Posts by Reiny

Total # Posts: 39,945

Math
dy/dx=2-8(3x+4)^-0.5 y = 2x + (16/9)(3x + 4)^(-3/2) + c or y = 2x + (16/9)(1/?(3x+4)^(3/2) + c but (0, 4/3) lies on it , so 4/3 = 2(0) + (16/9)(1/4^(3/2) + c 4/3 = (16/9)(1/8) + c c = 6 y = 2x + (16/9)(3x + 4)^(-3/2) + 6 check my algebra, should have written it out on paper ...

math
(a,b) ---> reflected across the x-axis ---> (a, -b) (a,-6) ---> translated 5 units to the right ---> (a+5, -b)

math
There must be a 90° angle, that is, two of the lines must be perpendicular, or the slopes of two of the lines must be negative reciprocals of each other. So .... take the slope of the 3 lines and check for the above property. A longer method would be to find the lengths of...

Lesson 2 Unit 2 Connexus SS
Just listened to Bob Marley's story about them, called Buffalo Soldier.

math
prob(spots) = 12/180 = 1/15 so of the 1200 frogs, (1/15)(1200) should have spots, so .. how many should not have frogs ? or prob(not spots) = 14/15 number who don't have spots = (14/15)(1200) = ... You will of course get the same answer from either method, right ?

Pre calc
Arora gave you a detailed solution to this type of question here: https://www.jiskha.com/display.cgi?id=1516371278 follow the same steps, and stick to one name

math
How about an indirect proof: Assume that ?(a+b) = ?a + ?b , for all a, b > 0 all we need is one counter-example to show my assumption is false: is ?(9 + 16) = ?9 + ?16 ??? LS = ?25 = 5 RS = 3 + 4 = 7 RS ? LS so I have a case where my assumption is false, all done

Algebra 1
4^-2 = 1/4^2 = 1/16 <----- positive (-4)^-2 = 1/(-4)^2 = 1/16 <------ positive (-4)^-3 = 1/(-4)^3 = 1/-64 <----- negative mhhhh ?

Algebra
plug in your values into I = PRT 480 = P(.04)(6) solve for P check your answer by finding the interest.

Geometry
I am sure Bosnian meant: ( x + 18 )² + ( y + 7 )² = 6² , since the radius is 6, not 12 ( x + 18 )² + ( y + 7 )² = 36

Trigonometry
if cot x = 5/?11 , then tan x = ?11/5 and x must be in quads I or III construct your right-angled triangle with opposite to angle x as ?11 and adjacent as 5 r^2 = 11 + 25 = 36 r = 6 then cscx = 6/?11 ins quad I csc x = -6?11 in III your choices are missing the quad III angle.

Math (money)
Damon already answered this for you. Why are you re-posting and posting under a different name ? https://www.jiskha.com/display.cgi?id=1516294634

Math
so you are adding 2(.25) m or .5 m to each side old area = 1.5^2 m^2 = 2.25 m^2 new area = 2^2 m^2 = 4 m^2 increase = ....

Maths
in x years: Mr. Lee --- 56+x Sam ---- 4 + x 56+x = 5(4+x) solve for x

math - probability
PS, your question made the point: "Keep in mind, the coins are not tossed simultaneously." The outcomes of two coins tossed simultaneously or a single coin tossed twice in succession would be the same. The same would be true for 3 coins tossed simultaneously or a ...

Math
original side --- x original area = x^2 new side = (3/4)x new area = (9/16)x^2 so new square has area of 9/16 of the old or the areas of similar shapes are proportional to the square of their corresponding sides so 3/4 ----> 3^2/4^2 = 9/16

Math
R -- right = .99 W -- wrong = .01 prob(all correct) = C(60,60) (.99^60) (.01)^0) = .00^60 = ... prob(59right,1wrong) = C(60,59)(.99^59)(.01^1) = .... Prob(58right,2wrong) = ....... ** (see above and adjust) prob(at least 2 wrong) = 1 - ** you try the others.

