Tuesday

November 24, 2015
Total # Posts: 35,768

**pre calc**

S1: 2 is a factor of 1^2+7*1 and so on. Clearly, since if n is odd, n^2 and 7n are both odd, so their sum is even if n is even. n^2 and 7n are both even, so their sum is even. Or, if n is odd (2k+1)^2+7(2k+1) = 4k^2+4k+1+14k+7 = 2(2k^2+9k+4) and similarly for even n=2k
*October 9, 2015*

**math**

4x+5y=10 2x+3y=8 x = -5 y = 6 Now just find 3x+4y
*October 9, 2015*

**Pre-calculus**

9^(2x-6)=6^(8x-5) (2x-6) log9 = (8x-5)log6 (2log9)x - 6log9 = (8log6)x - 5log6 x = (6log9 - 5log6)/(2log9 - 8log6) you can massage that a few ways, but that's the idea
*October 9, 2015*

**Math**

see http://www.jiskha.com/display.cgi?id=1444227515
*October 9, 2015*

**Trig**

after t seconds, Michael has gone 2t ft and Alyssa has gone 3t feet. So, the distance z between them using the law of cosines, is found using z^2 = (2t)^2 + (3t)^2 - 2(2t)(3t)cos60° so, plug in your time (in seconds!) and find z.
*October 9, 2015*

**precalc**

looks like our calculator agree!
*October 9, 2015*

**precalc**

Draw triangle LBM where the ball is at B; angle B is 158°. Using the law of sines, if the ball's distance from M is x, then x/sin9° = 23/sin158°
*October 9, 2015*

**Algebra**

(x+3)/(x+8)-(x-8)/(x-3) =[(x+3)(x-3) - (x-8)(x+8)]/[(x+8)(x-3)] =[(x^2-9)-(x^2-64)]/[(x+8)(x-3)] = (-9+64)/[(x+8)(x-3)] = 55/[(x+8)(x-3)] You probably forgot to use parentheses to keep track of quantities. But aside from that, what did you do with your denominator?
*October 9, 2015*

**geometry**

since DB bisects the angle ABC, the two smaller angles are equal. So, 12x+24 = 20x+16 So, find x, and you can figure the angles.
*October 9, 2015*

**MATH HELP PLEASE**

4718(1+.05/4)^(4n) = 5323 (1.0125)^(4n) = 1.1282 4n = log(1.1282)/log(1.0125) n = 2.4 or, roughly 2 1/2 years
*October 9, 2015*

**Math**

-2+5x-7=3x-9+2x collect constants and x's on each side: 5x-9 = 5x-9 Since both sides are the same, it will be true for any value of x at all!
*October 9, 2015*

**Calculus**

using shells, v = ∫[0,1] 2πrh dy where r = 1-y and h = √y - y^2 v = 2π∫[0,1] (1-y)(√y - y^2) dy = 11π/30 using washers, v = ∫[0,1] π(R^2-r^2) dx where R = 1-x^2 and r = 1-√x v = π∫[0,1] ((1-x^2)^2-(1-√x)^...
*October 9, 2015*

**Maths**

|a|-3/4=-5/8 |a| = -5/8 + 3/4 = 1/8 clearly, a = 1/8 or -1/8
*October 9, 2015*

**math**

As always, draw a diagram. The parabola has vertex at (1,0) and opens to the right. The line x=2 intersects the parabola at (2,1) and (2,-1). So, you will be revolving the sort-of-semicircular chink around the line y=-2, which is below the curve. So, as you say, v = ∫2&#...
*October 9, 2015*

**Maths**

|a|-3/4=-5/8 |a| = -5/8 + 3/4 = 1/8 clearly, a = 1/8 or -1/8
*October 9, 2015*

**Maths**

L1 has intercepts at A:(-6,0) and B:(0,4) L2 has gradient -3/2 and passes through (0,4), so L2 is y-4 = (-3/2)(x-0) 3x+2y-8 = 0 L2 passes through B:(0,4) and C:(8/3,0) So, if you plot the points, you can see that you have a triangle with base along the x-axis, and its third ...
*October 9, 2015*

