Friday
July 31, 2015

Posts by Reiny


Total # Posts: 30,509

Math 222
-5x+2y=16 y = 2x+7 Tika, Doesn't the 2nd equation tell you what the value of y is ?? Just replace the y in the 2y of the first equation with the value of y in the second. Give it a try, it is really easy. Let me know what you got.
April 27, 2015

Math
since sinØ = opposite/hypotenuse = -3/5 you should recognize the 3-4-5 right-angled triangle. You are also told the the angle (or triangle) is in the I, II, or IIIrd quadrant. But isn't sinØ negative only in III of those given? so x = -4, y= -3 thus tan&...
April 27, 2015

Math 222
solve each one separately if you want 2x-1 ≥ -3 2x ≥ -2 x ≥ -1 4x+5 ≥ -19 4x ≥ -24 x ≥ -6 but they are connect with AND, so ... x ≥ -1 AND x ≥ -6 Now thing about, what numbers are both greater than or equal to -1 AND -6 Place the...
April 27, 2015

MATH
This question makes little sense to me. Are the times given based on how long each one could row the boat? Why would you let Dale row for 10 minutes, if Abby ran do it it 1 minute? Anyway, taking your data at "face-value" .... A=1 B=2 C=5 D=10 I would use A for all ...
April 27, 2015

Math 222
rate charged by first mechanic --- x rate charged by second mechanic -- y "sum of their rates is 165" ---> x+y = 165 "first mechanic worked 10 hours" ---> 10x "the second mechanic worked 5 hours" --- 5y "Together they both charged a ...
April 27, 2015

Math 222
-2x + 9y = 3 -3x - 4y = 22 first equation times 3 -6x + 27y = 9 second equation times -2 6x + 8y = -44 add the new equations: 35y = -35 y = -1 sub back into original -2x + 9y = 3 -2x - 9 = 3 -2x = 12 x = -6 x= -6 , y = -1 of course you should realize that there are many other ...
April 27, 2015

Math 222
Both our last two replies posted at the same time. NO, both numbers are NOT 12 Look at your question, it said one is 23 less than the other, how can they be both 12 ? This is why definitions of your variable are so important. I defined by smaller as x, so it is 12 I defined by...
April 27, 2015

Math 222
yes, that would be one of the answers, remember it asked for two answers. You should verify your answers against the original conditions to eliminate any doubt
April 27, 2015

Math 222
smaller number --- x larger number ----- x+23 x + x+23 = 47 easy to solve....
April 27, 2015

math
How did you decide it was B ?
April 27, 2015

Statistics PLEASE HELP
prob(both defective) = (2/8)(1/7) = 1/28 prob(at least one good) = 1 - 1/28 = 27/28
April 27, 2015

math
True , the surface area of similar objects is proportional to the square of the sides (1/2)^2 = 1/4
April 26, 2015

Math
multiply each term by 3 3y + 9 = x x - 3y - 9 = 0
April 26, 2015

calculus check
correct
April 26, 2015

Calculus
how about L'Hopital's Rule limit = 7/( (1/2)(x+4)^-(1/2) ) = 14(√(x+4) = 14(2) as x---> 0 = 28
April 26, 2015

Calculus
number ' (t) = 100e^t + 75t number (t) = 100e^t + (75/2)t^2 + c assuming at opening (t=0) no people were in the zoo, 0 = 100e^0 + (75/2)(0) + c c = -100 number(t) = 100e^t +(75/2)t^2 - 100 so when t = 2.666.. (at 9:40 am) number(2.666...) = 100e^2.6667 + 37.5(2.666..) - ...
April 26, 2015

Analytic Geometry
slope of 1st line = (-2-6)/(5+1) = -8/6 = -4/3 slope of 2nd line = (7+4)/(1-3) = -11/2 angle made by 1st line = tan^-1 (-4/3) = 126.87° angle made by 2nd line = tan^-1 (-11/2) = 100.30° angle between them = 26.565° or tan(angle between) = (-4/3 + 11/2)/(1 + (-4/3...
April 26, 2015

algebra
9(x^2 - 8x + ....) + 4(y^2 + 4y + ....) = -124 9(x^2 - 8x + 16) + 4(y^2 + 4y + 4) = -124 + 144 + 16 9(x-4)^2 + 4(y+2)^2 = 36 divide each term by 36 (x-4)^2 /4 + (y+2)^2 /9 = 1
April 26, 2015

