Sunday
July 13, 2014

Posts by Reiny


Total # Posts: 26,788

Algebra confused/Thank you
You should be able to read the solution. http://www.wolframalpha.com/input/?i=plot+3x+%2B+2y+%3D+5+%2C+4x+−+3y+%3D+1

maths
a+bi = √(1+i)/√(1-i) = √(1+i)/√(1-i) * √(1-i)/√(1-i) = √(1 - i^2) / (1-i) = √(1 - i^2) / (1-i) * (1+i)/(1+i) = √2(1+i)/2 = √2/2 + √2/2 i so a = √2/2 and b=√2/2 and a^2 + b^2 = 2/4 + 2/4 = 1

Algebra
Put Hobbinton at the origin (0,0) on the x-y grid then Tom's house would be (12,-16) distance from (0,0) to (12,-16) = √(12^2 + (-16)^2) = √400 = 20

math
prob(c) = 1/4 prob(not c) = 3/4 so you are looking for c c notc = (1/4)(1/4)(3/4) = 3/64 c notc c = (1/4)(3/4)(1/4) = 3/64 notc c c = (3/4)(1/4)(1/4) = 3/64 prob of your event = 3(3/64) = 9/64

Algebra
the way you typed it, there is very little simplification I multiplied top and bottom by x^2 to get (x^3 + 3 - 36x + 3x^2)/(x^3 + 3x^2) , and that's about it. If you meant: ( (x+3/x^2 -36/(x+3)) /( (x+3)/x ) it would be something totally different. I can't guess what y...

MATH
Pick any x say, x = 0 y = 2(0)-5 = -5 ----> the point (0,-5) how about x = 4 , (or any x you feel like) then y = 2(4) - 5 = 3 --- the point (4,3) plot (0,-5) and (4,3) , join the with a straight line, extend the line to any length you feel like

math
that would be 8 - choose - 4 = C(8,4) = 8!/(4!4!) = 70

trig
For your first one, You should recognize those numbers as belonging to the 30-60-90° right-angled triangle which would make c = 1 If you didn't notice that, you could use the cosine law c^2 = 2^2 + √3^2 - 2(2)(√)cos30° = 4 + 3 - 4(√3)(√3/2) ...

math word problems
original: x by x area = x^2 new dimensions: (x+3) and (x+2) new area = (x+3)(x+2) = x^2 + 5x + 6 x^2 + 5x + 6 - x^2 = 46 5x = 40 x = 8 original was 8 by 8 check: old area = 64 new is 11 by 10 new area = 110 change in area = 110-64 = 46 , yeahh!

Precalculus
#3 Those are permutations since the order matters a) start with a vowel: 2*5*4 = 40 , you were right b) all consonants, means we only pick from 4 4*3*2 = 24 , you were right c) all vowels, you are right with 0 since we only have 2 vowels and we need 3 d) all consonants , repet...

Math - Business Calc.
I noticed an error in Damon's solution 4th line : V = (17-2h)(5-2h)h = (17-h)(5h-2h^2) should be : V = (17-2h)(5-2h)h = (17-2h)(5h-2h^2) I had h = 1.1445

Algebra - Help!!
I did a synthetic division of x^3 - 7x + 6 by x+3 to get the other dimension of x^2 - 3x + 2 , looks like a)

Math
Where is the second equation ?

algebra math
so she need one of 10, 11, or 12 prob of that = 3/12 = 1/4

Algebra
LCD is 24x -9y/(12x) + 28y/(12x) - 2y/(12x) = 17y/(12x)

Math
x^3 - x^2 - x + 8 = 0 tough one - it does not factor tried x = ±1, ±2, ±4 , none worked so no rational root what about real roots? let f(x) = x^3 - x^2 - x + 8 for f(-1) = -1 -1 +1 +8 = 7 for f(-2) = -8 - 4 + 2 + 8 = -2 so there is a real root between -2 a...

math
Did you make a sketch? I have a right-angled triangle with a base of 15 and a height of 4, (10 ft - his 6 ft) so in relation to your angle of elevation Ø, we have the opposite and the adjacent, suggesting tanØ = 4/15 arctan = 14.93° So to the nearest degree: ...

