Monday

July 28, 2014

July 28, 2014

Total # Posts: 1,493

**algebra**

represent the unknowns using variables: let x = shortest piece let y = 2nd longest piece let (x+y) - 6 = longest piece *according to the 2nd statement* set up equations: (1) x + y + (x+y) - 6 = 58 *total length must be 58* (2) 5x = y + (x+y) - 6 - 10 *according to 3rd statemen...

**math**

to add, just add the similar terms,, for terms with variable (which, in this case, is x), add their numerical coefficients -- the number beside the variable,, therefore: 3x + 2x + 5 - 3 5x + 2 so there,, :)

**math**

transfer one of the terms containing squareroot (in this case the first one) to the other side: sqrt(x-1) = 11 - sqrt(x+10) then square both sides: x - 1 = 121 - 22*sqrt(x+10) + x + 10 transpose all terms without squareroot on one side of the equation: x - 1 - 121 - x - 10 = -...

**math**

All the face cards (i.e., kings, queens, and jacks) are removed from a standard deck, and one card is drawn from the remaining cards. Let A be the event that a red card is drawn, and let B be the event that a spade is drawn. What is

**trig**

is the "0" in the problem, the angle theta? if it is, cos(3pi/2+[theta]) = sin [theta] *expand cos(3pi/2+[theta]), cos(3pi/2)cos(theta) - sin(3pi/2)sin(theta) = sin [theta] *cos(3pi/2) = 0 and sin(3pi/2) = -1, thus: -(-sin [theta]) = sin [theta] sin [theta] = sin [th...

**Math**

factor out x in numerator and denominator to cancel,, it then becomes: (x^2-4y^2)/(3x^2-2xy-8y^2) factor both numerator and denominator: [(x-2y)(x+2y)]/[(x-2y)(3x+4y)] cancel (x-2y), therefore: (x+2y)/(3x+4y) so there,, :)

**Math 12**

let y = sin x the equation then becomes: 2y^2 + y - 6 = 0 then factor: (2y - 3)(y + 2) = 0 y = 3/2 and y = -2 therefore: sin x = 3/2, x = 2*pi*n + arcsin 3/2 ; and sin x = -2 , x = 2*pi*n + arcsin (-2) , where n = integer *but note that arcsin 3/2 and arcsin (-2) are undefined...

**algebra**

let x = over time (in minutes) therefore, 29.95 + 10x = 99.95 10x = 99.95 - 29.95 10x = 70 x = 7 minutes total minutes billed is 300 + 7 = 307 minutes so there,, :)

**math**

solve for c,, transpose 2 to other side (right side of equation) but with opposite sign,, positive becomes negative: 4c = 18 - 2 4c = 16 then divide every term by 4 to get c: 4c/4 = 16/4 c = 4 so there,, :)

**math**

first, get the equation of the chord: slope, m = (y2-y1)/(x2-x1) m = (0+4)/(-2-4) = -2/3 slope of the line: y - y1 = m(x - x1) *just choose one point (for y1 and x1 to substitute),, in this case, i chose the first point: y - 0 = (-2/3)(x + 2) *transform this into standard form...

**math**

use distance formula to get distance (length of sides) between two points: length = sqrt((y2-y1)^2+(x2-x1)^2) use midpoint formula to get midpoint of one side/length: midpoint = ((x1+x2)/2,(y1+y2)/2) *for sure, the answer in (b) is twice the answer in (a) [of course with respe...

**Math**

*integer: any WHOLE number including zero (can be positive or negative) *positive integer: 2, 5, 7 *negative nonzero integer: -3, -4, -1 so there,, :)

**algebra**

solving for r,, (1-r)/(1+r) = 2/3 *do cross multiplication: (1+r) is multiplied by 2, then 3 is multiplied by (1-r): 3(1-r) = 2(1+r) 3 - 3r = 2 + 2r *transpose similar terms to one side of equation (all terms with r on left side, and constants on right side): -2r - 3r = 2 - 3 ...