Math
18sin^2 Ø +3cosØ - 17 = 0 18(1- cos^2 Ø) + 3cosØ - 17 = 0 18 - 18cos^2 Ø + 3cosØ -17 = 0 18cos^2 Ø - 3cosØ -1 = 0 (6cosØ + 1)(3cosØ - 1) = 0 cosØ = -1/6 or cosØ = 1/3 Ø = 1.738.. or &...
April 26, 2015

math
Sales of the $12000 which are over $5000 = $7000 so total commission = .06(5000) + .12(7000) = ..
April 26, 2015

math
Let the side parallel to the highway be y ft let each of the other two sides be x ft So 2x + y = 680 y = 680-2x area = xy = x(680-2x) = 680x - 2x^2 which is a parabola opening downwards, and you want its vertex. Since you are doing this type of question, you must have learned ...
April 26, 2015

calculus
integral of (3x^2+2x+4) dx f(x) = x^3 + x^2 + 4x + C given (f(1) = 10 10 = 1 + 1 + 4 + C C = 4
April 26, 2015

Calculus
need their intersection: x^2 - 4x + 3 = x + 4 x^2 - 5x - 1 = 0 was hoping for "nicer" values, but anyway.... x = (5 ± √29)/2 height of our region within those x values = x+4 - (x^2 - 4x + 3) = 1 + 5x - x^2 area = ∫(1 + 5x - x^2)dx from x = (5-&#...
April 26, 2015

Math
I will use l for lambda and m for mu Plane1: (x,y,z) = (2,1,1) + l(-2,1,8) + m(1,-3,-9) Plane2: (x,y,z) = (2,0,1) + s(1,2,1) + t(1,1,1) You want the x's, the y's and the z's to be the same 2 - 2l + m = 2 + s + t s + t + 2l - m = 0 , #1 1 + l - 3m = 0 + 2s + t 2s + ...
April 25, 2015

math
use the first two ordered pairs, since we are told the function is linear (2,1) and (4,-2) slope = (-2-1)/(4-2) = -3/2 To hear , " I don't know how to do this kind of stuff" is not a good thing. Finding slope between any two points is fundamental and pretty basic.
April 25, 2015

calculus
let the radius of the water level be r m let the height of the water be h m make a sketch and by similarity: h/r = 6/3 h/r = 2 h = 2r or r = h/2 V = (1/3)π r^2 h = (1/3)π (h^2/4)(h) = (1/12)π h^3 dV/dt = (1/4) h^2 dh/dt so when h= 2 and dV/dt = 12 12 = (1/4)((4)...
April 25, 2015

trigonometry pls help
According to my sketch, sinØ = 28/32 Ø = ... I assume you have a calculator
April 25, 2015

trigonometry pls help
You don't state where Ø is, I will assume it is one of the two equal angles at the base. a) tan 45 = height/18 height = 18tan45 = 18 b) repeat with tan 55 = height/18 c) since area = (1/2)(36)(height) the larger the height, the larger the area. you do the calculations.
April 25, 2015

math
2cos^2 Ø - sinØ -1=0 2(1-sin^2 Ø) - sinØ - 1 = 0 -2sin^2 Ø - sinØ +1 = 0 2sin^2 Ø + sinØ - 1 = 0 (2sinØ + 1)(sinØ - 1) = 0 sinØ = -1/2 or sinØ = 1 case1: sinØ = -1/2 Ø must be in ...
April 25, 2015

math
At the start: number of fives ---- 4x number of tens ----- 3x $140 in fives = 28 notes so he has 4x-28 of the fives left over he also spent 2/5 of his tens, so he has 3/5 of the tens left or he has 3/5(3x) or 9x/5 tens left over (4x-28)/( (9x/5)) = 2/3 12x - 84 = 18x/5 60x - ...
April 25, 2015

math
There are actually 4 solutions, from Jai's: tanØ = 1/2 so by the CAST rule, Ø is in either the first or the third quadrant Ø = 26.6° ---- Jai's answer Ø = 180+26.6= 206.6° if tanØ = 1 Ø = 45° , ----- again, Jai'...
April 25, 2015

