x new numbers: math ----- 1.4(5x) = 7x geography-- 1.5(7x) = 10.5x science ----- 1.75(8x) = 14x new ratio = 7x : 10.5x : 14x = 7 : 10.5 : 14 = 14 : 21 : 28 = 2 : 3 : 4
69. ### calc

or Newton's method: let y = lnx - x^3 + 1 dy/dx = 1/x - 3x^2 newx = x - (lnx - x^3 + 1)/(1/x - 3x^2) = (1 - 3x^3 - lnx + x^3 - 1)/(1/x - 3x^2) = (-2x^3 - lnx)/(1/x - 3x^2) guess: x = .5 newx1 = .3545... newx2 = .38789... nrwx3 = .39042.. newx4 = .39044046 newx5 = .39044046...
70. ### Math

log?62 = a , 4^a = 62 , I know 4^3 = 64 , so a = appr 3 , but a < 3 log?36 = b , 6^b = 36, so b = 2 log?10 = c , 3^c = 10, I know 3^2 = 10 , so c = appr 2, but c >2 log?20 = d , 5^d = 20 , I know 4^2 = 25, so d < 2 order: log?20 , log?36 , log?10 , log?62
71. ### Calculus

Looks pretty straight forward ... f(x)=9x^(1/3) + (9/2)x^(4/3) f ' (x) = 3x^(-2/3) + 6x^(1/3) f''(x) = -2x^(-5/3) + 2x^(-2/3) for relative max/min, f'(x) = 0 3x^(-2/3) + 6x^(1/3) = 0 3x^(-2/3) (1 + 2x) = 0 3x^(-2/3) = 0 ---> no solution or 1+2x = 0 x = -1/2 ...
72. ### Calculus

Your lack of brackets leave the interpretation of the equation very ambiguous. e.g. do you mean: f(x)=9x^(1/3) + (9/2)x^(4/3) ? please retype before I attempt it
73. ### Maths

What is a rectangular pentagonal garden? Where is point A ?
74. ### Algebra 2

or , assuming you meant : 4* 4^(x/2) =1024 4^(x/2 + 1) = 4^5 x/2 + 1 = 5 x/2 = 4 x = 8 If you meant: 4* (4^x)/2 =1024, the way you typed it (4^x)/2 = 256 4^x = 512 xlog4 = log512 x = log512/log4 = 4.5
75. ### Math

Your hyperbola has centre (0,1) , a = 3, and b = 1 vertices would be (3,1) and (-3,1) To sketch this hyperbola I would faintly sketch a rectangle with corners at (3,2), (-3,2) , (-3,0) and (3,0) One asymptote would run through (3,2) and (-3,0) and of course (0,1) slope = 1/3 y...
76. ### math

I noticed that the coefficients of y are ± 1 , so ... add the first and the second: 6x = 1 x = 1/6 , well that was lucky add the second and third: 3x + 3z = -3 x + z = -1 1/6 + z = -1 z = -7/6 sub into the last: 1/6 + y - 7/6 = 6 times 6 1 + 6y - 7 = 36 y = 42/6 = 7
77. ### math

Did you make a sketch? draw a horizontal at the 3 m height, and you will get a right-angled triangle with sides 12 and 5. You might recognize the 5-12-13 right-angled triangle, if not ... h^2 = 5^2 + 12^2 = 25 + 144 = 169 h = ?169 = 13 m
78. ### physics

I am going to do this question with actual numbers let u0 = 20 m/s let v0 = 28 m/s let á = 5 m/s^2 let â = 4 m/s^2 case 1: á = 5 m/s^2 then u0 = 5t+ c when t = 0 , 20 = 0 + c velocity1 = 5t + 20 similarly velocity2 = 4t + 28 distance1 = (5/2)t^2 + 20t + k, ...
79. ### Math

just translate and use your definitions of an AS a+3d = a+4d - 3 d = 3, hey, we got the common difference already a+6d = 3(a+4d) a + 6d = 3a + 12d -2a = 6d = 18 a = -9 check: terms are: -9 -6 -3 0 3 6 9 12 15 .... all conditions check out.
80. ### Math

