Friday
July 1, 2016

# Posts by Reiny

Total # Posts: 35,119

math
yes recall that (a/b)^n = a^n/b^n so (1/a)^-n = 1^-n / a^-n but (1)^anything = 1 = 1/a^-n
February 28, 2016

math
for the first one: (-1)^(2n) = +1 2n is an even number, so when you multiply -1 an even number of times you get a positive e.g. (-1)^12= ( (-1)^2 )^6 = 1^6 = 1 but (-1)^13 = (-1)^12 (-1) = (+1)(-1) = -1 so if you raise (-1)^odd, you get -1 which answers the second part since ...
February 28, 2016

FINANCE
PV of loan = .75(3250000) = \$2,437,500 paym = 15800 n = 12(35) =420 let the monthly rate be i 2437500 = 15800( 1 - (1+i)^-420)/i 154.2721519 i = 1 - (1+i)^-420 This is a very nasty equation to solve. Back in the "good ol' days", we used a method called ...
February 28, 2016

Finance
If she has 2500,000 and she gets 12.5% per year in interest, she would earn \$312,500 per year right now. Heck!, she should retire right now but according to your question 2.5 million(1.125)^n = 7.5 million 1.125)^n = 3 n log 1.123 = log3 n = appr 9.3 years
February 27, 2016

precal
It said diameter = 22, so radius is 11 I used 2πr = 2(11)π = 22π
February 27, 2016

precal
circumference = 2π(11) = 22π inches so in 1 minute a point on the rim covers 31(22π) or appr 2142.566 inches since linear velocity = distance/time ....... your turn.
February 27, 2016

math
sinØ = y/r = 1/9 ---> y = 1, r = 9 Make a sketch of the triangle in quad II so x^2 + y^2 = 9^2 x^2 + 1 = 81 x^2 = 80 x = ±√80 = ±4√5 but we are in II, so x = -4√5 sinØ = 1/9 ---> the given cosØ = -4√5/9 tan&...
February 27, 2016

Mathematics
you have to use the product rule, with your notation, it would be d(uv) = uv' + vu' = (-8sin(2x))(cos(3x)) + (4cos(2x)(-3sin(3x) ) = -8sin(2x)cos(3x) - 4sin(3x)cos(2x)
February 27, 2016

math
To make 10 L in total you will need x L of the 18% solution and 10-x L of water. .18x + 0(10-x) = .12(10) .18x = 1.2 x = 1.2/.18 = 120/18 = 20/3 He needs 20/3 L or 6 2/3 L of water. (btw, a Russian would never dilute his alcohol)
February 27, 2016

Calculus Pre Test Questions Monday Part 4
your symbols came out strange. Is 3􏰄<t􏰄<3.01 supposed to say 3 ≤ t ≤ 3.01 ?
February 27, 2016

Calculus
So you have a split function f(x) = 4-x^2 for x<1 f(x) = 2x+1 for x > 1 (you don't say what happens at x = 1 ) first slope = -2x, second slope is a constant 2 a) (-1,3), since x<1, slope = -2(-1) = 2 b) (2,5), since x > 1, slope = 2
February 27, 2016

Calculus
2a) I will assume you mean f(x) = 3/(x+1) I would write it f(x) = 3(x+1)^-1 then f ' (x) = -3(x+1)^-2 = -3/(x+1)^2 at P(2,1), slope = -3/(3)^2 = -3/9 = -1/3 h(x) = 2/√(x+5) = 2(x+5)^(-1/2) h ' (x) = -1(x+5)^(-3/2) = -1/( √(x+5) )^3 you finish it
February 27, 2016