**algebra**

6 - 3 - 7 + 9 = 5 so there,, :)

**algebra**

function value? do you mean values of f(x) at certain values of x? if so, it just tells as that they have the same values, for instance, at x = -1, f(x) = -1 at x = 0, f(x) = 0 at x = 5/2, f(x) = 5/2 so there,, :)

**Algebra**

there is no restriction for x so x can be any real number,, :)

**advanced math**

since there is e^4t multiplied to cos(2t), there is s-shifting: from e^4t, we know that a = 4,, we also know that L{cos 2t} = s/(s^2 + 4) , therefore: L{e^4t(cos 2t)} = (s-a)/((s-a)^2 + 4) = (s-4)/((s-4)^2 + 4) so there,, =)

**solve please**

substitute the first equation to the second: x(2x + 2) = 12 2x^2 + 2x - 12 = 0 x^2 + x - 6 = 0 (x+3)(x-2)=0 x = -3 and x = 2 substitute x values to either equations and solve for y: first equation: if x = -3, (-3)y = 12 y = -4 if x = 2, (2)y = 12 y = 6 so there,, =)

**geometry+algebra**

i think you forgot to specify the figure (if it is a parallelogram, triangle, lines, etc) are AC and DC sides? if so, of what figure?

**Math(Please help)**

(1) 3sqrt2 - 8sqrt 128 *note that 128 has factors 2 and 64 (and 64 is a perfect square), therefore: 3sqrt2 - 8sqrt(2*64) [sqrt of 64 is 8] 3sqrt2 - 8*8sqrt2 -61sqrt2 (2) distribute or multiply the exponents of each term inside the parenthesis to 2/15: 8^(2/15) x^3(2/15) y^(-1/...

**algebra**

8-1-y = 7 *absolute value sign removed 7-y = 7 -y=7-7 y=0 so there,, =)

**geometry**

*bisect means divide it into two equal parts. since JK bisected LM at J, LJ = JM therefore, JM = 23 cm so there,, =)

**12th grade maths**

the second one: make the subject (p) p+3=qp+r/(2) ..is wrong,, must be: ans: p=r-6/(2-2q) the third one: make the subject (r) p(r-q)=2+3(q-r) ..is lacking parenthesis,, must be: ans: r=(2+3q+pq)/(p+3) the last one is wrong,, y=r-qp/(x) *transpose r to left side y-r = -qp/x *mu...

**12th grade maths**

i think i've already answered that one,, you re-posted it right? so there,, =)

**math**

yes. =)

**algebra 8th**

first get the least common denominator (LCD),, what is the common multiple of 5 and 8, or what is the smallest number in which it is divisible by 5 and 8? i get LCD = 40 :this is the denominator therefore, for the numerator multiply 40 to the fractions: 40[2/5 - 7/8] 2(8)-7(5)...

**Math**

do you mean, [(-1)^3]-[(-1)^4]+[(-1)^5]-[(-1)^6] ? if it is, [(-1)^3]-[(-1)^4]+[(-1)^5]-[(-1)^6] (-1) - 1 + (-1) - (1) simplifying, we get -4,, so there, =)

**9th grade**

i think it means to name the corners. planes could also be interpreted as the faces of the triangular prism, to their intersection could be the corners,,

**College Algebra**

let x = time it takes for them to be 45.6 miles apart (in hours) recall: (speed)*(time)=distance >>since they travel in opposite directions, the distances between the station to their present location will be added. 10x + 9x = 45.6 19x = 45.6 x = 2.4 hours so there,, =)

**3rd grade**

it is already in standard form! =) standard form is writing the number using digits.

**geometry**

let A = area of rectangle let w = width of rectangle area of rectangle = length * width, therefore: A = 9w then plug-in values for the width in the formula: (a) if w=1, A = 9*1 = 9 sq. in (b) if w=8, A = 9*8 = 72 sq. in (c) if w=9, A = 9*9 = 81 sq. in (d) if w=11, A = 9*11 = 9...

