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# Recent problems solved by 'eggsarecool'

 Linear_Equations_And_Systems_Word_Problems/437485: find the 2 consecutive integers such that the square of the 2nd integer added to the 3 times the 1st is equal to 1771 solutions Answer 302626 by eggsarecool(46)   on 2011-04-18 17:44:19 (Show Source): You can put this solution on YOUR website!Ok so we have two consecutive integers Lets call the first 1 a, and the second one a+1 Now the formula, So we have the second one squared plus 3 times the first one=177 now we need to solve for a, so we will expand the giving us collect like terms, and move the 177 to the left side. you can factor this or if you are not comfortable with factoring you can use the quadratic formula Now if we factor we get which gives us , Now I am assuming they wanted the positive intergers, so you have a=11, and then a+1=12. So you integers are 11 and 12
 Rational-functions/430398: y= Hi! For this problem, what would the domain be? I am so confused... Please help me! Thank you and have a great day!!! :)1 solutions Answer 298920 by eggsarecool(46)   on 2011-04-02 23:52:59 (Show Source): You can put this solution on YOUR website!Ok, So for functions that are a fraction, the denominator cannot equal zero. So you solve to see what is not allowed, factoring gives you , and that gives you and , so x cannot equal 0 or 3. As for how to express this answer Domain:(,0)U(0,3)U(3,)
 Human-and-algebraic-language/426834: find the two numbers whose sum is 27, such that five times the smaller number is one less than three times the larger number1 solutions Answer 297899 by eggsarecool(46)   on 2011-03-29 13:32:32 (Show Source): You can put this solution on YOUR website!Let's call x the smaller number and y the larger number. So we have and Now rearrange the first equation to say and substitute into the second equation. -> -> -> Now that we have plug into to get 50+1=3*y}}}-> -> So your ordered pair is (10,17)
 Human-and-algebraic-language/427792: The sum of a number and four times its reciprocal is 29/5.Find the number 1 solutions Answer 297813 by eggsarecool(46)   on 2011-03-28 22:57:14 (Show Source): You can put this solution on YOUR website!The sum of a number and four times its reciprocal is 29/5.Find the number Let's call the number n. The reciprocal would be So the formula should look like. now multiply every term on both sides by n, the in the will cancel to become 1, leaving you with 4*1=4 multiply both sides by 5. subtract from both sides now you have a solvable quadratic equation, that factors into. So or -> divide both sides by 5
 Human-and-algebraic-language/428488: One number plus sixteen times its reciprocal is equal to ten. I tried n+16n=101 solutions Answer 297809 by eggsarecool(46)   on 2011-03-28 22:49:17 (Show Source): You can put this solution on YOUR website!ok so what happened here is that the reciprocal means One number plus sixteen times its reciprocal is equal to ten. So the formula should look like. now multiply every term on both sides by n, the in the will cancel to become 1, leaving you with 16*1=16 subtract 10n from both sides. now you have a solvable quadratic equation, that factors into. So or
Geometry_Word_Problems/291783: The length of one leg of a right triangle is 2 cm less than three times the length of other leg. The area of the triangle is 48 cm^2. Find the length of each leg. Please show work! thank u
1 solutions

Answer 210921 by eggsarecool(46)   on 2010-04-13 16:38:07 (Show Source):
You can put this solution on YOUR website!
Ok so lets call one leg x
The other leg is three times the length 3x and 2 cm less so 3x-2.
The Area of a triangle is
For a right Triangle the base is one leg and the height is the other leg.
We also know that the Area is 48.
So Multiply by 2 to cancel the
Subtract 96 from both sides.
Factor out the 3.
Use the qudratic formula to solve/
 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=129 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 6.17890834580027, -5.17890834580027. Here's your graph:

And since you cannot have a negative length in a triangle, is the length of the leg we called x. To find the length of the other leg multiply by 3 and then subtract 2 to get the length of the other leg.

So the length of the other leg is

 Trigonometry-basics/285156: Find an equivalent expression for cos 3x in terms of powers of cos x. cos 3x = cos (2x + x) = cos 2x cos x - sin 2x sin x <----Using cos(u + v) = cos u cos v - sin u sin v = (cos^2x - sin^2x) cosx - (2 sinx cosx) sinx = cos^3x -sin^2x cosx - 2sin^2x cosx I'm stuck up to here.... 1 solutions Answer 206777 by eggsarecool(46)   on 2010-03-25 10:10:30 (Show Source): You can put this solution on YOUR website!Going back to this step (cos^2x - sin^2x) cosx - (2 sinx cosx) sinx You need to use identities So Simplify. And everything is now in terms of powers.