math
PV = 25000(1.03)^-28 = $10,926.92 i = .12/4 = .03 n = 7(4) = 28

Math
the above factor of x^3 - 1 factors to (x-1)(x^2 + x + 1) the x-1 = 0 gave us x = 1 x^2 + x + 1 = 0 x = (-1 ±√-3)/2 or x = (-1 ± i√3)/2

Math
5x^4=5x x^4 - x = 0 x(x^3 - 1) = 0 x = 0 or x^3 = 1 x = 0 or x = 1 There are also two complex roots, but I don't think you have studied that. Let me know if you did.

math
second question: How can Frank be a jacket ? third question: What language is this: "what is the fraction of the amount that he that he needs to saved" What does that mean?

math 1 question!!!!!!
Didn't Ms Sue just prove to you that is is C ??

correction - math
subtract them as they sit -y = 4 y = -4 back into the first: x -3(-4) = 25 x + 12 = 25 x = 13 x = 13, y = -4 , you had them opposite.

Math
correct

Math
adults --- x girls ----- 4x boys ------5x (note x: 4x : 5x = 1 : 4 : 5) "6 more boys than girls" ---> 5x = 4x+6 x = 6 so we had 6 adults, 24 girls, and 30 boys, (satisfying all our conditions stated)

Math
nope f(-3) = (-3)^2 - 5(-3) + 1 = 9 + 15 + 1 = 25

If 12 people are playing in a tournament and?
number of subsets of 2 elements from a sample space of 12 = C(12,2) = 66

Math
yes

Math
f(4) = 16+9 = 25 g(-1) = 24-4 = 20 so what is the problem?

Math ~ Check Answers ~
use the first pair of points (2,1) and (4,0) slope = -1/2 so y = mx + b ----> y = -(1/2)x + b sub in (4,0) 0 = (-1/2)(4) + b b = 2 y = (-1/2)x + 2 use our non-used point to check: does (6,-1) lie on it? LS = -1 RS = (-1/2)(6) + 2 = -3+2 = -1 your answer is good.

Algebra 1--Please, help me!
((n-5)/(n^2 - 2n -3)) / ((n-3)/(n^2 -4n - 5)) multiply both sides by (n^2 - 2n -3)(n^2 - 4n - 5) , sometimes called cross-multiplying n^3 - 4n^2 - 5n - 2n^2+ 8n + 10 = n^3 - 2n^2 - 3n - 3n^2 + 6n + 9 -n^2 = -1 n^2 = 1 n = ± 1

word problem?
prob(going to amusement park) = 8/18 = 4/9 so number of the 225 who would go = (4/9)(225) = 100 notice Ms Sue's equation will yield the same answer.

Algebra 1
did that for you here http://www.jiskha.com/display.cgi?id=1401816411 #2, was also done somewhere, can't find it, so ... The way you typed it: 2/t + 4/3t = 4/t + 2 times 3t 6 + 4t^2 = 12 + 6t 4^2 - 6t - 6 = 0 2t^2 - 3t - 3 = 0 t = (3 ± √33)/4 somehow I don'...

Scientific notation
area = (5x10^4)(6x10^3) = 30x10^7 = 3.0 x 10^8 m^2

Probability???
yes, but I would rather have you think of (1/520)(7800) = 7800/520 ---> see, there is your division by 520 = 15

Math
|5m-11| = 9+3m case 1: 5m-11 = 9+3m 2m = 20 m = 10 case 2 -5m + 11 = 9+3m -8m = -2 m = 1/4 product of answers = 10(1/4) = 5/2 oe 2.5

Algebra 1--Please, help me!
let the amount to be added by x ml so we have 300+x ml of the new mixture .3(300+x) = .4(300) 3(300+x) = 4(300) 900 + 3x = 1200 3x = 300 x = 100 Add 100 ml of water check: Do we have the correct amount of acid? in original: .4(300) = 1200 ml in new: .3(400) = 120 ml -----> ...

Algebra/can you ck my anwers
my sum was 1770 divide that by 25 gave me a mean of 70.8 your mean of 1616 should have hit you as absurd. range is correct, your median and mode sound logical

Algebra 1--Please, help me!
#3 no need for all those brackets ... (d + 2)/(d + 8) = (-6)/(d + 8) multiply both sides by (d+8) d+2 = -6 d = -8 ahhh, trick question. Notice in the original, d≠ -8 So there is no solution. #4 correct #5 handled by bobpursley #6 (x -6)/(x^2-6) = (-4)/(x-4) x^2 - 10x + 2...

