Posts by Reiny
Total # Posts: 40,977

algebra 1
You did not state a question, but I assume you want to find the amount. you have P = 3000 i = .065 t = ???? (you did not give me that) so just replace the t in amount = 3000(1.065)^t , evaluate and you are done. 
math
3 books and 2 pens worth RM135 while 2 books and 3 pens worth RM 140. Calculate the price for each item. 3b + 2p = 135  times 3 > 9b + 6p = 405 2b + 3p = 140  times 2 > 4b + 6p =280 subtract them: 5b = 125 b = 25 sub back into one of the first equations to get p 
Finance
In the standard compound interest formulas, the payment is made at the end of the month. So I will consider today's payment to be a down payment. Balance owing = 38500690 = 37810 let the monthly rate be i the number of payments = 68 690( 1  (1+i)^68)/i = 37810 There is ... 
Math
yes 
Trig
Look up how to find the area of a triangle using Heron's Formula. Once you have the area in square feet, multiply that by 3. 
Math 6th grade
The first place can be filled by 4 different flags, leaving 3 flags that go go in the second spot, leaving 2 flags that can go in the third spot, leaving you with 1 flag for the last spot, so, the number of ways = 4*3*2*1 = 4! = 24 
math
since ?961 = 31 , see https://www.jiskha.com/display.cgi?id=1531557433 
math
Using the following dinky 1980's style program in GWBASIC 10 for a = 1 to 30 20 for b = 1 to 30 30 for c = 1 to 30 40 if sqr(a*a+b*b+c*c) = 31 then print a,b,c 50 next c 60 next b 70 next a if got the following: 5,6,30 < Steve's answer 6,14,27 6,21,22 14,18,... 
math
What was asked for? the only thing you can really do is give an approximation, the was it sits it is a real number in exact form 
MATH  circles, circles, circles
A circle can cut another circle in at most 2 places. So any new circle cuts Think along the lines of the "handshake" problems 2 people can shake hands in 1 way , C(2,2) 2 circles can intersect in 2 ways >2x1 = 2 3 people can shake hands in 3 way , C(3,2) 3 ... 
Math
certain speed  x mph slower speed  x6 mph time at certain speed = 56/x time at slower speed = 56/(x6) 56/x + 56/(x6) = 16 multiply each of the 3 terms by x(x6) you will get a quadratic, according to my definition, x > 6 , so reject any invalid answers after you ... 
SAT math
r(n) = (n7)[(n+1)7][(n+2)7] r(1) = .... wherever you see an n, replace it with 1 r(1) = (17)[(1+1)  7][(1+2)  7] just work it out. Watch the order of operation, let me know what you get. 
Math
If you see two or more ordered pairs with the same x value but different y valued, then the relation is NOT a function, so what can x not be ?? e.g. suppose x = 1 , then we would have (1,3) and (1,4). That would be a nono so x ? 1 What other values of x have that ... 
7 math
I count 8 variations of this question that you have now posted. You have been given answers by Steve, Ms. Sue, and bobpursley. What are you looking for ?? 12xyz and 6xy are both terms there are 15 different factors of 12xyz , 12, x, y, z, 12x,..... there are 7 different ... 
Math
number of screws  x number of pegs  2x number of nails  x3 x3=15 > x=18 so he used 36 pegs 
MathSine wave function
Our equation should have the form: h = a sin k(t  Ø) + d since the range of the up/down (ud) is 50 cm a = 25 It dows 5 ud's in 15 seconds, so we have a period of 1 ud/5 sec then 2?/k= 3 > k = 2?/3 so far we have h = 25 sin (2?/3 t) + 100 we also have to move ... 
Math
1/3  2/3 = 1/3 2/9  1/3 = 1/9 , so it is NOT arithmetic 1/3 ÷ 2/3 = 1/2 2/9 ÷ 1/3 = 2/3 , so it is NOT geometric let's change them to ... 2/3, 1/3, 2/9, 1/6 , .... = 2/3, 2/6, 2/9, 2/12, .... = 2/(3*1) , 2/(3*2) , 2/(3*3), 2/(3*4), .... mmmmhhhh? 
