Monday

January 26, 2015

January 26, 2015

Total # Posts: 28,751

**Algebra**

notice that for every increase of 1 in the x, the y increases by 2 so slope = 2 or, more formally, take the fist two points (1,1) and (2,3) slope = (3-1)/(2-1) = 2 so y = 2x + b sub in the first point (1,1) 1 = 2(1) + b b = -1 y = 2x - 1 check the remaining points to make they...
*November 1, 2014*

**Algebra**

I assume you want it 'simplified' and that you forgot the brackets (8-6i)/(3i) = (8-6i)/(3i) * i/i = (8i - 6i^2)/(3i^2) = (6 + 8i)/-3 or =( -6 - 8i)/3 hint for the second... multiply top and bottom by (4-2i)/(4-2i)
*November 1, 2014*

**Math**

simply solve ... .07x + .15(x+1500) = 1545 where x is the amount invested at 7%
*November 1, 2014*

**Maths**

Please type your question in proper English. "d" is the common variable for the difference between consecutive terms of an AP and not as a substitute for "the".
*November 1, 2014*

**math**

Finding the distance between 2 points and finding the midpoint between 2 points should be part of your repertoire of common and memory-recall-ready formulas if you want to study math for (a,b) and (c,d) Distance = √( (c-a)^2 + (d-b)^2 ) midpoint = ( (a+c)/2 , (b+d)/2 ) ...
*November 1, 2014*

**Algebra**

so a#b =(a+b)/2 then ((1#2)#2)#4 = (1.5#2)#4 = 1.75#4 = 2.875 or = 23/8 or ((1#2)#2)#4 = (3/2#2)#4 = (7/4)#4 = 23/8
*November 1, 2014*

**Algebra**

P(g(x)) = p(4-3x) = 4 + 2√(4 - 3x + 2) = 4 + 2√(6-3x) remember we cannot take the square root of a negative, so 6-3x≥0 -3x ≥ -6 x ≤ 2 so the largest value of a is 2
*November 1, 2014*

**MATHS**

I will need 2 zeros (0 can't be in front) 3 ones 3 twos 3 fours ... 3 sevens 2 eights 2 nines total = 29 for b) we can save the 2 nines, (the 3 sixes will suffice) so they can save 2 cards
*November 1, 2014*

**Maths**

Prob(m) = 1/5 prob(S) = 4/5 Possible outcomes in best of three" MM --- (1/5)(1/5) = 1/25 MSM -- ((1/5)(4/5)(1/5) = 4/125 SMM -- ((4/5)(1/5)(1/5) = 4/125 SS ---- (4/5)(4/5) = 16/25 ----> Sue wins SMS -- (4/5)(1/5)(4/5) = 16/125 ----> Sue wins MSS -- ((1/5)(4/5)(4/5...
*November 1, 2014*

**Algebra**

πr^2 = 2πr r^2 - 2r = 0 r(r-2) = 0 r = 0 , the trivial answer or r = 2 So the diameter is 4 a/b = 2/3 or 2b = 3a, or b = 3a/2 (a+5)/b = 5/6 5b = 6a + 30 5(3a/2) = 6a + 30 times 2 15a = 12a + 60 a = 20 and b = 3(20)/2 = 30 the fraction was 20/30 y < √x by 4 y...
*October 31, 2014*

**Math**

factor is 10^8.8/10^7.1 = 10^1.7 = appr 50 times as strong
*October 31, 2014*

**Math**

number of quarters ---- x " he has one more dime than he has quarters" ---> dimes ---- x+1 now for the "value" of coins equation: 25x + 10(x+1) = 115 25x + 10x + 10 = 115 35x = 105 x = 3 etc
*October 31, 2014*

**Width of a square**

How can 45/10 = 3.5 ?? 45/10 = 4.5
*October 31, 2014*

**math**

You are looking for those values of x, so that y = (x+5)/(x-2) lies above the x-axis first of all, x ≠ 2 or else we are dividing by zero critical values are -5 and 2 investigate x < -5, say x = -10 then y = -/- = + , that's good investigate between -5 and 2, say x...
*October 31, 2014*