Math
1. 78.5° would be the answer if the angle had been acute, but you wanted the angle in the 4th quadrant so Ø = 360 - 78.463 = 281.5° check by taking cos 281.5° 2. Again you want -90 ≤ Ø ≤ 90, which would be quadrant I or quadrant IV but for...
April 25, 2015

Math
From the equation I can tell that Diane started with $450 , (x=0) and her account increased by $30 per week
April 24, 2015

6th Grade Math Help Please
A rational number is a number which can be expressed exactly as a fraction or a ratio. so your coordinates would NOT contain any square roots.
April 24, 2015

algebra 2
yup, correct again (instead of 30x2power we can type 30x^2 on here)
April 24, 2015

algebra 2
I agree, good job
April 24, 2015

Interest
what is 10000(1.015)^4 ??
April 24, 2015

maths
In effect for each jump , he gains 1 foot. after 1 jump, he is 39 feet from the top after 2 jumps he is 38 feet from the top ... after 10 jumps he is 30 feet from the top .... after 37 jumps he is 3 feet from the top So on the 38th jump he is at the top, and we will assume he ...
April 24, 2015

math
9th term = a+8d = 12 17th term= a+16d = 28 subtract them 8d = 16 d = 2 sub into a+8d = 12 a = -4 4th term = a+3d = -4 + 6 = 2
April 24, 2015

Algebra
let the time passed since Chelsea left be t hrs So Chelsea went for t hrs Sarah went for t+1 hrs When they meet, they both have covered the same distance, so 75t = 55(t+1) 75t = 55t + 55 20t = 55 t = 55/20 or 2.75 hrs Chelsea went for 2.75 hrs of 2 hrs and 45 minutes Sarah ...
April 24, 2015

Math
4 S's 2 P's 4 I's number of permutations = 11!/(4!4!2!) = 34650
April 24, 2015

Algebra
I really don't know where Steve got his numbers from. Making a sketch I have a triangle with sides 165 and 80 and an angle of 65° between them, so by the cosine law x^2 = 80^2 + 165^2 - 2(80)(165)cos 65° = 22467.87789 x = appr 149.9 miles Using vectors we have (...
April 24, 2015

math
no After taking out any two, you could have the following cases: R W B 4 4 2 4 2 4 2 4 4 3 3 4 3 4 3 4 3 3 let's take the 3 3 4 situation prob of that having happened = C(4,1)xC(4,1)xC(4,0)/C(12,2) = 16/66 = 8/33 The other two cases of choosing 2 different colours = 8/33 ...
April 24, 2015

7th grade math
It says to find the equivalent equation containing no fractions. It did not ask to find the solution, so (2/3)x - 1 = 1/2 multiply each term by 6 , the LCD 6(2/3)x - 6(1) = 6(1/2) 4x - 6 = 3 which is choice A
April 23, 2015

Analytic Geometry
make a sketch label the intersection withe the y-axis as (0,y) I have two similar triangles and by ratios (6-y)/3 = (6+y)/6 18+3y = 36-6y 9y=18 y=2 so the sides of the smaller right-angled triangle are 3 and 4, and I recognize the 3, 4, 5 triangle the other triangle is 6 , 8, ...
April 23, 2015

Math
slope = (4-(-3))/(4-2) = 7/2
April 22, 2015

math
The wording is too nebulous. Are the balls numbered from 1 to 75 ? Are you just asking , "What is the probability of picking a 7, then a 14 , and then a 21 ? That is very straight-forward? Once you have that probability, multiply it by 500.00
April 22, 2015

math
ok, how about you trying some of these. They are rather simple probability question and you should be able to do them. Where are you having your difficulty?
April 22, 2015

math
prob(2reds) = (8/14)(7/13) = ..
April 22, 2015

math
prob(red, then yellow) = (8/14)(6/13_ = ...
April 22, 2015

Algebra IMPORTANT
I see 5 terms, not 3. You will need brackets to identify the terms
April 21, 2015

