Saturday
January 21, 2017

Posts by Reiny

Total # Posts: 37,337

algebra
original: width --- x length --- 5x , (it said so) new dimensions: length = 5x - 3 width = x+10 perimeter = 2* width + 2*length = 2(x+10) + 2(5x-3) = 374 2x + 20 + 10x - 6 = 374 12x = 360 x = 30 So the original rectangle had a width of 30 m and a length of 150 m
November 14, 2016

algebra
4b/2 + 3 = 11 + b 2b + 3 = 11 + b, since 4/2 = 2 2b - b = 11-3 b = 8 or 4b/2 + 3 = 11 + b multiply every term by 2 4b + 6 = 22 + 2b 4b - 2b = 22 - 6 2b = 16 divide both sides by 2 b = 8
November 14, 2016

math
the effective distance: 16 km east and 8 km north ---> right-angled triangle hint: Pythagoras
November 14, 2016

math
Poorly worded question. Are we to assume that some questions were skipped, and no reward or penalty for skipped questions? I will assume that. rights ---- x wrongs --- y skipped -- 40-x-y) 5x - 3y + 0(40-x-y) = 70 5x - 3y = 72 y = (5x-70)/3 , clearly 14 ? x ? 40 , x+y ? 40 ...
November 14, 2016

Math
Now: Benny ---- x years Apple ---- 38-x 6 years ago: Benny ---- x-7 Apple ----- 38-x - 7 = 31-x 31-x = 3(x-7) solve for x, and sub into my definitions
November 14, 2016

Maths
let the perpendicular height be 4x let the slant height be 5x (4x)^2 + 6^2 = (5x^2 16x^2 + 36 = 25x^2 carry on, of course you would reject the negative value of x after taking the square root at the end.
November 14, 2016

Maths
Think of the 5 kids standing in a row, and in each row changing positions 1 ---> 3 2 ---> 5 3 ---> 1 4 ---> 2 5 ---> 4 At the start,,,: 1 2 3 4 5 ---> A B C D E after 1 round: 3 4 1 5 2 ---> C D A E B after 2 round: 1 5 3 2 4 ---> A E C B D after 3 ...
November 14, 2016

math
depends where you want the water spout to be. It would make sense to have the spout at the origin. Then the zeros of the function would be (0,0) and (8,0) and the vertex would be at (4,6) height = a(x - 4)^2 + 6 but (0,0) lies on it, thus: 0 = a(0-4)^2 + 6 16a = -6 a = -3/8 ...
November 14, 2016

Aljebra
original number in first box --- x original number in 2nd box --- 123-x after shift: first box ----- x-10 2nd box --- 123-x + 10 = 133-x 133-x = 2(x-10) solve for x
November 13, 2016

Math
3?(x - 1) + 6 when x = 26 = 3?25 + 6 = ....
November 13, 2016

pre algebra
adult tickets ---- x children tickets --- 2x + 15 solve for x: 12x + 5(2x+15) = 1920
November 13, 2016

pre algebra
follow the same method and steps I just showed you in your other posts. The two questions are of the same structure.
November 13, 2016

intermediate maths
granddaughter's age---- x James' age --------- 6x 2 years from now: granddaughter's age --- x+2 James' age ---------- 6x + 2 6x+2 = 5(x+2) solve for x
November 13, 2016

Algebra
speed of slower rider --- x km/h speed of faster rider ---- 2x km/h distance gone by slower = 3(x) = 3x distance gone by faster = 3(2x) = 6x 3x + 6x = 90 9x = 90 x = 10 rate of slower rider = 10 km/h rate of faster rider = 2(10) = 20 km/h
November 13, 2016

Calculus
let the point of contact be P(a,b) let A be (1,7) slope of AP = (b-7)/(a-1) the closest point would be where the tangent at P is perpendicular to AP 2y dy/dx = 1 dy/dx = 1/(2y) so at P, the slope of the tangent is 1/(2b) so (b-7)/(a-1) = -2b b-7 = -2ab + 2b -b = -2ab + 7 2ab...
November 13, 2016

math
In a parallelogram Abcd angle add ??? side an ???? e ????? x+y ???? wow!
November 13, 2016

