Friday
August 1, 2014

Posts by Reiny


Total # Posts: 26,926

mat/117
Use the formula like I showed you in your other post

mat/117
-3x^2+3x+9=0 x^2 - x - 3 = 0 x = (1 ±√13)/2

Algebra
The wording is poor. Did you mean: " The numerical value of the area of the rectangle is 25 more than the numerical value of 4 times the width" ? if so, then ... width --- x length -- x+4 x(x+4) = 4x + 25 x^2 + 4x = 4x + 25 x^2 = 25 x = 5 The width is 5 units (length...

Algebra
slope = (4 -(-9))/(-3 - (-2)) = 13/-1 = -1 Surely you must have the definition of slope in your notes or in your text.

Algebra
x - y ≥ 2 -y ≥ -x + 2 y ≤ x - 2 draw the line y = x-2 and shade in the region below the line. Since the line is included, make it solid (had it been y < x-2, you would have drawn a dotted line to show it is excluded.)

Math
double the first: 6x - 2y = -24 x + 2y = -18 add them: 7x = -42 x = -6 back into the second: -6 + 2y = -18 2y = -12 y = -6 x = -6 , y = -6

Algebra
I would use substitution, from the 1st: y = 5x-18 sub into the 2nd: -4x - 2(5x-18) = -6 -4x - 10x + 36 = -6 -14x = -42 x = 3 y = 5(3)-18 = -3 x=3 , y = -3

College math
let each of the two equal sides be x let the single side by y then y+2x = 5500 y = 5500 - 2x area = xy = x(5500-2x) = -2x^2 + 5500 Since you labeled it "college" math, I will assume you know Calculus d(area)/dx = -4x + 5500 = 0 for a max of area 4x = 5500 x = 1375 y ...

stats
must be an old-type "crank on the wall" from The Waltons era .... anyway .... I will assume that none of your 6 digit numbers can start with a zero, and that numbers may be repeated, so we can't have a number with no 8 prob of no 8 = 8 x 9^5/(9x10^5) so prob that...

math
i = .105/12 = .00875 n = 12(30) = 360 payment ( 1 - 1.00875^-360)/.00875 = 130000 payment = $1189.16

Math
In 1959 the inch was internationally defined in terms of the centimetre 1 inch = 2.54 centimetres So if you want any precision you have to go back to that basic definition. c) 80 in = 80(2.54) cm = 203.2 cm = 2.032 metres once you have converted to any of the metric units, the...

math
cost of computer = .8(825) = 660 original amount of money --- x 12x/100 + .25(88/100)x +1320 + 660 = x 34x/100 - x = -1980 66x-100x = -198000 x = 3000 check: car repairs = .12(3000) = $360.00 leaves --- 2640.00 food = .25(2640) = 660 amount to parents = 1320.00 computer = 660 ...

math
Using proper algebra: number of lights --- x white = x/2 red = (1/3)(x/2) = x/6 blue = 4 yellow = 10 x/2 + x/6 + 4 + 10 = x times 6 3x + x + 6(14) = 6x 84 = 2x x = 42 42 lights in total check: whites = 21 leaves 21 red = (1/3)of 21 = 7 sum = 21 whites + 7 red + 4 blue + 10 yel...

typo - math
just noticed a typo should have said: if 3 decimal places divide by 1000 but you probably figured that out anyway.

math
1. count the number of decimal places, in this case there are 2 divide by 100 -----> 12/100 2. reduce the fraction to lowest terms 12/100 = 3/25 (if 1 decimal place, divide by 10 if 2 decimal places, divide by 100 if 3 decimal places divide by 100 etc e.g. .2568 = 2568/1000...