Math
2 errors error #1 : -1 - (-4) = -1 + 4 = 3 So review your subtraction of integers 2nd error: you can't switch direction in your subtraction your points where (-1,-4) and (0,-1) You started by subtracting the first y from the second y, and then you subracted the second x ...
April 21, 2015

Math
Did you not follow the method I showed you for the same kind of question in your previous post?? Are you just guessing at an answer, hoping some somebody will do it for you correctly? How did you arrive at the answer A ?
April 21, 2015

Math
let's take the first pair: (0,-4) and (1,-3) : slope = (-3-(-4))/(1-0) = 1/1 = 1 (I guess C is wrong) second pair: (1,-3) and (2, -2): slope = (-2+3)/2-1) = 1 mmmhhh? third pair: (2,-2) and (3,-1) = (-1+2)/(3-2) = 1 well, now, what do you think??
April 21, 2015

Algebra-VERY IMPORTANT
we need 2 values which have a sum of 10 how about 6 and 4 x^2 + 10x + 24 = (x+6)(x+4) , k = 24 how about 2 and 8 x^2 + 10x + 16 = (x+2)(x+8) , k = 16 how about -12 and 22 x^2 + 10x - 264 = (x+22)(x-12) , k = -264 etc. an infinite number of different values of k are possible
April 21, 2015

math
Assuming the same rate and the same time: amount/5800 = 720/4500 amount = 5800(720/4500) = 928
April 21, 2015

Math
To be a GS , any number divided by its previous one must produce the same result first pair: -6/9 = -2/3 2nd pair: 4/-6 = -2/3 3rd pair: -8/3 /4 = -2/3 yes!, common ratio is -2/3 you do the 2nd problem.
April 21, 2015

Math
The scale factor is 1 : 64 , not 1 : 64 inches, ratios don't have units It means that 1 inch in the model is 64 inches in reality 1 foot in the model is 64 feet in reality 1 metre in the mode is 64 metres in reality etc x feet in the mode is 20 feet in reality x/1 = 20/64 ...
April 21, 2015

geometry
-2 √15 / (6- √13) = -2 √15 / (6- √13) * (6+√13)/(6+√13) = (-12√15 - 2√195)/(36-13) = -(12√15 + 2√195)/23
April 21, 2015

Math
"the rule is add 4, subtract 1" ---> in effect is adding 3 term(n) = 5 + 3n so term(10) = 5 + 3(10) = 35 Emma is correct
April 21, 2015

calc
in general the inverse of a b c d is 1/(ad - bc) times d -b -c a e.g. 5 4 2 2 inverse is 1/(10-8) times 2 -4 -2 5 = 1 -2 -1 2.5 Apply this rule to your matrix
April 21, 2015

calc
We can only take inverses of square matrices. I see 2 numbers in the first row, but 3 in the second row. Are there supposed to be brackets? Is it i 3 (1+i) - i ??
April 21, 2015

math
let the height be h cm so 2(7h) + 2(5h) + 2(5)(7) = 4.65 cm^2 14h + 10h + 70 = 4.65 24h = negative this question is bogus, once you realize that the area of the base alone would be 35 cm^2, without even considering the other surfaces. How can the total be only 4.65 cm^2
April 21, 2015

MATH
total cost = 1.05(875) = 918.75 so you made 7 payments of 100, leaving you with a balance of 218.75 when the 8th payment is due Penalty is 39 + .1425(218.75) = 70.17 Your wording does not make it clear, on what amount the 14.25% interest is charged. I assumed it would ...
April 21, 2015

Math
Since the time is less than one year, I will use simple interest. R = I/(PT) = 685.13/(6300(270/365)) = appr .147 or appr 14.7% None of your answers match this, but my calculations are correct
April 21, 2015

Math
i = .16/4 = .04 n = 4(2) = 8 amount = 2500(1.04)^8 =3421.42 your textbook still has tables??? how old is this?
April 21, 2015

math
"without the use of tables" ?? - then how about just using a calculator ? ( I am being facetious) Here is the method I actually taught in medieval times, and remember we had no calculators either. http://www.johnkerl.org/doc/square-root.html
April 21, 2015

Math Help
r = (1/16)/(1/32) = 2 term(12) = a r^11 = (1/32) (2)^11 = (1/32)(2048 = 64
April 21, 2015

