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# Recent problems solved by 'Earlsdon'

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 Equations/22349: My son needs your help in solving this problem. Find the solution set for the system of equations 3X + 2Y = 3 -5X + Y = 8 Thanks 1 solutions Answer 10835 by Earlsdon(6291)   on 2005-12-11 22:36:03 (Show Source): You can put this solution on YOUR website!Solve the system of equations: 1) 3x + 2y = 3 2) -5x + y = 8 Multiply equation 2) by 2 then subtract equation 1) from the result and solve for x. 2) -10y + 2y = 16 1) -(3x + 2y = 3) ----------------- 3) -13x = 13 Divide both sides by -13 x = -1 Now substitute this into equation 1) and solve for y. 1) 3(-1) + 2y = 3 -3 + 2y = 3 Add 3 to both sides. 2y = 6 Divide both sides by 2. y = 3 Solution: (-1, 3)
 Expressions-with-variables/22286: please help me siplifyig1 solutions Answer 10812 by Earlsdon(6291)   on 2005-12-11 13:21:16 (Show Source): You can put this solution on YOUR website!Simplify: First, and Now, and Now add the two fractions, common denominator is xab. =
 Polynomials-and-rational-expressions/22131: Factor the polynomial as the product of factors that are irreducible over the real numbers. Then write the polynomial in completely factored form involving complex nonreal, or imaginary numbers. x to the 4th power + 7x to the second power - 181 solutions Answer 10811 by Earlsdon(6291)   on 2005-12-11 13:11:54 (Show Source): You can put this solution on YOUR website!Factor: This is as far as we can go for part 1. Factor completely:
 Graphs/22293: I do not know if this is in the right category but... the question is- Find the equation of the line that has a y-intercept of 3 and a slope of 0 {thanks alot}1 solutions Answer 10808 by Earlsdon(6291)   on 2005-12-11 12:56:30 (Show Source): You can put this solution on YOUR website!First, a slope of 0 means that the line is horizontal. The slope-intercept form of the equation is: where m is the slope and b is the y-intercept. Since m = 0 and b = 3, just substitute these values into the general form. or See the graph of this line below:
 Equations/22291: can you please explain how to solve this? x/6 + 3x/7 = 25 Please and Thanks!!!1 solutions Answer 10807 by Earlsdon(6291)   on 2005-12-11 12:46:31 (Show Source): You can put this solution on YOUR website!Solve for x: Add the fractions on the left side. Common denominator is 6 X 7=42 Multiply both sides by 42. Finally, divide both sides by 25.
 absolute-value/22277: -6(14)-|4(-2)-3^2| The answer I came up with was 85 can anyone please help.1 solutions Answer 10799 by Earlsdon(6291)   on 2005-12-11 10:13:53 (Show Source): You can put this solution on YOUR website!Simplify: -6(14)-|4(-2)-3^2| = -84-|-8-9| = -84-|-17| = -84-17 = -101
 Rational-functions/22186: I am stuck on this problem. Jacob is standing at the edge of a 3000 foot deep canyon. He kicks a ball into the air with a initial upward velocity of 32 feet per second. when will the ball return to the height from which it was kicked? I can get it to , but i get stuck trying to factor that.1 solutions Answer 10769 by Earlsdon(6291)   on 2005-12-10 16:29:46 (Show Source): You can put this solution on YOUR website!The general form of the equation for the height of an object propelled upward with an initial velocity of v from an initial height of h is , and since the depth of the canyon by which Jacob is standing is really irrelevant, your initial equation is correct. The initial height is zero feet. Now you would like to find out at what time (t) will the ball return to its initial height of 0 ft. Setting h(t) = 0 ft. you can write: Solve for t by factoring -16t from both sides. Apply the zero product principle. Add 2 to both sides. The ball will return to its initial height of 0 ft. in 2 seconds. Check: Set t = 2 Solve for h. ft.
 logarithm/22212: Simplify: 1 solutions Answer 10764 by Earlsdon(6291)   on 2005-12-10 15:57:17 (Show Source): You can put this solution on YOUR website!Simplify: Apply the Quotient rule for logarithms: to the left side. The right side is rewritten because: If then , so: Multiply both sides by (x+3) Subtract 243 from both sides. Subtract 5x from both sides. Divide both sides by 76.