Math
Key concept: they will have travelled the same distance time taken by the slower train  t hours time taken by the faster train  t2 hrs 125(t2) = 75t solve for t , sub into either 75t or 125(t2) 
Math
total  x son gets x/3 leaves 2x/3 for the 4 daughters so 2x/3 ÷ 4 = 2x/12 = x/6 each daughter gets 1/6 of the total check: 1/6+1/6+1/1+1/6+1/3 = 1 
Math
width  x m length = x+1 m area = x(x+1) x(x+1) = 6 expand, arrange in the usual quadratic form, and solve. I assume you know how to solve basic quadratics, or else you wouldn't have these types of problems. 
Quadratic Equations
For two equal roots, the discriminant has to be zero, ... b^2  4ac = 0 16  4(3)(m) = 0 16 = 12m m = .... For no real roots, b^2  4ac < 0 , so .... 
Quadratic Equations Word Problem
length including border = 12 + 2x width including border = 8 + 2x area including border = (12+2x)(8+2x) = ..... area of just the pool = 12(8) = .... the difference would be the area of the border. then (12+2x)(8+2x)  12*8 =44 simplify and solve for x I assume you know how to ... 
geometry
Carefully study this example then adapt it to your particular problems. They do a good job of outlining the steps. I suggest you print out these steps, then follow them https://patch.com/newjersey/wyckoff/findorthocenterofatrianglegeometry_eb93cdab 
Calculus
What part of the answer I gave you on Wednesday to the same question did you not like ? https://www.jiskha.com/display.cgi?id=1530696164 
negative numbers 6th grade
Good grief, this is the same type as the one I just answered for you. Just follow the same steps. 
negative numbers 6th grade
first change those silly fractions to useful fractions 9(5/3)÷(10/3) = 9(5/3)(3/10) = 9/2 
probability
So there are a total of 20 games, of which they win 13 so prob(wind) = ..... 
math, algebra
Kenny, how about this given A > B , e.g. A = 10, B = 3 then what is BA ?? would it not be 7 then, then for B(BA) > 0 , B would have to be negative, so B ? 3, but B = 3 will work and for the above example AB < 0 , so I and III are both correct how about letting ... 
Math
I have a feeling James meant to say: "Mabel bought some notepads for $56. If she had been given a discount of 30% , she would be able to buy 40 notepads more. Let the original price be x Number of notepads bought when paying $56 = 56/x discounted price = .7x Number of ... 
Math
The way it stands: 4 times the length of 18 ft, 4 inches, then subtract 3 ft for the doorway. Multiply that by 1.69 more realistic: Will there be any cutoff waste ? What happens it you can only buy the trim in 8 ft lengths? This question is much too simplistic. 
algebra
Did you notice that two of the points have the same y value of 20 so the vertex must lie on x = 1 midway between the two x's , (because (2 + 4)/2) = 1 ) So, let the quadratic be y = a(x1)^2 + c for the point (0,4) 4 = a + c for the point (4,20) 20 = 9a + c subtract ... 
algebra
I will assume you are solving. 8y=7+14x > 14x  8y = 7 18y2=7x > 7x + 18y = 2 I suggest multiplying the 2nd by 2, then subtracting them. That will eliminate the x's , then solve for y. You know what to do next. 
Maths
in one minute the minute hand has moved 360/60 or 6° in one minute the hour hand has moved (360/60) ÷ 12 = .5° so the angle between them has changed by 6.5 = 5.5° = 5° 30' 
Calculus
Did you make your sketch? then Area (or distance) = (1/2)(.3)(0 + 24.5) + (1/2)(.7)(24.5+27.8) + (1/2)(.6)(27.8+28.3) + (1/2)(.4)(28.3+29.0) = .... I will let you do the arithmetic. 