Algebra 1 (Reiny)
Sorry I misread your original question So here is the correct one: right now : amount of orange juice = .25(8) = 2 cups amount of apple juice = .75(8) = 6 cups let the amount of pure orange juice to be added be x cups so just looking at the orange juice: 2 + x = .4(x+8) times ...

algebra
Bosnian was right in his first post. (think I will have a third cup of coffee to wake up)

algebra
sorry, did not register the "linear" part, and concentrated on the "increasing" actually I think it is a), the slope between any two points is 3/2 all points satisfy the equation 3x-2y=7 http://www.wolframalpha.com/input/?i=interpolate+%281%2C-2%29%2C%283%2...

algebra
correct http://www.wolframalpha.com/input/?i=plot+%281%2C-3%29%2C%283%2C5%29%2C%285%2C11%29%2C%287%2C18%29

statistics
You have the subtraction backwards A score of 90 is above the mean, so the z-score should be positive z-score = (90-84)/8 = +.75

Algebra 1--Please, help me!
Argggghhh Duplicate question Didn't see that Steve had already answered it

Algebra 1--Please, help me!
cups of orange juice --- x cups of apple --------- 8-x .25x + .75(8-x) = 4.(8) 25x + 75(8-x) = 40(8) I will let you finish it 2. For your type of perfect-square trinomial the first and last terms would have to be positive. ---- the -9 takes this one out of the category. It is ...

Algebra 1--Please, check my answer!
correct

Trig
(320cos120 , 320sin120) + (35cos60 , 35sin60) you should be familiar with the trig ratios of the 30-60-90 triangle, and the multiples of those angles using the CAST rule = (320(-1/2) , 320(√3/2) + (35(1/2) + 35(√3/2) = (-160 , 160√3) + (35/2 , 35√3/2) =...

Algebra
Your equation doesn't even match your given data length --- x width ---- 2x - 2 area = x(2x-2) = 82 2x^2 - 2x - 82 = 0 x^2 - x - 41 = 0 use the formula ... x = (1 ± √165)/2 = appr 6.92 or some negative length = 6.92 , length = 11.85 check: 6.92x11.85 = appr 82

statistics
Looks like that professor is still giving those A's See the first 3 "Related Questions" below

algebra
let the number of boxes be x 45x + 4000 = 11200 I will let you solve this equation.

trigonometry, check please
I got 10.064.. which to the nearest tenth is 10.1

Algebra ll
hope you got -23 -48

trigonometry ans.
yes, to the nearest foot it is 66 ft

trigonometry ans.
correct in reference to your angle you are involving the opposite and the adjacent side since tanØ = opposite/adjacent your choice of tangent was correct.

algebra.can you ck my answers
216 = 6^3 <-----> log6 216 = 3 How did you ever get 0 as an answer? That is not even an equation ! I suggest you memorize the definition of logs 16-(1/4)^-2 1/2 No idea what that is supposed to be. Was that supposed to be an equation like your question suggested?

math
so the $72.09 represents 70% of the original price .7x = 72.09 x = 72.09/.7 = $102.99 check by taking off 30% of that

Math
you would have 6 equal surface areas 6x^2 = 24 x^2 = 4 x = √4 = 2

Math
length of side of the larger --- x length of side of the smaller -- y x+y = 5 So what do we see? We see 4 side faces of the larger = 4x^2 we see 4 side faces of the smaller = 4y^2 If we look straight down, we see a small face on top of the large face exposing the edge of the l...

Math
Since you already have the second part, let's work on the number of pennies , dimes and quarters we have to make $5.98 number of pennies -- x number of dimes ---- y number of quarters -- 52-x-y x + 10y + 25(52-x-y) = 598 x+10y + 1300 - 25x - 25y = 598 -24x - 15y = -702 8x ...

Algebra
amount into lower rate account --- x amount into higher rate account --- 8000-x .04x + .07(8000-x) = 480 4x + 7(8000-x) = 48000 4x + 56000 - 7x = 48000 -3x = -8000 x = 8000/3 = 2666.67 amount into CD = $2666.67

Algebra 1
Since F lies on DE, all we need is the equation of DE We don't even need F slope DE = (-2-2)/(-3-3) = 2/3 so y = (2/3)x + b but (3,2) lies on it, so 2 = (2/3)(3) + b b = 0 y = (2/3) x is the equation check: F is the origin (0,0) which satisfies y = (2/3)x A rather strangel...