Math
Just follow the definition: a*b means 3a^2+b 3*1 means 3(3^2) + 1 = .....
November 13, 2016

Math
number correct --- x , 0 ? x ? 20 number wrong ---- y number skipped ---- 20-x-y 5x - y + 0 = 72 y = 5x - 72 y ? 0 if x = 14, y = -2 , not possible if x = 15 , y = 3 , skipped = 2 if x = 16, y = 8 , not possible , x+y>20 so he got 16 right, 8 wrong, and skipped 2 check: 5(...
November 13, 2016

Math
not arithmetic nor geometric gave up and checked with Wolfram found: term(n) = (7(3^n) - 3)/6 http://www.wolframalpha.com/input/?i=pattern+%7B3,+10,+31,+94%7D quite obscure, perhaps more terms would have helped.
November 13, 2016

Math
mmmhhhh when x=1 , 3+2x = 3+2(1) = 5 when x=2, 3+2x = 3+2(2) = 7 when x = 3 ..... continue
November 13, 2016

Math
number of girls --- x number of boys --- (5/11)x x - (5/11)x = 114 (6/11)x = 114 x = 114(11/6) = .... take over
November 13, 2016

Math
1:2:1/2 = 2:4:1 -----> ratios usually are not expressed in fraction form let their shares be 2x, 4x, and x but x = 48 so 2x = 96 and 4x = 192 add them up
November 13, 2016

Calculus
You did not do exactly the same, your slope was -3/5, different from mine. (another example of why I prefer traditional class room instructions, where the learning of math is not just "answer based" )
November 13, 2016

Calculus
How did you get the slope to be -3/5 ?? let the x-intercept be A(a,0) and the y-intercept be B(0,b) label point (3,5) as P By ratios in similar triangles: (a-3)/5 = 3/(b-5) ab-5a-3b+5 = 15 b(a-3) = 5a b = 5a/(a-3) Area of triangle = (1/2)ab = (1/2)(a)(5a/(a-3) ) = 5a^2/(2a-6) ...
November 13, 2016

Math
right now: x + 7x = 976 x= 122 Aaron has 122 cards and Ben has 854. after the give-away of k cards: ben has 854-k Aaron has 122+k Aaron has 3 times as many as Ben 122+k = 3(854 - k) 122+k = 2562 - 3k 4k = 2440 k = 610 check: after the exchange Ben has 854-610 = 244 Aaron has ...
November 12, 2016

Maths
3^9 + 3^12 + 3^15 + 3^n = 3^9(1 + 3^3 + 3^6 + 3^(n-9) ) = 3^9(757 + 3^(n-9)) 3^9 is a perfect cube, so all we need is (757 + 3^(n-9)) to be a perfect cube, clearly n >9 perfect cubes past 757 with 3^(n-9) as the 2nd number: 1000 243 <---- well, that was lucky 1331 574...
November 12, 2016

Calculus
let the height be h then h^2 + b^2 = 20^2 h = (400-b^2)^(1/2) Area = (1/2)(bh) = (1/2)(b)(400 - b^2)^(1/2) d(Area)/dt = (b/2)(1/2)(400-b^2)^(-1/2) (-2b db/dt) + (1/2)(db/dt)(400 - b^2)^(1/2) = -b^2 (db/dt)/?(400-b^2) + (1/2)(db/dt)?(400-b^2) when b = 11 and db/dt = 4 d(Area)/...
November 12, 2016

math
number of ways to give the fruits = 5!/(3!2!) = 10 (you could list them) Bananas at least two days in a row: BABAB is the only case where two or more B could not be together. Look at your list from above prog(at least two B's in a row) = 9/10
November 12, 2016

maths
Susan's age now ---- x Mary's age now ------3x Three years ago: Susan ---- x-3 Mary ----- 3x-3 x-3 + 3x-3 = 22 continue
November 12, 2016

Algebra
good road ---- x km poor road ----- 48-x km time on good road = x/72 time on poor road = (48-x)/48 x/72 + (48-x)/48 = 3/4 times 144 , the LCD 2x + 3(48-x) = 108 carry on, easy from here
November 12, 2016