Math
let each leg's length be x cm so the base is (1/2)x + 3 so .... x + x + x/2 + 3 = 73 2x + x/2 = 70 my suggestion: multiply each term by 2, and it becomes very easy

Math
No! The president can be chosen in C(12,1) ways the VP can be chosen in C(11,1) ways the 2 shoe-shiners in C(10,2) ways the 2 polish selectors in C(8,2) ways, leaving C(6,6) for advertising. multiply these .... 12x11x45x28x1 = 166320

Geomtry
Since you have bisected the 90° angle, ?A = 45° and ?B = 45° so you have isosceles triangles, and AC = CD = your given

simple algebra
H - K = log(A/C) H - k = logA - logC logA = H - K + logC A = 10^(H - K + logC)

Math
let's intersect them: x^2 - b = -x^2 + b 2x^2 = 2b x = ± ?b then y = 0 So the points of intersection are (?b,0) and (-?b,0) Their vertices are (0,b) and (0,-b) Which makes the lengths of their diagonals equal to 2b and 2?3 Since the area of a rhombus is the product ...

graph showing solution - math
Here is the graph of (x+y)^2 = x-y http://www.wolframalpha.com/input/?i=plot+(x%2By)%5E2+%3D+x-y

math
let log9(x-y) = a ----> 9^a = x-y then log3(x+y) = a ---> 3^a = x+y from 9^a = x-y (3^2)^a = x-y (3^a)^2 = x-y 3^a = ?(x-y) Thus: x+y = ?(x-y) (x+y)^2 = x-y The solutions that appear obvious are: x = 0, y = -1 x = 1, y = 0 But, I squared the equation, so all answers must...

math
You got it

math
Hint : if ABC = 2880 and AB = 360 how about finding ABC/(AB) = 2880/360 C = .... Now do the same with AC = 160 , so now you also have B From there it is easy to find A

Algebra. Formalizing relations and functions
You forgot to indicate your choice. What does O/ mean? I have never seen that.

math
given a point (a,b) and the slope of the line of m, the equation in the form required is: y - b = m(x - a) now which of the given equations fits that pattern ?

Math
Actually, the radius is 30 ft , not 15 so area = ?(30)^2 square feet = .....

adenda - Mathematics
looks like the " I " also fits vertical as well as horizontal symmetry

Mathematics
vertical line symmetry: M, A, T, H, I horizontal line symmetry: H, E, C none: S so, more than one line: H

Math
The point is that simply giving you the answer would not serve any purpose. Ok, suppose you had $3.00 (or 3 boys), and your friend had twice as much, (the ratio of 2 : 1) , how much would your friend have ??

math
length x width = area 7.5w = 60 w = 60/7.5 = ....

math
I am sure you meant: (x + 2)^11 there will be 12 terms in the expansion. they are: x^11 + V(11,1) (x^10)(2) + C(11,2) (x^9)(2^2) + ... + C(11,9) x^2 (2^9) + C(11,10) x^1 (2^10) + 2^11 which term contains x^2 ?? calculate it.

Consumer Math
I suggest you follow the instructions in the steps outlined for you. Looks very straight-forward to me look in your notes or textbook to see how you can find the z-score. As for tables, they are really not used anymore, there are enough on-line charts or applets to find the ...

Algebra
Using the formula that you must know: PV = payment( 1 - (1+i)^-n )/i i = .066, n = 30 plug in those values in your calculator and calculate. Let me know what you got.

Algebra II
Just looking at the equation, we can tell that the vertex is (-2,2) and the parabola opens upwards. So clearly, it cannot cross the x-axis. So clearly, no real solution

maths
They are all equal, so set pairs equal. 1st and last ---> 3a+2 = b+3 or 3a - b = 1 ** 2nd and last ---> 3b - a = b+3 or a - 2b = -3 *** from ** , b = 3a-1 sub into *** a - 2(3a-1) = -3 a - 6a + 2 = -3 -5a = -5 a = 1 , then b = 3-1 = 2 the sides are 5 units each and the ...

algebra
you want the max value of -10x^2 + 100x - 210 = -10(x^2 - 10x + ... - .....) - 210 I am completing the square = -10(x^2 - 10x + 25-25) - 210 = -10( (x-5)^2 - 25) - 210 = -10(x-5)^2 + 250 - 210 = -10(x-5)^2 + 40 Max is 40 when x = 5 how does that fit into the given answers? ...

math
you already did it

Math
subbing x = -1 into the first equation gives you 3(-1) - 10 = -13, so it satisfies the first subbing x = -1 into the 2nd equation gives you -2(-1) - 15 = -13, so it satisfies the 2nd as well (-1,-3) must be the intersection point, or the solution to y=3x-10 and y=-2x-15

Math
If you are just testing if 3 numbers form a Pythagorean triple that is easy. Assume the largest is the hypotenuse, (it has to be!) and test (smallest)^ + (middle one)^2 = largest^2 e.g. is 5, 12, 13 one of those? is 13^2= 5^2 + 12^2 ? is 169 = 25 + 144 ? YES, so you got one! ...