Algebra 1
#1 and #2 ok #3, I agree with you, there is little that can be done All I could see is to divide top and bottom by 2g #4 ok #5, careless error, 2/2p = 1/p , not p #6 you have a common denominator, so add them 8m^2/(4m^5) = 2/m^3 #7, according to BEDMAS, division is done in the...

Math
if arithmetic, then 8 - (5+x) = (1+2x) - 8 8 - 5 - x = 1 + 2x - 8 -3x = -10 x = 10/3 check: terms are 25/3 , 8 , 23/2 or 25/3 , 24/3 , 23/3 which is an AS

Math
Sum(all terms) = a/(1-r) = 200/(1/2) = 400

statistics
Tools like this below replace tables traditionally found at the back of textbooks http://davidmlane.com/hyperstat/z_table.html enter your mean and sd, click on "above" for "exceeds 0.83" and enter the data to get .1587 ,or .159 correct to 3 decimals

College Algebra
Your last one 3/(x-4)=7/(x-8) is the easiest of the three equations just multiply each side by (x-4)(x-8) , which is sometimes called "cross-multiplying" 7(x-4) = 3(x-8) 7x - 28 = 3x - 24 4x = 4 x = 1

College Algebra
z^2 +iz -(5+i) = (2-5i)^2 + i(2-5i) - (5+i) = 4 - 20i + 25i^2 + 2i - 5i^2 - 5 - i = 4 - 20i - 25 + 2i + 5 - 5 - i = -21 - 19i

Math
value = 84000(.8)(.9)^4 = ....

College Algebra
(-5 - i)/(3 - 3i) = (-5 - i)/(3 - 3i) * (3+3i)/(3+3i) = (-15-15i -3i -3i^2)/(9 - 9i^2) = (-15 - 18i + 3)/(9 + 9) = (-12 - 18i)/18 = -2/3 - i (-5/2)i / ((-1/5)i ) = (-5/2) / (-1/5) = (-2/5)(-5/1) = 2 (-2i)^3 = -8i^3 now i^3 = (i^2)(i) = -i so -8i^3 = -8(-i) = 8i I do not unders...

College Algebra
expand it 3.14 i - 3i^2, but i^2 = -1 = 3.14 i + 3 or in the form a+bi 3 + 3.14 i

algebra
multiply both sides by (x+7)(x+3) , some people call it cross-multiplying 5(x+3) = 3(x+7) 5x + 15 = 3x + 21 I will let you finish it from here.

Math
looks like a geometric series with a = 3 r = 2 sum(n) = a(r^n -1)/(r-1) 765 = 3(2^n - 1)/1 255 = 2^n -1 256 = 2^n 2^8 = 2^n n = 8 there are 8 terms

math
1st times 2 8x + 18y = 20 5x + 18y = 19 subtract them 3x = 1 x = 1/3 sub x = 1/3 into the 1st and solve for y to get y = 26/27

Math
yes, good job however, you should reduce 26/56 to 13/28

decimals
so the number would look like 12.ab given: a+b = 9 b is odd, a is even, b>a easy to see that a=4, b=5 or a = 2 , b = 7 or, if we count 0 as even a = 0 , b = 9 12.45 12.27 12.09

MATH
prob(pink) = 4/14 = 1/7 prob(not pink) = 1 - 1/7 = 6/7

Math
all these are standard angles for which you should know the trig ratios cos 180 = -1 , look at the cosine curve sin 90 = 1 , look at the sine curve cot 45 = 1/tan45 = 1/1 = 1 , look at your 45-45-90 triangle csc 30 = 1/sin30 = 1/(1/2) = 2 , look at the 30-60-90 triangle sec 24...

calculus
I assume you meant f(x) = x √(10 - x^2) and not the way you typed it Of course the function would only be defined for -√10 ≤ x ≤ √10 f' (x) = x (1/2)(10-x^2)^(-1/2) (-2x ) + (10-x^2)^(1/2) = (10 - x^2)^(-1/2) [ -x^2 + 10-x^2] = (10-2x^2)/ͩ...