**maths**

I will assume you meant: 1/( (x+2)(x+3) ) - 1/( (x-4)(x-5) ) what about it? are you simplifying?
*October 31, 2014*

**Math, Can someone check my answers?**

all 3 are correct
*October 31, 2014*

**Thanks Steve - Pre Calculous**

for keeping an eye on me. I just have to read more carefully, I read it as sinx = 1/4
*October 31, 2014*

**Pre Calculous**

my keystrokes on my calculator: 2nd sin .25 = to get 14.478° but the sine is positive in I and II so x could also be 180 - 14.478 = 165.522° there are an infinite number of solutions, just add/subtract 360° to any existing answer to produce more.
*October 31, 2014*

**Math Calc**

divide by 7 sinØ = 6/7 Ø = arcsin (6/7) = appr 58.997° Did you use a calculator? my keystrokes: 6 ÷ 7 = 2nd sin = to get my answer
*October 31, 2014*

**Math Arc Length**

circumf = 2πr = 2π(4.9) = 9.8π so 360° of arc = 9.8π units and 1° of arc length = 9.8π/360 = 49π/1800 units Maybe they didn't like your decimal, but your answer is correct
*October 31, 2014*

**Calculus**

dy/dx = 4x + 5 dy = (4x + 5)dx so for your given data dy= (20+5)(.1) = 2.5 so the other one the same way
*October 31, 2014*

**math**

amount poured into canister --- x g amount in canister = 5026 + x amount left in bag = 4157-x g 5026+x = 2(4157-x) 5026 + x = 8314 -2x 3x = 3288 x = 1096 amount left in bag = 4157-1096 = 3061 g
*October 31, 2014*

**trigonometry**

LS = sinx(cos2x) + cosx(sin 2x) RS = sin(3x) = sin(2x + x) = (sin 2x)cosx + (cos 2x) sinx = LS I am using sin(A+B) = sinAcosB + cosAsinB
*October 31, 2014*

**Math Please Check**

you have found the variables which will yield the maximum and minimum , but you have not found the actual max or min When t = 0 (you had x = 0) h(0) = 0-0 = 0 when t = 2, h(2) = 8 - 12 = -4 also h(-1) = -1 - 3 = -4 so you have a local max at (0,0) and a local min at (2,-4) for...
*October 30, 2014*

**business maths**

I have no idea what your equation is supposed to say or do. Since you are talking about a "focal date", I will assume you have learned to make a time line. label it "now" or 0, 1,2,3 months I place the debt above the line , and the payments below the line, ...
*October 30, 2014*

**geometry**

not enough data all we know is that the total area of pool plus walkway is 72 units^2 so 9x8=72 , perimeter = 34 6x12 = 72 , perimeter = 36 4x18 , perimeter = 44 etc
*October 30, 2014*

**pre-algebra**

so the area of each of the smaller squares = 100/25 = 4 ft^2 so each side of the smaller square must be 2 ft
*October 30, 2014*

**can't figure it out**

Bob, looks like you missed that silly little negative sign in front of the 5 too, just like I did when I answered this question the first time for Ernie, John, and now Charlie . One would assume that he would check back to his previous post before posting the same question ...
*October 30, 2014*

**Math 11**

So you have a tetrahedron area of one of the triangles = (1/2)(16)(16)sin60 = 128(√3/2) = 64√3 Counting the base there are 4 faces, so surface area = 4(64√3) = 256√3 = appr 443.4 cm^2 If you don't want to count the base, multiply by 3 instead of by 4
*October 30, 2014*

**Math**

A two-term ratio can not be equal to a constant looks like a typo
*October 30, 2014*

**math really need help!**

done, look back
*October 30, 2014*

**oops math please help**

didn't notice that little - in front of the 5 f(x+2) = -5(x+2) + 6 you finish it this time
*October 30, 2014*

**math please help**

replace the x with x+2 f(x+2 = 5(x+2) + 6 = 5x + 16
*October 30, 2014*

**Math-urgent-**

huh? how many times are we to subtract ? on the other hand ... 11/12 ÷ 3/4 = (11/12)(4/3) = 44/36 = 11/9
*October 30, 2014*