**Maths**

why plug in 3 for x? Why change the polynomial? x^2 + 2kx - 3k = 0 the discriminant is (2k)^2 - 4(1)(-3k) = 4k^2 + 12k For two equal roots, the discriminant must be zero. 4k^2+12k = 4k(k+3) = 0 k = 0 or -3 k=0: clearly x^2=0 has two equal roots k = -3: x^2-6x+9 = (x-3)^2 has ...
*October 9, 2015*

**Algebra**

(8+12)/(4*5)=1
*October 9, 2015*

**Algebra**

24000(1+.0685/12)^(12*18) = 82,067.98
*October 9, 2015*

**math**

It's a little easier to check if you mark your answers with the questions. Saves a lot of scrolling back and forth. However, the wily teacher opens a 2nd window to avoid that, too! #1: 20/2 – 32 – (-2)2 = 10 - 32 - (-4) = 10 - 32 + 4 = -22+4 = -18 Since that'...
*October 9, 2015*

**Algebra**

in 2 hours, Molly was 54 miles ahead. Mark was going 18 mi/hr faster, so it took him 54/18 = 3 hours to catch up. But 3 is not the answer to the question ...
*October 9, 2015*

**Physics/trig**

as you recall, the equation of motion is y = tanθ x - g/(2(v cosθ)^2) x^2 So, plugging in your numbers, y = 0.664x - 0.00806x^2 That's a parabola with vertex at x=41.2
*October 9, 2015*

**pre calculus**

This is just a standard linear programming problem. For x breakfast packages and y afternoon packages, you want to maximize p=1.50x+2.00y subject to x/3 + y/2 <= 45 2x/3 + y/2 <= 70 Now just use your favorite linear programming tools.
*October 9, 2015*

**pre calculos**

Just substitute k for n and you have Sk. Same for k+1. Sk+1: 1∙2+2∙3+...+k(k+1)+(k+1)(k+2) = [(k+1)(k+2)(k+3)]/3 Can't get much simpler than that.
*October 9, 2015*

**math**

shift 3 left scale by 2 vertically reflect in x-axis In this case, the order does not really matter. Try them and see.
*October 9, 2015*

**prasanna high school**

been done. http://www.jiskha.com/display.cgi?id=1444216542
*October 9, 2015*

**math - eh?**

Not sure what you are saying here. When you say the building and the pole are at equal angles, do you mean the top of the building, or the bottom? The top of the pole, or the bottom?
*October 9, 2015*

**Maths**

-(x^2+3x)+7 3 = 2 * 3/2, so -(x^2 + 3x + 9/4) + 7 - 9/4 -(x + 3/2)^2 + 19/4
*October 9, 2015*

**Math**

Not to mention gazillions of others, like 99/100 87/150 1234124/2468247 and so on. I didn't see anything about having a single digit in the bottom or top.
*October 9, 2015*

**Math**

well, it has to double three time to be full, right?
*October 9, 2015*

**math**

well, 20 = 4*5 25 = 5*5 So, what do you think?
*October 9, 2015*

**Math**

not quite. 6 pizzas makes 48 slices 3 1/4 pizzas are 26 slices. So now, how many slices were left over? How would you interpret Janet's suggestion?
*October 9, 2015*

**pre calculus**

well, just plug in k and k+1 for n. You need to prove that if Sk is true, then Sk+1 is also true. Then, if you can show that S1 is true, then S2,S3,... are all true as well. 1+4+...+(3k-2)+(3(k+1)-2) = Sk+3(k+1)-2 = k(3k-1)/2 + 3(k+1)-2 = (k(3k-1) + 6(k+1)-4)/2 = (3k^2-k+6k+6-...
*October 8, 2015*

**math**

how much did each eat? Heck, they told you that. Convert each fraction to decimal to compare. 0.5 is 1/2. 2/3 = 0.666 and so on
*October 8, 2015*

**Math**

The one-digit factors of 54 are 1,2,3,6,9 so, which three of those add to 14?
*October 8, 2015*

**Science**

All the energy ultimately comes from the sun.
*October 8, 2015*

**trig**

nice formulas. Is there a question in there somewhere?
*October 8, 2015*

**math**

you want to add some parentheses, or at least some spaces, so we can work with that? As written, using the normal order of operations, you have 4-x^2/x^2+7x+12/2x-4/x+3 4-1+7x+6/x-4/x+3 3+7x+2/x+3 6 + 7x + 2/x I doubt that is what you had in mind.
*October 8, 2015*

