The center will lie at the intersection of the perpendicular bisectors of the line segments (chords) joining the points. If we label the points A,B,C, then The midpoint of AB is at (-5/2,2) The slope of the chord AB is 4/5 The line AB is y = 4/5 (x+5) The slope of the radius t...
-3 + i^2y = -3-y The conjugate of x^2+y + 4i is x^2+y -4i so, we want -3-y = x^2+y - 4i In no case is that ever true We can have -3-y = x^2+y, but there's no way to get the -4i I suspect a typo in the problem.
#1. The kth odd number is 2k-1 Think about it : 1,3,5,... #2 It will be a multiple of 60. So, what's the biggest 3-digit multiple of 60? #3 There are 203 numbers from 101-303. Knock off one end, since both are odd, and half of the remaining 202 are even. #4 same thing #5 5...
2 3/4 = 2 + 3/4 1 1/4 = 1 + 1/4 add them up to get 2+1 + 3/4 + 1/4 = 3 4/4 = 4
Write each expression using a single exponent.
when dividing, just subtract exponents: 5^10 / 5^7 = 5^(10-7) = 5^3 because 5^10 = 5*5*5*5*5*5*5*5*5*5 5^7 = 5*5*5*5*5*5*5 divide, and seven of the 5's cancel, leaving only 3 in top: 5^3 76^11 / 76^5 = 76^(11-5) = 76^6
csc(4θ+3) sin(5θ-6) = 1 That's surely an odd sort of expression. Still, since cscθ = 1/sinθ, we have sin(5θ-6) = sin(4θ+3) So, we want 5θ-6 = 4θ+3 θ = 9 That seems kind of big, so what if we consider that sin(π-x) = sin(x)....
72000(1+.80n) = 87840 1+.80n = 1.22 and so on to get n
v = x^3, so dv/dt = 3x^2 dx/dt = 6(2t+1)^2
since multiplication is commutative, 3 * 10^6 * 2 * 10^12 = 3*2 * 10^6 * 10^12 = 6 * 10^18 the other is analogous. Just recall that 30*10^13 is not scientific notation.
3x^2+2x-x^2+3 3x^2-x^2+2x+3 (3-1)x^2 + 2x + 3 2x^2 + 2x + 3 not much to do -- just combine the x^2 terms. We used commutativity of addition and distributive property.
cosA/(1-tanA) + sinA/(1-cotA) cosA/(1-tanA) + sinAtanA/(tanA-1) (cosA - sinAtanA)/(1-tanA) (cos^2A-sin^2A) / cosA(1-tanA) (cos^2A-sin^2A)/(cosA-sinA) cosA+sinA sure you don't have a typo somewhere?
since cosA = 5/13, sinA = 12/13 Now just use those values in your double-angle formulas.
wolframalpha.com is your friend. For #26, see http://www.wolframalpha.com/input/?i=table+2x^2-4+for+x+%3D+-3+..+5
help needed with math
Was something wrong with the solution I posted here? http://www.jiskha.com/display.cgi?id=1401907573
4/52 * 4/51
#14. For each x, place a 3. f(3) = 4*3-4*3-7 = -7 Same way for #16 However, I suspect a typo, since 4x-4x-7 = -7 for any value of x.
clearly, 4y = (2/3)x - 8 so, 24y = 4x-48 -4x + 4x-48 = 32 -48 = -32 No solution exists
Can you help me find the answers?
#10 14-11*1 = 14-11 = 3 14-11*2 = 14-22 = -8 ... #12 23+1 = 24 23+2 = 25 ...
Find the common difference or ratio in each..?
6: r = 1/4 8: r = -2 That should do it.
