3√(3/8) = 3(√(1/4 * 3/2) = 3 * 1/2 √(3/2) = 3/2 √(3/2) Not sure that's any simpler, but the radicand doesn't have any factors which are perfect squares. It'd also be √(27/8) Now, if you meant ∛(3/8), that would be ∛(3 * 1/8...
3x^2 √(5x) * 3√(3x^3) = 9x^2 √(5x*3x^3) = 9x^2 √(15x^4) = 9√15 x^4
cost: 40*3.20 = 128.00 after spoilage there are only 32 dinners to sell Now, if the 32 dinners are supposed to cover the entire cost + 80% markup, that would mean they must sell at a price p such that 32p = 1.80*128 p = 7.20 So, the $1 discount is a 13.9% discount off the mark...
#1 2x(x-12) = -40 x(x-12) + 20 = 0 x^2-12x+20 = 0 (x-2)(x-10) = 0 #2 3x^2 + 2x = 12 - 7x 3x^2 + 9x - 12 = 0 x^2+3x-4 = 0 (x+4)(x-1) = 0 #3 8√-63 = 8√63 i #4 |7+24i| = √(7^2 + 24^2) = 25 #5 (4-7i)(2+3i) = 8 - 14i + 12i - 21i^2 = 29-2i
DOS is a text-based interface. Commands are typed in. Unless you know the command name and the path to its location, you are SOL. Windows is a GUI (Graphical User Interface) where you move the cursor to icons and click to perform actions.
( tanx + cotx )² = tan^2 + 2 + cot^2 = sec^2 - 1 + 2 + csc^2 - 1 Now it should be easy.
the graph can be seen here: http://www.wolframalpha.com/input/?i=plot+y%3D|x^2+%2Bx-2|+for+-4+%3C%3D+x+%3C%3D+3 That should make it easy to answer the other questions. If not, come on back and show where you get stuck.
Not quite: A: x-coordinate of the vertex, also of the axis of symmetry B: not a quadratic at all; just a line C: the discriminant D: likely the parent equation E: quadratic formula. Note how the roots are equally spaced around x = -b/2a
h(t) gives the height for any value of t. For this problem, wherever you see a t, substitute 40: h(40) = 81.69 + 2.39*40
first, it's "whether" not "weather". Look at the coefficient of x^2. Since x^2 is always positive, the parabola grows upward if the coefficient is positive, and downward if it is negative. The easy way to find the vertex and axis is to complete the squa...
in the two hours between the buses, the first bus has traveled 60 miles. So, the other bus must make up 60 miles at 50 mi/hr, which will take 60/50 hours. Add that time to the bus's departure time.
Algebra help ASAP please
I'm sure you can factor x^2-x-2, no? This is the same things (2x+1)(x-1) Not quite sure what it has to do with #1, though #2 ok #3. Since the top and bottom are of equal degree, there should be no unbalanced x's between the top and bottom (6x^2+4x)/(2x^2+4x) = 2x(3x+2)...
9(1.06^5x + 1) = 15 (1.06^5x + 1) = 15/9 1.06^5x = 2/3 5x log 1.06 = log (2/3) x = log(2/3) / (5log 1.06)
by the time you get to calculus, you certainly should know how to plug in a value and evaluate a function! Where do you get stuck? (a) q(5) = 10300*e^(-0.34*5) = 1882 (b) as you know, if y = e^u y' = e^u u' And, as you know, the derivative is the rate of change. So, q&...
the amount of acid in each part must total the acid in the mixture, so .05x + .09(40-x) = .06(40) Now just solve for x, the amount of 5% acid.
the max or min of a quadratic is at the vertex of the parabola. I expect you can determine whether the vertex is a max or a min. So, since the vertex is at x = -b/2a, (2) -3x^2-6x-9 the vertex is at x = -6/(2*-3) = 1 y(1) = -18, so the vertex is at (1,-18) (3) the vertex of y-...
the midpoint is halfway from one to the other. That means its coordinates are the average of the x- and y- values of the two points: (-1,-4) Note that -1 is halfway from 2 to -4 (3 away from both ends)
math (algebra honors)
(x+2)^3 - x^3 = 386 6x^2 + 12x + 8 = 386 x^2 + 2x - 63 (x+9)(x-7) the shorter side is 7 check: 9^3-7^3 = 729-343 = 386
algebra word problem
when the cyclist starts, the runner is 5 miles ahead. So, he needs to make up 5 miles at 13 mi/hr, which takes 5/13 hours.