**algebra**

times 2 14 + 6t = 6 - t 7t = -8 t = -8/7
*October 30, 2014*

**Math**

should have been y-1 = (1/4)(x-1) y = (1/4)x - 1/4 + 1 = (1/4)x + 3/4
*October 30, 2014*

**Algebra**

ahhh, your slope is not zero look at your 3/0 we CAN'T divide by zero , 3/0 is undefined If you look at your sketch , your line will be a vertical line Anytime you have a vertical line, your slope will be undefined and the equation will simply be x = some constant look at ...
*October 30, 2014*

**math**

c + 2s = 10.30 3c + 2s = 18 subtract them 2c = 7.7 c = 3.85 sub back into the first equation to get 3.85 + 2s = 10.3 2s = 6.45 s = 3.23 so c + s = 7.08
*October 30, 2014*

**Equation ratio**

if 5x = 4.5y then y/x = 5/4.5 = 10/9 y : x = 10 : 9
*October 30, 2014*

**Math**

7/3 = rear/2 3rear = 14 rear = 14/3 or 4 2/3 turns or 3 pedal turns = 7 rears 1 pedal turn = 7/3 rears 2 pedal turns = 14/3 rears
*October 29, 2014*

**Math**

yes (4/3)π r^3 = 1767.1 r^3 = 21.864.. r = 7.4999 or appr 7.5 m check: (4/3)π(7.5)^3 =1767.145..
*October 29, 2014*

**Math**

The least common multiply (LCM) of 12 and 20 is 60 So to make 60 burgers, we need 60/12 or 5 patty packages, and 60/20 or 3 bun packages.
*October 29, 2014*

**Math**

According to your equation, the object was 125 m above ground (t=0) , when it was shot solve for h = 0 , this will give you the two times it is on the ground -5t^2 + 120t + 125 = 0 divide by -5 t^2 - 24t - 25 = 0 (t-25)(t+1) = 0 t = -1 or t = 25 but, this only makes sense for ...
*October 29, 2014*

**Trigonometry**

2cosxcsc2x = cscx LS = 2cosx(1/sin 2x) = 2cosx(1/(2sinxcosx) = 1/sinx = csc x = RS sin^2 2x = 4 sin^2 x cos^2 x will use the same identity as in the first one: namely, sin 2x = 2sinxcosx LS = sin^2 2x = (sin 2x)(sin 2x) = (2sinxcosx)(2sinxcosx) = 4 sin^2 x cos^2 x = RS cot 2&...
*October 29, 2014*

**Calculus**

Let the height of the ballon be h ft then tanØ = h/60 h = 60tanØ dh/dt = 60 sec^2 Ø dØ/dt we know dh/dt = 8 when h = 25 tanØ = 25/60 = 5/12 construct a right-angled triangles with opposite side 5 and adjacent side 12. By Pythagoras the ...
*October 29, 2014*

**math**

What is the transformation ? Does it match with any of the "Related Questions" below? the first one has the same coordinates.
*October 29, 2014*

**Math**

look at some example 3/2= 6/4 = 60/40 = 12/8 = .. what do you think?
*October 28, 2014*

**Trig**

(1+sinx)=cos^2 x 1 + sinx = (1 - sin^2 x) (1 + sinx) = (1+sinx)(1-sinx) divide both sides by 1 + sinx 1 = 1 - sinx or sinx = 0 easy to solve if you have to solve
*October 28, 2014*

**Math**

volume of cylinder = π(5^2)(12) = ... volume of cone = (1/3)πr^2 h solve (1/3)π(5^2)h = π(5^2)(12) after getting your answer it should be obvious why it is so.
*October 28, 2014*

**Math**

insufficient data e.g. do the 12 boys play ONLY soccer ? etc
*October 28, 2014*

**Algebra**

ratio of movie to band posters = 120:100 = 6/5 after selling 24 movie posters she has 96 so 96/x = 6/5 6x = 480 x = 80 so she has to sell 100-80 or 20 band posters
*October 28, 2014*