Math: Ratios
iphone owners --- 5x Samsung users --- 3x 5x - 3x = 500 etc

Math
Log3(log9x) = 1 , use your definitions log a x = b <------> x = a^b log9 x = 3^1 9^3 = x x = 729

maths
Assuming he has only reds, blues, and whites blue beads ---- x red beads ----- x+20 total of blues and reds = 2x + 20 white beads = 95-(2x+20) = 75 - 2x 75-2x = 2(x+20) 75-2x = 2x + 40 -4x = -35 x = 35/4 , which is not a whole number the question is bogus, do you have a typo? ...

Check this - Algebra2A
Arora said: "If y varies directly with x, then that means, whenever x increases by a certain amount, y proportionally increases by the same amount. " not true Your answer of 15, even though correct, has nothing to do with the question, I can get 15 in an infinite ...

Algebra2A
"y varies directly with x" ---- y = kx, where k is a constant given: when x = 2, y = 6 6 = 2k k = 3 so your equation is : y = 3x when x = 5 , y = .... or direct variations can be solved by simple ratios 6/2 = y/5 2y = 30 y = .... (same as above)

Math
number of white patches ---- x 5x + 5(27) = 540 solve for 5x , the area of the white patches

Precalculus
since ? radians = 180° we have ? radians in a straight line or one complete rotations is 2? radians, so ......

Logarithms
log x x^(m-1) + 1 = m LS = log x x^(m-1) + 1 = (m-1)log x x + 1 , (using the rule log a^n = nloga) = (m-1)(1) + 1 , since log n n = 1 = m-1 + 1 = m = RS

MATh
If Bob starts with $46 and you spend $12 or if Sue starts with $42 and you spend $12 who will have the larger amount left ???

Math
yes, both are correct

Math
Just apply your definitions: sum(n) = a(r^n - 1)/(r-1) sum(5) = a((-3)^5 - 1)/(-3-1) = -61 a(-244/-4) = -61 61a = -61 a = -1 so term(5) = ar^4 = -1(-3)^4 = 81 #2: you have a GP with a = 38500, and r = 1.03 you want sum(6), so apply the above formula

Algebra
abc = (ab)c = (ab)c in your list of properties, which one matches this pattern. Simplify the expression. (2x/9+8)-8 = 2x/9 + 8 - 8 = 2x/9 Solve the formula for g s=1/2gt^2 multiply both sides by 2 2s = gt^2 isolate the g by dividing both sides by t^2 2s/t^2 = g Solve the ...

Math PLZ HELP
the way you typed it ... 5-4?5/10 = 5 - 2?5/5

Logarithms
4^x+6(4^-x)=5 4^x + 6/4^x = 5 let 4^x = y , so you have y + 6/y = 5 y^2 + 6 = 5y y^2 - 5y + 6 = 0 (y - 2)(y - 3) = 0 y = 2 or y = 3 case1: 4^x = 2 (2^2)^x= 2^1 2^(2x) = 2^1 2x = 1 x = 1/2 case2: 4^x = 3 take log of both sides, and follow through with log rules log(4^x) = log3 ...

check this - math
You do NOT need a common denominator for multiplication and division of fractions. 3/4 x 5/2 = simply 15/8 the answer given by anonymous of 3/4*10/4 is not incorrect, but it can be reduced. = 30/16 = 15/8

Algebra
for a cube , side^3 = volume so side = (343x^12) = 7x^4

Math
Der Umfang einmal herum = 2(Laenge + Breite) = ... Aber du gehst zweimal herum, so .....

Me sue plz help math
What is your question? I sketched the first one, if you join PR, you can see that you have 2 congruent triangles, so angle S = 120° by the sine law you can find the other angles and PR the other question is the same thing.

