Tuesday
February 9, 2016

Posts by Jai

Total # Posts: 1,926

algebra
(3x+6)/(4x+12) / (x^2 - 4)/(x-3) first, to divide, we get the reciprocal of the divisor (or the second term/ term at the right) and the operation will be multiplication. reciprocal is just interchanging the numerator and denominator terms. thus, (3x+6)/(4x+12) * (x-3)/(x^2 - 4...
June 4, 2011

Math - Domain of Composite function
f(x) = sqrt(x) g(x) = 2x + 12 thus, (fog)(x) = sqrt(2x + 12) note that to get the domain, you must get the intersection of the 3 function domains. for f(x) = sqrt(x), x cannot be less than zero thus the domain is [0 , +infinity) for g(x) = 2x + 12, x can be any real number ...
June 3, 2011

math
to multiply, just multiply the radicands (terms inside the radical sign): sqrt(3*3) - sqrt(3*21) sqrt(9) - sqrt((3^2)*7) 3 - 3*sqrt(7) hope this helps~ :)
May 30, 2011

math
note that you can combine them right away when the radicand (term inside radical sign) are not the same/equal. observe that 45 and 125 can be factored to: 45 = 3*3*5 = (3^2)*5 125 = 5*5*5 = (5^2)*5 thus, we can take 3 and 5 respectively from each term, and it becomes (4*3)*...
May 30, 2011

math
you just multiply the radicands (terms inside the radical sign): sqrt(2) * sqrt(6) = sqrt(12) but we can further simplify this to: sqrt(12) = 2*sqrt(3) hope this helps~ :)
May 30, 2011

algebra
1.042 x 10^3
May 29, 2011

math
2.24 x 10^(-5) note that since the exponent of 10 is negative (which is -5), we just move the decimal point 5 places to the LEFT, or: 0.0000224 hope this helps~ :)
May 29, 2011

math
hmm, i'm not sure with that "reduce to 5/8". i interpreted it in two ways: A.) 5/8 as a number: let n = number thus, n - 33 = 5/8 n = 33 5/8 B.) 5/8 of the original n - 33 = (5/8)n n - (5/8)n = 33 (3/8)n = 33 n = 33*8/3 n = 88 hope this helps~ :)
May 27, 2011

Algebra
(c^2 - 1)(c^2 + 1) (c - 1)(c + 1)(c^2 + 1)
May 26, 2011

algebra
there are many ways to solve for the vertex. i think the easiest is to first find the derivative and solve for x: f(x)=x^2-10x+21 f'(x) = 0 = 2x - 10 2x = 10 x = 5 now substitute this back to original: f(5) = 5^2 - 10*5 + 21 f(5) = 25 - 50 + 21 f(5) = -4 thus vertex is at...
May 26, 2011

algebra
5x^2 = 48x 5x^2 - 48x = 0 x(5x - 48) = 0 therefore, x = 0 and x = 48/5 there are two solutions, and they are both real numbers. hope this helps~ :)
May 26, 2011

algebra
how to do this: first, from the equation, we get b or the numerical coefficient of x. from the given, b = 2. then divide this by 2: 2/2 = 1 and square it: 1^2 = 1 thus, the number that we're looking for is 1: x^2 + 2x + 1 =(x + 1)^2 hope this helps~ :)
May 26, 2011

algebra
(1/7x^2 - 2/5)(1/2x + 1/2) to do this, first multiply the 1/7x by the two terms on the second parenthesis (that is, 1/2x and 1/2). then also multiply -2/5 by the terms on the second parenthesis. and add them all. (1/7x^2)*(1/2x + 1/2) = (1/14)x^3+(1/14)x^2 (-2/5)(1/2x + 1/2...
May 26, 2011

math
22 * 5/8 = 13.75
May 26, 2011

Math
(3/17)x = 12 to get x alone, you divide both sides by the numerical coefficient (number before the variable) of x. 3/17 divided by itself is 1 and thus thus x = 12 / (3/17) to divide by fraction, you get the reciprocal of the divisor (that is, the 3/17) and change the division...
May 25, 2011