**Algebra**

NA : SA = 5 : 3 , SA : E = 3 : 2 So, NA : SA : E = 5 : 3 : 2 = 5x : 3x : 2x given: NA = 30 5x = 30 x = 6 then NA = 30 SA = 18 E = 12
*October 28, 2014*

**Algebra**

correct
*October 28, 2014*

**math**

let the width of one of the pens be x, let its length be y so we have 8x + 5y = 720 y = (720 - 8x)/5 = 144 - 8x/5 area = 4xy = 4x(144 - 8x/5) = 576x - (32/5)x^2 d(area)/dx = 576 - 64x/5 = 0 for a max of area 64x/5 = 576 64x = 2880 x = 45 largest total area = 4(45)(144 - 8(45)/...
*October 28, 2014*

**Cal.**

Since you did not define what your x and y are, I have no way of checking what you did In my sketch, I let the distance from the man to the light be x m, and the length of his shadow as y m then by ratios , 2/x = y/12 xy = 24 x dy/dt + y dx/dt = 0 when x=4, y=6 and dx/dt = 2.2...
*October 28, 2014*

**math**

width --- x length --- 2x+6 2(x) + 2(2x+6) = 102 carry on
*October 28, 2014*

**Algebra**

pick any pair to find the "slope" I took the first two pairs slope = (1840-1000)/60-40) = 42 so using the 1st point: e-1000 = 42(t-40) e - 1000 = 42t - 1680 42t - e = 680 or e = 42t - 680 all "points" satisfy my equation
*October 28, 2014*

**probability ?????**

time = distance/rate = 121/65 = 1.8615 hrs = 1 hr and 51.7 minutes
*October 28, 2014*

**math**

1st simplified: x + 2y = -1/2 2nd simplified: x + 2y = -1/2 same line, so infinite number of solutions
*October 28, 2014*

**trigonometry**

Did you make a sketch? I have a right-angled triangle with hypotenuse of 54 and a base angle of 90-32 or 58° sin 58 = y/54 y = 54sin58° = ... (the north distance) cos58 = x/54 x = 54cos58 = .... (the west distance)
*October 28, 2014*

**math**

Fran --- x Pete ---- 6x Hannah --- y y + x = 120 y+6x = 230 subtract them 5x = 110 x = 22 then y = 98 Hannah has $98 (Fran has 22 and Pete has 132
*October 27, 2014*

**math**

5 nickels 4 nickels, 5 pennies 3 nickels, 10 pennies 2 nickels, 15 pennies 1 nickel, 20 pennies 25 pennies. so 6 combinations
*October 27, 2014*

**math**

geeeshhh .... 2 inches represent 35 miles 1 inch represents 35/2 or 17.5 miles, so 5 inches represent 17.5(5) or 87.5 miles
*October 27, 2014*

**Calculus**

In just about any introductory Calculus book this type of question appears as a lead-in to the topic of "rates of change" Make a diagram, label the height y and the the base length x then x^2 + y^2 = 13^2 differentiate with respect to t (time) 2x dx/dt + 2y dy/dt = 0...
*October 27, 2014*

**Math**

3^-1 m/min = (1/3) m/min so time = distance/rate = 33/(1/3) = 99 minutes
*October 27, 2014*

**algebra. help!**

1st correct 2nd ... Poorly worded make a Venn diagram and fill in the data, according to your data, 130 play only basketball, 120 play both and 100 play only baseball so 220 for all of baseball circle is correct
*October 27, 2014*

**math**

2/5x-9 < 9/10 times 10 4x - 90 < 9 4x < 99 x < 99/4 if you meant to type 2/(5x-9) < 9/10 we would have a totally different problem, but you didn't type that
*October 27, 2014*

**NO Nicole -Trig**

your step from cos8t=3sin8t to 8 = 3tan8t is totally invalid, that would be pure mathemagics test your value, it does not work
*October 27, 2014*

**Trig**

you are ok up to 8t = arctan 1/3 make sure your calculator is set to radians, and then 8t = .32145 or 8t = π + .32145 t = .04022 or t = .43292 we know the period of tan 8t is 2π/8 or .7854 so we could add this to any previous answer to get more correct answers, as ...
*October 27, 2014*