Maths
without a calculator... let a=20142014 then 20142015 = a+1 then 20152015 = a + 1 + 1000 = a+1001 then 20152014 = a+1000 20142015×20152014 – 20142014 ×20152015 = (a+1)(a+1000) - a(a+1001) = a^2 + 1001a + 1000 - a^2 - 1001a = 1000
November 12, 2016

Algebra
2x^3 - 5x^2 - 5x - 1 = 0 let f(x) = 2x^3 - 5x^2 - 5x - 1 try f(1) = 2 - 5 - 5 - 1 ? 0 try f(-1) = -2 - 5 + 5 - 1 ? 0 try f(1/2) = 1/4 - 5/4 - 5/2 - 1? 0 try f(-1/2) = -1/4 - 5/4 + 5/2 - 1 = 0 , yeahh! so (2x + 1) is a factor and x = -1/2 by long algebraic division, which I ...
November 11, 2016

Math -fractions word problems
total number of students ---- x number of boys ----- (3/7)x number of girls ------(4/7)x (4/7)x = (3/7)x + 4 times 7, the LCD 4x = 3x + 28 x = 28 boys: (3/7)(28) = 12 girls = 28-12 = 16
November 11, 2016

intergrated science
I will assume that Calculus is part of your integrated science course. a = 2 then v = 2t + c at the beginning of the observation, t = 0 , v = 24 so 24 = a(0) + c ----> c = 24 v = 2t + 24 when t = 8 v = 2(8) + 24 = 40 m/s or, simply .... for each of the 8 seconds the ...
November 11, 2016

calculus
your values of x = -2, 3 are the x-intercepts, and you don't need a derivative to find them dy/dx = (x-3)(2/3)(x+2)^(-1/3) + (x+2)^(2/3) = (1/3)(x+2)^(-1/3) [2(x-3) + 3(x+2)] = (1/3)(5x)(x+2)^(-1/3) = 0 for a max/min of y ----> 5x = 0 or (x+2)^(-1/3) = 0 ---> no way ...
November 11, 2016

math- Trigonometry
I agree with Scott. For the given date, the calculations are correct. In reality, the question is absurd. Using Pythagoras, the height of the lighthouse would have to be appr 8.9 km high. and, using our given angle of 65.91..° tan 65.91 = height/4 height = 4tan 65.91 = ...
November 11, 2016

Math
or 15 machines 15 minutes to make 500 raviolis 75 machines 15 minutes to make 2500 raviolis 75 machines 15(2.4) minutes to make 2500(2.4) raviolis 75 machines 36 minutes to make 6000 raviolis (the 2.4 comes from 6000/2500)
November 11, 2016

maths
I assume you are solving? from the 2nd: y = -2x-4 sub into the first 3x - 2(-2x - 4) = 1 3x + 4x + 8 = 1 7x = -7 x = -1 back into y = -2x - 4 y = -2(-1) - 4 = -2 x = -1 , y = -2
November 11, 2016

Math
Assuming that x is the length of the missing parallel side ... area of trapezoid = (x+15)(10)/2= 5x + 75 area of triangle = (1/2)(15)(10) = 75 5x + 75 < 2(75) 5x < 75 x < 15 but clearly x has to be positive 0 < x < 15 looks like a common sense type of question ...
November 11, 2016

finite math
mortgage after downpayment = 140,000 i = .09/12 = .0075 n = 30(12) = 360 payment = p p(1 - 1.0075^-360)/.0075 = 140000 p(124.2818657.) = 140000 p = $1126.47
November 11, 2016

finite math
Follow the same steps I just showed you here http://www.jiskha.com/display.cgi?id=1478848733
November 11, 2016

Math
1/6 of the 3/2 pepperoni's remain or 1/4 this is (14)/4 or 1/16 of the original amount
November 11, 2016

Math
distance covered in one rotation = 25? inches 65 miles/hr = 65*12*5280 inches/hour = 65*12*5280/3600 inches/sec number of rotations = 65*12*5280/3600 ÷ (25?) = 14.56.. / sec or appr 15 rotations per second check: distance in 1 second = 14.56*25? = appr 1143.5 inches = ...
November 11, 2016