**algebra**

enter your polynomials at http://calc101.com/webMathematica/long-divide.jsp and see all the details
*October 8, 2015*

**geometry**

assuming RST are collinear points, in that order, RS+ST=RT, so hmmm. If R bisects ST, and 5x=7 is a typo for 5x+7, then since SR=RT, 5x+7 = 15x-1 10x = 8 x = 4/5 But you may have had other things in mind. Remember, we cannot see what diagram you have in front of you. Nor can ...
*October 8, 2015*

**Pre Calculus**

(a) if you mean (3f+2g)(1) then that is 3f(1)+2g(1) = 3*50 + 2(-5) = 140 (f◦g)(-1) = f(g(-1)) = f(-3) = 10 f(x) = x^2 g(x) = x/(x+4) h(x) = g◦f = f/(f+4) = x^2/(x^2+4)
*October 8, 2015*

**math**

see related questions below
*October 8, 2015*

**math**

pick any five values for x. Multiply each by 18. Plot those points. Can you see what a useless exercise it is for you to ask us to plot a graph and verify it? Sheesh.
*October 8, 2015*

**Math**

one-digit factors of 54 are 1,2,3,6,9
*October 8, 2015*

**Math**

Let 2x be the least. Then the next 3 even integers are 2x+2, 2x+4, 2x+6 So, add them up: 2x + 2x+2 + 2x+4 + 2x+6 = 2x Now solve for x, and ... Extra credit: We used 2x to make sure it was an even number. What would have happened if we had just used x instead?
*October 8, 2015*

**Pre-Calc**

the same way you would simplify 2/3 + 3/2. Put it all over a common denominator: tan/(1+sec) + (1+sec)/tan = [tan^2 + (1+sec)^2]/(tan(1+sec)) = (tan^2 + 1+2sec+sec^2)/(tan(1+sec)) = (sec^2-1+1+2sec+sec^2)/(tan(1+sec)) = (2sec^2+2sec)/(tan(1+sec)) = 2sec(1+sec)/(tan(1+sec)) = ...
*October 8, 2015*

**Math Help**

oh, please...
*October 8, 2015*

**Math (Quadratics)**

You'll need to use the quadratic formula on that one. Or, completing the square, 8x^2+2x-4 = 0 8(x^2 + x/4) = 4 8(x^2 + x/4 + 1/64) = 4 + 8/64 8(x + 1/8)^2 = 4 + 1/8 (x + 1/8)^2 = 33/64 x + 1/8 = ±√33 / 8 x = -1/8 ±√33/8 x = (-1±√33)/8
*October 8, 2015*

**Algebra i need serious help**

Sorry, I only give jocose help. Since 3-x = -(x-3) |x-3| = |3-x| for all values of x
*October 8, 2015*

**Division need help urgently plz**

all you want is the last digit. So, look at the powers of 7: 7^1 = 7 7^2 = 49 7^3 ends in 3 7^4 ends in 1 since 3*7=21 913 = 4*228 + 1 So, 7^913 = 7^4^228 * 7 thus, it ends in 7
*October 8, 2015*

**Algebra 2**

try using ^ for powers. That is y^3 means y cubed. The formatting has messed things up to where they are incomprehensible.
*October 8, 2015*

**Physics**

220 km/hr = 2.20 * 10^5 m/hr So, there must be a headwind of 2.8-2.2 = 0.6 * 10^5 m/hr. That is, a wind blowing north at 60 km/hr
*October 8, 2015*

**Math**

paycheck: x food: 1/6 x, leaving 5/6 x house: 3/5 of 5/6 x = 1/2 x, leaving 1/3 x bills: 1/3 of 1/3 x = 1/9 x, leaving 2/9 x entertainment: 1/4 * 2/9 x = 1/18 x, leaving 1/6 x so, 150 = 1/6 x x = 900
*October 8, 2015*

**math please help!!**

the graph is concave down where 16e^-x^2 (2x^2-1) < 0 that is where 2x^2-1 < 0 x^2 < 1/2 so, f is concave down on the interval (-1/√2,1/√2)
*October 8, 2015*

**Math 125**

It appears that the number of calculators sold, as a function of the amount of discount (x) is p(x) = 10000+400x so, just plug in x=20 for the demand at $75.
*October 8, 2015*