 Quadratic_Equations/22247: Help, I am so lost! Thanks in advance!! Find the x-intercepts. y = x^2 – 4x + 4 1 solutions Answer 10762 by Earlsdon(6291)   on 2005-12-10 15:31:02 (Show Source): You can put this solution on YOUR website!To find the x-intercepts, set y = 0 and solve for x. Solve by factoring. Apply the zero product principle. You will have a double root. If then, A double root. See the graph:
 logarithm/22248: Good Afternoon, I am trying to work out some problems but I don't know what I am doing. Can someone please help me? Here is the question. log8x=2/31 solutions Answer 10761 by Earlsdon(6291)   on 2005-12-10 15:23:13 (Show Source): You can put this solution on YOUR website!Solve for x: Apply the product rule for logaritms: logMN = logM + logN So: Subtract log(8) from both sides. Rewrite in exponential form: logx = y means b^y = x You can do this on your calculator. Check:
 Evaluation_Word_Problems/22232: kavita secured 12 marks out of 20 in maths and 10 marks out of 15 in science.in what subject was her performance better? in a certain class there are 30 boys and 20 girls.What is the percentage of the number of boys and that of the girls? monthly incomeof an employee is Rs 1800.he saves 10% of his income.how much does he save? a man earns Rs 4750 per month.how much will he earn in 12 years? babasaheb sells his car for Rs 96000 through an agent.He gives the agent 5% of commission. how much does the agent recieve as commission?1 solutions Answer 10746 by Earlsdon(6291)   on 2005-12-10 12:10:17 (Show Source): You can put this solution on YOUR website!1) Here, you need to compare 12/20 with 10/15. To do this, you must re-write the fractions with a common denominator. First, it might be helpful to reduce the fraction to their simplest forms. Now re-write each fraction with a common denominator of 15. Ok, so we really didn't need to simplify this fraction. Now compare: with Kavita's performance was better in science than it was in maths 2) The number of boys (30) plus the number of girls (20) means that there was a total of 50 pupils in the class. The percentage of boys is is given by: [(# of boys)/(# of pupils)]*100 The percentage of boys is: % Similarly, the percetage of girls is given by: [(# of girls/# of pupils)*100] The percentage of girls is: % 3) The employee saves 10% of Rs 1800. Change the percentage to its decimal equivalent: 10% = 0.1 and multiply this by 1800 to find the employee's savings. The employee saves Rs 180 4) Earnings per month = Rs 4750 Earnigs per year = Rs 4750 /month * 12 months /year = Rs 57000/year Earning for 12 years = Rs 57000/year * 12 years = Rs 684000 in 12 years. 5) The agent receives 5% of Rs 96000. Change the percent to its decimal equivalent: 5% = 0.05 and multiply this by 96000 to find the agent's fee. The agent receives Rs 4800
 Inequalities/22208: Satchi found a used bookstore that sells pre-owned videos and CDs. Videoa cost \$9 each, and CDs cost \$7 each. Satchi can spend no more that \$35. Write an inequality that represents this situation.1 solutions Answer 10722 by Earlsdon(6291)   on 2005-12-09 20:08:44 (Show Source): You can put this solution on YOUR website!You can let V = number of videos and C = number of CDs.
 Travel_Word_Problems/22167: If it takes a Dell Dimension-8300 computer 4 hours to crack a UNIX password file and Gateway E-6100 computer twice as long to crack the same password file, how long would it take the two of them, working together (assume we can get two of them to work together) to crack the file, if each computer works at its respective individual speed? 1 solutions Answer 10713 by Earlsdon(6291)   on 2005-12-09 12:59:45 (Show Source): You can put this solution on YOUR website!If the Dell computer takes 4 hrs to crack the password file, then it can crack 1/4 of the file in 1 hour. If the Gateway computer takes 2(4) = 8 hrs to crack the same password file, then it can crack 1/8 of the file in 1 hour. Working together, the two computers can crack (1/4 + 1/8 = 3/8) of the file in 1 hour. Therefore, it would take them 8/3 hours, working together to crack the entire password file. 8/3 hours = 2 hours 40 minutes.