Statistics
prob(ace) = 4/52 = 1/13 prob(5 aces with card replaced each time) = (1/13)^5 = ....
November 10, 2016

Math
did you notice that the third difference is 3 ? So it is a cubic messing around a bit I got term(n) = (n^3 - n^2 - 4)/2 so term(6) = (216 - 36 - 4)/2 = 88
November 10, 2016

math
68/104 = 17/26 This question has two correct choices as answers. Poorly designed question.
November 10, 2016

matha
What part of my previous reply to your same question did you not like ? http://www.jiskha.com/display.cgi?id=1478784506
November 10, 2016

Math
This year: number of middle schoolers --- 2x number of high schoolers ----- 7x but 2x = 18 x = 9 So this year there are 18 middle schoolers, and 63 high schoolers. Total = 81 Since all we know from the previous year is the ratio of 1:8 , and there were more last year: possible...
November 10, 2016

Math
I have no idea what that first part of your post is supposed to be. your problem: 53+59+65+...+233 We have to know how many terms. a=53, d=6, n= ? term(n) = a + (n-1)d 233 = 53 + 6(n-1) 180 = 6n - 6 6n = 186 n = 31 sum(31) = (31/2)(first + last) = (31/2)(53+233) = 4433 which ...
November 10, 2016

Math
(Log75+log9+log5)÷(log5+log45) = log(75*9*5) / log(5*45) = log 3375 / log 225 = log(25*9*15) / log(25*9) = log(5^2 * 3^2 * 15)/log(5^2 * 3^2) = log( 15^2 * 15) / log (15^2) = (log 15^2 + log 15)/ log 15^2 = (2log15 + log15)/(2log15) = 3log15/(2log15) = 3/2 I think I ...
November 10, 2016

math
After eliminating all the weird symbols, I got: Triangle ABC is a right triangle with right angle at A. Suppose AX is an altitude of the triangle, AY is an angle bisector of the triangle, and AZ is a median of the triangle, and angle XAY = 13°. If X is on BY, then what is ...
November 10, 2016

Math
let the sides be 2x, 3x, and 4x (notice 2x:3x:4x = 2:3:4 ) but 2x = 15 find x, then sub into my definitions
November 10, 2016

Algebra
one number ---- x the other ------(1/2)x x + (1/2)x = 18 double each term 2x + x = 36 continue
November 10, 2016

matha
I think you missed a zero in the original value, if the present value is 1,000,000, then after a 5% depreciation you have 95% left or 950,000. Insert or delete the zero as needed.
November 10, 2016

Math grade 6, 4 operations
Let the number of years be x 10+x + 7+x = 41 2x = 41 - 17 2x = 24 x = 12 It will happen in 12 years. check: in 12 years: Deepak will be 22 his brother will be 19, the sum will be 41
November 10, 2016

Math grade 6, 4 operations
Retype your question in English please.
November 10, 2016

Maths
Translate into English. "One-fourth of the sum of a number and seven is four less than three times the number." If the number is x (1/4)x + 7 = 3x - 4 x/4 - 3x = -11 times 4 x - 12x = -44 -11x = -44 x = 4
November 10, 2016

math
how about 3457 ?
November 10, 2016

math
4-8 -(-2) -17 = -4 + 2 - 17 = -2 - 17 = -19
November 10, 2016

math
17(1/2)^(t/5730) = 10 (1/2)^(t/5730) = 10/17 take log of both sides and use rules of logs (t/5730) log .5 = log10 - lot17 t/5730 = (1 - log17)/log.5 t = 5730(1 - log17)/log .5 = appr 4387 years
November 9, 2016

statistic
enter your data http://davidmlane.com/normal.html
November 9, 2016

Algebra- Word Problem
your second equation: 4x + 2y = 56 2x + y = 28 2x+y = 28 x+y = 40 subtract: x = -12 you are correct, the question is bogus!
November 9, 2016

Math algebra
amount of water added ---- x gallons .6(2500) + 0.0x = .25(2500 + x) solve for x
November 9, 2016