Algebra
number of fifties --- x number of tens ---- x+14 number of twenties -- 2x+4 50x + 10(x+14) + 20(2x+4) = 1720 Solve for x, and all shall be revealed.
February 27, 2016

math
Use the discriminant property if we have real roots, then b^2 - 4ac > 0 px^2-p+10=2(p+2)x px^2 - p + 10 = 2px + 4x px^2 - 2px - 4x + 10 = 0 px^2 + x(-2p-4) + 10 = 0 b^2 - 4ac > 0 (-2p-4)^2 - 4(p)(10) > 0 4p^2 + 16p + 16 - 40p > 0 4p^2 - 24p + 16 > 0 p^2 - 6p + 4...
February 27, 2016

math
for 2 equal roots, b^2 - 4ac = 0 9p^2 - 4(p)(p+q) = 0 9p^2 - 4p^2 - 4pq = 0 5p^2 - 4pq = 0 p(5p - 4q) = 0 p = 0 or p = 4q/5 but p≠0 or else we don't have a quadratic, so p = (4/5)q
February 27, 2016

math
You must be talking about the simple interest formua I = PRT 700 = 3500(r)(4) r = 700/(14000) = ...
February 27, 2016

Geometry
"One Secant has 4 and x" is not clear. Is 4 the length of the entire secant or just the part inside the circle? In general, if you have two secants to the same circle (whole of secant #1)(outside part of secant#1) = (whole of secant#2)(outside part of secant#2) So ...
February 27, 2016

Algebra 2
y = -.23x + 56.78 or y = (-1/2)x + 3
February 27, 2016

math
speed of private jet --- x mph speed of commercial jet --- 2x-143 mph They both went the same distance, so ... 4(2x - 143) = 6x solve for x
February 27, 2016

algebra
f(x)-g(x) = 9x^3+2x^2-5x+4 -(5x^3-7x+4) = 9x^3+2x^2-5x+4 -5x^3+7x-4 = 4x^2 + 2x^2 + 2x looks like you are correct
February 27, 2016

Alg2
Why make things complicated ? Just solve it .... (1/4)x-3=(1/2)x+8 times 4, the LCD x - 12 = 2x + 32 -x = 44 x = -44 Where does y come from in the pairs of equations?
February 27, 2016

calculus
I see 4 questions posted in quick succession. You have given no indication of any start to these on your part, nor have you told us where your problems are. This looks like an assignment or homework. Surely you realize that if just do these questions for you, you will not ...
February 27, 2016

Math
let the number of boys be 5x and the number of girls be 6x 5x+6x=44 11x=44 x=4 so we have 20 boys and 24 girls (notice 20:24 = 5:6)
February 27, 2016

financial maths
i = weekly rate = .0665/52 = .001278846 n = number of payments = 52(15) = 780 Amount repaid = present value of loan = 200( 1 - 1.001278846^-780)/.001278846 = appr \$98,677.00
February 27, 2016

math
Alice --- x Peter --- x+5 John ---- 2x+10 5 years from now: John -- 2x+15 Alice -- x+5 2x+15 = 3(x+5) -x = 0 x = 0 This question is bogus, even though the answer meets the original conditions. Unless Alice was just born, it makes little sense i.e. Alice -- 0 years Peter --5 ...
February 27, 2016

math
let the 3 numbers be x, x+1, and x+2 3x = x+1 + x+2 3x = 2x+3 x = 3 Finish it up, and check my answer to see if it meets the given conditions
February 27, 2016

math
what is 4x3 ?
February 27, 2016

algebra or algebra1
Not sure of your unusual notation. did you mean |x-6| is multiplied by 7 ? Ok, then ... f(-1) = |-1-6|7 - (-1) = 49+1 = 50
February 27, 2016

Math Word Problem
same type of problem as your previous post .... students --- x adults ----- y x+y = 110 ---> y = 110-x 13.5x + 16.5y = 1581 sub the first into the second: 13.5x + 16.5(110-x) = 1581 13.5 + 1815 - 16.5x = 1581 -3x = -234 x = 78 So 78 students and 32 adults
February 27, 2016

Math Word Problem
Look at the response to this question last night by both Steve and I. All you have to do is change the original second equation, and solve. http://www.jiskha.com/display.cgi?id=1456542484
February 27, 2016

Maths
You have your thinking backwards. an example of the above would be both 12 and 30 are divisible by 3 then their difference is divisible by 3 check: difference = 30-12 = 18 is 18 divisible by 3 ? YES actual proof: let the two numbers be kx and ky. kx and ky are both divisible ...
February 26, 2016

