Posts by Reiny

Total # Posts: 39,510

geometric progression
given: a= x^-4 ar^7 = x^52 use substitution: (x^-4)r^7 = x^52 r^7 = x^59 r = x^(59/7) 2nd term = ar = (x^-4)(x^59/7) = x^(31/7) matching it with x^t ---> t = 31/7

Math
or: if right angled, then two lines must be perpendicular slope between 1st point and 2nd = 2/3 slope between 1st and third = -1/5 slope between 2nd and 3rd = -3/2 notice that 2/3 and -3/2 are negative reciprocals of each other, thus , yes we have a right-angled triangle

Math - Im soooo lost need help fast
if you have two points (x1, y1) and (x2, y2) the slope = (y2 - y1)/(x2 - x1) OR (y1 - y2)/(x1- x2) so for your first one: (6,5) (3,1) slope = (1-5)/(3-6) = -4/-3= 4/3 OR slope = (5-1)/(6-3) = 4/3 , same result Do the same for #5, be careful with the subtraction of negatives. I...

math
a) is correct b) banks do not lend out money for 4 years at simple interest, they use compound interest. You will have to answer c) first, that is , find the monthly payment c) i = .09/12 = .0075 n = 4(12) = 48 paym = ? 4600 = paym( 1 - 1.0075^-48)/.0075 you should get $114.47...

Math
This is a quadratic. It can only factor over the rational numbers if the discriminant is a perfect square. What do you think?

math
To be a perfect square, the number must be factorable into pairs of equal factors e.g. 144 = 2x2 x 2x2 x 3x3 10 = 2x5 15 = 3x5 20 = 2x2x5 30 = 2x3x5 So the LCM would be 2x2 x 3 x 5 So to pair them up, we will need another 3x5 So the least square divisible by 10,15,20, and 30...

math
smaller number ---- x larger number ----- 2x product means we multiply them, so x(2x) = 98 2x^2 = 98 x^2 = 49 etc

Math
I will guess we are just evaluating these. I will do the first one, you show me how you did the rest 8q + 6 for q = 2 = 8(2) + 6 = 16 + 6 = 22

Business Math
only difference would be in the time fraction for I = PRT 220/365 in the first case, and 220/360 in the second. (I assume my Canadian and the US methods are the same)

math?
You didn't tell us how long he is paying for the trip.

Algebra 2
consider 8^x = 25 take logs of both sides and use your log rules xlog8 = log 25 x = log25/log8 = appr 1.55 so x ? 1.55 test some values: x = 0, 8^0 = 1 which is ? 25 x = -5 , 8^-5 = .0000305.. which is ? 25 we can easily see that all negative values of x will work let's ...

correction = Math
wrong! your answer's ratio would be 5 : 17 which is not 2:5 number of males --- 2x number of females --- 5x 5x - 2x = 12 3x = 12 etc ....

APY-math
let the equivalent annual rate be i daily rate = .031/365 = .000084931 1.000084931^365 = 1+i 1+i = 1.031484143 i = annual = .03148 annual rate = .03148 or appr 3.15% Scott's answer would be the instantaneous rate at .0314855 which of course would be very close to the daily...

Liberal are maths
prob(red, red) = (20/36)(19/35) = ....

Math
10 4/17 ÷ 4 5/9 = (174/17) ÷ (41/9) use your rule for division of fractions to continue

Math helppp
The angle between their flight paths is 110° I sketched the triangle and used the cosine law. x^2 = 450^2 + 380^2 - 2(4500)(380)cos110° = 463870.889 x = ?463870.889 = appr 681 km or using vectors and the actual angles let v = (450cos320, 450sin320) = (344.72,-289.25) ...

math 7/8 grd
let d = -6.9, valid for d > -7 -6.9+s > -3 s > 3.9 which is NOT s > 4 Yup, Steve is right, we have one exception which rules out my entire solution.

math 7/8 grd
subtract them, (valid since both inequality signs are the same) d+s - d > -3 - (-7) s > 4

Math
I agree http://www.wolframalpha.com/input/?i=pattern+%7B0,6,15,27%7D

algebra
replace x with 1 f(1) = 5(1) + 4 = .....

Algebra
dimensions of a rectangular prism , (a box), consist of 3 constants, the length, the width and the height "dimensions 11 by 9 by 3. 23 in 297 in 318in 159in" makes no sense to me "I think the answer is c 318 in". What does that mean? Volume would be measure...

