# Posts by Jai

Total # Posts: 1,998

**Algebra 2**

x^3 + y^(-2) to evaluate means you substitute the value of x and y which are given in the problem. first, recall some laws of exponents. if a term is raised by a negative number, it is also equal to its reciprocal raised to the that number but positive in sign. for example, 5...

**maths**

first we represent unknowns using variables. let x = number of girls in the hall since the the total number of children is 335, let 335 - x = number of boys in the hall then we set-up the equation. since 1/4 of the girls and 2/5 of the boys are swimmers and their total is 110...

**Algebra 2**

recall some laws of exponents. a term which is raised by a negative number is also equal to its reciprocal raised to that number with positive sign. for example, 3^(-2) = (1/3)^2 thus, we can rewrite it as, (1/x)^4 substituting x = 2, (1/2)^4 (1/2)*(1/2)*(1/2)*(1/2) 1/16 hope ...

**Algebra II**

S = (-1/2)gt^2 + vt S + (1/2)gt^2 = vt vt = S + (1/2)gt^2 v = [S + (1/2)gt^2]/t , or v = S/t + (1/2)gt hope this helps~ :)

**Algebra II**

first represent the unknowns using variables. let x = first multiple of 10 since consecutive multiples of ten has difference of 10 (example 40 and 30 has a difference of 10), let x + 10 = second multiple of 10 let x + 20 = third multiple of 10 then we set-up the equation. from...

**math**

6*e^(-4t) = 2 e^(-4t) = 1/3 take the ln of both sides: ln [ e^(-4t) ] = ln (1/3) -4t = ln (1/3) t = -(1/4)*(ln (1/3)) or t = (1/4)*(ln 3) hope this helps~ :)

**math**

note that you can combine exponents if they have the same base. thus, we change the 4 (first term) to 2^2 since the base on the second term is equal to 2: 3 x 4^(1/4) - 12 x 2^(-3/2) 3 x (2^2)^(1/4) - 12 x 2^(-3/2) also, since 12 = 2*2*3 = (2^2)*3, 3 x (2^2)^(1/4) - (3*2^2) x ...

**algebra**

(5x-4)/3 = 12 5x - 4 = 36 5x = 36 + 4 5x = 40 x = 8 hope this helps~ :)

**college meth**

i interpreted this as: -128 / 4^2 + 6 - 1 recall PEMDAS: Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction. this is the order in which operation must be done first. therefore, -128 / 8 + 6 - 1 -16 + 6 - 1 -11 hope this helps~ :)

**geometry**

since AD bisects BC, point D is therefore the midpoint of B and C. recall that the formula for midpoint is given by MP = ( (x1 + x2)/2 , (y1 + y2)/2 ) where (x1,y1) and (x2,y2) = coordinates of B and C substituting, D = ( (5+3)/2 , (-1+5)/2 ) D = ( 8/2 , 4/2 ) D = (4, 2) hope ...

**maths**

we can rewrite 2:40 as 14:40 then we subtract, 14:40 - 9:50 since 40 is less than 50, we add an hour to it or 60 minutes, while we subtract 1 from 14: 13:100 - 9:50 4 : 50 = 4 hours and 50 minutes hope this helps~ :)

**algebra**

in the second line of your solution, 2*(-3x^2) = -6x^2 not 6y^2. thus, -3x^2 + 4xy + 7y^2 - 6x^2 + 10xy + 22y^2 -9x^2 + 14xy + 29y^2 ..for the second problem, i think there are typos. please check the problem again. also, 100^2 is not equal to 200.

**algebra**

-4^6 = -(4*4*4*4*4*4) = -4096

**chemistry**

recall that density is mass per unit volume, or d = m/V substituting, 8600 kg/m3 = 2 kg / V V = 2/8600 V = 0.00023256 m^3, or in mL, V = 232.56 mL hope this helps~ :)

**math/algebra**

to do this you can either just factor it out (if it is factorable) or use quadratic formula. since it's factorable, (x + 4)(x - 3) = 0, thus x = -4 and x = 3 using quadratic formula: x = [-b +- sqrt(b^2 - 4ac)]/(2a) where a = numerical coefficient of x^2 b = numerical ...

**algebra**

11 + 12^2 - (-11)*12 11 + 144 + 132 155 + 132 287 you should perform multiplication operation (the -11*12) first, not subtraction (not the 144-11). -(8m) - (-7m + 2) -8m + 7m - 2 -m - 2 you should distribute the negative sign to the terms inside the parenthesis. thus their ...