Math 221
Third time for this question. Surely your text or notes must have your "Cowling's Rule" state and explained. Since I have no idea what it is, .......

math
288π , not 268 TT = appr 904.78 cm^3

math
volume of a cylinder is π r^2 h you are given r and h, take it from here.

math
volume of given tank = (45)(70)(10) cm^3 = 31500 cm^3 number of packages = 31500/3000 =10.5 but since we probably can't buy half a package, there will be 11 packages needed

math
according to your wording of the problem, term(n) = √term(n-1) - 2 or √term(n-1) = term(n) + 2 square both sides term(n-1) = term(n) ^2 + 4term(n) + 4 for n = 3, term(3) = 1 term(2) = 1^2 + 4(1) + 4 = 9 term(4) = √term(3) - 2 = -1 so we can't go any highe...

math (xi)
looks like the definition of dy/dx for y = secx we know dy/dx = (sec x)(tan x) so lim [sec(x+h)-sec x]/h h>0 = (secx)(tanx)

math
sum of 20 = 10(2a + 19d) = 10(2a - 38) = 20a - 380 sum of 22 = 11(2a + 21d) = 11(2a - 42) 22a - 462 22a - 462 = 20a - 380 2a = 82 a = 41 first term is 41

math
1960 ---> term10 = a + 9d = 2400 1990 ---> term40 = a + 39d = 600 subtract them 30d = -1800 d = -60 then a + 9(-60) = 2400 a = 2940 sum40 = 20(2(2940) + 39(-60)) = 70800

Calculus Help!
let the number of additional dollars be x new price = 7.5+x number of tickets sold = 1500 - 95x Revenue = (7.5 + x)(1500-95x) = 14250 + 787.5x - 95x^2 d(Revenue)/dx = 787.5 - 190x = 0 for a max of Revenue 190x = 787.5 x = 4.14 ticket price = 7.5+4.14 = $11.64 number of tickets...

math
5(3^2) + 3(3)(-3) - (-3)2 = 45 - 27 - 9 = 9

Math
2[-3(2x+4)+8(3x-2)] = 2[-6x-12+24x-16] = 2[18x-28] = 36x - 56

Math
suppose the radius of the original cone is r then the base area of the original is πr^2 Now, the radius of your half-size cone is r/2 so the base area = π(r/2)^2 = πr^2/4 = (1/4) πr^2 Thus the base area of the scaled down cone = 1/4 of the base area of the ...

statistics
Find the z-score of each. The one with the higher z-score is a "better score"

math
You must mean 6 square root of 3, or 6√3 let each side be 2x then x^2 + (6√3)^2 = (2x)^2 x^2 + 108 = 4x^2 3x^2 = 108 x^2 = 36 x = 6 So each side is 12 units long

Math
with replacement: prob = (13/52)(13/52)(26/52) = 1/32 without replacement: prob = (13/52)(12/51)(24/50) = 12/425

algebra
Katie's share ---- x Brandy --------- 2x Steph-----------x-3 x + 2x + x-3 = 56 4x = 59 x = 14.75 Katie --- $14.75 Brandy --$29.50 Steph---$ 11.75 check: 14.75+29.50+11.75 = 56 All is good.

Math
Fraction of female drivers = 48/106 = 24/53 So according to this experimental data number of female drivers = (48/106)(190 million) = appr 86 million

Calculus 2
yup, didn't see that perfect square

Calculus 2
let y = x^5/10+1/(6x^3) here is a picture of y = x^5/10+1/(6x^3) from 3 to 6 http://www.wolframalpha.com/input/?i=plot+y+%3D+x%5E5%2F10%2B1%2F%286x%5E3%29+from+3+to+6 arc length = ∫√( 1 + (dy/dx)^2) dx from 3 to 6 dy/dx = x^4/2 - 1/(2x^4) (dy/dx)^2 = x^8/4 - 1/2 + ...

Alegbra
slope of #1 is 7 slope of #2 is .... -3y = 21x + 7 y = -7x - 7/3 to be perpendicular, the slopes would have to be opposite reciprocals of each other that is, the 2nd would have had to have a slope of -1/7 no, they are NOT perpendicular

Math
first conditions: x+4 ≥0 ---> x ≥ -4 and 3x+10 ≥0 ----> x ≥-10/3 so we know that x ≥ -10/3 case 1: x+4 = 3x+10 -2x = 6 x = -3 case 2: -x-4 = 3x+10 -4x = 16 x = -4 , also no good, because of above restriction So x = -3 check: if x = -4 LS = |...