**algebra**

The only one slightly difficult is #2 |y+4| < 1 then y+4 < 1 AND -y-4 < 1 y < -3 AND -y < 5 y< -3 AND y > -5 so -5 < x -3 in general, for inequalities, if you have |some stuff| < k , then separate them with AND (the intersection) |some stuff| > k...
*October 27, 2014*

**College Algebra**

8% less ----> 100% - 8% = 92% or .92 .92x = 146000 x = 146000/.92 = $158,695.65
*October 27, 2014*

**Pre-Calc/Trig**

Both of your equations are quadratics the standard form, sometimes called the vertex form, of a quadratic takes the form y = a(x-h)^2 + k , where the vertex is (h,k) your first equation is in intercept form, so the x of the vertex must be midway between -3 and 4 which would be...
*October 27, 2014*

**math**

What am I looking at ? I this a matrix equation? What is x ?
*October 27, 2014*

**algebra**

factor top and bottom = (x-6)(x+5)/( (x-5)(x+5) ) = (x-6)/(x-5) , x ≠ -5
*October 27, 2014*

**maths**

take a $1 investment 1 + 1(5)r = 8/5 5r = 8/5 - 1 = 3/5 r = 3/25 or .12 or 12%
*October 27, 2014*

**Calculus: need clarification to where the #'s go**

looks like you defined d to be the distance of the point from the origin y = 2(4x+4)^(1/2) y^2 = 4(4x+4) = 16x + 16 d = √(x^2+y^2) = ( x^2 + 16x + 16)^(1/2 dd/dt = (1/2)(x^2 + 16x + 16)^(-1/2) (2x + 16) dx/dt so when x = 3, y = 8 and dx/dt = 5 . Plug away dd/dt = (1/2) (...
*October 27, 2014*

**Math**

I will assume you have a typo and on the third day she sold 1/4 of what was left and 1/4 of a peach, or else it does not follow the pattern let x be the number of peaches at the start. number sold in 1st hour = x/2 + 1/2 = (x+1)/2 number left after 1 hour = x - (x+1)/2 = (2x...
*October 26, 2014*

**Calculus**

f(x) = sinx ---> f ' (x) = cosx g(x) = cosx ---> g ' (x) = -sinx so we want -sinx = cosx -sinx/cosx = 1 tanx = -1 I know tan 3π/4 = -1 and tan 7π/4 = -1 and the period of tanx is π since 3π/4 + π = 7π/4 we can just state that first ...
*October 26, 2014*

**algebra**

done, look back
*October 26, 2014*

**Algebra**

I think you placed some of those brackets in the wrong places, I am sure you meant f(x) = 1/(x-64) + 1/(x^2 - 64) + 1/(x^3 - 64) (the way you have them, they serve no purpose) remember we can't divide by zero, so x-64 ≠ 0 , ---- x ≠ 64 x^2 - 64 ≠ 0 ----&...
*October 26, 2014*

**Calculus**

let y1 = r dy1/dr = 1 let y2 = r^3 dy2/dr = 3r^2 when is dy2/dr = 12(dy1/dr) ? 3r^2 = 12(1) ? r^2 = 4 r = 2
*October 26, 2014*

**Calculus**

Let P(x,y) be any point on the parabola. According to the stated condition √( (x-8)^2 + (y-6)^2 ) - √( (x-5)^2 + (y-2)^2 ) = c, where c is that constant we could find c by plugging in (8,6) , a point on the parabola, but there is no need for it messy looking ...
*October 26, 2014*

**Calculus**

x^2 - xy + y^2 = 9 2x - x dy/dx - y + 2y dy/dx = 0 dy/dx(2y - x) = y - 2x dy/dx = (y-2x)/(2y-x) at x-intercept: y = 0 x^2 - 0 + 0 = 9 x = ± 3 when x = 3, dy/dx = (0-6)/(0-3) = 2 equation of tangent: y = 2(x-3) y = 2x - 6 when x = -3 , dy/dx = (0 + 6)/(0+3) = 2 equation ...
*October 26, 2014*