Math
They are the same thing. e.g. suppose there are 2 possible outcomes to some experiment, A and B and prob of event A is 5/19 then the prob of B is 1  5/19 = 14/19 odds in favour of event A = (5/19) ÷ (14/19) = (5/19)(19/14) = 5/14 or 5 : 14 or odds in favour of event A... 
probability with casework
Damon, if we follow your interpretation, the outcomes would be dddd dddc  (2/3)(2/3)(1/3) ddcd ddcc  (2/3)(1/3)(1/2) dcdd dcdc  (1/3)(1/2)(1/3) dccd dccc  (1/3)(1/2)(1/2) then there would be 4 outcomes that end with a coin, for a total of 4/27 + 1/9 + 1/18 + 1/12 = ... 
probability with casework
Let D be the outcome of a die at the end of a turn C be the outcome of a coin at the end of a turn Make a tree diagram we start with D we have either a D or a C at the end of the first toss, two branches from the D, we have a D or C at the end of the 2nd toss (the beginning of... 
Math
Read carefully, the wire is attached 40 ft from the top, so the wire is attached 110 ft above the ground. So now it becomes very simple, a rightangled triangle with base angle of 40°, and an opposite side of 110 ft. We want the hypotenuse h, so sin40° = 110/h solve ... 
Algebra
for the zeros of 2x(x+5)^28x 2x(x+5)^28x = 0 2x( (x+5)^2  4) = 0 x = 0 or (x+5)^2 = 4 x = 0 or x+5 = ±2 x = 0, 3, 7 proof: http://www.wolframalpha.com/input/?i=solve+2x(x%2B5)%5E28x+%3D0 I have no idea where you got your answers from, but they are not the zeroes ... 
Pure maths
Why did you post this? Could you not do .... https://www.google.ca/search?source=hp&ei=lAk5WeqNJLJ5gK9qqWICg&q=199%2B8799%2B687997345852&oq=199%2B8799%2B687997345852&gs_l=psyab.3...1775.1775.0.3547.3.2.0.0.0.0.176.176.0j1.2.0....0...1c.2.64.psyab..1.1.350.6..35i39k1.351.... 
Maths
after giving .6x to his brother, he has .4x left he gives half of those to the cousin. So he has .2x left .2x = 36 x = 180 
math
simplify (9/12)(8/11) 
Math
I read that as 14 8/15 m and 4 2/3 m , 14/8/15 makes little sense. P = 2L + 2W 14 8/15 = 2(4 2/3) + 2W 218/15  28/3 = 2W 2W = 26/5 W = 13/5 m or 2.6 m btw, metric units of measurement usually aren't stated as fractions like that, it would defeat the beauty and purpose of ... 
MATH
?8 = ?(4*2) = ?4*?2 = 2?2 
Quadratics
For the equation ax^2 + bx+ 9 = 0 to have only one solution, (the parabola touches the xaxis at one point only) , the discriminant has to be zero, that is b^2  4a(9) = 0 b^2 = 36a a = b^2/36 Also MsPi suggested subbing in the given point (1,25) 25 = a(1)^2 + b(1) + 9 a+b = ... 
Trig
I made a sketch saw that I had a triangle with sides 36 and 27 and a contained angle of 116° So, using the cosine law: let the distance between them be x x^2 = 36^2 + 27^2  2(36)(27)cos116 = 2877.19... x = appr 53.64 miles, which agrees with Daniel's answer. 