Calculus
I agree with your derivative, and I a agree with your idea of (x-y+2)/(x-y+4)= 0 for the horizontal tangent. Now consider where the zero could come from. It certainly can't come from the denominator, since we can't divide by zero (this will be considered in the next ...

maths
man-days = 6(20) = 120 rate of man = 1/120 , where 1 represents the work done rate of boy = 1/240 x(10)(1/120) + x(5)(1/240) = 1 , where 1 represents the work x/12 + x/48 = 1 x(1/12 + 1/48) = 1 (5/48)x = 1 x = 48/5 = 9.6 days or since 1 boy does the job of 1/2 man, 5 boys ---&...

math
by definition |-25| = 25

math
There are several algorithms: 1. ----- This method seems to be taught these days: for ax^2 + bx + c vs. 2x^2 - x - 10 - multiply a times c -----> 2(-10) = -20 - now look for factors of -20 which will add up to b our b = -1 so a few quick tries shows (-5)(+4) = -20 and -5+4...

Math
I am guessing they want to express 4 minutes to 90 seconds as a ratio 4 min : 90 s = 240 s : 90 s, now we have the same units = 240 : 90 = 8 : 3

trigonometry
This question has nothing to do with trig, it is simply a Pythagorean application. x^2= 10^2 + 15^2= 325 x = ?325 = appr 18 km

Math2
The answer to my example was 3x + 15 which consists of 2 terms, thus we have a binomial. Of course it could also be called a polynomial, which is the general classification "poly" from the Greek meaning many or several so check off: A, and C

Math2
use an example: 3(x+5) = 3x + 15 how many terms do you see? What does the bi in binomial mean ? What does the mono in monomial mean? How can it be A) and B) ???

math
Well, we know it can't be A, since it is changing we know it can't be B, since it is not growing not C or D, since it clearly is not linear. is it exponential ? yes Is it decay, is it getting less ? Yes so .....

Geometry
correct

algebra
Looks like they used the same textbook back in 2011 https://www.jiskha.com/display.cgi?id=1321919895

algebra
B's current age ---- x F's current age ---- 29-x 7 years ago: B's age = x-7 F's age = 29-x - 7 = 22-x x-7 = 2(22-x) solve for x , and sub into my definitions

Geometry
direct application of the cosine law, using the fact that the largest angle is opposite the largest side .... 158^2 = 110^2 + 137^2 - 2(110)(137)cosØ 30140 cosØ = 5905 cosØ = .195919... Ø = appr 78.7° Answer accordingly.

math
Volume of a sphere =(4/3)? r^3 you have 3 of them, so the total volume = 4? (6^3) cm^3 = 864? cm^2 or appr 2714 cm^3 (why use such a poor approximation of ? if almost all calculators have the ? constant built in ? I am sure you are going to use a calculator anyway. )

math
What is 690 pi/(20?) ? , (assuming your pi = ?)

Geometry
Kayla, you were given the exact answer of 2?10 by "cyliner", which is 6.3245553... which correct to 1 decimals would be 6.3 so .....

Algebra
first one: you have a rectangle + half a circle = 5*8 + (1/2)? (4^2) = ... can you see why the radius of the semicircles is 1/2 of 8 ? 2nd: area of circle = ?(2^2) = appr 12.566 inches^2 You didn't say what the square is like, I will assume the circle touches the square on...

Math
ummhhh, a single book would be 16 ways

arithmetic mean
(x + 30(9) )/31 = 10 x + 270 = 310 x = 40

Mathematics
f(x) = 2x + 5 and g(x) = x^2-1 the f(g(x)) = f(x^2 - 1) = 2(x^2 - 1) + 5 f(g(x)) = 2x^2 - 2 + 5 = 2x^2 + 3 check: try x = 6 g(6) = 36-1 = 35 f(35) = 2(35) + 5 = 75 in my answer of f(g(x)) = 2x^2 + 3 f(g(6)) = 2(36) + 3 = 75

Math
straight application of a linear function. let E = mL + k, where E is the force, and l is the load, and k is the constant given : when L = 20, E = 14 20m + k = 14 when L = 30, E = 20 30m + k = 20 subtract them: 10m = 6 m = 6/10 = .6 back into 20m + k = 14 12 + k = 14 k = 2 so ...

Probability
I answered this question yesterday when it was posted under "Angel" https://www.jiskha.com/display.cgi?id=1515201345 Why did you repost it ?? I stand by those answers for a) and b) c) is open for debate since it is ambiguous. here is the other way to do a) Prob(all 5...