Geometry-Help PLZ
if three cubes are stacked, the other three are stacked too, and they are put together, the figure i see is a rectangular prism of lengths 6, 4 and 2. getting the SA of a rectangular prism, SA = 2LW + 2LH + 2WH SA = 2(6*4) + 2(6*2) + 2(4*2) SA = 48 + 24 + 16 SA = 88 sq units. ...
May 25, 2011

Geometry-Help PLZ
recall surface area and volume of cube is given by SA = 6*s^2 V = s^3 where s = length of a side the volume becomes 1/8 of original so V' = 8 cubic units. thus, 8 = s^3 s = cuberoot(8) s = 2 (new length) the surface area of a cube of this length is SA = 6*(2^2) SA = 24 sq ...
May 25, 2011

physica
recall that the motion of the stone is uniformly accelerated motion (because it accelerated due to gravity). thus we can use the formula: h = vo*t - 1/2(g)(t^2) where h = height vo = initial velocity t = time g = acceleration due to gravity = 9.8 m/s^2 substituting, h = vo*(1....
May 25, 2011

math
true.
May 25, 2011

math
false. it's 1/[2*sqrt(x)]
May 25, 2011

math
because it is undefined at x = 3.
May 25, 2011

Algebra
do you mean these are the roots of the quadratic equation you want to find? if so, from its roots, 2 and -4, (x-2)(x+4) x^2 + 2x - 8 hope this helps~ :)
May 25, 2011

algebra
to find f(0), we just substitute x = 0: f(x) = [x^2 - 3x + 2] / x + 1 f(0) = [0^2 - 3(0) + 2] / (0 + 1) f(0) = 2/1 = 2 hope this helps~ :)
May 25, 2011

Geometry-help
it's D. because 27/3 = 9 -> which must be the product of the remaining two lengths that are not given.
May 25, 2011

algebra
2(a^2)b - 7a - 9b
May 25, 2011

geometry
recall that lateral area (area on the sides, not the top or the bottom) of a cylinder is given by, LA = 2πrh where r = radius h = height π = "pi" equal to 3.14 (constant) substituting, LA = 2*(3.14)*5*22 LA = 690.8 cm^2 recall that the surface area of ...
May 24, 2011

algebra
to get the slope, we first transform this into slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. x + 5y = 10 note that in slope-intercept form, y is the only term on the left side, and all other terms on the right side. thus, 5y = -x + 10 then ...
May 24, 2011

algebra
x-intercept occurs at y = 0. thus from the given equation, we set y = 0: -25x + y = 15 -25x = 15 x = -3/5 thus x-intercept is at (-3/5 , 0) y-intercept occurs at x = 0. thus from the given equation, we set x = 0: -25x + y = 15 y = 15 thus y-intercept is at (0 , 15) hope this ...
May 24, 2011

Geometry -need help
recall that the surface area of cylinder is given by SA = 2πr^2 + 2πrh where r = radius h = height π = "pi" equal to 3.14 (constant) substituting, SA = 2*(3.14)*3^2 + 2*(3.14)*3*9 SA = 226.08 in^2 then we divide this by his speed, 40 in^2/5 min: 226.08...
May 24, 2011

math
we need to divide both sides of the equation by 0.8 to get T alone: 0.8T = 24 0.8T / 0.8 = 24 / 0.8 T = 30
May 24, 2011

algebra
note that this equation is already in the slope-intercept from: y = mx + b , where m is the slope and b is the y-intercept. thus in the given, y = 2x + 6 the slope is 2. hope this helps~ :)
May 23, 2011

algebra
6y -6 < 5y - 3 6y - 5y < -3 + 6 y < 3 hope this helps~ :)
May 23, 2011

algebra
7+3x < 19 we just solve it like a normal equation (not an equality). 7 + 3x < 19 3x < 19 - 7 3x < 12 x < 4 hope this helps~ :)
May 23, 2011

algebra
5 - 9y - 2y < 27 we just solve it like a normal equation. 5 - 11y < 27 -11y < 27 - 5 -11y < 22 y > -2 note that when dividing both sides by a negative number, the inequality sign becomes its opposite. like here, both sides are divided by -11, and thus the sign ...
May 23, 2011

maths
first convert the time given in hours. 2 hours & 30 min = 2.5 hours then recall that speed is just distance traveled over time, or v = d/t substituting, v = 220/2.5 v = 88 km/hr hope this helps~ :)
May 23, 2011

math
x-intercept occurs at y=0. thus we substitute it to the given equation, y = x^2 + 4x - 12 0 = x^2 + 4x - 12 0 = (x-2)(x+6) x = 2 and x = -6 at these values of x, y is zero. thus the x-intercepts are (2,0) and (-6,0) hope this helps~ :)
May 23, 2011