Quantitative Aptitude
I have no idea what this is supposed to mean. Looks like a series of random statements.

Math
total number of students ---- x number of girls = (2/7)x number of boys = (5/7)x number of girls with glasses = (1/2)(2/7)x = (1/7)x number of boys with glasses = (1/3)(5/7)x = (5/21)x given: (5/21)x = 10 solve for x, and sub into my definition

Trigonometry
N45W ---> an angle of 135° using trig notation. So we are de-composing your vector into its vertical and horizontal displacement. horizontal: 99cos 135 = 99(-?2/2) = appr - 70 metres vertical : 99 sin 135° = appr 70 metres notice if you construct a right-angled ...

Math/calculus
165 = 180-15 or = 120+45 or = 90+75 I will pick 120+45 tan 165 = tan(120+45) = (tan120 + tan 45)/(1 - tan120tan45) ** 2 we know tan 45=1 tan120 = -tan60 , by the CAST rule = -?3 , from the 30-60-90 triangle so back in ** tan165 = (-?3 + 1)/(1 - (-?3)(1)) = (1 - ?3)/(1 + ?3)

Math
to be a multiple of 3, the sum of the digits must be a multiple of 3 For 74A52B1, 7+4+A+5+2+B+1 must divide evenly by 3 19 + A+B must divide by 3 then 18 +A+B+1 must divide by 3 A+B+1 must divide by 3 So A+B could be 2, 5, 8, 11, 14, 17, no more in the second: 326AB4C the same...

Math/calculus
f (x) = 3cos (4pix -pi/2) -2 = 3cos (4?(x - 1/8) ) - 2 <---- a horizontal shift of 1/8 to right period = 2?/(4?) = 1/2 On the x-axis mark off 0, 1/8, 2/8, 3/8 and 4/8 the magnitude of your cosine curve is 3, so on the y-axis, mark off 5 or 6 units above and below Knowing ...

Math/calculus
Using the standard "compass heading" http://www.allstar.fiu.edu/aero/fltmidcomp.htm that would be 120° based on standard trig notation. what If I told you the plane ends up at (125(1.5)cos120°, 125(1.5)sin125°) ??

Math
let the smaller be x then the larger is x+4 so x + x+4 = 90 2x = 86 x = 43 so how about 43 and 47. Did you skip that pair ? You knew the were only 4 apart, so just about equal and half of 90 is 45 , so ....

Math
For linear equations, - if in your solution, the variable drops out, and you end up with a true statement, there will be an infinite number of solutions. e.g. 3x - 9 = 3(x-3) solving you get 0 = 0, which is true, so infinite number - if in your solution, the variable drops out...

Algebra 2
all good except #8 8. it asked for the actual solutions. x^2 - (-x^2 - 6)^2 = 36 x^2 - (x^4 + 12x^2 + 36) = 36 x^2 - x^4 - 12x^2 - 36 = 36 x^4 + 11x^2 + 72 = 0 no real roots, the discriminant is negative. http://www.wolframalpha.com/input/?i=plot+x%5E2+-+(y+-+6)%5E2+%3D+36+,+y...

Math Posttest Connexus 09:Posttest 9:Solving Two-
Are you even reading the question?? Your reply to Ms Sue suggests that you are merely looking for the answer. You want an average of 200 Your first day sales were good, there were 6 over your goal your second day not so good, you were 15 short of the goal. take it from there

Math
See the post I answered for you

Math
look back at your post that was answered

Math
https://www.jiskha.com/display.cgi?id=1510589905

No to Pizza - Math
dividing 754 by 13 will give you the distance per hour you then have to multiply by 8 or use a simple ratio: x/8 = 754/13 x = 8*754/13 =...... notice I performed the same steps as above

math
first step is correct: 2075 – 1195 = $880 now you want the percentage based on the original amount, so 880/1195 = ... now change that to a percentage You have to learn to get a "feel" for numbers 1195 is almost 1200 the increase is 880 or about 3/4 so 8.8% is a ...

Math
All 3 are wrong. Are you just guessing, hoping that somebody will just give you the answer. Show me what you did to get your answers, that is the only way I can help you.

@ Kira
Don't just yell out answers, no learning takes place by doing that.