Math
case 1: 1-x = 2x-5 -3x = -6 x = 2 case 2: -1+x = 2x-5 -x = -4 x = 4 x = 2 or x = 4 but by definition of absolute value, 2x-5 ≥ 0 2x ≥5 x ≥ 5/2 so x = 4

Math
The width of 12 m governs the value of x We must have 12 - 2x > 0 x < 6 the square garden must have sides less than 6 m each.

Math
What part don't you understand ? there are 25 skittles, of which 15 are green so prob of green = 15/25 = 3/5 since you are returning the one you picked, the second prob is the same as the first so prob(2green) = (15/25)(15/25) = (3/5)(3/5) = 9/25

RE: ALGEBRA
Improvement over your last post. 25x^2 - 10x = 0 5x(5x-2) = 0 5x = 0 ---> x=0 or 5x-2=0 ---> x = 5/2

Algebra
I suspect a typo, your wording indicates that it should have been a quadratic. the way you have it ... 25^2 - 10x = 0 625 = 10x x = 625/10 = 125/2 or 62.5

Math
prob(2 green) = (15/25)(15/25) = 9/25

math
argggh, what kind of a texbook would mix metric with non-metric units ?? anyway ... 20 inches = 20(2.54) cm = 50.8 cm one rotation would cover 2π(50.8) cm or 319.1858. (I stored it on calculator) 150 km/h = 150(1000)100)/3600 cm/s = 4166.666.. cm/s number of revolutions =...

math
cost of one item --- x .2x = 16 x = 16/.2 = 80 So two items without tax would cost 160

maths
good question, Olivia, since if 3x+3 = 0 we would have 0/(6y+1) = 3 0 = 3 which would be nonsense. Jonel was just "lucky" to get the correct answer, since x = -1 works in the simplified equation x = 6y but not in the original equation.

maths
from the given equation, 18y + 3 = 3x+3 18y = 3x x = 6y then 7x/3y = 42y/(3y) = 42/3 = 14 =

Math
width = 2x+2 length = 4x + 4 2(2x+2)(4x+4) = 216 2(2)(x+1)(4(x+1) = 216 4(x+1)^2 = 54 take √ of both sides 2(x+1) =√54 = 3√6 x+1 = 3√6/2 x = 3√6/2 - 1 = appr 2.67 the pool is 7.35 m by 14.70 m check: 2(7.35)(14.7) = 216.09 , not bad

silly typo - Math
the third last line of the solution should of course be (x-2)^2 = 28 and the conclusion line: can't have a negative side, so x = √28 + 2

Math
let the shortest side be x then the longer side is x+5 and the hypotenuse is x+7 (x+7)^2 = x^2 + (x+5)^2 x^2 + 14x + 49 = x^2 + x^2 + 10x + 25 x^2 - 4x - 24 = 0 x^2 - 4x + .... = 24 + ... , going to complete the square x^2 - 4x + 4 = 24+4 = 28 (x+2)^2 = 28 x-2 = ± ͩ...

math
assuming you are using the [..] operator to have the same meaning as (..) we have Limit x^2/sinx , as x ---> 0 using L'Hopitals Rule lim x^2/sinx = lim 2x/cosx , as x ---> = 0/1 = 0 verification: http://www.wolframalpha.com/input/?i=plot+y+%3D+x%5E2%2Fsinx looks at x...

or - Math
√(4x+1) = 2 - √(x+1) square both sides (√(4x+1) )^2 = (2 - √(x+1) )^2 4x+1 = 4 - 4√(x+1) + x+1 4√(x+1) = 4 - 3x square both sides again 16(x+1) = 16 - 24x + 9x^2 16x + 16 = 9x^2 - 24x + 16 9x^2 - 40x = 0 x(9x-40) = 0 x = 0 or x = 40/9 HOWEVE...