**algebra1**

i think you forgot to type the expression or the function,, anyway, all you have to do is to substitute the values of r, s, and t (which is r=6, s=5, t=3, and so on..)to the expression and solve it,, i hope i was able to help,, =)

**math**

the sin-1 and sin would just "cancel each other" (i dont mean like it would become sin/sin or something) therefore,, sin^-1(sin 7pi/6) = 7pi/6 so there,, =)

**math**

do you mean this?: (x^(9y^(-4)))^6 if it is, it should be: x^(54/y^4) so there,, =)

**algebra**

first, represent the unknown using variables: let x = number of 2-point shots let y = number of 3-point shots then set-up the equations. for the first statement, total score is 26, so: 2x + 3y = 26 for the second statement, total number of shots is 11, so: x + y = 11 using sub...

**Algebra**

first, represent the unknowns: let x = length of the 1st piece let 4x + 5 = length of the 2nd piece (as the second statement of the problem says) then set-up equation: x + (4x + 5) = 100 *total length of the two pieces must be 100 ft solve: 5x + 5 = 100 5x = 95 x = 19 ft 4x + ...

**Geometry**

since no conditions are given for the sides of triangle, i think you can draw a triangle with arbitrary length of sides,, then, name the corners/angles as A, B, C (or any three letter you like) then, choose 2 angles,, for example you chose A and B. to bisect the angle, get a c...

**math**

first, find the least common denominator (LCD) of 7 and 8,, LCD is 56: x/7 + x/8 = 8/7 *multiply both sides by 56* (x/7)(56) + (x/8)(56) = (8/7)(56) 8x + 7x = 64 *combine similar terms* 15x = 64 x = 64/15 so there,, =)

**algebra**

to solve for x, first, transpose all terms which does not contain x,, thus we have to transpose the term 3y to the right side of equation, but the sign must be the opposite: 3x + 3y = 9 3x = 9 - 3y *positive 3y becomes negative after transposing after that, divide the numerica...

**math**

for #2, just equate the exponents, since they have the same base: 7^(x^2-x)=7^6 x^2 - x = 6 x^2 - x - 6 = 0 *factor* (x-3)(x+2) = 0 x=3 and x=-2 note: check if there is extraneous root by substituting the roots back to the original. for #3, i interpreted this as log with base ...

**Math**

first, recall that speed, v, is distance traveled over a certain period of time: v=d/t thus t=d/v *we'll need this equation later* represent the unknowns using variables: let x = average speed of motorboat (in kph) let y = average speed of rowing (in kph) set-up the equati...

**algebra**

you have to find the least common multiple of 2, 3, 4, 5 and 6. thus, LCM = 60 now, add 1 to 60, and check if the new number is divisible by 7,, 60 + 1 = 61 61/7 = 8 remainder 5 61 is not divisible by 7,, thus repeat this process using multiples of 60,, try 120,, 121/7 = 17 re...

**MATH 2B Calculus **

first, graph the two equations (in one cartesian plane) then get the points of intersection: x+7=y^2 *this is the second equation x=y^2-7 substitute this to the first: y^2-7+4y=14 y^2+4y-21=0 (y+7)(y-3)=0 y=-7 and y=3 substitute these back to obtain corresponding values of x: ...

**math**

a star polygon with n points and point angle, X, has a dent angle of: dent angle = (360/n) + X therefore, in your question, n=6 and X=30: dent angle = (360/6) + 30 = 90 source: teach.valdosta.edu/plmoch/MATH3162/Spring%202009/11-3.pdf

**math**

you need to know first the number of star-tip points,, for N star-tip points, and dent angle A: point angle = Y - (360/N)

**math**

first represent: let b = base of original parallelogram let h = height of original parallelogram let 2b = base of new parallelogram let 2h = height of new parallelogram Area of original, A = bh Area of new, A2 = (2b)(2h) = 4bh = 4A therefore, it is true that when the size tran...

**math**

sorry, i don't get it,, where are O, P and P'' located?