Statistics
Number of possible choices of 5 members from a total of 15 = C(15,5) = 3003 a) number of all teachers = C(10,5) = 252 so prob(5 teachers) = 252/3003 = 12/143 b) 3 teachers, and 2 students prob = C(10,3) * C(5,2)/3003 = .... c) not clear with the wording. Is it exactly 3 ...

Math
by (64?69/63)3 do you mean: - (64?69/63)^3 ? - (64?69/63)?3 ? - (64?69/63)/3 ? , or some other combination? in any case, none of them can be expressed as a power with base 6

statistics / probability
What is (18/30)(17/29) ?

Calculus
30 mph = 30/3600 miles/sec = 1/120 mps 50 mph = 1/72 mps v = at + c when t = 0, v = 1/120, so c = 1/120 v = at + 1/120 when t = 4, v = 1/72 1/72 = 4a + 1/120 4a = 1/180 a = 1/720 miles/sec^2 v = (1/720)t + 1/120 if the distance is s s = (1/1440)t^2 + (1/120)t + k when t = 0, s...

maths
What Scott did makes perfect sense to me. Perhaps you will understand it better if we use the standard definitions. term(1) = a = 5 term(3) = a+2d = 245 so: 5 + 2d = 245 2d = 240 d = 120 So the 3 terms are 5, 125, and 245 There is only one answer, not two like you stated. If ...

Math
.13x = 660 x = 660/.13 = appr 5077

But, but, .... algebra
It said that the sides form an AP, not the angles for angles 30, 60, 90, the sides would be 1 , ?3, and 2, which do not form an AP

math
length of wire = circumference = ?D = 21? metres or appr 66 m cost = 4(21?) = 84? = 263.89 or appr Rs 264

Algebra
D+(1/4)D+........+D(1/4)^n-1 = D(1 + 1/4 + 1/16 + (1/4)^(n-1) ) = D(geometric series of n terms, with a = 1, r = 1/4) sum(n) = a/(1-r) , as n ---> ? = 1/(1-1/4) = 1/(3/4) = 4/3 so the amount = D(4/3)

math
are you looking for something like: 9.5 + 30 + 5.5 < 9.65+30.1+5.835 < 10 + 30 + 6 45 < 9.65+30.1+5.835 < 46 so the sum is between 45 and 46

Ratios
let number of students choosing soccer be 8x, and the number of students choosing baseball be 3x 8x = 56 x = 7 so students choosing soccer is 56 students choosing baseball is 21 note: 56+21 =77, so as was noted, how does the 132 enter the picture

math
x-4 = 16 - x solve for x or ... from -2 to 4 is 6 so add 6 to 4

math
It means we replace x with -3, wherever we see it f(x) = x^2 - 5x - 2 f(-3) = (-3)^2 - 5(-3) - 2 = ......

math
I would do it this way: LS = (sinx+1)/(1-sinx) = (sinx+1)/(1-sinx) * (sinx+1)/(1+sinx) = (sinx+1)^2 /(1 - sin^2 x) = (sinx + 1 )^2 / ((1+sinx)(1-sinx)) = (1+sinx)/(1-sinx) RS = ( tan x + sec x )² = (sinx/cosx + 1/cosx)^2 = ( (sinx+1)/cosx)^2 = (sinx+1)^2/cos^2 x = (sinx+1...

math
2sec^2 x - 3tanx - 5 = 0 2(1+tan^2 x) - 3tanx - 5 = 0 2 + 2tan^2 x - 3tanx - 5 = 0 2tan^2 x - 3tanx - 3 = 0 tanx = (3 ± ?33)/4 tanx = 2.18614... or tanx = -.68614... x = 1.14178... or x = ? + 1.14178 = 4.283376 or x = ? - .60136 = 2.5402 x = 2? - .60136 = 5.68182 x = 1....

Math
Steve, thanks for the catch.

Math
The key is a good diagram. On mine I labeled the window position as A and the base of the building as B, so AB = 30 I labeled the top of the flag pole as P, and its base as Q So BQ = 25 We can find PQ by PQ^2 = 30^2 + 25^2 PQ = .... No look at triangle AQP, angle APQ = 90+44...

Math
I don't see anything. Tried the usual tests for polynomial and exponential sequences. Wolfram found no pattern either: http://www.wolframalpha.com/input/?i=pattern+%7B0.2+,+4+,+3+,+10+,+14%7D

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