Math
You could visualize it by looking at the face of a clock and imagining a circle around the face. There would be 12 markings on it (the knots of your string) the first marking could be 1:00 , the second at 4:00 and the third at 8:00 now count the number of hours between the ...

Algebra
Your function would be: f(x) = (x-1)(x-2)(x+2)(x+3) = (x^2 - 4)(x-1)(x+3) expand it further to see which one matches. That way you will not have to "guess" what the correct version is.

Math
Well, in a parallelogram, opposite angles are equal and adjacent angles add up to 180° Take it from there.

Algebra
F(x)=x^2+8x+15 complete the square, you must know this procedure! = (x^2 + 8x + 16 - 16) + 15 = ( (x+4)^2 - 16) + 15 = (x+4)^2 - 1

Algebra
not enough data

Algebra I
so the new line must be y = (-1/5)x + b which automatically rules out a) and d) plug in the point (-10,3) and find b to decide which of the remaining choices is it.

Math
The number ---- x the reciprocal of the number --- 1/x "The reciprocal of a number decreased by the reciprocal of twice the number" ---- 1/x - 1/(2x) 1/x - 1/(2x) ? 2 2/2x - 1/2x ? 2 1/x ? 2 1 ? 2x 2x ? 1 x ? 1/2 test: let x = 1/4 reciprocal --- 4 twice the number...

Math
1(1/2)^(t/5730) = .921 .5^(t/5730) = .921 take log of both sides and use log rules ... (t/5730) log .5 = log .921 take over

Math
let the rate be r 101(1 + r)^10 = 160 (1+r)^10 = 160/101 = 1.58418... take 10th root of both sides to get 1+r subtract 1 from that, then change to a percent

Math
So each square has an area of 16 units^2, so each side is 4 units. the circle on each square will have a radius of 2 units, for an area of ?(2^2) or 4? so the left over from each square is 16 - 4? units or 4(4 - ?) Now, how many squares did you have ?

Calculus
looking at your answer for y' I will assume you meant: y = x^2/(x^2 + 3) your first derivative is correct, I suspect you used the quotient rule. So why not use it also to get y'' y'' = ( (x^2 + 3)^2 (6) - 6x(2)(x^2 + 3) (2x) )/(x^2 + 3)^4 = ( 6(x^2+3)^2 - ...

Math - Accounting
Assumption on 9% I will assume that the rate is 9% per annum, compounded monthly, so ... i = .09/12 = .0075 n = 30(12) = 360 Paym= ? 125000 = paym( 1 - 1.0075^-360)/.0075 find paym. "The total payment over the term of the loan is" I suppose they want you to multiply ...

Mathematics
First bottle: unit price .... £55/80 ml = 68.75 cents/ml 2nd bottle: 50 ml at £45 plus 50 ml at £22.50 or 100 ml for £67.50 unit price = £67.50/100 = 67.50 cents/ml so what do you think?

Math
with distribution: 6( 1/2 + 2/3) + 3/4) = 3 + 4 + 9/2 =7 9/2 or 11 1/2 or 23/9 without distribution: add up the 3 fractions in the bracket, first obtaining a common denominator, then multiply that by 6 , reduce your fraction answer to lowest terms You MUST get the same answer.

Math
Yes, there would be no solution. If your variable disappears and you end up with a FALSE statement, there is no solution e.g. x +8 = x - 6 if your variable disappears and you end up with a TRUE statement, there will be an infinite number of solutions. That is, every possible ...

Math
no, what you typed makes no sense to me notice in 5^3, 5 is the base and 3 is the exponent so your ^3 has no base what does 8+^7 mean? did you mean 8^7 ??

Math
retype using the convention ^ to show exponents e.g. 5^3 means "5 to the third" or (5)(5)(5)

Math
#3 x/-10 > 6 , we are going to multiply by -10 so the inequality sign must reverse ... x < -60, so ------ C all others are correct

Pre-Calc
"bearings" to indicate direction is often misunderstood so you should stick with the conventional method used in trigonometry I will use vectors, so ... (400cos10° , 400sin10°) = R + (50cos90° , 50sin90°) where R is the required vector (393.923, 69....

algebra
If Karen deposits $x in the 2.5% account, how much does she deposit in the other account ?? if her interest from the first account is .025x , what is ther interest from the 2nd account ?? (sum of the two interests) = 850 take over

Algebra
I had assumed you found the new perimeter to be 4(x+3) = 4x + 12 so 4x + 12 = 2x+40 I had formed that equation for you, no solve it.