48000(1+.0428/12)^18 = 51,176.82
math Study guide
1A 2B 3C 4C 5B Whenever there is replacement, then the events do not affect each other. Or, if the events are unrelated, as with dice and spinners, they are independent. 6: 1/2 * 1/2 = 1/4 7: 1/2 * 3/6 = 1/4 8: 20 total marbles, so 7/20 * 6/20 9: 1/2 * 3/6 (primes are 2,3,5) 1...
math question check
4/10 * 2/10 = 2/25
just plug in a value for n and compute the value for C. For example, if 10 people attend, n=10, and C = 10*10+26 = 126 So, the pair for that would be 10,126 Now use your numbers and finish it up.
that's "whether" not "weather". visit wolframalpha.com and just type in a function. It will show you the graph and other information. Be sure to note how interprets you input. You may need to use some parentheses to ensure proper evaluation. The graph r...
No, that's 0.15 * 20 Look. 15% means you expect 15 wins in 100 tries. 20 is only 1/5 of 100, so you expect 1/5 as many as 15, or 3. 0.15*20 = 3 That is, 15% of 20 is 3.
well, what is .15 * 20 ?
math - eh?
Can't say, since you have only presented an approximation to a question. Read what you posted, then supply all the missing data, so we have something to work with.
can't say, since you don't say how big the sides are. Also, I assume you mean that 1 litre covers 5m^2 of area. In any case, figure the area to be painted, in m^2, and then multiply that by R26/5m^2
Geometery - incomplete
you need to describe the diagram. What is the relationship between the angles? Suppose I ask you what color the fruits are. Have an answer? Also, try using symbols. The usual format is If m<1 = 43°, what is m<2? There is even an angle symbol which you can use: ∠
looks pretty standard to me. To play around with functions and their graphs, you can visit wolframalpha.com and just type in your function. For example, http://www.wolframalpha.com/input/?i=x^2-9
The usual reference level is 10^-12 W/m^2 Here, you have 2.37*10^-5 W/cm^2 = 2.37*10^-1 W/m^2 The dB level is thus 10 log(2.37*10^11) = 10*11.37 = 113.7 dB
x^2-144 = (x-12)(x+12) x^2+7x-60 = (x+12)(x-5) 3x-36 = 3(x-12) 9x-45 = 9(x-5) So, since dividing by a fraction is the same as multiplying by its reciprocal, we really have (x-12)(x+12) / (x-5)(x+12) * 9(x-5) / 3(x-12) Now you can see that almost everything cancels out, leaving...
they all satisfy x-2y = 1
the park is 150 by 450, making a perimeter of 1200 ft 1200/10 = 120 seconds G
MATH HELP PLEASE & THNX!
revenue = price * demand = pq = p(300000-15000p) cost for q copies is 4q profit = revenue-cost = p(300000-15000p)-4(300000-1500p) = -15000p^2 + 306,000p - 1,200,000 maximum profit is thus at p = 306000/30000 = 10.20
Just a guess: 3/5?
solve for x in 150*1.03^x = 300 1.03^x = 2 x log1.03 = log2 x = log2/log1.03 = 23.45 years
(2^x ln2 - e^x)(2^x+e^x) - (2^x-e^x)(2^x ln2 + e^x) --------------------------------------------------------------- (2^x+e^x)^2
just plug and chug, using the quotient rule (2^x ln2 - e^x)(2^x+e^x) - (2^x-e^x)(2^x ln2 + e^x) --------------------------------------------------------------- (2^x+e^x)^2 You can "simplify" that to
just plug and chug, using the quotient rule (2^x ln2 - e^x)(2^x+e^x) - (2^x-e^x)(2^x ln2 + e^x) ------------------------------------------------------- (2^x+e^x)^2 You can "simplify" that to
Excuse me? You developed your own function. The price after r rate increases is 6.40 + 0.1r so, for r=0, the price is 6.40 for r=8, the price is 6.40+.1*8 = 7.20 Between those two prices, she'll make at least $1500. Take a look at http://www.wolframalpha.com/input/?i=plot+...