Algebra
February 26, 2016

Math
using the definitions: a+2d + a+8d = 20 2a + 10d = 20 a + 5d = 10 ** a+11d - (a+3d) = 32 a+11d - a - 3d = 32 8d = 32 d = 4 sub into ** a + 20 = 10 a = -10 state your conclusion.
February 26, 2016

Math Word Problem
number of 4-credit courses --- x number of 5-credit courses --- y x+y = 52 4x + 5y = 22 This has no positive x and y solutions. Check your question or your typing How can a total of 52 courses yield only 22 credits, unless they failed most of the courses ???? Even if courses ...
February 26, 2016

math
You don't say what kind of a prism. I will assume it is a rectangular prism, (fancy word for box) each cube has a volume of (1/2)^3 or 1/8 inches^3 number that will fit the box = 56/(1/8) = 448 cubes e.g. the box could have been 4 in by 7 in by 2 in for a volume of 56 ...
February 26, 2016

Pre calculus
Do you really think that somebody will give their free time and help you after such a rude and disrespectful response to one of our valuable and trusted tutors ? I certainly don't feel such an inclination.
February 26, 2016

Math
Your equation is correct now, you are told that m = 3 solve: 3.95(3) + 8.95b = 47.65
February 26, 2016

Maths
Look at the expression (x-1)^2 When you square anything, the result is always positive unless you squared zero, which would stay at zero. 3(x-1)^2 > 0 divide by +3 (x-1)^2 > 0 now for what value is x-1 equal to zero? x-1 = 0 x = 1 now take any value of x you want, ...
February 26, 2016

correction
28 is not correct you are selecting 4 toppings from 7 This is a 'combination' type question number of ways = C(7,4) = 7!/(5!2!) = 35 If you care about the order in which the toppings are put on the sundae then it would be P(7,4) = 7x6x5x4 = 840 , which is not one of ...
February 26, 2016

math
Yes, all are correct 5 people in a backseat? Sounds cozy.
February 26, 2016

Math
area of ||gram = (1/2)(a+b)(height), where a and b are the parallel sides 246 = (1/2)(a+b)(20.5) a+b = 24 So all we know is that the two parallel sides add up to 24, so not enough info
February 26, 2016

Math
Notice this is NOT an arrangement, the word "choose" is a give-away that you are dealing with combinations. so you want to select 5 from 7 = C(7,5) = 7!/(5!2!) = 21 you are correct!
February 26, 2016

Math
You should not just "think" it is 24. You should be absolutely and definitely be sure of yourself 4x3x2x1 = 24
February 26, 2016

Mathematics
you can do more than one step at a time if they don't affect each other 3{[7(8-2)+4]-[2(2•8-5)+6]} = 3{[7(6)+4]-[2(16-5)+6]} = 3{[42+4]-[2(11)+6]} = 3{[46]-[22+6]} = 3{[46]-[28]} = 3{18} = 54 so you are right, notice the use of the = sign at the beginning of each new ...
February 26, 2016

Math - Help!
Sandy, I have made many errors and mistakes. Sometimes we read a question too quickly and miss something. In my case I just call it a "senior moment, lol
February 26, 2016

Math - Help!
It said: P(sum is greater than 5) so we have to exclude those equal or less than 5 11 12 13 14 21 22 23 31 32 41 -----> there are 10 of those, leaving 26 to be > 5 so prob(sum> 5) = 1 - 10/36 = 26/36 = 13/18 or by using the 26 count directly prob( sum > 5) = 26/36...
February 26, 2016

Math - Help!
first one is correct prob(sum > 5) = 1 - prob(sum ≤ 5) = 1 - 10/36 = 26/36 = 13/18 Don't add a new question as a reply to another post, in this case your own. One might think it has been answered and it gets overlooked .... Your answer to the cell phone question ...
February 26, 2016

Dividing Polynomials
We usually put them in order of highest to lowest in terms of exponents. That way by just looking at the first term exponent we can tell what degree the polynomial has e.g. 7x^5 - 4x^2 + 3x +9 is a fifth degree polynomial
February 26, 2016