 Complex_Numbers/285171: Please help me with this problem (1/3 - i)^21 solutions Answer 206775 by eggsarecool(46)   on 2010-03-25 09:56:48 (Show Source): You can put this solution on YOUR website!i is defined as the So we have. Now we FOIL. Simplify. note that And now put back as i since that is what teachers expect. So
 Trigonometry-basics/285166: can you show me the steps on how to change the trig identity of tanxcosx=cotx(secx-cosx) ?1 solutions Answer 206772 by eggsarecool(46)   on 2010-03-25 09:41:23 (Show Source): You can put this solution on YOUR website!Ok so lets rewrite everything in terms of and So we have Multiply everything out. common denominator of on the right. we know that So
 test/285170: evaluate given function for f(3) and f(-2) f(x)=x^2+4x-11 solutions Answer 206770 by eggsarecool(46)   on 2010-03-25 09:33:14 (Show Source): You can put this solution on YOUR website! means plug in 3 for x so we get So
 Graphs/285162: Determine whether the graphs of the equations are perpendicular. 5x-8y=3, 5y-8x=2. Are the graphs of the given equations perpendicular?1 solutions Answer 206769 by eggsarecool(46)   on 2010-03-25 09:30:32 (Show Source): You can put this solution on YOUR website!To do this you need to solve both equations for y, once you have done this you will be able to see the slopes and that will tell you if they are perpendicular. So add 8y to both sides. subtract 3 from both sides. And divide through by 8. So the slope is that comes from the number attached to the x. For the next equation. Add 8x to both sides. And divide through by 8. So the slope is The definition for two lines to be perpendicular is that the slope of one must be the negative reciprocal of the slope of the other. The negative reciprocal of is and we only got so they are not perpendicular.
 Graphs/285160: solve inequality. express answer in interval notation.. -3 <= 3 - 2x <= 91 solutions Answer 206767 by eggsarecool(46)   on 2010-03-25 09:20:56 (Show Source): You can put this solution on YOUR website! The first step will be to subtract 3 from all 3 parts. Now divide by -2. And remember to reverse the <= signs when dividing by a negative. Expressed in interval notation this is [-3,3]
 Linear-equations/284715: the line passes thru (4,-7) and is perpendicular to the line whose equation is x-2y=3 write an equation in slope intercept form satisfying the given conditions1 solutions Answer 206571 by eggsarecool(46)   on 2010-03-24 10:06:52 (Show Source): You can put this solution on YOUR website!The first step in such a problem is to solve the given equation for y. So subtract x from both sides. Now divdie everything by -2. The number attached to the x is the slope of this line, To get a line that is perpendicular you need to take the negative reciprocal which would be or just -2. We now do m stands for slope so we have. Now you plug in (4,-7), 4 for x and -7 for y to get the line that passes through that point and solve for b. add 8 to both sides. Going back to you will now put in the b you found. And is your final answer.
 Miscellaneous_Word_Problems/284748: A student may pay \$1.50 for a single bus ticket or \$5.75 for a package of 5 tickets. If a student requires 40 tickets, how much does she save by buying all of the tickets in packages of 5 rather than buying 40 single tickets? (A) \$54.25 (B) \$34.00 (C) \$14.00 (D) \$8.25 (E) \$4.251 solutions Answer 206567 by eggsarecool(46)   on 2010-03-24 09:51:00 (Show Source): You can put this solution on YOUR website!Ok so to buy 40 tickets in packets of 5 means youe need 8 packets. So 8 packets of 5 tickets costs . So 40 tickets in packets costs \$46 Now for single tickets . So buying 40 single tickets costs \$60 The differance is the ammount he saves . So he saves \$14 Which is answer C
 Coordinate-system/237326: what is the equation of the line tangent to the circle x^2+y^2=25 at the point (3,4) ? I don't know how to go about this sum. Please solve and explain thanks1 solutions Answer 174522 by eggsarecool(46)   on 2009-11-10 12:11:17 (Show Source): You can put this solution on YOUR website!You need to implicit differentiation for this problem and solve for So we have. The derivative is the 2y produces the because y is a function so you have to apply the chain rule to it. So now. And x and y are given by (3,4) giving x=3 and y=4. (,) So Now for the tangent line you have. so we have Giving us Add 4 to both sides. 4 can be rewritten as And that is your tangent line.