If possible, I prefer to work without fractions (27\8)A+7=(4\9)-3A times 72 243A + 504 = 32 - 216A 459A = -472 A = -472/459 I verified this answer in the left and right sides.
81. ### Algbra

Here is a quick way to find the slope of a line, if written in the form Ax + By + C = 0 the slope of the line is -A/B so for #1 -2x=-10y+6 ---> 2x - 10y + 6 = 0 , slope = -2/-10 = 1/5 x+5y=3 ---- slope = -1/5 so the lines have different slope, so they must intersect in 1 ...
82. ### Alegbra 1

Bill, you have now posted this same question 7 times since yesterday. You received a variety of ways to get the answer. Ms Sue even told you not to post it again, so here it is once more
83. ### Math

this is probably a question asking for EXACT values 37.5 = 1/2 of 75 and 75 = 30+45 so find tan75 = tan(30+45) = (tan30 + tan45)/( 1 - tan30*tan45) = (1/?3 + )/(1 - 1/?3) = (1+?3)(?3 - 1) recall tan 2A = 2tan A/(1 - tan^2 A) tan 75 = 2tan37.5/(1-tan^2 37.5) let tan37.5 = x (1...
84. ### Algebra 2/ Intermediate

I will assume you mean: log4(x-6)= -1 then .. x-6 = 4^-1 x-6 = 1/4 4x-24 = 1 4x = 25 x = 25/4
85. ### Math

geeeshhh let her income be x (1/4)x + (1/12)x + (1/2)x + 10000 = x times 12 3x + x + 6x + 120000 = 12x 120000 = 2x x = 60,000
86. ### Math Help

did you notice: 12-9=3 15-12=3 so what is your verdict ?
87. ### Should be the last one

You probably did 3^2 instead of 2^3 --- neither one of which requires a calculator
88. ### Should be the last one

make sure you follow the order of operations 4 + 3(10 - 2^3) = 4 + 3(10 - 8) = 4 + 3(2) = 4 + 6 = 10 how did you get 11 ??
89. ### correction - MATH

since V = pi(r^2)h if we double r and h new V = pi(2r)^2(2h) = 8pi r^2 h so it increased 8 times or, since they gave you the volume after doubling in the second sentence, just divide 401.9/50.2 = 8.0059... or 8 times or volume of similar objects varies directly with the cube ...
90. ### math

nothing to solve, you don't have an equation. If you are simplifying .... 3loga(2x+1)-2loga(2x-1) = loga(2x+1)^3 - loga(2x-1)^2 = loga [ (2x+1)^3 / (2x-1)^2 ] not really simplifying, just changing it around a bit
91. ### Mathe

Did you make a sketch ? Draw a perpendicular from the centre to the chord and you have a right-angled triangle. h^2+ 6^2 = 8^2 h^2 = 64-36 = 28 h = ?28 cm
92. ### Math again ;-;

First you have to expand using the distributive property 5x + 2(x + 6) , remember multiplication comes before addition according to BEDMAS = 5x + 2x + 12 = 7x + 12
93. ### Algebra 1

Since the two y values must be the same .... 2/5 x- 17 7/10 = -5/2 x + 20 2x/5 - 177/10 = -5x/2 + 20 I suggest we multiply each term by 10 4x - 177 = -25x + 200 take over , (the x value is a whole number, but the y isn't)
94. ### math

Well, if n is a whole number, then 2n will always be even. When you add 1 to any even, the result will be odd. So 2n+1 is always odd by writing it as 2n^3+n^2+6n+3 = (2n+1)(n^2 + 3) I have shown that one of the factors, namely (2n+1), will always be an odd number, thus 2n^3+n^...
95. ### math

let's factor it ... 2n^3+n^2+6n+3 = n^2(2n+1) + 3(2n+1) = (2n+1)(n^2 + 3) what kind of a number is 2n+1 ??
96. ### Geometry

let the other endpoint be (a,b) recall how to find the midpoint: for the x-coordinate, add up the x's of the endpoints , then divide by 2 for the y-coordinate, add up the y's of the endpoints , then divide by 2 so for the x of the endpoint: (a+7)/2 = 2 a+7 = 4 a = -3 ...