Your equation looks good. So, just solve it and you get (250-5r) (6.40+0.10r) >= 1500 -.5r^2 - .7r + 1600 >= 1500 .5r^2 + .7r - 100 >= 0 Now, solve the left side using the quadratic formula, and you find that .5r^2 + .7r - 100 = 0 at x = -22.8 and 8.8 Between those tw...
r:m = 4/15:1/3 = 4/15:5/15 = 4:5
well, you know that 1/3 pi r^2 * 8 = 250 So, now just solve for r.
23010(1+.029/2)^(2*9) = 29816.29
math word problem
If he buys x packs of batteries, we wan to find out how many packs it takes to cost more than the price of the charger and batteries. 7x > 15.39 x > 2.2 So, after using the rechargeable batteries 40 times, they will be the better buy.
Algebra/not sure what to do Thank You
just pick any value for x and evaluate y at that point. x=0: y=2*0-1 = -1 So the point is (0,-1) x=-5: y=2(-5)-1 = -11 So the point is (5,-11) x=17: y=2*17-1 = 33So the point is (17,33) and so on for any x value you want. You can also pick y, but then you have to work backward...
Can't tell. The two bases are equilateral triangles, but the three lateral faces are rectangles of area 6. But is the prism tall and skinny, or short and fat? You must know either the height of the prism, or the side length of its bases. If the bases are of side 2s, then e...
55° + 360k are all coterminal for any integer k. 9/5 π + 2kπ are all coterminal for any integer k. So, pick a positive and negative k
since 81 = 3^4, we have 3^-4 = 3^(2x-1) -4 = 2x-1 x = -3/2 logx + 3/logx = 4 log^2(x) - 4logx + 3 = 0 (logx-1)(logx-3) = 0 logx = 1,3 x = 2,8 check: 1+3/1 = 4 yes 3+3/3 = 4 yes
us always, draw a diagram. Label one of the acute angles θ. The side opposite is 4 and the side adjacent is 3. (Note: the hypotenuse is not a side!) The hypotenuse is 5, since 3^2+4^2=5^2 Now, review your trig definitions. sinθ = opposite/hypotenuse = 4/5
sin 40° = x/80
sin 70° = 25/x As usual for trig problems, draw a diagram. In this case, label the angle at the ground 70°. You want the hypotenuse (x), and have the side opposite the angle (25).
Not sure what "compounding amount" means. If you mean the final amount after adding the interest, just apply the usual formula, which you surely have. A = 700(1+.015/12)^(12*8) = 789.19 To find just the interest, subtract the original $700, leaving just $89.19
if the bot has speed b, and the stream has speed s, then since time=distance/speed, 12/(b-s) + 40/(b+s) = 8 16/(b-s) + 32/(b+s) = 8 b=6 s=2 check: 12/4 + 40/8 = 3+5 = 8 16/4 + 32/8 = 4+4 = 8
You forgot the minus sign. -4p < 36 p > -9 That's just shorthand for switching sides of the inequality: -4p < 36 -36 < 4p -9 < p
3000/(pi*75) = ?
What happens if the square does not share sides with the triangle? If the vertices of the triangle are at (0,0),(6,0),(0,12), then if one side of the square is on the hypotenuse, and one corner is at (s,0), another is at (0,2s), so the hypotenuse has length √5 s. Now, we...
trig angle of elevation
The rim is only 4 feet above his eyes, so 4/x = sin 12.5° we don't really care how far horizontally he is from the basket. All that stuff about 15 feet and stepping back is just noise. The final picture is just a 12.5° angle with a 4-ft height difference.
Math please help
don't let those fractional exponents confuse things. What you have is just (x^1/5)^2 + x^1/5 - 6 = 0 That's just like u^2+u-6=0 So, just factor it to be (x^1/5 + 3)(x^1/5 - 2) = 0 x^1/5 = -3 or 2 x = -243 or 32
18% compounded 12 times per year give 1.5% per month. So, 6 years = 72 months.
3(x+2) = 3*x + 3*2 = 3x+6 an identity 3(x+4) = 3*x + 3*4 = 3x+12 ≠ 3x+4 not only not an identity, but not even conditional. There is no value of x which makes it true!