Math
a+3d = 27 a+6d = 64 subtract them 3d = 37 d = 37/3 a + 3(37/3) = 27 a = -10 term(9) = a+8d = -10 + 8(37/3) = 266/3 check: term(4) = a+3d = -10 + 3(37/3) = 27 term(7) = a+6d = -10 + 6(37/3) = 64
April 21, 2015

Maths, functions
At ground level, h = 0 1+15t-4.9t^2 = 0 4.9t^2 - 15t - 1 = 0 Solve using the quadratic equation, using only the positive solution.
April 21, 2015

algebra
width ---- x length ----y 2x + 2y = 124 x+y=62 y = 62-x xy = 912 x(62-x) = 912 62x - x^2 - 912 = 0 x^2 - 62x + 912 = 0 (x-24)(x-38) = 0 x = 24 or x = 38, then y = 38 or y = 24 the doormat is 24 by 38
April 20, 2015

Maths
Samuel K. Simultaneous ?
April 20, 2015

college algebra
amount of 14% solution --- x amount of 6% solution ----- 28-x solve for x: .14x + .07(28-x) = .08(28) I suggest multiplying each term by 100 to get rid of those pesky decimals
April 20, 2015

Calculus
Let's see what this looks like https://www.wolframalpha.com/input/?i=plot+y+%3D++%28e%5E-x%29%28sin%28x%29%29 f ' (x) = e^-x(cosx) - sinx (e^-x) = 0 for max/min e^-x(cosx - sinx)=0 e^-x = 0 ---> not possible or cosx = sinx tanx = 1 x = pi/4 or -3pi/4 sub that back ...
April 20, 2015

Math
we were given that t = 4 so we had to "freeze" the situation at t = 4 That gave us tan O = 4/25 so we have a right-angled triangle with opposite 4 and adjacent 25. Since we need the secant of that angle and secant = 1/cosine , and cosine = adjacent/hypotenuse, so...
April 20, 2015

Math
let the angle be Ø, so we have tanØ = h/400 h = 400 tanØ dh/dt = 400 sec^2 Ø dØ/dt but dh/dt = 8t 400 sec^2 Ø dØ/dt = 8t dØ/dt = t/(50sec^2 Ø) so for the given case of t = 4 h = 4(4^2) = 64 tanØ = 64/400 = 4...
April 20, 2015

Math
y = (e^x + x)^x I would take ln of both sides ln y = x ln(e^x + x) now use the product rule (dy/dx)/x = x(e^x + 1) + ln(e^x + 1) dy/dx = y(x(e^x + 1) + ln(e^x + 1)) I don't know what kind of simplification you need , but you could sub back the original y value dy/dx = ( (e...
April 20, 2015

Trig
According to my sketch , we have a cosine law problem x^2 = 140^2 +60^2 - 2(60)(140)cos 110° = ...
April 20, 2015

Calculus
Here was my first answer http://www.jiskha.com/display.cgi?id=1429478661 In a subsequent reply you said you were confused. Now you simply repost the same question for a third time. Exactly what did you not understand in my answer?
April 19, 2015

Math
let original piece of material be x by x inches after cut-out, the base will be x-4 by x-4 and the height will be 2 so 2(x-4)^2 = 72 (x-4)^2 = 36 take √ of both sides x - 4 = 6 x = 10 the original piece was 10 by 10 inches
April 19, 2015

Math 10
I see a common factor of 12xy so ....
April 19, 2015

Calculus
look back before reposting
April 19, 2015

Pre-Calculus
Hasn't the boat effectively traveled 9 km north and 8 km west? Don't you have a right-angled triangle with sides 8 and 9 and we have to find the hypotenuse ? Go for it, don't go to decimals btw, I get √145, which cannot be written as a mixed radical
April 19, 2015

7th grade math
I did not answer your question the first time you posted it, since it looks like an obvious "homework dump" The first 4 questions simply require that you sub in the values and test. #5, what happened to the x and to the y value of the original point? -looks like 4 ...
April 19, 2015

Math
Easiest way is to use 2 variables let x be the speed of the boat in still water let y be the speed of the current so going downstream the boat is going x+y mph going against the current it is x-y mph now use your formula, we need t = d/r time upstream = 40/(x-y) time ...
April 19, 2015