If all we have is one side and one angle, there's no way to determine any of the missing info. Now, if we're working with a right triangle, then the side opposite the angle is x/59 = tan 35° But since this is geometry, not trig, I don't know whether that's ...
Quick math help
Looks like an exercise set using factoring by grouping. 4n^3+4n^2-16n-16 4(n^3+n^2-4n-4) 4(n^3-4n + n^2-4) 4(n(n^2-4) + (n^2-4)) 4(n+1)(n^2-4) 4(n+1)(n-2)(n+2) 9k^3-15k^2-3k+5 3k(k^2-1) - 5(k^2-1) (3x-5)(k-1)(k+1) 60m^3+48m^2-20m-16 4(15m^3 + 12m^2 - 5m - 4) 4(5m(3m^2-1) + 4(3...
Calc Help :(((((
As x->∞, only the highest powers are relevant, so we wind up with the limit of 7x^(5/3) / -2x^(8/5) = -7/2 x^1/15 -> -∞ Or, you can divide top and bottom by x^(5/3) and then throw away all the fractions with x in the bottom
the distance between the trains grows at 115+95 = 210 mi/hr So, it will take 504/210 hours to get 504 miles apart.
Algebra 1 (Reiny)
It's not clear just what you mean by "the greatest number" If you put 72 of each berry into each tart, you can make only 1. If you put 36 of each kind of berry into each tart, then you can make only 2 tarts, with 36 blueberries left over. If you put 3 raspberries...
Use standard enthalpies of formation to determine ΔHorxnfor: 3NO2(g) + H2O(l) → 2HNO3(aq) + NO(g) -133.5 = Delta H Find the change in internal energy for this reactioion.. ???? In KJ
pi * 6^2 * 5 ft^3
If the first digit is t (for tens) and the 2nd digit is u (for units), then u = 5t+2 5t = u+3 Sorry, no solution. Care to rethink it?
#1 - no way to know, without some information about the pressure. #2,3 just remember that mass = density * volume Look up the density of ice and aluminum, and you're almost done.
get a better table
the powers are 0,5,6,10
5n+25q = 620 5q+25n = 620+320 now just solve for q.
Or, post your results and we can verify them.
assuming you just need to confirm your answers, I'll say none |x+.5|>1.5 monotone over any interval not including the x-values -2,-.5,1 up: x<-2 and x>1 down: -2<x<1 no inflection http://www.wolframalpha.com/input/?i=|x^2+%2Bx-2|
ummm, that would be x^2 + x^2 = 2x^2 just as 4x+7x = 11x and 4+10 = 14 just collect all the terms with the same power x^2 means 1x^2, so x^2+x^2 = 1x^2 + 1x^2 = 2x^2
However, they are asking for the smallest square greater than 64, which is 81. Note that -8^2 = -(8^2) = -64 (-8)^2 = +64
if the building is at distance d from the tree of height h, draw a diagram to see that (150-h)/d = tan 50° h/d = tan 22° plugging in the numbers, h+1.19d = 150 h = 0.40d So, we have h = 94.3 d = 37.7
If we convert the dimensions to inches, then the kitchen is 1224 by 216 inches. 1224/28 = 43.7 216/28 = 7.7 So, assuming no fractional tiles are to be reused, we need 44*8=352 tiles. The only weird thing about this problem is the idea of a kitchen 102 feet long!!! Is there a t...
they are not integers they may be negative
Algebra 2 Homework
#1 x^2+10x+9 = x^2+10x+25 + 8-25 = (x+5)^2 - 16 Since the vertex is at (-5,-16), the axis of symmetry is at x = -5 Or, you can consider that the roots are at -9 and -1, and the axis is midway between the roots, or at x = -5. #2 3x^2+12x+16 = 3(x^2+4x) + 16 = 3(x^2+4x+4) + 16-3...
This is explained in detail at http://jwilson.coe.uga.edu/emt725/Cylinder/OneSol.cyl.html nothing fancy, just basic algebra.
vertical travel: y = 15t horizontal travel: x = 35t actual distance: d = √(x^2+y^2) = √(15t)^2 + (35t)^2) = 5√58 t At t=60, d=2285 m Assuming the rocket does not run out of fuel and go ballistic (literally)
what does it matter how many are in the family? (2+1)*8 = 24 Now, if you wanted to know how many pieces each member of the family gets, it should be clear what comes next.
after each step, the bag has 3 fewer candies than before. So, starting with 50 candies, after 16 steps, there are just 2 candies left in the bag. During those 16 steps, 64 candies have been removed. If you are allowed to remove the last two, then that makes 66. It's a bit ...
the average age of the two extremes is 5. So, with 4 children, 20 is a reasonable guess. I think if you listed all possible ages (including twins and triplets) you will come up with a figure close to 20.