**prealgebra**

you have to substitute the value of t given in the problem to the equation to get v,, therefore: v = (-1/2)(4) + 5 v = 3 therefore, the point is at (4,3) assuming that v is the vertical axis and t is the horizontal axis of rectangular coordinate plane,, so there,, =)

**Science**

H+ + Base = conjugate acid of Base therefore, (a) NH3 (b) HCO3^- (c) H2S (d) H2O so there,, =)

**math**

first represent: let x = first number let x+1 = second number let x+2 = third number *note: since they are consecutive, the difference between them is 1,, that's why it's x, x+1, x+2 set up the equation and then solve for x: x+x+1+x+2=90 3x+3=90 3x=87 x=29 *first numbe...

**math**

(5/(t^5))^1/2 you can rewrite this as: (5t^(-5))^1/2 therefore,, (1/2)*(-25t^-6)*(5t^(-5))^(-1/2) so there,, =)

**Math**

first, determine the x1 and x2, as well as the y1 and y2: *note: i will rename the given points as A and B,, first point, A(-16, -19) -16 is the x-coordinate of point A = x1 -19 is the y-coordinate of point A = y1 second point, B(-18, -20) -18 is the x-coordinate of point B = ...

**math**

first solve for y: 35-5y=0 -5y=-35 y=7 *you can actually rewrite this as: 0x + y = 7 notice the equation has a definite value of y (which is 7) while you can substitute any number on x (since when it is multiplied by zero, the product is always zero),, y is therefore independe...

**MATH**

is P multiplied by B? if it is, P*B = 1/3 *divide both sides by B P*B/B = (1/3)/B P = 1/(3B) so there,, =)

**math**

first get the area of circle: A = pi(r^2) A = pi(20^2) A = 400*pi sq. cm then multiply this to the price of pizza per sq. cm to cancel the sq. cm units and obtain the price of pizza,, so there,, =)

**Math**

get the derivative to get the maximum/minimum: y = sinx + cosx y' = 0 = cosx - sinx cos x = sin x x=pi/4 *the value of x in which y is max x=-(pi/4) *the value of x in which y is min you can actually check this by graphing the equation,, so there,, =)

**Algebra 2**

(1.) first, graph the equations,, there are various ways how to graph them,, for linear equations, i usually get the x- and y- intercept (*x- and y- intercepts are points*): *note: to get x-intercept, set y=0 and solve for x,, to get y-intercept, set x=0 and solve for y,, >...

**Math**

gradient of a line is also the "slope" of the line,, and m = y/x = tan (theta), where theta is the angle of inclination,, therefore, m = tan (75) = 2+sqrt(3) = 3.73 so there,, =)

**math157**

for the letter: determine first how many letters are possible,, there are 3 *S, P, Y for the first number: how many are possible,, there are 10 *0,1,2,..9 for the second number: since no repetition is allowed, there only 9 possible,,, then multiply: 3*10*9 = 270 possibilities ...

**Math**

i'm not sure about this (if it requires some formulas), but i used extrapolation: X Y 0 1 33 2 140 y therefore, (y-1)/(y-2)=(140-0)/(140-33) y=5.24 so there,, =)

**math**

as v goes to c, v^2 becomes c^2 and c^2/c^2 = 1,, therefore m becomes mo/sqrt(1-1) or mo/0 which is undefined,, according to this, no such thing can exist with speed equal to the speed of light,, so there,, =)

**algebra**

recall the form of a quadratic equation: y = a(x-h)^2 + k where, (h,k) is the vertex,, since the given equation is in that form (where a=3, h=4, and k=6), the vertex is at (4,6) *there is an alternative solution, but this is used in higher math,, if you already know how to dif...

**Maths**

i also got the same equation: ln [(x+4)(x+2)] = 2 ln (x^2+6x+8) = 2 x^2+6x+8 = e^2 x^2+6x+(8-e^2)=0 thus, you have no choice but to use quadratic formula: (where a=1, b=6, c=8-e^2) [-6+-sqrt(6^2-4(1)(8-e^2))]/2(1) [-6+-sqrt(36-32+4e^2)]/2 [-6+-sqrt(4+4e^2)]/2 *factor out 4 [-6...