Math
rate = distance/time = 3(.25)miles / 4.5 min but 4.5 min = 4.5/60 hrs = .0075 hrs = .75/.0075 mph = 10 mph
November 9, 2016

maths
n = 5 payment --- p i = .06 p(1.06^5 - 1)/.06 = 30000 I get p = $5321.89
November 9, 2016

Algebra 2
It appears that there are at least 3 numbers let the first be x then the second is x+2 and the third is x-4 x + x+2 + x-4 ? 30 3x ? 32 x ? 10 2/3 Assuming that your numbers are whole numbers x could be 5, 6, 7, 8, 9, or 10 possible cases: 5, 7, 1, .... ---> others that add ...
November 9, 2016

Math
Number of games in one round = C(10,2) = 45 but they are playing two rounds, so total number of games = 90
November 9, 2016

Math
I read that as: ?(2x - 1) = x-2 square both sides 2x-1 = x^2 - 4x + 4 x^2 - 6x + 5 = 0 (x-5)(x-1) = 0 x = 5 or x = 1 since I squared, both answers must be verified in the original equation, if x = 1 LS = ?(2x-1) = ?1 = 1 RS = 1-2 = -1 so x ? 1 if x = 5 LS = ?(10-1) = 3 RS = 5-...
November 9, 2016

Math
remember, consecutive angles in a parallelogram have to be supplementary, that is, they add up to 180° let the angles be x and 3x x + 3x = 180 continue ....
November 9, 2016

math
Volume of water rise = ?(6^2)(2) = 72? volume of 1 sphere = (4/3)?(1.5)^3 = 4.5? number of spheres that caused the rise = 72?/4.5? = 72/4.5 = 16
November 9, 2016

Math
x+y=82 x-y = 16 add them to solve for x subtract them to solve for y
November 9, 2016

Calculus AB
first find the point where y = 1 x^2 + 2x(1) + 1 = 4 x^2 + 2x - 3 = 0 (x+3)(x-1) = 0 x = -3 or x = 1 but in quad I, the point is (1,1) use implicit differentiation: 2x + 2x(dy/dx) + 2y + 3y^2 (dy/dx) = 0 dy/dx (2x + 3y^2) = -2x - 2y dy/dx = (-2x - 2y)/(2x + 3y^2) = (-2-2)/(2+3...
November 9, 2016

Math
8/12 = x/9 solve for x
November 9, 2016

Math
(f o g)(x) is defined as f(g(x)) so f(g(x)) = f(x-1) , remember f(x) = 3x+4 f(g(x)) = 3(x-1) + 4 = 3x + 1 , same as bob or f(g(x)) = 3g(x) + 4 = 3(x-1) + 4 = 3x + 1 , like bob had in #2 (f o g)(-2) = f(g(-2)) ----> g(-2) = (-2)^2 = 4 = f(4) = 3(4) + 2 = 14 last one: Here is...
November 9, 2016

The Tangent Function
Label the original position as A and the second position as B, top of the lighhouse as P and its base as Q. ABQ is a straight line, AB = 40, angle B=25°, angle PAQ = 30°, AQ = x, and PQ = h I used to teach this question is 2 ways: 1. In triangle PBA, angle PAB = 150&...
November 9, 2016

9th grade algebra (completing square)
You seem to have a good grasp of doing these. I verified most of your answers by subbing them back into the original equation. All the ones I tried were correct. I suggest you take your calculator and test your answers.
November 9, 2016

correction - math
Y = 2x^2 + 3?x is NOT a function, since a quadratic must have the form y = ax^2 + bx + c that is, the exponents of the x term can only be 2 or 1 the term ?x is x^(1/2) Furthermore, the graph of a quadratic function is a parabola, the graph of Y = 2x^2 + 3?x looks like this, ...
November 9, 2016

Math
Since no condition is stated, that number would be C(9,5) or 126 There seems to be something missing here.
November 9, 2016

pre calc
amount = a (1/2)^(t/k), where k is the half-life period when t = 2, amount = .7a .7a = a(1/2)(2/k) .7 = (.5)^(2/k) take log of both sides and use log rules log .7 = (2/k)log .5 2/k = log .7 / log .5 = .514573... k = 2/.514573.. = 3.887 days the half-life is 3.89 days check: ...
November 8, 2016