maths
b = a-2 c = a+1.5 d = c+1.5 = a+1.5 + 1.5 = a+3 a+b+c+d = 66.5 a + a-2 + a+1.5 + a+3 = 66.5 4a = 64 a= 16 box A = 16 box B = 14 box C = 17.5 box D = 19 check: sum = 66.5 All is good.

math
Your statement is false (25+5)(25-5) ≠ 0 it is (30)(20) = 600 What were you trying to do? To "solve" an equation, it must contain a variable Your expression shows the "difference of squares" could be done as 25^ - 5^2 = 625 - 25 = 600

College Algebra
What about it ? did you mean (15x^2-23x-21) / (3x-7) ? are we graphing y = (15x^2-23x-21) / (3x-7) ? are we solving (15x^2-23x-21) / (3x-7) = 0 ?

math
I would let the width = x then the length is x+120 and x(x+120) = 6400 x^2 + 120x - 6400 = 0 which factors to (x-40)(x+ 160) = 0 x =40 or x = -160, which is not possible, can't have negative width width is 40, length is 40+120 = 160 check: area = 40(160) = 6400 , yup!!

math
I will assume you mean (3x-4)/(4x+2) use the quotient rule ... y = (3x-4)/(4x+2) dy/dx = ( (4x+2)(3) - (3x-4)(4) )/(4x+2)^2 = (12x + 6 - 12x + 16)/(4x+2)^2 = 22/(4x+2)^2 or = 11/(2(2x+1)^2)

Math
correct, assuming that repetition of letters and numbers is allowed

Algebra
really ? isn't x^2 a perfect square? isn't 121 a perfect square ? ---- 11^2 = 121 Don't we subtract (-) to take the difference between 2 numbers? Now what do you think??

algebra
http://www.wolframalpha.com/input/?i=plot+4y%3Dx%2B8%2C+x%3D2%2F3y%2B2

Statistics/Probability
prob(Saturday) = 1/7 prob(not Saturday) = 6/7 prob(exactly 4 of 15 years is a Saturday) = C(15,4) (1/7)^4 (6/7)^11 = appr .1043 at least 2 Saturdays ----> 1 - (case of 0 Saturday + case of 1 Saturday) = 1 - (6/7)^15 - C(15,1)(1/7)(6/7)^14 = .6534 check my arithmetic

Algebra II
I will assume p5 is meant to be p^5 and 2x2 is meant to be 2x^2 , then p^5 + 2x^2 + 3px + 17 = 0 2x^2 + 3px + p^5 + 17 = 0 a quadratic with a = 2 , b = 3p and c = p^5 + 17 for real roots: 9p^2 - 4(2)(p^5 + 17) ≥ 0 9p^2 - 8p^5 - 136 ≥ 0 using Wolfram to solve, I got...

precalculus
make a sketch of the positions at t = 0, 1, 2, 3, and 4 and you will see that you need something like height = 5sin(π/2)t + 8 to meet your condition of 6:00 o'clock position being 3 m we do a 1 second shift to the right, height = 5sin [(π/2)(t-1)] + 8 check: when...

math
prob(male) = .4 prob(female) = .6 prob(5 of 6 are male) = C(6,5) (.4)^5 (.6) = ... prob(at least 4 of the 6 are boys) = prob(4 boys) + prob(5 boys) + prob(6 boy s) = C(6,4) (.4)^4 (.6)^2 + C(6,5) (.4)^5 (.6) + .4^6 = --- all boys = .4^6

Algebra
first of all, write it in its general form ax^2 + bx + c = 0 t^2 - 6t + 3 = 0 a = 1, b = -6 , c = 3 t = (-b ±√(b^2-4ac) )/(2a) = (6 ± √(36-4(1)(3))/2 = (6 ± √24)/2 = (6 ± 2√6)/2 = 3 ± √6 No complex roots here.