 expressions/237328: What is the simplified solution to -2^2-(-2)^3? And what are the steps?1 solutions Answer 174519 by eggsarecool(46)   on 2009-11-10 11:59:09 (Show Source): You can put this solution on YOUR website!I am assuming you did not lose any parentheses. So this has to do with order of operations. parentheses take precedence over everything and then exponents take precedence over multiplication and subtraction. For the first term you square first and then multiply. But for you have to cube before multiplying by -1. So we have
 Trigonometry-basics/237320: PLEASE HELP ME SOLVE THIS TRIGONOMETRIC FUNCTIONS: Given that sin0=-1/2 and 0 lies in quadrant lV,find the following value.sec 0 the possible answers are: a)-2 b)square root of 3/2 c)(2/square root of 3)/3 1 solutions Answer 174517 by eggsarecool(46)   on 2009-11-10 11:53:03 (Show Source): You can put this solution on YOUR website!I am going to replace theta with x since i have no way to make the computer display theta. So what we have is. The referance angle that makes sin equal to is 30 degress or If we want this angle in the 4th qudrant we get or So we know that our angle is 330 degrees or We also know that So we need to find out what cos(x) is to find sec(x). So we need to find cos of 330 degrees. The referance angle was 30 degrees and . Cos is positive in the 4th quadrent so And is So And if you rationalize this. So choice C is the correct answer.
 Linear-equations/237318: 1 solutions Answer 174511 by eggsarecool(46)   on 2009-11-10 11:38:03 (Show Source): You can put this solution on YOUR website! Ok so distribute first to remove parentheses. Now combine like terms. Add 6v to both sides. Subtract 2 from both sides. And divide both sides by 9.
 Triangles/237317: For a right triangle, what is the area with side A of 12 and the side B of 10?1 solutions Answer 174509 by eggsarecool(46)   on 2009-11-10 11:35:06 (Show Source): You can put this solution on YOUR website!The area of a triangle is Now for a right triangle sides A=12 and B=10 are the base and the height. So your area is So the area of your triangle is 60.
 Numeric_Fractions/237314: , two over three x -7 = 5 or 1 solutions Answer 174506 by eggsarecool(46)   on 2009-11-10 11:32:04 (Show Source): You can put this solution on YOUR website!Not sure which you wanted so I will solve both. For we will multiply both sides by Giving us When we distribute the 5 Now add 35 to both sides. and divide both sides by 15. Now the other interpretation of your problem. For this one you would need to get a common denominator first. So With the common denominator we have. Now we will multiply both sides by 3x. Giving us Add 21x to both sides. Divide both sides by 36.
 Quadratic_Equations/234434: translate the problem into a pair linear equations in two variables.solve using elimination or substitution. andy has 14 coins made up of quarters and half dollars, and their total value is \$4.25.How many quarters does he have? 1 solutions Answer 172845 by eggsarecool(46)   on 2009-11-02 22:53:28 (Show Source): You can put this solution on YOUR website!Ok so lets say that Andy has x quarters and y half dollars. So And now for the values of the coins. Each quarter is worth 0.25 and you multiply by x, and each half dollar is worth 0.5 and you multiply by y. When you add them up you get the amount the coins are worth. So Putting this into the second equation gives us. Distributing the 0.25 gives us. Combine like terms. Subtract 3.5 from both sides. Divide both sides by 0.25. We now know that and we can plug this into to gives us So and
 Numbers_Word_Problems/234098: The sum of two numbers equals eighteen. The total of three times the smaller and two times the larger is 44. 1 solutions Answer 172666 by eggsarecool(46)   on 2009-11-02 11:34:34 (Show Source): You can put this solution on YOUR website!The sum of two numbers equals eighteen. The total of three times the smaller and two times the larger is 44. Ok so we have two unknown numbers. We will call the smaller one x and the larger one y. So and Now we have a system of equations. And we can write Now when you see x in the second equation replace it with This gives us. Subtract 48 from both sides. Divide both sides by -1. And x was so So and
 Polynomials-and-rational-expressions/234082: what does it mean to refer to a 20-in TV set or a 25-in TV set? Such units refer to the diagonal of the screen. A 15-in TV set also has a width of 12 inches. What is its height? What is the height of a 15-in TV?1 solutions Answer 172663 by eggsarecool(46)   on 2009-11-02 11:12:39 (Show Source): You can put this solution on YOUR website!This problem is done using the Pythagoran theorem. Which says that This says that the two shorter sides of a right triangle squared equal the long side squared And the triangles longest side is the diagnol line across the tv set. So we know the diagnol of the tv is 15, so And we know the leangth is 12 so This gives you that Since b is the height of your triangle the height is 9.
 logarithm/234094: solve for x: 59.2=42.5(1.64)^x1 solutions Answer 172662 by eggsarecool(46)   on 2009-11-02 11:06:16 (Show Source): You can put this solution on YOUR website!solve for x: So first we divide both sides by 42.5 Now we will take ln of both sides. This helps because there is a property of logarithms that says the following In english it basically allows you to take the exponent outside the logarithm. So applying this to our equation gives us. Now I will move the x outside. Now all that is left is to divide both sides by Using a calculator you can get a decimal value of.