**algebra**

A. (x-6)(2x+3) B. (2x-9)(7x+4) C. (x-1)(x+1)(x+3)

**math**

(x+3)(x-3)(x-2) (x^2 - 9)(x - 2) x^3 - 9x - 2x^2 + 18 x^3 - 2x^2 - 9x + 18 hope this helps~ :)

**maths**

1000^1000 = (10^3)^1000 = 10^3000 ..it's like, 3000 zeros written on the right of 1. hope this helps~ :)

**science**

recall that acceleration is the change in velocity over time, or a = Δv / t substituting, 2 = Δv / 6 Δv = 12 m/s hope this helps~ :)

**PreCal**

first recall that the form of polar coordinate is (r, θ) to convert polar coordinate to rectangular coordinate, we do this: (r*cos θ , r*sin θ) in the problem, r = 40 and θ = 62. thus, (r*cos θ , r*sin θ) (40*cos 62 , 40*sin 62) (18.78 , 35.32) ...

**math**

since the amount of money the theater makes is a function of the number of people, it is dependent on the number of people. let n = number of people let m = amount of money since a ticket costs 2 dollars, the amount of money would be m = 2n, or in function form, m(n) = 2n ...

**Math**

on the fourth line of your solution, 2(4) = 8, not 16. thus, = 15 - 8 - 4/2 = 15 - 8 - 2 = 5 hope this helps~ :)

**math**

x = 6 + y y = -z/3 substituting, x = 6 - z / 3 thus letter (c).

**Chem**

neutral Nitrogen has an atomic number of 7 (from periodic table) thus it has 7 protons and 7 electrons (equal +p and -e). Since it is an ion with charge -3, it means that it gained 3 electrons. therefore, N^-3 has 7 protons and 10 electrons. hope this helps~ :)

**geometry**

since it's already factored, you can equate each factor to zero and solve for x. 2x - 3 = 0 2x = 3 x = 3/2 x - 5 = 0 x = 5 4x + 7 = 0 4x = -7 x = -7/4 note that there are three values of x. hope this helps~ :)

**Math**

first represent unknowns with variables. let x = games that they tied let x+1 = games that they lost let (x+1)+2 = games that they won then we set-up the equation. since the total games is 12, x + x+1 + (x+1)+2 = 12 x + x + 1 + x + 3 = 12 3x + 4 = 12 3x = 8 x = 8/3 = 2.67 ...

**science**

recall that speed is distance travelled over time. thus we calculate the speed of each. let's also make sure that the units of speed for both are the same. Car: (convert first the units) 240 km * (1000 m /1 km) = 240000 m 2 hr * (3600 s / 1 hr) = 7200 s v = d/t v = 240000/...

**science**

i think you forgot to include here the time given. because speed is distance travelled over time, but the only given here is the distance.

**Geometry**

...but we need to see the figure.

**geometry**

recall the form, y - y1 = m(x - x1) where m = slope (x1 , y1) = point on the line substituting, y - (-2) = (2/3)*(x - 5) y + 2 = (2/3)x - 10/3 y = (2/3)x - 10/3 - 2 y = (2/3)x - 10/3 - 6/3 y = (2/3)x - 16/3 *the slope-intercept form is in the form y = mx + b. hope this helps~ :)

**Chemistry**

(a) to get the weight/volume percent, we just divide the mass of the compound to the volume, and multiply by 100: 25 g / 1000 mL * 100 = 2.5 % w/v (b) recall that molarity is moles of solute per liter of solution. thus first get the number of moles of the compound by dividing ...

**Maths**

cos (theta) = -0.25 theta = cos^-1 (-0.25) there are two answers: theta = 104.48 degrees = 3.65 radians and, theta = -104.48 degrees = -3.65 radians hope this helps~ :)

**Trig**

0 - 5(-1) 0 + 5 5

**Trig**

we only to find the angle formed between 2 and 3 (represents where the longer hand points when 15 minutes). notice that, as the longer hand of clock moves, the shorter hand also moves. the maximum angle that it can move in an hour is 360/12 = 30 degrees (occurs if the longer ...

**geometry**

(9m+2)(m-3) to multiply this, use FOIL method: F = multiply first terms (9m & m) O = multiply outer terms (9m & -3) I = multiply inner terms (2 & m) L = multiply last terms (2 & -3) then add all the products. therefore, 9m * m = 9m^2 9m * -3 = -27m 2 * m = 2m 2 * -3 = -6 9m^2...

**algebra**

y = (-7/4)x - 1 since the points given will satisfy the given equation, we just substitute the value of x-coordinate to variable x in the equation to get y: for x = -4, y = (-7/4)*(-4) - 1 y = 7 - 1 = 6 thus the first point is (-4,6) for x = 0, y = (-7/4)*0 - 1 y = -1 thus the...