Math
let me guess, you want to know the speed of the east-bound ship. looks like a Pythagorean problem: (24(22.2))^2 + (24t)^2 = 863^2 ..... see if you can get appr 28.28 km/h

math
a+3d = -3 a+8d = 12 subtract: 5d = 15 d = 15/5 = 3 a + 9 = -3 a = -12 common difference is 3 sum(7) = (7/2)(-24 + 6(3)) = -21

trigo
slope of y = -mx is -m, but m is a positive number, so the slope is negative the slope is also equal to tan Ø the tangent is negative in quadrants II and IV, but x > 0 in IV so 270° < Ø < 360°

math
√3 is an irrational number, which is a subset of the real numbers

math
salary in 1st year --- x salary in 3rd year = x(1.03)^2 salary in 4th year = x(1.03)^2 (1.05) salary in 5th year = x(1.03)^2 (1.05)^2 x(1.03)^2 (1.05)^2 = 100000 x = 100000/((1.03)^2 (1.05)^2) = $87,180.84

Algebra
hint: How many wheels does a tricycle have ? how many wheels does a bicycle have? tri ?? bi ??

Math
amount = 500( 1.08^8 - 1)/.08 = ....

math
.10(1) + .025(1) = x(2) same type as your previous post, I will let you finish it.

math
.02(25) + .06(35) = x(60) 2.6 = 60x x = 2.6/60 = .04333.. The resulting concentration is 4 1/3 %

maths
assuming that all available digits must be used at least once: largest : 44210 smallest: 1024 now multiply them

math
width --- p length -- p+1 p(p+1) = 6 p^2 + p - 6 = 0 easy to solve by factoring...

math
from smallest to largest of the 7 consecutive EVENS x, x+2, x+4, x+6, x+8, x+10, x+12 middle is x+6 x+6 = 48 x= 42 smallest is 42

Math
Using Calculus .... x+y = 11 ---> y = 11-x S = 1/x - 1/y = 1/x - 1/(11-x) = x^-1 - (11-x)^-1 dS/dx = -1/x^2 - 1/(11-x)^2 = 0 for a max/min of S -1/(11-x)^2 = 1/x^2 -x^2 = 11-x^2 -2x^2 = 11 x^2 = -11/2 No real solution , there is no maximum see Wolfram http://www.wolframalph...

math
Looking back I see many posts by you involving the quadratic equation and its properties, You have shown no sign that you have attempted any of them, nor did you indicate where your problems lie. The intent of this forum is not to simply do homework or assignments for you. for...

maths
I suspect a typo, since I get 2/(x+p ) = 1/r x+p = 2r ---> linear equation x = 2r-p , which only has one root

maths
For any quadratic, complex roots or irrational roots always come as conjugate pairs so if one root is 2 + i√3, the other must be 2 - i√3 sum of those roots = 4 product of those roots = 4 - 3i^2 = 7 In any quadratic of the form x^2 + px + q = 0 the sum of roots = -p...

math
first reduce the equation to x + 6y - 3 = 0 Since the new line is perpendicular, it must be 6x - y + c = 0 plug in (2,4) 12 - 4 + c = 0 c = -8 new equation: 6x - y - 8 = 0

maths
Since in a square, the diagonals bisect each other, 5x+9 = 5+3x 2x = -4 x = -2

maths
the quadratic must have been (x-tan30)(x-tan15) = 0 x^2 - xtan30 - xtan15 + tan30tan15 = 0 x^2 + x(-tan30 - tan15) + tan30tan15 = 0 comparing this to x^2 + px + q = 0 p = -tan30 - tan15 and q = tan30tan15 then 2 + q - p = 2 + tan30tan15 - (-tan30 - tan15) = 2 + tan30tan15 + ta...