**College Algebra**

first, represent: let x = the length of the original square let x+7 = the length of the new square since area of square is (length of side)^2: A=s^2 225=(x+7)^2 225=x^2+14x+49 *transpose all terms to one side x^2+14x-176=0 (x-8)(x+22)=0 *get only the positive since there is no...

**algebra**

first, represent: let x = amount of 20% acid used (in mL) let 100-x = amount of 100% acid used (since the total volume of the 2 acids mixed must be 100) therefore, 0.2x + 1(100-x) = .4(100) *note: 0.2 = 20%, 1 = 100%, .4=40% 0.2x + 100-x = 40 -0.8x=-60 x = 75 mL of 20% acid, a...

**geometry**

recall the formula for midpoint: (Xm,Ym)=([X1+X2]/2, [Y1+Y2]/2) therefore, (X1+X2)/2 = (-2+1)/2 = -1/2 (Y1+Y2)/2 = (6+2)/2 = 4 (Xm,Ym) = (-1/2,4) so there,, =)

**calculus**

note: to check if the given equation is symmetric to x-axis or y-axis or origin (that is, y=x),, *symmetric to x-axis: change y to -y and substitute to the given equation. if it goes back to original form, therefore, it is symmetric to x-axis. otherwise, it is not. *symmetric ...

**math algebra**

b^2 - 4ac ==> this is the discriminant note: for real numbers a, b and c,, *if b^2 - 4ac < 0 : 2 imaginary roots *if b^2 - 4ac = 0 : 1 real and distinct root *if b^2 - 4ac > 0 : 2 real and distinct roots

**math**

the equation you got is correct,, =) first, note that x (which is the height of the box) cannot be negative, since there is no negative height,, equating V to zero, x=0, 1, 9 now, get some values in between (and if you want, get also a value greater than 9), and check if the d...

**algebra **

first, represent them as variables: let x = four-passenger cars let y = six-passenger cars set up the equations [since two unknowns, you must have two equations]: (1) 4x+6y=92 ==> since 92 people altogether (2) y=x-3 ==> since three less six-passenger cars then you can s...

**Exponents and Logs (Math)**

first, express 4 as a power of 2,, 4=2^2 then divide both sides by 2^2 2^(-x+1)/2^2 = 8^x *note, at the right side of equation, 4 and 2^2 canceled each other* then recall some laws of exponents. since on the left side, the numerator and denominator have the same base (which is...

**geometry**

since they are parallel, and you can only draw points in the area between them (because points must have equal distances from the lines), the figure you would get is a line parallel and equidistant (means has the same distance) to the given lines,, so there, =)

**Math - Vectors**

mutually orthogonal=the three of them are orthogonal (or perpendicular) to each other,, [angle between them is 90 degrees] first recall the formula for the dot product. for any given vectors A and B, A(dot)B=|A||B|cos(theta) where |A| and |B| are the magnitude of vectors A and...

**Math**

you can also do cross multiplication to check if two fractions are equal,, in this case, 2*45 = 90 (numerator of first fraction * denominator of the second) 18*5 = 90 (denominator of first fraction * numerator of the second) therefore, they are equal, and they make a proportio...

**math**

is this just solve for K? if it is, transpose the term v/2 to the left side of equation, getting K=B+v/2

**GEOMETRY 4.6**

one way to solve this (but a little time-consuming) is to first get the distances of all the sides of triangles EFG and JKL using distance formula: d=squareroot of [(x2-x1)^2+(y2-y1)^2] after getting the distances, use the law of cosines: a^2=b^2+c^2-2ac(cos A) where: a, b, an...

**math**

you have to solve for x,, here are the steps: =) (1)distribute the 4 on x+4 and the 7 on x-2, getting 4x+16=7x-14 (i.e. just multiply 4 by x and 4 by 4 to get 4x+16 on left side, and do the same on other side) (2)combine similar terms, to simplify, transpose the term 7x on lef...

**Math**

nope. 20 is not the common denominator,, on the given, i think you mean 3/(w+4) + 4/5w ,, first thing, multiply BOTH the numerator and denominator of the terms with their common denominator, which is (w+4)(5w),, therefore, (3/(w+4) + 4/5w)*(5w)(w+4)/(5w)(w+4) ==> some terms...