**math**

first, represent unknowns with variables. let x = measure of angle 2 let 4x-5 = measure of angle 1 (according to the first statement of problem) then set-up the equation. since the angles form a linear pair, their sum must be equal to 180. thus, x + 4x - 5 = 180 5x = 180 + 5 ...

**Math**

just follow MDAS: Multiplication, Division, Addition Subtraction. this is the sequence that should be followed when there are multiple operations. however, for operations involving only Multiplication and Division, you can solve them left to right. for example, 6 / 3 * 4 2 * 4...

**math**

first we represent unknowns with variables. let x = number of $3-tickets since the total number of tickets ($3 and $5) is equal to 272, let 272-x = number of $5-tickets then we set-up the equation. to get the total cost, we multiply each price of the ticket with their number. ...

**science**

recall that speed is distance traveled over a certain time, or v = d/t substituting, v = 400/90 v = 4.44 m/s hope this helps~ :)

**chemistry**

first we write the balanced chemical reaction: C + 2 H2 -> CH4 *note that Hydrogen is diatomic in nature (that's why it's H2, not H) then to get how much H2 reacted (in grams), we use the data of Carbon. 1 g of Carbon reacted, thus to get the number of moles of C, ...

**algebra**

first we represent the unknowns using variables: let x = measure of angle 4 let 3x+4 = measure of angle 3 (from the second statement) then we set-up the equation. since the angles form a linear pair, their sum is equal to 180 degrees. therefore, x + 3x + 4 = 180 4x + 4 = 180 ...

**chemistry**

do you mean density of Na2CO3 of 1 dm^3 volume? if so, we first find its density. Since sodium carbonate only, assume that it is anhydrous (no water/hydrate). from density data found in some books, density of Na2CO3 is 2.54 g/cm^3. then we get the corresponding mass for a ...

**Math**

just substitute the value of radius to the equation: surface area = SA = 4*pi*r^2 SA = 4*3.14*(3960^2) SA = 1.97 * 10^8 miles^2 hope this helps~ :)

**algebra 2**

first, represent unknowns with variables: let x = width let x+5 = length (according to first statement) then set-up the equation. recall that the perimeter of a rectangle is given by P = 2L + 2W therefore, 58 = 2(x + 5) + 2x 58 = 2x + 10 + 2x 58 = 4x + 10 48 = 4x x = 12 cm (...

**science/math please help**

density = mass/volume density = 500 / 250 density = 2 g/mL

**algebra**

left and right sides of frame = 1 + 1 = 2 in top and bottom sides of frame = 1 + 1 = 2 in therefore the total length and width are: L = 8 + 2 = 10 in W = 8 + 2 = 10 in recall that area of rectangle is given by A = L*W A = 10*10 A = 100 in^2 hope this helps~ :)

**Math**

first we represent the unknowns using variables: let x = measure of angle 4 let 3x+4 = measure of angle 3 (from the second statement) then we set-up the equation. since the angles form a linear pair, their sum is equal to 180 degrees. therefore, x + 3x + 4 = 180 4x + 4 = 180 ...

**SCIENCE**

recall that the rate of energy being transferred is given by: q = -kA(dT/dx) where q = energy per unit time (in Watts) k = thermal conductivity (W/m-K) T = temperature (in Kelvin) x = distance (in meters) assuming steady-state heat transfer (meaning, at a particular location, ...

**PHYSICS**

recall that the rate of energy being transferred is given by: q = -kA(dT/dx) where q = energy per unit time (in Watts) k = thermal conductivity (W/m-K) T = temperature (in Kelvin) x = distance (in meters) assuming steady-state heat transfer (meaning, at a particular location, ...

**Mathematics**

both irregular and regular have 5 sides and 5 corners. also, both have the same TOTAL/SUM of the interior and exterior angles. regular pentagon has sides of equal lengths, while irregular pentagon has sides of not equal or varying lengths. hope this helps~ :)

**chemistry**

the heat released or absorbed is given by the formula, 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 ...

**Math**

L^2*pi*a- 2L*pi*x + pi*x^2 = 0 first we can factor out pi from all terms and cancel it out: pi*[ L^2 * a - 2Lx + x^2 ] = 0 L^2 * a - 2Lx + x^2 = 0 a*L^2 - 2x*L + x^2 = 0 since it looks like a quadratic equation now (where L is the variable), we can use quadratic formula to ...

**mechanical**

recall that maximum range occurs at angle = 45 degrees. also, the max height in projectile motion is given by: y,max = (Vo)^2 * sin^2 (theta)/(2g) where Vo = initial velocity theta = angle of release g = acceleration due to gravity = 9.8 m/s^2 note that max height occurs at ...