 Linear-equations/233545: write equation,in slop-intercept from,(3,4)and(5,8)1 solutions Answer 172400 by eggsarecool(46)   on 2009-11-01 01:25:54 (Show Source): You can put this solution on YOUR website!Ok so first we need the slope. You compute this using Where m is your slope. So you have (3,4) and (5,8) Giving us So Now to write the the equation you can pick (3,4) or (5,8) So it will look like or I will use the first point (3,4). So now we have Next multiply out the two on the right hand side. Now add 4 to both sides. This gives you your final answer of
 Geometric_formulas/232854: what would the answer be for 1 solutions Answer 171968 by eggsarecool(46)   on 2009-10-29 11:50:15 (Show Source): You can put this solution on YOUR website!Ok so we have What you can do in algebra is flip both sides of an equation. So will become and which is really will become So now we have. Now you divide both sides by two. Dividing a fraction can be confusing so you can multiply by instead of dividing by 2. Giving us.
 Systems-of-equations/232857: A motel charges 80.00 per day for double occupancy and 70 pr day for single occupancy. If 80 rooms are occupied one night for a total of 5800.00 how many rooms of each type are occupied?1 solutions Answer 171967 by eggsarecool(46)   on 2009-10-29 11:44:51 (Show Source): You can put this solution on YOUR website!A motel charges 80.00 per day for double occupancy and 70 pr day for single occupancy. If 80 rooms are occupied one night for a total of 5800.00 how many rooms of each type are occupied? Ok I am goint to define as the number of single occupancy rooms. And what this tells us is that is the number of double occupancy rooms. So now we set up the equation. So it is the number of single occupancy rooms times the single rate + the number of double occupancy rooms times the double rate = to the total amount made by the hotel. Solving the equation. Subtract 6400 from both sides. And divide both sides by -10. this tells us that there were 60 single occupancy rooms since I defined as single occupancy. And double occupancy was , so So there must be 20 double occupancy rooms.
 Trigonometry-basics/232805: Please help prove identity: thank you1 solutions Answer 171966 by eggsarecool(46)   on 2009-10-29 11:37:19 (Show Source): You can put this solution on YOUR website! Two formulas you need are and the other is Using these we can rewrite the left side to become. Now we distribute the that is on the outside. this proves your identity.
 Polynomials-and-rational-expressions/232845: find: 2x/(x^2-9) + (1-2x)/(x^2-4x+3)1 solutions Answer 171965 by eggsarecool(46)   on 2009-10-29 11:23:54 (Show Source): You can put this solution on YOUR website!I am assuming you want this solved for 0 So first we need a common denominator We will start by factoring the current denominators. Now for the common denominator. Now your denominator cannot equal to zero since you are not allowed to divide by 0. so x cannot equal to 1, 3, or -3. Since the bottom cannot equal 0 the only time the fraction will equal 0 is when the numerator equals 0. Now we multiply out the numerator. Next we combine like terms. Now we set the numerator equal to 0 and solve. Add 7x to both sides. Divide both sides by 7.
 Numeric_Fractions/232846: I need help with COMPLETELY factoring out the polynomial 3x3-12x1 solutions Answer 171961 by eggsarecool(46)   on 2009-10-29 11:07:08 (Show Source): You can put this solution on YOUR website!I need help with COMPLETELY factoring out the polynomial Ok first step would be to factor out which leaves us with Now we can use the differance of squares formula which says that For us and This gives us we factored the using difference of squares.
 Expressions-with-variables/232481: solve for the variable, first stating any restrictions. if there are no restrictions, state that 7/x+4 + 2/x-3 = 7x-21/x^2+x-121 solutions Answer 171791 by eggsarecool(46)   on 2009-10-28 13:07:21 (Show Source): You can put this solution on YOUR website!I am assuming this is the original problem, it wasn't completely clear. the next step is to rewrite the right hand side. Now we state the restrictions, these happen when you divide by 0. So x cannot equal to 3 or -4 Your next step is to create a common denominator on the left side. Now we will only pay attention to the numerators since the denominators match. This gives us. Now combine like terms. subtract 9x from both sides. add 13 to both sides Divide both sides by 2. This gives you the solution but since this is among the values that are not allowed your equation has no solution.