Mathematics
(4x+3y):(3x+5Y) = 6:7 (4x+3y) / (3x+5Y) = 6/7 28x + 21y = 18x + 30y 10x = 9y substitute y = 10 and solve for x 
geometry
Ok with x = 8 BUT, it asked for the length of RT and NQ if x = 8, RT = 7x5 = 56  5 = 51 notice that NQ = 5x+11 = 40+11 = 51, the same as required So your choice would be b) 
Math
consider 12:00 am , the hands will coincide. In on hour the minute hand makes one rotation, or 2?r inches = 2?(12) or 24? inches in the same time the hour hand will make 1/12 of a rotation. distance of hour hand = (1/12)(2?)(9) = 3?/2 inches So the difference = 24?  3?/2 = 45... 
math
charge = 5 + .75(k  4), where k is the number of kilometres. 43.25 = 5 + .75(k  4) solve for k 
pemdas
which I did 
pemdas
I read that as: 2/6 + (1/2)^2 + 1 = 1/3 + 1/4 + 1 = 4/12 + 3/12 + 12/12 = 19/12 
Math
xy^2 = 1 x(2y)dy/dx + y^2 (1) = 0 dy/dx = y^2/(2xy) at (1,1) , dy/dx = (1)^2/(2(1)(1))= 1/2 =  1/2 Now you have the slope and the given point. Find the equation of the straight line, using your method of choice. 
math
I will find the payment for the first case: let the payment be P i = .09/12 = .0075 n= 12(22) = 264 P(1  1..0075^264)/.0075 = 175000 P = .0075(175000)/(1  1.0075^264) = $1524.56 Now the new rate is said to be 10% repeat the above process, them compare the payments take the... 
Math
Very good, I agree with all your answers 
Rotations
I don't know at what level you are working at, but if you are into matrices, here is an excellent video that not only develops the rotation matrix but actually uses a 90° rotation as an example. https://www.youtube.com/watch?v=OYuoPTRVzxY If you don't know what a ... 
Math
I agree with your answers, good job 
math
original amount  x spent on food = 3x/5, leaving her with 2x/5 she spends 1/2 of that on a book, leaving her with (1/2)(2x/5) or x/5 so x/5 = 32 x = .... 
maths
The way you typed it, it is false. It needs brackets, but the number of variations to place those brackets is too great for me to start guessing what you meant. e.g. did you mean : tanx + (secx 1)/(tanx  secx)+1 = (1+sinx)/cosx or (tanx + secx 1)/(tanx  secx+1) = 1+sinx/... 
Geometry
I have my doubts that your teacher would use a notation or a concept that was never taught to you. What does your text say? Did you not attend your classes ? 
Geometry
I am not familiar with your notations. e.g. • T<3,6> ????? 
calculus2
Let a circle x^2 + y^2 = r^2 be rotated about the xaxis to create the sphere so we need volume = ?? y^2 dx from r to r or volume = 2?? y^2 dx from 0 to r because of the symmetry = 2?? r^2  x^2 dx from 0 to r = 2? [r^2 x  (1/3)x^3 ] from 0 to r = 2? (r^3  r^3/3) = 2?(2/3) ... 
Algebra
C(29,6) or ??? ways 
math
27 miles/1 hour = 27(5280) ft / (60(60))sec = 142560/3600 ft/s = 198/5 ft/s or 39.6 ft/s So if the cyclist goes 39.6 ft in 1 second, in 2 seconds he/she goes ...... 
Vectors
direction vector of AB = (3, 6, 6) < Steve had (3,4,6), a slight arithmetic error. x = 1 + 3t y = 2 + 6t z = 3  6t direction vector CD = (3,3,1) x = 3  3s y = 5  3s z = 3 + s setting the x's equal > 1+3t = 33s or 3t + 3s = 2 setting the y's equal... 
Calculus
h(t) = 0.8cost + 0.5sin2t v(t) = .8sint + .5cos(2t)(2) = .8sint + cos(2t) = .8 .8sint + cos(2t) = .8 time 10 8sint  10cos(2t) = 8 4sint  5cos(2t) = 4 , but cos(2t) = 2sin^2 t  1 4sint  5(2sin^2 t  1) + 8 = 0 4sint  10sin^2 t + 5 + 8 = 0 10sin^2 t  4sint  13 = 0 ... 
Math
Amount = principal(1 + i)^n your principal is 1400 i = .06 n = 8 + 5/12 = 101/12 you will definitely need a calculator, what answer did you get ? 