Math HELP HELP
x^2+4x-41 = x^2+4x + 4 - 4 - 41 = (x+2)^2 - 45 expand and simplify to verify my answer
November 8, 2016

pre calc
N = a (2)^(t/20), where N is the number of bacteria, t is the number of minutes, a is the initial count, our problem. counting 7:00 as zero time and 5:00 am as t = 10 hrs = 120 minutes 1000000 = a(2)^(120/20) 1000000 = a(2)^6 64a = 1000000 a = 1000000/64 = 15625 of the germs ...
November 8, 2016

Math
Did you even look at the solution I gave you here http://www.jiskha.com/display.cgi?id=1478637677 This is the same type of problem. btw, the denominator on the right side factors to (x+3)(x-1)
November 8, 2016

Algebra
"j vaires directly with m and inversely with p" ----> j = km/p plug in the given, and solve for k
November 8, 2016

MATH
Your second equation IS a quadratic function. since the highest power you see is x^2. Sorry if you misunderstood. btw, don't say "square root of x", that would be ?x the term is "x squared"
November 8, 2016

MATH
Small change to your definition. The highest power must be a square term. The degree of a polynomial is determined by the highest power, so in your case you would have a cubic because of the x^3 term a quadratic must have the form y = ax^2 + bx + c, where the a,b, and c are ...
November 8, 2016

Math
I will assume you meant: 2x/(x+1) + 3/(5x+5) = 0 the whole thing falls apart when the denominators are zero, since then we would be dividing by zero When does that happen? when x+1 = 0 x = -1 and 5x+5 = 0 5x = -5 x = -1 so x ? -1
November 8, 2016

Math
Look up the definition of a function in your text or in your notes. In a nutshell, it says that for every x there is one and only one y value So, if you see two or more y values for the same x, then it is NOT a function e.g. in the first I see (5,2) and (5,10) , so NOT a ...
November 8, 2016

Calculas-Differentiation
I have now done 2 of your quite straightforward questions. You MUST know how to do these type of relatively easy Calculus problems. Show me the steps of your solution so I can check it.
November 8, 2016

Calculas-Differentiation
The line y=1/4x+1 has a slope of 1/4 So the perpendicular has a slope of -4 y = 6 - x^2 dy/dx = -2x set -2x = -4 , and solve, then use your grade 9 method of finding the equation of the tangent
November 8, 2016

Algebra
amount of the 20% stuff ---- x gallons amount of the other stuff ---- 700-x .2x +.3(700-x) = .24(700) solve for x to reveal the mystery.
November 8, 2016

Calculas-Differentiation
dA/dt = 6t + 1/5 plug in t = 2 for dA/dt
November 8, 2016

trigonometry- hight and distance
At 45° the length of the shadow will also be h m
November 8, 2016

Math
x+y=16 x-y=3 just add them, to find x subtract them to get y
November 8, 2016

Algebra
in its standard form , at centre (0,0) a^2 = b^2 + c^2 4^2 = b^2 + 2^2 b^2 = 12 x^2 / 16 + y^2 / 12 = 1
November 7, 2016

Math
If you are picking just one student, prob(boy) = 12/29
November 7, 2016

Math
why not try it with something like (x+4)(2x-1) expand it and see how many products you have before simplifying
November 7, 2016

Math
to have an undefined slope, the line must be a vertical line. A vertical line has the form x = c, where c is a constant look at our point, its x value is -3 so the equation of your line is x = -3
November 7, 2016

math
radish seeds --- x pumpkins ----- x+6 x + x+6 + 40 = 80 solve for x
November 7, 2016

correction - Math
forget my previous post, did not notice the x^3 f(x)=4x^2-2x+3 ; g(x)=2x^3+4x-7 (f-g)(x) = 4x^2 - 6x + 10 - 2x^3 (f-g)(2) = 16 - 12 + 10 - 16 = -2 bobpursley was correct
November 7, 2016

Math
3rd one: f(x)=4x^2-2x+3 ; g(x)=2x^3+4x-7 (f-g)(x) = 2x^2 - 6x + 10 (f-g)(2) = 8 - 12 + 10 = 6
November 7, 2016

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