√32 = 4√2, so we have 4x*4√2xv^2 + v√2x^3 16x√2x√v^2 + v√2x√x^2 16xv√2x + vx√2x 17vx√2x
2:3 = 4:6, so draw the picture with 4 pencils and 6 pens
38*34 = 1292 you are correct
var=25 means std=5 113 is 12 below the mean, or 2.4 std So, what's P(Z < -2.4)
5^1 * 5^10 5^5 * 5^6 5^20 * 5^-9 In each case the sum of the powers is 11.
f(n) = 10(1.02)^n A: since f(0) = 10, we're looking for a growth of 11.04/10 = 1.104 1.104/.02 is about 50, so as a rough guess I'd go with a domain of [0,50]. B: y-intercept is the initial population (when n=0) C: (f(5)-f(1))/(5-1) = 0.21 Represents a constant growth ...
ly and solve for x.
try something simple, like 3 = x/2 You want x all alone, so get rid of that pesky fraction. Since 2/2 = 1, multiply both sides by 2 and you get 3*2 = x/2 * 2 6 = x Now, for your problem: 8/18 = x/225 You can clear the fraction on the left by multiplying by 18. 8/18 * 18 = x/22...
Choose the term to complete this sentence?
hmmm. I don't see any mention of a proposed experiment, so ...
area of sector is 60/360 * 81pi arc length subtended is 60/360 * 18pi For any other questions, you're on your own...
Just use the distributive property: n(n-1)-4 n*n - n*1 - 4 n^2-n-4 Since f(x) = x^2-4x+3, and you want f(-3), just replace all the x's with -3 and you have f(-3) = (-3)^2 - 4(-3) + 3 = 9+12+3 = 24
Algebra 1 (Reiny)
#1 no solution #2 ok #3 ok but I had to try two different ways of inserting parentheses before I got your answer. Grrr. The spacing in "t + 2" was especially deceptive. #4 x = 0 or 2 This time, overkill. Use parens as needed, but only as many as it takes to avoid amb...
since the denominator is the same on both sides, just work with the numerators: d+2 = -6 d = -8 BZZZT! But thanks for playing. Since the denominator is d+8, d = -8 is not in the domain, because that would cause division by zero. Before clearing fractions, be sure to note which...
Algebra 1--Please, check my answer!
You can go overboard with the parentheses. In this case, there's no confusion if you just write 1/x = 2/x^2 so, x/x^2 = 2/x^2 x = 2 check: 1/2 = 2/4 yes
Algebra 1--Please, help me!
(4x-3)^2 = 16x^2 - 24x + 9 You have -9. A perfect square will never end in a negative number.
add the two vectors and you get <539,0> + <43,43> = <582,43> arctan(43/582) = 4.2° As a bearing, that's E 4.2° N, or 85.8°
work with the amount of orange juice in each container. If x cups of 100% orange juice are added to 8 cups of 25% orange juice, she will wind up with x+8 cups of 40% orange juice. .25*8 + 1.00*x = .40(8+x) x = 2 check: There are 2 cups of oj in the 8 cups of 25% mix There are ...
sure. Two intervals that overlap at a single point. x+y >= 3 2x-3y <= 1 y <= x/2 The single point which satisfies all three equations is (2,1)
If the smaller diameter is d, the other is d+8 d + d+8 = 28 Now just find d, and figure d+8.
for polar coordinates, dA = 1/2 r^2 dθ since each tiny wedge of area can be considered a sector of a circle of radius r and angle dθ. So, since r = 8+4sinθ, a = ∫[0,2π] 1/2 (8+4sinθ)^2 dθ now just expand the quadratic and evaluate each term,...
If the positive direction is east, we have to add up the two velocities: 395 - 55 = 340 or, 340km/h east
since time = distance/speed, 12/s - 1 = 12/(s+1) Hint: 3 is one less than 4.
algebra - incomplete
no idea - how long did it fly?