Pre-algebra
8(4s-7) < 6(2s+4) 32s - 56 < 12s + 24 20s < 80 s < 4 hope this helps~ :)
May 23, 2011

Pre-algebra
-5(3e-2)<-2(6e+7) -15e + 10 < -12e - 14 -3e < -24 e > 8 *note that when dividing both sides of the equation by negative number, the sign changes to its opposite. like here, both sides were divided by -3 and the sign changes from < to >. hope this helps~ :)
May 23, 2011

Pre-algebra
-3(2b+4)>4(b+7) -6b - 12 > 4b + 28 -10b > 40 b < -4 *note that when dividing both sides of the equation by negative number, the sign changes to its opposite. like here, both sides were divided by -10 and the sign changes from > to <. hope this helps~ :)
May 23, 2011

Pre-algebra
48>3(w+7) 48 > 3w + 21 27 > 3w 9 > w or w < 9 hope this helps~ :)
May 23, 2011

Pre-algebra
-12(c-6)<120 -12c + 72 < 120 -12c < 48 c > -4 *note that when dividing both sides of the equation by negative number, the sign changes to its opposite. like here, both sides were divided by -12 and the sign changes from < to >. hope this helps~ :)
May 23, 2011

Pre-algebra
7(v+5)>56 7v + 35 > 56 7v > 21 v > 3 hope this helps~ :)
May 23, 2011

Math
but we need the figure to solve for this.
May 23, 2011

Math
you can answer this in two ways~ systematic way (lol): let x = units digit let y = tens digit from the second statement, (1) xy = 14 from the first statement, (2) 10x + y = 3(10y + x) - 9 from equation (1), we can express y in terms of x, yielding y = 14/x substituting this to...
May 23, 2011

Math
2x^2 + 7x -15 =0 (2x - 3)(x + 5) = 0 therefore, x = 3/2 and x = -5 hope this helps~ :)
May 22, 2011

physics
just imagine when you dribble. you use force (directed downward) from your hand to "throw" it downwards.
May 22, 2011

algebra
numerical coefficients : 2, 4, 8
May 22, 2011

algebra
(-8x^2-2x+4)+(x^2-9x+7) to add, we just combine the numerical coefficients (or the numbers before the variable) of the same variables (meaning same letters and same exponents). thus, (-8x^2 - 2x + 4 ) + ( x^2 - 9x + 7 ) -7x^2 - 11x + 11 hope this helps~ :)
May 22, 2011

chemistry
(1) assuming the gas is ideal, the volume becomes 1/3 of the original. (2) recall that STP, pressure is at 1 atm. assuming the gas is ideal, P1*V1 = P2*V2 where P1 = initial pressure V1 = initial volume P2 = final pressure V2 = final volume substituting, 1*2000 = (P2)*15 P2 = ...
May 21, 2011

math
i think you mean 3k^2 + 6k = 6 thus, we can re write this as 3k^2 + 6k - 6 = 0 note that we can factor out 3 from each term and cancel it. thus we can re write this as k^2 + 2k - 2 = 0 using quadratic formula, k = [-b +- sqrt(b^2 - 4ac)]/(2a) substituting, k = [-2 +- sqrt(2^2...
May 21, 2011

algebra2
to do this, we just multiply the exponents. [x^9]^11/7 x^(9*11/7) x^(99/7) hope this helps~ :)
May 17, 2011

Maths
|| means they are parallel. since AB and CD are parallel, they will never meet.. thus i think the first statement is wrong that they meet at point E.
May 17, 2011