Hmmm. 3/4 less than 3 is either 2 1/4 or 3/4. In either case, we have a crying baby.
(49w^5-28w^3)/7w= 49w^5/7w - 28w^3/7w = 7w^4 - 4w^2 Why did you add exponents, when I suggested you need to subtract when dividing? x^a/x^b = x^(a-b)
can you not compute 49/7 28/7 w^5/w and w^3/w? Just divide each term by 7 and by w. Hint: when dividing powers, subtract exponents.
you have added 11300m to the radius, so add 2pi*11300 m to the circumference. Doesn't matter how big the earth is; what matters is the increase in radius.
Rosge, dum la ŝliplaj tovoj Tre gire en l' ongefo borlis, Misgilis ĉiuj borogovoj, Tenrefoj dejmaj gorlis.
you can easily construct a 60° angle, so 30° and 15° are also easy. So, since 90+15=105, that also comes easily. So, lay out the given sides, construct the necessary angles, and take the necessary measurement. It might help to calculate it as well as a check.
20x+25y <= 5000 type that in at wolframalpha.com and it will show the shaded region
x+y=21 x = y-5 y-5+y=21 ...
since y=x^(3/2) y' = (3/2)x^(1/2) y'=1 when x = 4/9 and y = 8/27 so, the arc length is s = ∫[0,4/9) √(1+((3/2)x^(1/2))^2) dx = 1/2 ∫[0,4/9) √(9x+4) dx = 8/27 (2√2-1) As always, check my math
just solve for t in 103000(1+.075t) = 1000000
y = 1/2 x - 4 has x-intercept at (8,0) 3x - 4y + 4 = 0 has slope 3/4 so, your line is (using point-slope form) (y-0) = (3/4)(x-8)
if sold at price p, we need the revenue from 90% of the 600 lbs to be 1.60 times the cost of 600 lbs at $5.59: 600(1-.10)p = 600*5.59*1.60 p = $9.94
if you mean (fg)(x) that would be f(x)*g(x) = (x-11)(2x+12) = 2x^2-10x-132
For any set with n elements, there are 2^n subsets. But A is not a proper subset of itself, nor is Ø, so that leaves just 2^4-2 = 14. By the way, "the number" is singular, not plural.
Ya got me On Monday there was 1/2 bag left. That means 7/14 are left. If he is to eat a few more, then that means there are only 7/14 - 5/14 = 2/14 left after Tuesday's chow-down. But, the next largest candy leaves 1/3 of the bag full. 1/3 > 2/14, so eh? is that 1/3 of ...
I'll use the more common ^ instead of , which is often used for simple multiplication. 10^5 = 10*10*10*10*10 = 100,000 it's a simple power. 3^2 = 3*3 2^6 = 2*2*2*2*2*2 = 64 and so on.
algebra - questions
What, are we playing Jeopardy?
What, no ideas? A simple review of the properties of the named figures should provide the answers. Or at least allow you to eliminate some possibilities.
I'd say they are 1/66 times the lengths of AB,BC,CA respectively.
Hmmm. What is f(5)? 7 or 8?
as long as no two distinct pairs have the same 1st element, it is a function. So, what do you think?
well, you know that h/x = tan 39.8° h/(x+51.7) = tan 19.7° Now eliminate x and solve for h: h/tan39.8° = h/tan19.7° - 51.7 1.2h = 2.8h - 51.7 h = 32.3 check my math, but that's the method to my madness.
Note that each tree costs the same as 2 bushes. Nick can buy 2-6 trees and 0 bushes, or 4-12 bushes and 0 trees. Each tree can be replaced by two bushes, so it's fairly easy to see how to keep within budget by replacing each tree by 2 bushes.
earnings = 0.05 Af A+f is meaningless, since you can't add ft^2 and n. Af computes the total ft^2 mowed. For various earnings, you'd also need a vector of rates. Not sure how to do that with just vector operations. Say the rates were 0.05, 0.10, 0.07, 0.12,...
depends on the configuration of the pens. A longs skinny corral with 4 pens in a row? Or a rectangular corral with a 2x2 arrangement of pens? If the first, then we have two lengths and 5 widths. 2x+5y = 200 area = xy = x(200-2x)/5 = -2/5 x^2 + 40x the vertex of the parabola is...
apparently an = (-1)^n + 1/2^n as in -1/2, 5/4, -7/8 ... but I could be wrong...