**Calculus (math)**

Let the radius of the water level be r let the height of the water level be h by ratios, r/h = 12/23 12h = 23r r = 12h/23 V = (1/3)πr^2 h = (1/3)π(144h^2/529)h = (48π/529) h^3 dV/dt = (144π/529) h^2 dh/dt for the given data: 20 = (144π/529)(144) dh/dt ...
*October 25, 2014*

**Math**

just one tiny step needed: divide by -3 s ≤ -6 (remember when multiplying or dividing by a negative number, the inequality sign must be reversed)
*October 25, 2014*

**trig**

You will have to know the co-function properties notice that the 6 trig names come as sine vs cosine tan vs cotan sec vs cosecant we need only the first two sinx = cos(90-x) tanx = cot(90-x) secondly we have to know tan(-x) = -tanx and sin(-x) = -sinx tan(-17°) + sin24°...
*October 25, 2014*

**Math**

#1 and #2: isolate the term you are solving for e.g. 4y + 6x = 12 ---> 4y = -6x + 12 now divide everybody by the coefficient of the term you isolated divide by 4 y = (-6/4)x + 12/4 y = (-3/2)x + 3 for #3, I would first multiply every term by 2, the LCM 2y = x - 20 2y + 20...
*October 25, 2014*

**math**

What Sal is basically showing you in the video is this: look at the repeating decimal places , there are 2 digits in the repeating loop so, let x = .151515... because we have 2 digits repeating, let's multiply the equation by 100 100x = 15,151515... notice the decimal part...
*October 25, 2014*

**Math**

your volume is correct f) well , we know the block of ice must be 12 inches high , and must be a square of 15 in by 15 inches
*October 25, 2014*

**Pre-Calc/Trig**

Try to factor it as Steve told you in a previous post along the same type of question What methods have you learned? A common method these days seems to be "decomposition" multiply the first and last coefficients: 6(-35) = -210 Now look for 2 factors which when ...
*October 25, 2014*

**Math**

f(x) and y are interchangable so instead of f(x) = 3x^2 - x - 2 you can say y = 3x^2 - x - 2 so when x = 2 , y = 12 - 2 -2 = 8 which you had so you are dealing with the point (2, 8) the x is 2, the y is 8
*October 25, 2014*

**precalculus**

make you sketch in such a way that the roadway is the x-axis and the center of the cable is along the y-axis So the vertex of your parabola is (0,10) and your equation is y = ax^2 + 10 we know (200,90) must be a point on it, so 90 = a(40000) + 10 a = 80/40000 = (1/500)x^2 + 10...
*October 25, 2014*

**Precalculus**

according to my quick sketch you have to use the cosine law x^2 = 180^2 + 90^2 - 2(180)(90)cos 75° ... x = appr 179 miles
*October 25, 2014*

**geometry**

No idea what your diagram looks like.
*October 25, 2014*

**correction - Math**

original : x at end of 1st week we have 1/3 x left at end of 2nd week we have (1/3)(1/3 x) left = (1/3)^2 x at end of 3rd week we have (1/3)^3 x left so (1/27)x = 37 x = 999 So there were 999 leaves check: number falling off 1st week = (2/3)(999) = 666 number left = 333 number...
*October 25, 2014*

**math**

Amount it is less by = 45-25 = 20 as a percentage that is 20/45 =.44444.. or appr 44.4%
*October 25, 2014*

**maths**

Assuming you are just picking one card from the full deck each time It will always be out of 52 all you have to know is how many cards there are in your subject. e.g. b) there are 4 aces, so prob(ace card) = 4/52 = 1/13 d) yellow is not a basic property of a deck of cards so I...
*October 25, 2014*

**Math**

depends on the value of the discriminant D where D = b^2 - 4ac remember that if D > 0 we have 2 distinct real roots D = 0 we have 1 real root D <0 we have no real roots So take all 3 cases , I will do one them, you do the rest. D > 0 10^2 - 4(5)d > 0 -20d > -100...
*October 24, 2014*

**algebra**

done, check your other post
*October 24, 2014*

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