Algebra
#6, wrong -4-5(x+8) = -4 - 5x - 40 = -5x - 44 #7 wrong 3x+4(x-6)-3(x-7) = 3x + 4x - 24 - 3x + 21 = 4x - 3 #8. 8 + 8 < -28 , the answers make no sense according to the question, the statement itself is false #9. wrong R/15>-3 R > -45 you're batting 0/4, looks like ...
February 26, 2016

Algebra 2
I see so many things wrong here. Why are you taking 16-2x, when according to your question it should be 18-2x which is it? You also completely ignored the fact that the whole garden has an area of 200 f^2 Where did it say that the area of the walkway is zero? That is what you ...
February 26, 2016

algebra
f(x) = 2x+1 , g(x) = 3x+2 f(3) / f(2) = 7/8 then if f(x)=2x , g(x)=3x^3 f(x)/g(x)=2x/(3x^3) = 2/3x^2 end of problem, how easy was that
February 25, 2016

maths
let's see: 12^2 = 144 13^2 = 169 14^2 = 196 what do you think? if ^3√80 is to mean "the cuberoot of 80" then we could try this as well: 2^3 = 8 3^3 = 27 4^3 = 64 ....
February 25, 2016

Math
As a Canadian, I haven't seen a 50-cent coin in circulation for years. Anyway... I really don't understand what your question is. The area would be π(13.565^2) mm^2 = appr 578.082.. mm^2 "What is the ... tenth of a square millimeter? " 1/10 square mm = ....
February 25, 2016

Calculus
Just use the cosine law let x be the distance between them when the angle is Ø x^2 = 8^2 + 13^2 - 2(8)(13)cosØ x^2 = 233 - 208cosØ 2x dx/dt = 208sinØ dØ/dt dx/dt = (104sinØ dØ/dt)/x given: dØ/dt = .08 rads/min find : dx/...
February 25, 2016

Calculus
I assume these are Philippine pesos and there are 100 centavos in a peso. current subscribers --- 50,000 cost per minute = 800 centavos let the number of one centavo reductions be n subscribers = 50000 + 1000n cost per minute = 800 - n Revenue = (50000+1000n)(800-n) = 1000(50...
February 25, 2016

Mensuration
how far is it three times around ? Once you have that distance, and you know Time = Distance/rate you can do it.
February 25, 2016

math
Yes, a square is a rectangle, but a rectangle is not necessarily a square. A square is a subset of all rectangles. Similar to: Every girl is a human being, but not every human being is a girl.
February 25, 2016

Math Vector
Make a sketch. Since position vector like OA = 3i-5j set A as the point (3,-5), we also have OB = -7i+4j , placing B at (-7,4) let D be the midpoint of AB, D = (-2, -1/2) using the standard way to find midpoint. Also we know the centroid G is at (2,1) We also know that the ...
February 25, 2016

Math
Make a sketch If D divides AB in the ratio of 1 : 2, then DA = 1/3 BA similarly EA = 1/3 CA notice I was careful in the order I wrote EA, that way writing them as vectors would be the same. I will use the notation v(AB) for vector AB v(DE) = v(DA) + v(AE) = (1/3)v(BA) + (1/3)v...
February 25, 2016

algebra
ummmhhh, j+8 = 51 take over
February 25, 2016

Math
And I am equally bemused by your comment. What do you mean by "the answer" ? You have simply written down 4 numbers. What about them ? 13. SA of sphere is 4πr^2 = 4π(2√2)^2 = 32π m^2 Still trying to visualize your cone somehow wobbling on top of...
February 25, 2016

Algebra
right the equation is y = -(x)^3 , which is not exponential
February 24, 2016

algebra
What about it ? We could change it to .... 1/2[ln(x+1)^6+ln(x-2)] = 1/2[ln ( (x+1)^6/(x-2) ) = ln √((x+1)^6/(x-2)) but why ?
February 24, 2016

Mensuration
area of floor = 120 m^2 area of one tile = .5*.25 or .125 m^2 number of tiles = 120/.125 = 960 or we need 30 tiles along one wall, and 32 along the other wall, so 30*32 or 960 tiles carpet is 13 by 6 or 78 m^2, leaving 120-78 or 42 m^2 of the floor exposed
February 24, 2016