Algebra
(q-2)/4 * -2q/(q+5) to multiply, we just multiply numerator by numerator and denominator by denominator. thus, this becomes: (q-2)(-2q) / (4)(q+5) observe that we can factor 2 from numerator and denominator and cancel it, and this becomes: -q(q-2) / (2)(q+5) hope this helps~ :)
May 17, 2011

science
recall that current is voltage per resistance, or I = V/R *units of current in Amperes (A) *units of voltage in Volts (V) *units of resistance in ohms (Ω) substituting, 8 = 1.1/R R = 1.1/8 = 0.1375 Ω hope this helps~ :)
May 17, 2011

chemistry
first thing to do here is to balance the chemical equation. 2Na + Cl2 --> 2NaCl then we get the masses of Sodium and Chlorine from periodic table of elements in order to calculate the molar mass of NaCl. from periodic table, Na = 23 Cl = 35.5 thus, NaCl = 23+35.5 = 58.5 g/...
May 17, 2011

math help please !!!
*reposted -- because i think you haven't read my previous post in this problem* first, we solve for the initial velocity from the formula of the maximum height: h,max = [(vo)^2]/(2g) where vo = initial velocity g = acceleration due to gravity = 9.8 m/s^2 substituting, 30...
May 17, 2011

geometry
note that complement means the other angle in which their sum should be 90. thus to get the complement of each angle, we just subtract them from 90: 90 - 44 = 46 90 - 15 = 75 90 - 72 = 18 90 - 89 = 1 90 - 10 = 80 90 - 30 = 60 hope this helps~ :)
May 16, 2011

math
we'll solve this in two cases: Case I: absolute value is positive. |n+1| < 4 n+1 < 4 n < 3 Case II: absolute value is negative. |n+1| < 4 -(n+1) < 4 n+1 > -4 n > -5 getting the intersection (common between them) of the two answers, thus n must be ...
May 15, 2011

Algebra
the formula is wrong. it should be y = a(x-h)^2 + k where (h,k) is the center then to solve for a, you choose one of the points to substitute for the value of x and y. for instance you choose (-4,-1): y = a(x-h)^2 + k -1 = a(-4+3)^2 - 2 then solve for a. if you want to make ...
May 15, 2011

Algebra
yes~ :)
May 15, 2011

Algebra
yes, you're right. :)
May 15, 2011

Algebra-right question for Jai
the volume of a triangular prism is given by V = (1/2)*(B*H*L) where B = base H = height L = length thus the new volume becomes, V' = (1/2)*(2*B)(2*H)*L V' = 2*(1/2)*(B*H*L) or V' = 2*V thus the new volume is twice the original. note that first statement is tricky...
May 15, 2011

Algebra- word problem
sure~ :)
May 15, 2011

Algebra- word problem
original area: A = L*W A = 6*3 = 18 in^2 new area: A' = L'*W' A' = 8*5 = 40 in^2 the difference between these areas is the amount of wall space needed: 40-18 = 22 in^2 thus it's A. hope this helps~ :)
May 15, 2011

algebra
recall that the volume of a rectangular prism is given by V = L*W*H where L = lenght W = width H = height. if 4 is multiplied to both length and width, the new volume, V', is V' = (4L)*(4W)*(H) V' = 16*(L*W*H) or V' = 16*V thus the new volume is 16 times ...
May 15, 2011

algebra
oh, i see.. the choices are wrong. i guess you typed it wrong because "volume" is in the choices.. it must be "area" since it is the required. (and rectangles don't have volume)
May 15, 2011

algebra
original area: A = L*W new area: A' = (3L)*(3W) A' = 9*(L*W) or A' = 9*A thus there is no correct answer in the choices, since the new area is 9 times greater than the original. hope this helps~ :)
May 15, 2011

algebra
yes~ :) original area: A = L*W new area: A' = (3L)*(3W) A' = 9*(L*W) or A' = 9*A thus there is no correct answer in the choices, since the new area is 9 times greater than the original. hope this helps~ :)
May 15, 2011

Math
(a) to get this, we just use ratio and proportion: let x = weight of 150 books. 108 books : 30 kg = 150 books : x kg we can thus rewrite this as 108/30 = 150/x 3.6 = 150/x x = 150/3.6 x = 41.67 kg (b) we also use ratio and proportion here: let y = number of books that has ...
May 15, 2011

physics
recall that the volume of a sphere (geometry of the ball) is given by V = (4/3)πr^3 where r = radius π = 3.14 (constant) thus to get radius, we need to first get the volume from the given mass and density. recall that density is just mass per volume, or d = m/V ...
May 15, 2011