**Calculus**

∫[0,8] 8x-x^2 dx = 4x^2 - 1/3 x^3 [0,8] = 4*8^2 - 1/3 * 8^3 = 256 - 512/3 = (768-512)/3 = 256/3 Maybe you should have shown your work.
*October 8, 2015*

**Mathematics(XI)**

google is your friend: https://answers.yahoo.com/question/index?qid=20121228030540AAIm82k
*October 8, 2015*

**math**

since √y = 7-x, √x + (7-x)^2 = 11 √x = -x^2+14x-38 x = x^4-28x^3+272x^2-1064x+1444 x^4-28x^3+272x^2-1065x+1444 = 0 (x-4)(x^3-24x^2+176x-361) = 0 good luck with the cubic. But, if x=4, y=9
*October 8, 2015*

**Find x algebra help**

no easy algebraic way to do this. However, with a little thought, you should be able to come up with 3^2-1 = 2^3
*October 8, 2015*

**Pre-Calculus**

well, just plug in the values: f(x)-f(1) = (-3x+2)-(-3*1+2) = -3x+3 Now divide by x-1 and you have (-3x+3)/(x-1) = -3(x-1)/(x-1) = -3 For the other, the same thing: f(x+∆x)-f(x) = 2(x+∆x)-2x = 2x+2∆x-2x = 2∆x Now divide by ∆x and you have 2∆...
*October 8, 2015*

**math**

a < b x >= y etc. If you have some specific questions, it would be a bit more useful to see how they can be answered.
*October 8, 2015*

**Algebra**

Looks like 9!-1 to me. Now, if you want (9!-6!)/(9-3)! that's 503. What is that supposed to model?
*October 8, 2015*

**Math**

If the faster person takes x hours, then the slower person takes (x+1) hours. So, how much of the job gets done in an hour? 1/x + 1/(x+1) = 1/5 Now just find x.
*October 8, 2015*

**Calculus 1**

the light turns through angle θ where dθ/dt = 4π. If the light hits x km away from P, then x = 4tanθ So, knowing that tanθ = 1/4, plug in the numbers and find dx/dt: dx/dt = 4 sec^2(θ) dθ/dt
*October 8, 2015*

**calculus**

I'll let you do the discussion. You just need to recall that f' = x^3 - 3x f" = 3x^2 - 3 f is increasing where f' > 0 f is concave up where f" > 0 f has max/min where f'=0 f has inflection where f" = 0
*October 8, 2015*

**Geometry**

as with the supplementary angles problem, 4x = (90-x)+10
*October 8, 2015*

**Geometry**

two angles are supplementary if they add to 180. So, if one angle is x, the other is (180-x), and you have 2x = (180-x)-36 2x = 133-x 3x = 144 x = 48
*October 8, 2015*

**Calculus 1**

If the hands are separated by an angle θ, then using the law of cosines, the distance z between the tips is z^2 = 6^2 + 9^2 - 2(6)(9) cosθ The hour hand rotates at a speed of 2π/1440 radians/min, and the minute hand moves at 2π/60 radians/min. So, figure &#...
*October 8, 2015*

**Calculus 1**

at the moment in question, we have a 6-8-10 triangle. You know that tanθ = y/x = √(100-x^2)/x or, x tanθ = √(100-x^2) So, tanθ dx/dt + x sec^2θ dθ/dt = -x/y dx/dt Now just plug in your values to find dθ/dt
*October 8, 2015*

**Calculus 1**

You know that when the water has depth y, the surface of the water has radius (4/6)y So, at depth y, the volume of water is v = π/3 r^2 y = π/3 (4/9) y^3 dv/dt = 4π/9 y^2 dy/dt That's if no water is draining out. SO, adjust dv/dt when you get your answer above.
*October 8, 2015*

**math**

amt = ears/3
*October 8, 2015*

**HELP HELP CALCULUS**

u=5e^x u' = 5e^x y = e^u y' = e^u u' = e^(5e^x) * 5e^x or, y' = 5e^(x+5e^x) y" = 5(1+5e^x)e^(x+5e^x)
*October 7, 2015*

**Geometry**

I've solved this one ---thanks
*October 7, 2015*

**Geometry**

find the image, of o(-2,-1) after two reflections first across the line y=-5 and then across the line x=1
*October 7, 2015*