Mensuration
area of long strip = 80*10 or 800 m^2 area of shorter strip = 60(10) = 600 m^2 total = 1400 m^2 BUT, we counted the intersection twice so we subtract 10(10) or 100 m^2 are of the two "rmads" is 1300 m^2 cost = 1.2(1300) = 1560 units of money
February 24, 2016

Stats
balls numbered > 23 are 4 prob(drawing 2 which are > 23) = (4/27)(3/26) = 2/117
February 24, 2016

Trigonometry
Jack's distance from the building ---- x tan45 = 15/x ----> x = 15 for Maria: tan 60 = 15/y y = 15/tan60 = appr 8.66 ft they are 15-8.66 or 6.34 ft apart
February 24, 2016

Geometry (Law of Cosine or Sine)
For the given times, one car went 2.75(60) miles or 165 miles and the other 2.75(75) or 206.25 miles d^2 = 165^2 + 206.25^2 - 2(165)(206.25)cos125° = 108803.1087 d = √.. = 329.85 miles
February 24, 2016

math
2w + 3p = 16.50 4w+p = 15.50 double the first: 4w+6p = 33 4w + p = 15.50 subtract them 5p = 17.50 p = 3.50 into the original 2nd: 4w + 3.50 = 15.50 4w = 12 w = 3.00 Water costs \$3.00 per bottle, and \$3.50 per pretzel
February 24, 2016

they involve grouping, I will do the first and last. axny+abn+cxy+bc = an(xy + b) + c(xy + b) = (xy + b)(an + c) ... 2x^3+3x^2-2x^2y-3xy = x^2(2x + 3) - xy(2x + 3) = (2x+3)(x^2 - xy) = (2x+3)(x)(x-y) = x(2x+3)(x-y)
February 24, 2016

math
My crystal clairvoyance ball is a bit cloudy this morning. I just can't see your graph
February 24, 2016

Algebra
clearly (0,5) is the y-intercept, so all we need is the slope slope = (12-5)/(4-0) = 7/4 so y = (7/4)x + 5 b) good grief, another abuse of equations and variables. Just do the question! cost = 3.2(\$2.50) + \$6.90 = \$14.90
February 24, 2016

Algebra
y^2 = x+4 let x = 0 ---> y^2 = 4 , y = ± 2 let y = 0 x+4=0 ----> x = -4 A quick sketch will show a parabola with vertex (-4,0), opening to the right, and axis of symmetry the x-axis
February 24, 2016

Algebra
Why did you not just follow the instructions? All you need is the distance formula between 2 points. distance between the 2 points = √((4-1)^2 + (a-2)^2 ) = √(a^2 - 4a + 13) for #2, just set the two square roots equal to each other. Simplify like I did above, then ...
February 24, 2016

Algebra
you must drain the same amount as the amount you are going to add , to keep 15 L in there let that amount be x L so we are draining .4x L of antifreeze and then adding x L of pure antifreeze so .4(15) - .4x + x = .6(15) times 10 4(15) - 4x + 10x = 6(15) 60 + 6x = 90 6x = 30 x...
February 24, 2016

Maths
Are the ends semi-circles ? If so, then the curved part must come in 15 m on each end, leaving a straight length of only 20 m for the rectangle. outer area = rectangle of 20by30 + 1whole circle of radius 15 = 600 + π(225) = (225π + 600) m^2 inner area = 25by20 + &#...
February 24, 2016

geometry
Not aware of any special name given that point. How about calling is a "common point of concurrency"
February 24, 2016

math
good job, all are correct
February 24, 2016

Math
number of sweets --- s , where s < 200 number of students -- x case1 : 2x + 70=s case2 : 4x - 10 = s 4x - 10 = 2x+70 2x = 80 x = 40 then s = 80+70 = 150 ( or x = 4x-10 = 150) There are 150 sweets and 40 students
February 24, 2016

Math
multiply both sides by 7a 35 = 6a a = 35/6
February 24, 2016

Algebra
Did you mean ? (2x^3+9x-4x+10)/(x+5) I suspect a typo, or else why would you not have added the 9x and the -4x ? Is it 9x^2 ? What do you want to do with this ?
February 24, 2016