Algebra
Side of original square ---- x cm perimeter = 4x side of new square = x+3 New perimeter = ..... translate: "the perimeter of the new square is 40 more than twice the length of each side of the original square" ---> new perimeter you found above = 2x + 40 solve for x

Pre-Calc
According to my diagram, they ploughed at an angle of 135° to each other, one went .5 miles , the other 2.5 miles area = (1/2)(side1)(side2)(sin(angle between them)) = (1/2)((.5)(2.5)sin 135° = .... square miles

Maths
let each of the base angles be x then the vertical angle = 2(x+x) =4x solve for x: x + x + 4x = 180

Trigonometry
let the diameter be D ft in one rotation the belt moves D? ft. The wheel rotates at 360 rpm, or at 60 rotations per second In that 1 second the belt covers 40 ft. so 60(D?) = 40 D? = 2/3 D = 2/(3?) ft = appr .2122 ft or appr 2.546 inches

Calculus
If typed fully , this is one of the standard optimization problems, and it probably asked for a minimum sum of the areas. I will define my variables different from Steve's, mainly to avoid fractions let each side of the square be x let each side of the equilateral triangle...

Calculus
Ok, I did that, no what ?

Math
We have four possible outcomes: 1 ww ** 2 wb 3 bw 4 bb we want the cases marked by ** #1: ww, prob(first w) = 6/11 so the white gets transferred to B and prob(2nd w) = 4/8 = 1/2 prob(ww) = (6/11)(1/2) = 6/22 = 3/11

Math
Identical post to this https://www.jiskha.com/display.cgi?id=1510190947 which I had answered yesterday. Why are you reposting it ?

algebra
JoJo you were right -5(5) + 4 = -25 + 4 = -21 D

Maths
9:12:18 ---> a:b:12 9:12:18 = 3:4:6 = 6:8:12 state your conclusion

Math
key concept: at catch-up time, they both will have travelled the same distance rate of freight train ---- x mph rate of passenger ----- x+11 mph time taken by passenger = 20 hrs time taken by freight = 64 hrs distance covered by passenger tr. = 20(x+11) distance covered by ...

Calculus
You are correct, I don't know what I did to get the easy part of the problem, And your final answer is correct, good job.

Calculus
Khan Academy does a good job of introducing the MVT here: https://www.khanacademy.org/math/ap-calculus-ab/ab-existence-theorems/ab-mvt/v/mean-value-theorem-1 with an example using an actual function here: https://www.khanacademy.org/math/ap-calculus-ab/ab-existence-theorems/ab...

Calculus
I did not get this. for my average rate of change I had = (4sin4 - sin1)/3 = appr -.72858 f'(x) = xcosx + sinx by MVT, xcosx + sinx = -.72858 This is a nasty equation to solve, so I tried good ol' Wolfram http://www.wolframalpha.com/input/?i=solve+xcosx+%2B+sinx+%3D+-....

Algebra
incorrect @ Anonymous, don't just post answers, especially if they are wrong.

Algebra Help
ok, let's go with your messy-looking equation 7x - 3/5 ? 2/5 + x/5 7x - x/5 ? 2/5 + 3/5 (35/5)x - (1/5)x ? 5/5 (34/5)x ? 1 now multiply each side by 5 34x ? 5 now divide each side by 34 x ? 5/34 starting from my simplified version of 20x + 15x - 3 ? 2 + x 20x + 15x - x ? 5...

Algebra Help
4x + 3( x - 1/5) ? 1/5( 2 + x ) Just simplify it 4x + 3x - 3/5 ? 2/5 + x/5 don't like those fractions? , multiply each term by 5 20x + 15x - 3 ? 2 + x I am sure you can handle it from there, let me know what answer you get

MATH PLEASE HELP
no I hope you weren't guessing, hoping that somebody would just give you the answer. suppose you let t = 2, that is two days number of trees cut down would be 2(77) and the number of trees left would be 7820 - 2(77) now which of your choices follows that pattern for t days?