**Algebra**

12i

**Algebra**

by just observing the given equations, since they have the same slope, they are parallel and thus the system has NO solution since parallel lines never meet or has no intersection. to prove this using substitution: first choose one equation. then choose one variable (for ...

**Algebra 1**

to do substitution: you choose one equation, then represent one of the variables in terms in terms of the other. and finally substitute it the the other equation. (1) x - 5y = 10 (2) 2x - 10y = 20 here, let's choose equation (1), and let's represent x in terms of ...

**math**

just type this in your calculator: 878 + 956 + 1039 + 1497 + 1463 + 1277 = ? for the second question, it is finite (or definite), since the total number of escapees is specific and can be measured. hope this helps~ :)

**College Physics**

momentum = mass * velocity thus we first get the mass by dividing the weight by g. m = W/g m = 9700/9.81 m = 988.8 kg thus, momentum = p = mv p = 988.8 * 36 p = 35596.8 kg*m/s hope this helps~ :)

**maths**

first we add all the fractions: 1/3 + 1/8 + 1/6 to add them, we need the 'least common denominator' (LCD) of the three fractions. LCD is the smallest number that is divisible by 3, 8 and 6. the LCD of 3, 8 and 6 is 24. then we change all the denominators by 24. to get ...

**derivative calculus**

the derivative you got is correct. by distributing, we can further simplify this into: 32t + 8t^(3/2) + 2t^(3/2) - (5/2)t^(-1/2) 10t^(3/2) + 32t - (5/2)t^(-1/2) hope this helps~ :)

**MATH**

linear pair means the sum of the angles equal 180 degrees. therefore, 3x - 12 + 7x + 2 = 180 10x - 10 = 180 10x = 190 x = 19 finally, substituting this back to angle 1 and 2: Angle 1: 3(19) - 12 = 45 degrees Angle 2: 7(19) + 2 = 135 degrees hope this helps~ :)

**Translate the following situation into an inequali**

first, we represent the unknowns using variables. let x = outfits that Jane packed let x-1 = outfits that Charlie packed let 2x-5 = outfits that Loretta packed since "limited to a total of 24 outfits", it means that the maximum number of outfits is 24: x + (x-1) + (...

**“Charlie would like to pack one less outfit than J**

*re-posted* first, we represent the unknowns using variables. let x = outfits that Jane packed let x-1 = outfits that Charlie packed let 2x-5 = outfits that Loretta packed since "limited to a total of 24 outfits", it means that the maximum number of outfits is 24: x...

**chemistry**

(a) x = 273.15 Kelvin (b) p = freezing (c) heat of freezing (d) Q = melting (e) heat of fusion

**Math**

supplement means the measure of angle in which when added to the other angle equals 180 degrees. therefore, we just subtract the given from 180: 180 - 58 = 122 degrees hope this helps~ :)

**Math**

y = -4x^2 - 16x - 11 there are many ways to determine the vertex, but the easiest (for me) i think is to use derivatives. first we get the derivative with respect to x: y = -4x^2 - 16x - 11 y' = -8x - 16 then we equate this to zero (because vertex is a maximum or a minimum...

**Math**

y = -2x^2 + 12x - 13 there are many ways to determine the vertex, but the easiest (for me) i think is to use derivatives. first we get the derivative with respect to x: y = -2x^2 + 12x - 13 y' = -4x + 12 then we equate this to zero (because vertex is a maximum or a minimum...

**math**

(x + 5) -2(4x -1) = 0 x + 5 - 8x + 2 = 0 -7x + 7 = 0 -7x = -7 x = 1 hope this helps~ :)

**math**

note that the sum of the interior angles of a triangle is always equal to 180. thus to get angle H, F + G + H = 180 32 + 100 + H = 180 132 + H = 180 H = 180 - 132 H = 48 degrees hope this helps~ :)

**Algebra**

e^9 = -x

**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...

**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 ...

**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~ :)

**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)*...

**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~ :)

**algebra**

1.042 x 10^3

**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~ :)

**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~ :)

**Algebra**

(c^2 - 1)(c^2 + 1) (c - 1)(c + 1)(c^2 + 1)

**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...

**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~ :)

**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~ :)

**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...

**math**

22 * 5/8 = 13.75

**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...

**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. ...

**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 ...

**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....

**math**

true.

**math**

false. it's 1/[2*sqrt(x)]

**math**

because it is undefined at x = 3.

**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~ :)

**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~ :)

**Geometry-help**

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

**algebra**

2(a^2)b - 7a - 9b

**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 ...

**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 ...

**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 ...