.6b + .9g = 3/4 (b+g) .9g = .6b + 12 Now just solve for b and g
Look up in your Z table for the upper tail at 20% You can play around with this at http://davidmlane.com/hyperstat/z_table.html where you can set the mean and variance and explore various properties of the normal distribution
LCM(a,b) = a*b/GCF(a,b) so, 36 = a(a+6)/6 a^2 + 6a - 216 = 0 (a+18)(a-12) = 0 a = 12 So, the two numbers are 12 and 18
60*5 = x(x+5) x^2 + 5x - 300 = 0 x = 15 The two numbers are 15,20
if there are n even numbers (starting at 2, and not skipping any), then n/2 (2*2+(n-1)*2) = 420 n = 20 So, the largest is 40
AD/AB = DE/BC AD/6 = 20/8 AD = 15
factor it and set each factor to zero.
You can get excellent graphing help at http://rechneronline.de/function-graphs/ You can plot up to three functions at the same time, and set the x- and y- boundaries as desired. I expect that you plotted the points wrong, if it didn't look like a parabola. Your tables look...
6x-4<-34 or 3x+10>10 6x-4<-34 6x < -30 x < -5 or 3x+10>10 3x > 0 x > 0 You can see the solution graphed at http://www.wolframalpha.com/input/?i=6x-4%3C-34+or+3x%2B10%3E10
5r+4 < 5 5r < 1 r < 1/5
algebra - an attempt
s = 5rt t = s/(5-r) t = 25r/s t = r^2-5s t = s/(5r^2) I get t=s/(5r) which is not any of the choices listed. If you want to repost using similar notation, maybe we can help more.
lots of rules will produce that, but the easiest is f(x) = x-1
h/150 = sin 45°
(2x/15)^2 / (.15-x/15)(.2-x/15) (4x^2/15^2) / (x^2-5.25x+6.75)/15^2 The 15^2 cancel out, and we have 4x^2/(x^2-5.25x+6.75) 16x^2/(4x^2-21x+27)
well, there are 5280 ft/mi, so 15*5280 feet
better just stick with "trig" One of the first things to do is to learn the special angles with easy trig values: 0,π/6,π/4,π/3,π/2 Knowing those, you will see that sin π/3 = √3/2 You have -√3/2, so that means that your angle is i...
original fraction: n/(2n+4) modified fraction: (n+6)/(2n+4+6) = 7/13 13(n+6) = 7(2n+10) 13n+78 = 14n+70 -n = -8 n=8 So, the original fraction was 8/20 and the new value is 14/26 = 7/13
2/8 * 1/7
The month must begin on Monday, so there are 2 full weeks ending on Sunday. The 15th is thus the 3rd Monday.
you know PV=kT solve for V, then use density = mass/volume
ab:xy = 10:11 So, other sides are in the same ratio ac/xz = 10/11 14/xz = 10/11 xz = 15.4
we know that ∫cos(u) du = sin(u) ∫tan(u) du = -log cos(u) So, what we get here is (-1/3)sin(2-3x) - (-1/3)(-log cos(5-3x)) = -1/3 (sin(2-3x) + log cos(5-3x)) + C
y = a(x-(-1+√5))(x-(-1-√5)) = a(x^2+2x-4) the one passing through (0,-32) is y = 8(x^2+2x-4) Similarly for the other root pair.
Quick math help
I only see one variable: x Factored it is -7(x-1)(2x+3)
I'd say 8 8 balls and 8 straws for the base 1 ball and 8 straws for the edges
well, it would have to be (2x-7)(2x+3)(x-2) = 117 4x^3 - 16x^2 - 5x - 75 = 0 (x-5)(4x^2+4x+15) = 0 ...
2/(2/3) = 3 So, 3 people, each with 2/3 extra bag makes 2 extra bags.
The second formula is correct The games played are 32,16,8,4,2,1 a1=32, r = 1/2 and there are 6 rounds played. 32(1 - 1/2^6)/(1 - 1/2) = 32(63/64)/(1/2) = 63