Algebra/can you ck my answer
correct remember , this would be statistical probability

Precal, please help asap!
let's use the sine law ... sin B/34 = sin 117°/42 sin B = 34sin117/42 = .72129... B = 46.2° or by the CAST rule B could be 133.8° But, that would mean the angle has 2 obtuse angle, which is not possible so angle B = 46.2° and there is only one triangle poss...

maths
nasty and tricky the way you typed it did you mean: 3^(n-1) = 2^(n+1) ?? I sure hope so, and will assume that. take log of both sides log [3^(n-1) ] = log [2^(n+1) ] (n-1) log3 = (n+1) log2 n log3 - log3 = n log2 + log2 n log3 - n log2 = log2 + log3 n(log3 - log2) = log2 + log...

Math (Pre-calc)
1 rotation = 2π(14) or 28π inches In 1 minute he goes 280(28π) inches = 7840π inches In 1 hour he goes 60(7840π) inches = 60(7840π)/12 feet = 60(7840π)/(12*5280) miles = appr 23.3 mph sin(2π/3) = sin 120° = sin 60° = √3/2 ,...

Algebra 1
a) is correct, but you should have brackets around the complete denominator. The way you typed it, it is only divided by (2x+10) x(x + 10)/( (2x + 10)(2x + 9) ) b) So now we have an actual numerical case and let's just follow the same argument you did in a) blacks = 5 whit...

math
rise/run = 400/1600 = 1/4 = tan Ø Ø = appr 14°

math
number of sales = .2(150) = 30 commission = 6(30) = 180

Algebra
Since the positions are specific, this is a permutation, not a combination. number of ways = 33*32*31*30*29 = ...

Albebra
both numbers 2's ----> 22 less than 6 ----> 11 12 13 14 21 22 23 31 32 41 total = 10 , (not counting 22 twice) prob of your event = (36-10)/36 = 26/36 = 13/18

Albebra
that would simply be C(4,1) * C(13,5) / C(52,5) = 5148/2598960 = 99/49980 = 33/16660 = appr .00198 Note, I included the royal flush in the above, you did not say anything about exclusion. What about other hands that are both a flush and something else? e.g. what about the 4,5,...

Algebra
you want 2 out of the 4 aces prob = C(4,2)/C(52,2) = ....

math help plzzz!!!!!!!!!
-8<1-3(x-2)<13 let's just work on it as it sits -8 < 1-3x+6 < 13 -8 < 7-3x < 13 subtract 7 , (does not affect inequality sign) -15 < -3x < 6 divide by -3 , (switches the < to a > sign) 5 > x > -2 better form: -2 < x < 5

math help plzzz
the easy one first: 2(x+7)-4>5(x-3) 2x + 14 - 4 > 5x - 15 -3x > -25 x < 25/3 for the 1st, I don't know why you put brackets around the left side, since it serves no purpose did you mean 2/(5x) > 7 or (2/5)x > 7 I will assume the last case: mulitply both s...

trig
not enough information to make any distance calculations.

HeLP MATH !!!!
2.903t - 1.98 = 18 2.903t = 19.98 t = 6.88 years or 7 years from 2000 in the year 2007

math
how about cos 66° = 11.3/L L = 11.3/cos66 = appr 28 ft

Math
log7 49(3√(x^5) ) = log749 + log73 + log7 x^(5/2) = 2 + log7 3 + (5/2)log7 x it can't be evaluated unless you give me a value for x

math
You don't need an "angle of elevation formula" Just make a sketch and use your basic trig ratios I see it as tan Ø = 350/1000 = .35 Ø = appr 19.26°

hectorr
Why do you call this a fractional equation ? I see no fraction in the equation. 3[2x-(x+7)]=5(x-3) 3[x-7] = 5x - 15 3x - 21 = 5x - 15 -2x = 6 x = -3 check: if x = -3 LS = [3(-6 - 4] = 3[-10] = -30 RS = 5(-6) = -30 = LS my solution is correct.

trig length
Make a sketch to see that sin 69° = 603/L L = 603/sin69 = appr 562.95 m

6th grade math
a) let x=0 is 4(0) - 5 < 3 -5 < 3 ???, YES ... d) let x = 4 is 4(4) - 5 < 3 16 - 5 < 3 11 < 3 ??? , NO do the others the same way

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