Vectors
A point on the line is (-3,-1,-2) and the direction of the line is [-2,5,4] To find the equation of a plane I need another direction vector, using the point (-3,-1,-2) and the other point P(1,3,0) , I get [-4, -4, -2] or we could simply use [2,2,1] since you want the vector ...
April 19, 2015

math
did you make your sketch?? If you follow the standard definition of "bearing", I see it as a cosine law problem solve: x^2 = 5^2 + 10^2 - 2(5)(10)cos 150° ....
April 19, 2015

geometry
I can't follow your description
April 19, 2015

Calculus
I would start by sketching it http://www.wolframalpha.com/input/?i=plot+y+%3D+1+%2B+sin%282x%29%2C+y+%3D+e%5E%28x%2F2%29 So now for the hard part of finding their intersection. The left one is obviously (0,1) How do they expect you to solve 1 + sin(2x) = e^(x/2) ??, Have you ...
April 19, 2015

Trig
I will do it in parts for easier typing sinØ + cscØ = sinØ + 1/cosØ = (sinØcosØ + 1)/cosØ tanØ + cotØ = sinØ/cosØ + cosØ/sinØ = (sin^2 Ø + cos^ Ø)/sinØcosØ = ...
April 19, 2015

Precalculus Trig (Geometry)
So if you place the ellipse with centre at (0,0), we have a=19 and b = 13 , and the equation would be x^2/19^2 + y^2/13^2 = 1 or x^2/361 + Y62/169 = 1 Now if x = 5 25/361 + y^2/169 = 1 y^2/169 = 336/361 y^2 = 157.296... y = 12.54 adding on the 60 m it would be 72.54 m high. ...
April 19, 2015

Precalculus Trig (Geometry)
I would sketch a parabola with vertex at (0,20) opening downwards, and crossing the x-axis at (10,0) and (-10,0) then in vertex form the equation would be y = a(x-0)^2 + 20 = ax^2 + 20 but (10,0) lies on it, so 0 = a(100) + 20 x = -20/100 = -1/5 so we have y = (-1/5)x^2 + 20 ...
April 19, 2015

calc
wow http://www.wolframalpha.com/input/?i=integrate+5%2F%28t%5E3+%2B3%29 What methods have you been taught?
April 19, 2015

Finance
solve for n 3500(1.038)^n = 7000 1.035^n = 2 log both sides, and use log rules n log 1.035 = log 2 n = log 2/log 1.035 = appr 20.15 years
April 19, 2015

algebra
40000(.9)^n < 25000 .9^n < .625 take log of both sides and use log rules n log .9 < log .625 n < 4.46 yrs testing: 40000(.8)^4.5 = 24,897.24 40000(.9)^4 = 26244 4000(.9)^5 = 23619.60 So, I would say in 4 1/2 years
April 19, 2015

math
Now: son's age --- x Norman's age --- 4x Three years ago: son ---- x-3 Norman --- 4x-3 so x-3 + 4x-3 = 49 5x = 55 x = 11 the son is now 11 and Norman is 44 check: 3 years ago, son was 8 and Norman was 41 what is 41 + 8 ??
April 19, 2015

calculate the area of plane figures
I assume you want the area between. you need their intersection: x^2 = 8-x^2 ... x = ± 2 we can use symmetry and just go from 0 to 2 effective height = top curve - bottom curve = 8-x^2 - x^2 = 8 - 2x^2 integrate, and evaluate from 0 to 2
April 19, 2015

math
a) how many red or white balls are there ? b) how many yellow or reds are there ? c) how many non-reds are there ? How many balls are there in the bag in total? Well ??
April 19, 2015

Maths- Please help
Switch to the same units, metres. - good thing we are in metric diameter = 500 mm = 50 cm = .5 m so radius = .25 m height = 10 cm = .1 m volume of flywheel = π r^2 h = π(.25)^2 (.1) = .00625π m^3 mass = 750(.00625π) kg = appr 147.26 kg
April 19, 2015

Math
x/15 + x/10 = 1 multiply by 150 10x + 15x = 150 etc
April 19, 2015

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