maths
let the roots of the first be s and 4r let the roots of the second be s and 3r 1st: x^2 - 6x + a = 0 sum of roots = 6 product of roots = a s+4r = 6 and 4rs = a 2nd: x^2 - cx + 6 = 0 sum of roots = c product of roots = 6 s+3r =c and 3rs = 6 ---> rs = 2 so in 4rs = a , we hav...

maths
Sachins would have been (x-4)(x-3) = 0 x^2 - 7x + 12 = 0 Rahul's would have been (x-3)(x-2) = 0 x^2 - 5x + 6 = 0 Sachin was wrong with the 12, should have been 6 Rahul was wrong with the -5x , should have been -7x Equation should have been x^2 - 7x + 6 = 0 (x-6)(x-1) = 0 x...

algebra
amount of the 30% solution needed ---- x L amount of the 16% solution needed --- 5-x L .3x + .16(5-x) = .272(5) times 100 30x + 16(5-x) = 136 30x +80 - 16x = 136 14x = 56 x = 4 L 4 L of the 30%, and 1 L of the 16% solution would be needed.

math
For any linear equation in the form Ax + By + C = 0 , the slope is -A/B So for both of your equations, the slope is -1/3 thus they are parallel

Algebra
For a complicated equation such as yours, the most powerful method is probably Newton's Method. let y = 3x^2+4lnx+4 dy/dx = 6x + 4/x newx = x - y/(dy/dx) = x - (3x^2+4lnx+4)/(6x + 4/x) which simplifies to newx = (3x^2 - 4lnx)/(6x + 4/x) now use an iteration process, I star...

algebra
Vikky, what Steve is telling you that complex roots, as well as irrational roots, always come in conjugate pairs. e.g. if one root is 5 - 7i, then there has to be a matching 5 + 7i e.g. if one root is (4 + 3√5)/2 , then there has to be a (4 - 3√5)/2 So, if you know...

math
Using a ruler and compass, draw the base line of 9 inches. Set your compass to 6 inches, from the left end of the base draw an arc above the base line. Set your compass to 4 inches, from the right end of the base, draw an arc above the base line The intersection of the two arc...

Math
To be an arithmetic progression, (2t-1) - t = (2t+4) - (2t-1) solve for t

math
what is 60 + (2/5)(60) ?

algebra math
I don't see any obvious relationship, nor does Wolfram http://www.wolframalpha.com/input/?i=plot+%7B%282%2C3%29%284%2C5%29%286%2C4%29%288%2C6%29%2810%2C5%29%2812%2C12%29%2814%2C16%29%2816%2C22%29%2818%2C26%29%2820%2C32%29%7D

mat/simultaneous equation
I would use elimination here 1st times 3 ---> 6x - 15y = 39 2nd times 5 --> 25x - 15y = -75 subtract them: -19x = 114 x = -6 back into 1st -12 - 5y = 13 -5y = 25 y = -5 x = -6 , y = -5

calculus
Assuming we take the growth to be exponential , ... 5 e^(28r) = 7.5 e^(28r) = 1.5 ln both sides ln (e^(28r)) = ln1.5 28r = ln 1.5 r = .0145 the rate is 1.45% check: 5 e^(28*.0145) = 7.5

maths probability
Answered by MathMate a few days ago under a Physics heading http://www.jiskha.com/display.cgi?id=1403632512

math
In a 32:3 ratio, there are 35 parts 7 m or 700 cm divided by 35 = 20 cm by part So what do you think?

Math
I get 3t-9-20t+15 = 5-42t-7 25t = -8 t = -8/25

Math
I will assume you mean 120a^4b^2/(-24a^9b^-15) if so, then it would be -5 a^-13 b^17 or -5b^17/a^13

Algebra 1
Use this notation to indicate exponents: x^3 - x^2 - 4x + 4 = 0 grouping will work x^2(x - 1) - 4(x - 1) = 0 (x-1)(x^2 - 4) = 0 (x-1)(x+2)(x-2) = 0 so x = 1 , -2 , +2

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