Math
vector AB = (2,-10) vector CB = (8,-13) vector AB (dot) vector CB = |AB| |CB| cosØ , were Ø is angle ACB 16 + 130 = √104√233 cosØ cosØ = .937903... Ø = appr 20.3°
February 24, 2016

algebra or algebra1
Not sure about your invisible equations, but mine would be 42x = 62(x - 1/2)
February 24, 2016

Algebra
#3 x/5 + 6 = 10 x/5 = 4 x = 5(4) used to be 20, was not aware of any recent changes to 30 #4 -2(m-30)=-6m -2m + 60 = -6m 4m = -60 m = -15 #5 3.75x+3.7=1.7+1.75x 2x = -2 x = -1 one out of 4 easy questions correct! somebody has some serious work ahead of them!
February 24, 2016

algebra
first ---- x third ---- x-55 second ---- 220 - (x + x - 55) = 275- 2x "The sum of the first and second integers exceeds the third by 94" ---> x + x-55 = 275-2x + 94 4x = 424 x = 106 first is 106 third is 51 second is 63 check: sum = 106+51+63 = 220 , ok 1st + 2nd...
February 23, 2016

Math
ratio of their areas = 3^2 : 4^2 = 9 : 16 areas of circles = proportional to the square of their radii
February 23, 2016

algebra
.06x + .03(35000-x) = 1395
February 23, 2016

Calculus
Make a sketch. We will need to know where they intersect -x = 2-x^2 x^2 - x - 2 = 0 (x-2)(x+1) = 0 x = 2 or x = -1 height of region = 2-x^2 - (-x) = 2+x-x^2 area = ∫(2+x-x^2)dx from -1 to 2 = [2x + (1/2)x^2 - (1/3)x^3] from -1 to 2 = ... I will leave the arithmetic for you
February 23, 2016

Calculus
Make a sketch. No calculus needed, we have a triangle with straight lines Using some mental arithmetic and looking at my diagram, the base of my triangle is 4 units, and the height is 2 area = (1/2)(4)(2) = 4
February 23, 2016

Algebra
Why use a "system of equations", all the variables are easily defined . number of mezzanines --- x number of balconies ----- 3x + 78 number of main floor ---- x + 3x+78 + 435 = 4x + 513 59(4x+513) + 50(3x+78) + 40x = 73785 426x + 34167 = 73785 x = 93 back-sub into my...
February 23, 2016

Calculus
because of the symmetry, we can just go from x=0 to x=2 to find the area between y = x^2 and y = 4 that area = ∫4-x^2 dx from 0 to 2 = [4x - (1/3)x^3] from 0 to 2 = 8 - 8/3 - 0 = 16/3 so when y = b x= √b and we have the area as ∫(b - x^2) dx from 0 to √...
February 23, 2016

Algebra 2
February 23, 2016

college pre calculus
If the two top pieces are 5 units each, the bottom pieces are 12 units each, and if the center piece is 13 inches each, you are looking at two right-angled triangles, since 5^2 + 12^2 = 13^2 Thus the length of the cross pieces is fixed as well as the area. So this is not a ...
February 23, 2016

Math
the areas of similar figures area proportional to the square of their sides so area/12 = 3^2/1^2 area = 12(9) = 108 inches^2
February 23, 2016

Math
prob(red) = 17/60 prob(not red) = 43/60 have to exclude zero red, one red, and two red prob zero of 7 red = C(7,0) (17/60)^0 (43/60)^7 = appr .0971 prob one of 7 red = C(7,1) (17/60) (43/60)^6 = appr .2687 prob two of 7 red = C(7,2) (17/60)^2 (43/60)^5 = .3187 prob of getting ...
February 23, 2016

math
you define the variables, so that x+y = 40000 .08x + .06y = 2500
February 23, 2016

math
assuming you are drawing only two marbles prob(yellow, then yellow after replacement) = (6/15)(6/15) = 4/25
February 23, 2016

Math
Sliding the box through the circle length wise means that the circle must be able to at least as long as the diagonal. So you are right, D^2 = 4^2 + 4^2 = 32 D = √32 = appr 5.7
February 23, 2016

math
number of adults -- x number of chidren -- 12-x solve for x 8x + 5(12-x)=72
February 23, 2016