**math**

substitute: (2cos^2(theta)-1)^2 + (sin2(theta))^2 = 1 then recall some identities: *2cos^2(theta)-1=cos2(theta) *cos2(theta)=cos^2(theta)-sin^2(theta) *sin^2(theta)=1-cos^2(theta) therefore, it will become: (cos2(theta))^2 + (sin2(theta))^2=1 >>actually, here you can con...

**Math**

since you know y^2 in terms of x, you can substitute either of them to the other equation,, in this case, i will substitute the first equation into the second, getting: 1-x^2=x^2-3x+2 then combine similar terms to one side of the equation, yielding: 0=2x^2-3x+1 since it is fac...

**MATH**

you can also do it by recalling some properties of sin x and cos x: sin (-x) = -sin x cos (-x) = cos x since tan(theta) = (sin(theta))/(cos(theta)),, tan(-theta) = (sin(-theta))/(cos(-theta)) applying their properties we have: -(sin(theta))/(cos(theta)) which is equal to -tan(...

**math**

first, you will need to recall the identities,, some useful identities that will be applied here are: (a) 1/sec(theta)=cos(theta) ; and (b) cos(90-theta)=sin(theta) ,first, use identity (a) to change sec^2(90-theta) to 1/cos^2(90-theta),, ,then, use identity (b) to rewrite the...

**elementary math**

no. of ways = 20!/(11!*9!)

**math**

in order to graph a step function/greatest integer function,, you need values of x (not only integers but also with decimal), for example, if x=3, y=-5(3)=-15 ==> no problem since -15 is an integer if x=3.1, y=-5(3.1)=-15.5 ==>if not an integer, get the greatest integer ...

**math**

for the first part,, sorry, i am not sure about this,, if you only have ONE given equation for instance,, sin(x)=1 ==> the solution for this is x = pi*2+k*2pi, for k greater than or equal to zero (note: pi/2 is in radians which is also equal to 90 degrees), therefore sin x ...

**Math**

note: remember that if we have two unknowns in an equation, we need also two equations (with the two unknowns) to solve for their values,, first, work with the first and third given: (since both contains the same unknowns) 3g=d *substitute d to the other g^2=d=3g *transpose al...

**calculus**

yes, x must not be equal to -2 and -1 (-00,-2)U(-2,-1)U(-1,+00) *00==>infinity symbol (it should look like an 8 rotated 90 degrees clockwise..) *U==>union i hope i was able to help you.. =)

**Math**

first, imagine the front view of the cone,, it should look like an inverted triangle,, then draw the content (the water - horizontal line),, note that if you draw a vertical line bisecting the inverted triangle, you actually form a right triangle,, since you bisected it, get t...

**Calculus**

substitute the value of x: (2-1)^3tan[pi/2] = 1^3tan[pi/2] note: 3*tan (pi/2) = 3*[sin(pi/2)]/[cos(pi/2)] = 3/0 = infinity therefore, 1^infinity = 1 so there,, =)

**physics**

a force of 20N is exerted on a court for 10 seconds. How long must a 40N force act to produce the same impulse?

**college, structures**

the rectangular steel bar shown supports a concentric load of 13000lbf. Both ends are fixed. If te modulus of elasticity is 29x10^6 lbf/in^2, what is the maximum length the rod can be without experiencing buckling failure? P=13,000 lbf | _________________ .75 in | _______ | | ...

**History**

Hi, I need some help with this question: It is 1789 .....You are an educated member of the bourgeoise....You listen to the thinking of the philosophes and the physiocrats in the salon and you read what they say in the daily news...... WHAT DO YOU THINK IS THE IDEAL STATE? Tha...

**Weird question.........H.W due in tomrrow...quick**

OMG I was browsing the archives and saw this question. I know you might never see this post of mine, but I still want to try answering this. :) I think there are 59 pictures, because 59/2 = 28, with remainder 1 59/3 = 19, with remainder 2 59/4 = 14, with remainder 3 59/5 = 11,...

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