**Math**

well, geez -- get rid of the parentheses and collect terms! 4+2(x+5) / 14-2(x+5) = 4+2x+10 / 14-2x-10 = 14+2x / 4-2x = (7+x)/(2-x)
*October 7, 2015*

**Math**

v = pi r^2 h so, find h when pi*18^2 h = 31000
*October 7, 2015*

**math**

rearrange to y = 3x-6 That is called the slope intercept form. I suspect you can now tell the slope, eh? For the y-intercept, just set x=0 and find y.
*October 7, 2015*

**algebra**

(9^2)^p = 9^(2p) so, 2p = 8
*October 7, 2015*

**algebra**

3^5 = 243 Just going that far, you can see that none of the choices will do. I suspect a typo in your presentation.
*October 7, 2015*

**math**

I'll assume you mean (x+160)/5 = 2/(3x-2) (x+160)(3x-2) = 10 3x^2+476x-330 = 0 Now you can use the quadratic formula. If that's not what you meant, how about some parentheses to clarify the grouping?
*October 7, 2015*

**algebra**

(2.8 * 10^7)/(1.4 * 10^3) = (2.8/1.4)*10^(7-3) = 2.0*10^4
*October 7, 2015*

**ALGEBRA**

I think you'd do well to review your scientific notation. Any explanation I give here will just be a duplication of what you have already (I hope) read.
*October 7, 2015*

**ALGEBRA**

14,200,000 10,700,000 ---------------- 24,900,000 = 2.49x10^7 or, 1.42x10^7 + 1.07x10^7 = 2.49x10^7
*October 7, 2015*

**ALGEBRA**

3^2 * 3^-5 = 3^(2-5) = 3^-3 = 1/3^3 Your notation is very sloppy.
*October 7, 2015*

**algebra**

x = ±√20
*October 7, 2015*

**Math**

direct: y=kx or x=ky inverse: xy = k where k is a constant. So, check 'em out.
*October 7, 2015*

**math**

102 = 96*1.0625 So, 102 is 6.25% larger than 96
*October 7, 2015*

**Algebra 2**

an expression has no solution. An equation has a solution. Plugging in x = -9/4 results in a value of 3/56. Not sure whether that's what you want. Leaving in x as-is, the expression evaluates to (-3x-6)/14
*October 7, 2015*

**Alg2.**

what, you can't check it? Apparently not. In fact, your results row should be 4 -2 -1 1/2 7/4 25/8
*October 7, 2015*

**Calculus**

I think you mean y = √(11x + √(11x+√(11x))) y^2 = 11x + √(11x+√(11x)) If u^2 = 11x, u' = 11/(2√(11x)) y^2 = u^2 + √(u^2+u) 2y y' = 2u u' + (2u+1)u'/(2√(u^2+u)) 2y y' = u' (4u+1)/(2√(u^2+u)) Now ...
*October 7, 2015*

**Algebra**

Rotating 90° about the origin takes P:(x,y) -> P':(-y,x) So, plug in your numbers.
*October 7, 2015*

**Algebra**

A segment with endpoint a(3,1) and b(-1,-1) is rotated 90 degrees about its origin what are the new of a and b prime?
*October 7, 2015*

**math**

1000 * 1.05^18
*October 7, 2015*

**Algebra**

just solve for x when h=0. Clearly, it is only when x=0. If you mean h(x)=-32x^2/(140^2+x) If you meant it as written, h(x)=-32x^2/140^2 + x = x(1 - 64x/1225) h=0 when x = 1225/64
*October 7, 2015*

**Please help with MATH**

been there, done that. http://www.jiskha.com/display.cgi?id=1444251037
*October 7, 2015*

**Geometry**

Each quadrant contains 90°, starting from 0°. QI is 0-90° QII is 90-180° Or, going the other way, QIV is 0 to -90° QIII is -90 to -180° So, now what do you think?
*October 7, 2015*

**Geometry**

You are correct. An angle has its own measure, regardless of whether it is anywhere near another angle.
*October 7, 2015*

**Math**

assuming she answered all the questions, and got x wrong, then there were (50-x) correct. 2(50-x) - x = 85 Now just find x.
*October 7, 2015*

**Algebra 2**

you know the possible roots are ±8,±4,±2,±1 So, look for the easy ones first, using synthetic division. It's easy to find that there are no rational roots.
*October 7, 2015*