MATH
2?[((6561/4)+2430(729/2))((1/4)+(10/3)(9/2))] = 2?[ 1701/4  (17/12) ] = 2? [ 1280/3 ] = 2560/3 ? I have a feeling you messed up in the subtraction of the terms in the second bracket. 
geometry
Since you told me the two angles are equal .... 14b  22 = 11b solve for b 
MATH
If you meant (?4)(x) , then it is indeed 2x if you meant ?(4x) = 2x, then it is true only for x=0 and x=1, it is false for all other values of x let's solve ?(4x) = 2x square both sides: 4x = 4x^2 4x^2  4x = 0 4x(x  1) = 0 so x = 0 or x = 1 
MATH
I read that as: Find the intersection of y=?4x and y=x^2/4 the x^2/4 = ?(4x) x^2 = 4?(4x) square both sides: x^4 = 16(4x) = 64x x^4  64x = 0 x(x^3  64) = 0 x=0 or x = 4 if x = 0, y = 0 if x = 4 , y = ?16 = 4 the two curves intersect at (0,0) and (4,4) (notice the two points ... 
Math
Interpretation: I will see 4 cm of framing all around. Add 4 cm to each end of the width > width of frame = 32+8 = 40 cm length of frame = ..... area = length x width = .... 
Data
The prob of drawing any specific number is 4/36 = 1/9 expected return on one game = expectation(2) + expectation(3) + ... + expectation(10) = (1/9)(2) + (1/9)(3) + ... + (1/9)(10) = (1/9)(2+3+4+...+10) = (1/9)(45) = 5 so it will cost 20($5) or $100 to play the 20 games the ... 
Maths (money and finance)
What is 2500(1.09)^3 ? 
math
It would really help it you had put your answers with each of the questions. I am NOT going to keep scrolling up and down, trying to match your choices with the question, sorry. 
Math
The question was , "How many more litres are needed to fill it? the tank holds 36 litres, we both have that it already holds (1/6)(36) or 6 L 21 more are added, so now we have 27 L, which is 3/4 of the tank, so 9 more litres are needed to fill it. 
Math
Let the capacity of the tank be x litres (1/6)x + 21 = (3/4)x solve for x to find the capacity of the tank. I am sure you can take it from there, e.g. 1/6 of the tank is ... then 21 litres were added, how many more are needed to fill it ? 
Vectors
I set the x and y equations equal to each other to get: 4t  s = 11 t + 3s = 7 solving these, I got t = 2 and s = 3 which verified in the z value of 0 for both lines. So sub s=3 and t = 2 and it the corresponding lines and you get (x,y,z) = (5,5,5) 
Mathtrig
small typo: 2ndF cos (/13) should have been 2ndF cos (1/3) 
Mathtrig
by arcsec(3) you are looking for an angle Ø so that secØ = 3 or cosØ = 1/3 we know that the cosine is negative in quads II and III so Ø = 180°  70.53° OR Ø = 180° + 70.53° Ø = appr 109.5° or appr. 250.5° I ... 
Math
I assume you are proving this identity to be true. What have you done so far? 
Math
from 8x + 8y = 18 x + y = 9/4 x^2  y^2 = (x+y)(xy) , using the difference of squares 3/8 = (9/4)(xy) xy = (3/8) / (9/4) = (3/8)(4/9) = 1/6 so 2x  2y = ....... 
math
let the total be x solve : (2/3)x + (3/4)(1/3)x + 3 = x 2x/3 + x/4 + 3 = x suggestion: times 12 take it from there 
math
Assuming your equations are: 2a + 12b = 7 3a + 2b = 7 multiply the 2nd equation by 6 to get 18a + 12b = 42 then subtract the 1st, that will eliminate the b, and go from there 
Geometry
What do you call a triangle that has 2 equal sides ?? 
Vectors
You are right, at closer look I now see 1/14, with my failing eyesight I saw 1 1/14, which I changed to 15/14 so picking it up from ( (6)(1) + (2)(p) + (3)(2) ) = 7?(5 + p^2)(15/14) should have been ( (6)(1) + (2)(p) + (3)(2) ) = 7?(5 + p^2)(1/14) and then 2p = (1/2... 