Math
#1 to get this, we just use ratio and proportion. let x = weight of 1000 cm^3 liquid. 250 cm^3 : 125 g = 1000 cm^3 : x g thus we can rewrite this as, 250/125 = 1000/x solving for x, 2 = 1000/x 2x = 1000 x = 500 grams #2 here, we also use ratio and proportion. first we convert ...
May 15, 2011

algebra
to get this, you just substitute t=6 to the given equation: v = (-1/2)t + 3 v = (-1/2)*6 + 3 v = -3 + 3 v = 0 plot: h t t p : / / w w w 4 c . w o l f r a m a l p h a . c o m / Calculate/MSP/MSP412219fd25cdf0efbh880000587daeb9i9ea74bg?MSPStoreType=image/gif&s=11&w=424&h=166&cdf...
May 15, 2011

math
first, we solve for the initial velocity from the formula of the maximum height: h,max = [(vo)^2]/(2g) where vo = initial velocity g = acceleration due to gravity = 9.8 m/s^2 substituting, 30 = [(vo)^2]/(2*9.8) vo = sqrt(588) vo = 24.25 m/s (a) note that the motion of the ...
May 15, 2011

algebra
*reposted* 9t^4 + 7t - 45 t^3 + 10t note that when combining terms with variables, we just add the numerical coefficient of the same variable (and exponent). here, we can only combine 7t and 10t. thus 9t^4 + 7t - 45 t^3 + 10t 9t^4 + 17t - 45 t^3 rearranging, 9t^4 - 45 t^3 + ...
May 14, 2011

algebra
*reposted* 9t^4 + 7t - 45 t^3 + 10t note that when combining terms with variables, we just add the numerical coefficient of the same variable (and exponent). here, we can only combine 7t and 10t. thus 9t^4 + 7t - 45 t^3 + 10t 9t^4 + 17t - 45 t^3 rearranging, 9t^4 - 45 t^3 + ...
May 14, 2011

math
sin 90 = 1 hope this helps~ :)
May 14, 2011

math
sin 90 = 1 hope this helps~ :)
May 14, 2011

algebra
9t^4 + 7t - 45 t^3 + 10t note that when combining terms with variables, we just add the numerical coefficient of the same variable (and exponent). here, we can only combine 7t and 10t. thus 9t^4 + 7t - 45 t^3 + 10t 9t^4 + 17t - 45 t^3 rearranging, 9t^4 - 45 t^3 + 17t hope this...
May 14, 2011

Math
first observe that you are 24 years older than your son. also, since we are required of the ages, we represent these unknown ages using variables: let x = your son's age let x+24 = your age note that when your son's age is x years, you are three times as old. therefore...
May 14, 2011

Applied Physics
equilibrium means that all forces acting on the object are balanced / cancel each other out. it can also mean that the object is not accelerating. thus, an object can be in equilibrium whether it is motion or not, as long as forces are balanced. since it's said that it ...
May 14, 2011

Chemistry
to get the heat released or absorbed, Q = mc(T2-T1) where m = mass of substance (units in g) c = specific heat capacity (units in J/g-K) T2 = final temperature T1 = initial temperature **note: if Q is (-), heat is released and if (+), heat is absorbed now we can only apply ...
May 14, 2011

Chemistry
to get the heat released or absorbed, Q = mc(T2-T1) where m = mass of substance (units in g) c = specific heat capacity (units in J/g-K) T2 = final temperature T1 = initial temperature **note: if Q is (-), heat is released and if (+), heat is absorbed for water c = 4.184 J/g-K...
May 14, 2011

Math
X(bar) = 10,000 M = 1,000 D = 500 C = 100 L = 50 X = 10 I = 1 thus XMMDCLXII is equal to 12,662 hope this helps~ :)
May 14, 2011

mensuration
recall that the area of rectangle is given by A = L*W where L is length and W is width. substituting, A = 20*12 = 240 m^2 (we'll use this later) since there is 2 m wide path, (and thus there is total of 4 m on both sides), 20 - 4 = 16 m 12 - 4 = 8 m getting the area of ...
May 14, 2011

physics
hello~ you can find answers on google. just type "why candle flame up" , there are links discussing this topic. i can't post links here that's why~ ^^;
May 13, 2011