Math
original radius and height : r and h volume = ? r^2 h new radius = 3r new height = h/2 new volume = ? (3r)^2 (h/2) = (9/2) ? r^2 h ratio of old volume to new volume = ?r^2 h : (9/2) ? r^2 h = 1 : 9/2 = 2 : 9

math
an example of an exponential equation could be y = 3^x the variable is found as an exponent

math
The way you described the given graphs, neither one is correct q(x) = x or y = x is a straight line passing through the origin and forming a 45° with the x-axis Verification: http://www.wolframalpha.com/input/?i=plot+q(x)+%3D+x

Math
Instead of the triangle having sides 390, 280, and 180 let's use the similar triangle of 39, 28, 18 , the angles of course remain the same. looks like we need the angle opposite the side 18, using the cosine law: 18^2 = 39^2 + 28^2 - 2(39)(28) cosØ 2184cosØ...

Math
This question makes no sense. let Brock take x minutes, then Justin takes x-2 minutes, Jinping takes x+2 minutes first case: 1/x + 1/(x-2) = 1/10 , (you had 10 on the right side) This equation alone is sufficient to find x .... multiply each term by 10x(x-2) 10(x-2) + 10x = x(...

math
yes

math
correct so far. Now divide both sides by 10 since you dividing by a positive 10, the inequality sign stays as >

Algebra
yes, you are correct with choice c as to x > 4, the solution would be any number greater than 4. e.g. 7, 9.456, 1345, ?81, etc

math
cost = 15n + 95 , where n is the number of people attending replace n with 77 and evaluate to get the cost

mmmaaatthh
Interest = P*r*t, where P is principal, r is the rate as a decimal, and t is the number of years so.... 5 = P(.015)(12) solve for P A rather unrealistic question. You say that "no other money was deposited into or withdrawn from the account", so where does the annual...

maths
I am going to assume that you are using a comma instead of the North American period to indicated the decimal place, so I will read that as: f(x)= 1320/(1 + e^(5.1 - 0.66x)) , (why are you using the comma in the first number and then the period in 0.66 ??) so at introduction, ...

math
solve for x (3/8)x = 16.95

Calculus 1
Just noticed my "late-night" calculations have an errors and typos, sorry about that. corrected version: when 200 ft are let out, x^2 + 100^2 = 200^2 x^2 = 30,000 x = 100?3 secØ = 200/ (100?3) = 2/?3 sec^2 Ø = 4/3 tanØ = 100/100?3 = 1/?3 then my...

Calculus 1
let the angle be Ø, and the horizontal distance be x given : dx/dt = 9 find dØ/dt we have a right angled triangle, and tanØ =100/x xtanØ = 100 x sec^2 Ø dØ/dt + tanØ (dx/dt) = 0 *** when 200 ft are let out, x^2 + 100^2 = 200^2 x...

Math
rate of faster painter --- 1/x rate of slower painter -- 1/(x+4) combined rate = 1/x + 1/(x+4) = (x+4 + x)/(x(x+4)) = (2x + 4)/(x^2 + 4) 1/[(2x + 4)/(x^2 + 4)] = 2 (x^2 + 4x)/(2x+4) = 2 x^2 + 4x = 4x + 8 x^2 = 8 x = ?8 or appr 2.83 hrs

Math
let speed of current be x mph Roy's speed with the current = 4+x Roy's speed against the current = 4-x time with the current = 4/(4+x) time against current = 4/(4-x) total time = 5 4/(4+x) + 4(4-x) = 5 multiply each term by (4+x)(4-x) 4(4-x) + 4(4+x) = 5(4-x)(4+x) 16...

algebra
1484.40 = 1314 + r(5680) solve for r and express it as a percentage

algebra
I did this for you yesterday, and you even thanked me for it. What gives ? https://www.jiskha.com/display.cgi?id=1509977126

oops - Algebra 1
made an error, go with Damon and Scott

Algebra 1
let the equation be y = ax^2 + bx + c since (0,0) is a point on it 0 = 0+ 0 + c, so c = 0, and we can go with y = ax^2+ bx If (1, -2) lies on it ---> -2 = a+b if (-1,-4) lies on it ---> -4 = a - 4b subtract them: 2 = 5b b = 2/5 sub back in to get a and write your equation

Math
For a reflection in the y-axis (x,y) ----> (-x,y)

Math/Algerba
I strongly suggest you simply divide 62 by those numbers and your mystery shall be solved. I am sure you have a calculator if you cannot divide these in your head. btw, did you mean to list 1 twice in the last choice ?

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