Vectors
error in finding b b = ?(5+p^2) you need the dot product a dot b = a b cosØ ( (6)(1) + (2)(p) + (3)(2) ) = 7?(5 + p^2)(15/14) 2p = (15/2)?(5+p^2) 4p = 15?(5+p^2) 16p^2 = 225(5+p^2) 16p^2 = 1125 + 225p^2 209p^2 = 1125 No real solution, so no value of p ... 
Calculus
for your given example , dy/dx = 2x/(3y^2) so you set that equal to 4 2x/(3y^2) = 4 2x = 12y^2 x = 6y^2 now plug that back into the original y^3 = x^2 y^3 = 36y^4 36y^4  y^3 = 0 y^3(36y  1) = 0 y = 0 or y = 1/36 if y = 0, the x = 0 < **** if y = 1/36, then x = 6(1/... 
PreCalc
well, x^27x8 factors to (x8)(x+1) = 0 So the sides are (x8) and (x+1) So what are your thoughts on this? 
math
Glad you told me. Did you have a question? 
Calculus
Exact answer: volume = ? ? (sec^2 x) dx from 0 to ?/3 = ? [ tanx ] from 0 to ?/3 , since the derivative of tanx = sec^2 x = ?( tan ?/3  tan 0) = ?3 ? In your question, we have a case where the solution to find an approximate answer is more difficult than the actual solution ... 
Vectors
When s = 0 , we get the point (2,9) when t=3, we get the point (0,8) Using your intersection point that you already found, find the lengths of the 3 line segments using the "distance between two points" formula. To find the area, use Heron's Formula, which says ... 
Math
https://www.google.ca/search?q=Find+the+probability+that+you+throw+a+dart+and+land+in+the+region+labeled+%22G%22&rlz=1C5CHFA_enCA690CA690&tbm=isch&source=iu&ictx=1&fir=mEy256_2SOKM%253A%252COTpziutDtOkUGM%252C_&usg=__hp1tFrIfMKrhg0itf5IMc5zxeBE%3D&sa=X&ved=... 
Math
Did you make your sketch? It should show an angle of 108° between XY and YZ by the cosine law: XZ^2 = 115^2 + 75^2  2(115)(75)cos 108° XZ = ..... or vector XY = 115(cos42, sin42) = (85.46165... , 76.95...) vector YZ = 75(cos30 , sin 30) = (64.9519.. , 37.5) XZ = (... 
math
It is C(52,5), trust us another approach: suppose you had to pick them in a specific order, then the number of ways would be 52x51x50x49x48 which is the same as 52! / 47! or P(52,5) But the order does not matter, as you said, so we have to divide by 5! the number of ... 
Math
Here is how I do these: sin^1 (.65) I know from CAST that the sine is positive in quadrants I and II so 2ndF sin .65 gave me .70758... That is my quad I angle, so ?  .70758 or 2.434 would be the quadrant II angle of course adding/subtracting 2? will yield other answers: my ... 
algebra
Prob(boy from 7th grade) = 7/10 Prob(boy from 8th grade) = 2/4 = 1/2 Prob(2 boys) = (7/10)(1/2) = 7/20 
calculus2
Let me know what you get, they probably want an "exact" answer. 
calculus2
Notice that at the intersection of the two curves, x = ?/3 and we have symmetry, so we can take the area from 0 to ?/3, then double area = 2? (8cosx  sec^2 x) dx from 0 to ?/3 = 2[8sinx  tanx] from 0 to ?/3 = 2(8sin ?/3  tan ?/3  (8sin 0  tan 0 ) = ...... your turn 
Algebra
The simplest ratio of sides of a rightangled triangle is the 3:4:5 ratio so we have 9:x:y, clearly x = 12, and y = 15 check: 9^2 + 12^2 = 15^2 , YES