Math- college
to get this, we just use ratio and proportion: let x = miles travelled with 24 gallons 22 miles : 1 gallon = x miles : 24 gallons therefore, 22/1 = x/24 x = 22*24 x = 528 miles hope this helps~ :)
May 13, 2011

Math- college
(a) to get this, we just divide 1148 by 13. type this in you calculator: 1148 / 13 the answer must be 88.308. since the number of bags can not be decimal, we only take the whole number, which 88 sand bags. (b) to get this, we multiply the number of bags used (which is 88) by ...
May 13, 2011

Math
first let's represent their weights using variables: let C = weight of one piece of cake let A = weight of one apple let H = weight of one cherry from the first statement, (1) 2C = A + H for the second statement, (2) A = 5H + C now we need to find how mach does cherries ...
May 13, 2011

Algebra 8th
do you mean "square root" for the "radical"? if so, 2[sqrt(8) + sqrt(5)] note that we cannot combine the radical terms since their radicands (term inside the radical sign) are not equal. but we can rewrite this as 2[2*sqrt(2) + sqrt(5)] 4*sqrt(2) + 2*sqrt(5...
May 13, 2011

Calculus
recall that the derivative of cos^-1 (x) or arccos (x) is -1/[sqrt(1-x^2)] * dx thus the derivative of cos^-1 (x^2) -(2x)/[sqrt(1 - x^4)] note that the 2x is the dx that came from the derivatice of the term inside the cos^-1, which is x^2. hope this helps~ :)
May 13, 2011

Math
to convert PERCENT to DECIMAL, we move 2 decimal places to the LEFT. thus for 0.06%, we move 2 decimal places, and it becomes: 0.0006 now we know the decimal, we can convert this to fraction. first we count the places to the right of decimal point. there are 4 decimal places (...
May 11, 2011

Geometry
recall that length of arc is given by s = r*theta where r = radius theta = angle in radians first we convert the given angle to radians: 20 * pi/180 = pi/9 = 0.349 rad substituting, s = 1*0.349 s = 0.349 s = 0.35 (nearest hundredth) hope this helps~ :)
May 11, 2011

physics
(a) the motion of the book is projectile, and uniformly accelerated motion. thus we use the formula, h = ho + vo*t - (1/2)*g*t^2 where h = final height ho = initial height vo,y = initial vertical velocity = vo*sin(theta) t = time g = acceleration due to gravity (9.8 m/s^2) ...
May 11, 2011

physics
..what do you want to solve?
May 11, 2011

math
note that 36/9 is also equal to 4. thus we look for fractions that is also equal to 4. the denominator of 4 is 1 (any number divided by 1 is itself). thus we only multiply the numerator and denominator by the same number to get an equivalent fraction. for instance, let's ...
May 11, 2011

math
do you mean x^(2-n) ? if so at x = 8, 8^(2-n) = 0 , we can rewrite this as (8^2)/(8^n) = 0 64/8^n = 0 note that this equation has no solution and only at n-> infinity, it will approach zero. also at x=-8, it has no solution. hope this helps~ :)
May 11, 2011

science
in physics, note that mass is different from weight. mass has units in kilograms, grams, etc., while weight has units of Newton. (Newton = kg*m/s^2) to determine weight, we use the formula W = m*g where m = mass (in kg) g = acceleration due to gravity = 9.8 m/s^2 substituting...
May 11, 2011

Physics(Please Help!!)
* means multiply or times / means divided by to solve, input this on your calculator: 77.18 x 9.81 x 5.83 / 4.37
May 9, 2011

geometry: volume of cone
recall that volume of cone is given by V = pi*(r^2)*h/3 where pi = 3.14 (constant) r = radius h = height if r becomes (1/2)r, V,new = pi*[(1/2)r]^2*h/3 V,new = 1/4[pi*(r^2)*h/3] V,new = (1/4)V thus multiplied by 1/4. hope this helps~ :)
May 9, 2011

math!!!!
you use the distance formula: d = sqrt[ (x2 - x1)^2 + (y2 - y1)^2 ] where (x1,y1) = first point (x2,y2) = second point hope this helps~ :)
May 9, 2011

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