#1 If the sides are x and y, then x^2+y^2 = 68^2 (not √68) xy = 16 so, y = 16/x x^2 + 256/x^2 = 68^2 x^4 - 68^2 x^2 + 256 = 0 since 256 = 4*64, we have (x^2-4)(x^2-64) x = 2 or 8 (discard the negative roots) #2 If the cardboard is of side x, then (x-8)(x-8)4 = 784 x^2 - ...
If you mean square root, use √ and some parentheses. Do you mean 3 ln e = √(7x) - 3 ln 6 ?? If so, recall that ln e = 1 3 ln 6 = ln 6^3 I still doubt that's what you want. It still looks bogus.
those double minuses make a +, so you really have -39+24+64 leading minus signs make some people uncomfortable, so bob moved it to the end.
Algebra - Math HW HELP!
just work with the clues. The number's digits are abcde palindrome means it is abcba tens digit must be 1 or 2, so b=1 or 2 a2c2a a1c1a c*a = 54, so c=9 and a=6 or vice-versa 92629 62926 91619 61916 c+a=15 well, we already knew that with the 9 and 6 divisible by 4 knocks o...
Assuming a $26 budget per table, you have 8 favors and 8 flowers. The 8 flowers cost 8*2.50 That leaves for the favors, cost = (26-8*2.50)/8 Better be cheap favors! And if your total budget is $26 for all the tables, forget it, since the flowers for a single table already cost...
10% = 1/10 So, it rises 1/10 as far as it runs horizontally: .2km or 200m
It might be helpful to rescale things by letting u = (x-30)/30 so the u-values go from 0 to 5. Then, since we are expecting an exponential relationship, see whether you can find something that fits ∆y/∆u = ky + c See where that takes you
No reason to stop there. Factor out all those 3's: 81(x^2+1)(x-1)(x+1) If you must pick one of those choices, then use the last one, since it factors the 9x^2-9 as well. (factor completely!)
if the tortoise is last, then you just have to worry about the other 5 animals. So, in how many ways can you arrange 5 things?
If the vertex of the parabola is at (0,630), then the arch is modeled by y = (630/315^2)(315^2-x^2) = 630 - 2/315 x^2 If the work is being done at a position c ft to the right of the vertex, it will be at the point (c,y(c)), on a line with slope 1/5. Unfortunately, this makes ...
math [linear equations]
If you can plot points, remember that two points determine a line. So, pick two easy points and plot them. Then draw a line through them. So, what's easy? How about letting x=0 or y=0? That gives us 0-y=5 y = -5 x-0=5 x=5 So, our two points are (0,-5) and (5,0) Now it shou...
Excuse me? You already know that the length is 20 more than the width. So, if the width is 80, the length is 100. Sure enough, 80*100 = 8000 Or, since you know the width is 80, and area = length*width 8000 = 80 * length length=100 Don't forget your algebra I now that you...
Trying to match the question with the choices sure stumps me. Using similar triangles, if we label the vertices of the triangle P,K,F, and the library L, then we have ∆LPF ~ ∆KLP we want the distance LP and FP, and we have LP/2 = FP/KP LP/8 = KP/FP so, LP/2 = 8/LP ...
you can play around at http://davidmlane.com/hyperstat/z_table.html and do all kinds of neat Z-table stuff. Just enter your mean and std and you can see the areas (probabilities) for various kinds of calculations.
#1 ok, though I'd write it as 4.00t + 25.00 Lose all that "x" stuff, if for no other reason than because "x" is often used as a variable. "*" is better for explicit multiplication. #2 where did 350 come from? If t shirts are ordered, then t of...
the slope of the line is ∆y/∆x, so m = 6/7 Now you have a point and a slope, so the line is y-4 = 6/7 (x-0) or y-10 = 6/7(x-7) and you can massage them to whatever form you like, and convince yourself that they are really the same equation.