 Linear_Equations_And_Systems_Word_Problems/22175: Find the lenght of a rectangle meeting the specified conditions. The perimeter is 108 feet and the length is 80 percent of the width.1 solutions Answer 10712 by Earlsdon(6291)   on 2005-12-09 12:52:50 (Show Source): You can put this solution on YOUR website!Start with the formula for the perimeter of a rectangle: where L = Length and W = Width. P is given as 108 feet, and L = 0.8W, so: Simplify and solve for W. Divide both sides by 3.6 feet. feet.
 Graphs/22174: How do you graph an equation using rise over run?1 solutions Answer 10711 by Earlsdon(6291)   on 2005-12-09 12:44:13 (Show Source): You can put this solution on YOUR website!Rise over run is the definition of the slope, m, of a line. If your equation is in the slope-intercept form: , the slope is given by m and the y-intercept is given by b. For example, let's say that you wanted to graph the line whose equation is: Remember that you need only two points to define a straight line. The y-intercept is y=4, so mark a point on the y-axis at y=4. The slope m is 2/3, so that's rise = 2 and run = 3 and since the sign of m is positive, the slope of the line will be leaning to the right. Then, starting at the point y=4, go up (rise) 2 and then go right (positive) 3 and mark your second point. Now join the two points with a straight line and you have your graph. Here's what it should look like on the graph:
 Complex_Numbers/22152: Find the real-number solutions of the equation:1 solutions Answer 10683 by Earlsdon(6291)   on 2005-12-08 23:47:26 (Show Source): You can put this solution on YOUR website!Solve for x: Factor 2x^2 Apply the zero product principle. and/or If then, If then, The solutions are: x = 0 (A double root) x = 3
 Linear_Equations_And_Systems_Word_Problems/21992: First let me say I'm an old guy (52 years old)! Here is my problem, my 25 year old daughter has challenged me to solve this problem: What is the sum of the solution of the equation 3x^2 + 11x = 4 (three x squared plus 11x equals four She gave me the answer as negative three and two-thirds, and has challenged me to show how she arrived at this answer. Quite frankly, I have no idea. Any help would be greatly appreciated! Thanks, "Old Guy Dad" 1 solutions Answer 10610 by Earlsdon(6291)   on 2005-12-07 20:04:15 (Show Source): You can put this solution on YOUR website!Well, hang in there "old man"! (I'm 73!) First, let's find the solutions or roots, as they are commonly called. First subtract 4 from both sides of the equation. Solve this quadratic equation by factoring. Now apply the zero product principle. and/or If then, and If then, The roots are: So their sum is: = -3 1/3 Your daughter is correct!
 Linear-systems/21988: 1. 18-3y=5 2. -14+9a=38 3. 14r+8=32 4. 37-58b=2041 solutions Answer 10609 by Earlsdon(6291)   on 2005-12-07 19:51:05 (Show Source): You can put this solution on YOUR website!The principal idea here is to isolate the variable to one side of the equation. This is done by "undoing" (doing the opposite operation on) whatever has been done to the variable. 1) 18 - 3y = 5 Isolate the y-term by subtracting 18 from both sides of the equation. -3y = 5-18 -3y = -13 Now divide both sides by -3 y = 13/3 y = 4 1/3 2) -14+9a = 38 Add 14 to both sides to isolate the a-term. 9a = 38+14 9a = 52 Now divide both sides by 9. a = 52/9 a = 5 7/9 3) 14r+8 = 32 Subtract 8 from both sides. 14r = 24 Now divide both sides by 14. r = 24/14 r = 1 5/7 4) 37-58b = 204 Subtract 37 from both sides. -58b = 167 Now divide by -58. b = -(167/58) b = -2 51/58
 Graphs/21959: My line is (-7, 2) ; (-7, -2). Obviously this is a horizontal line. Also, this does not have a y-intercept. How would I find the equation of this line? In the formula y = mx+b, would "b" represent the x-intercept in this case? Thank you in advance!1 solutions Answer 10607 by Earlsdon(6291)   on 2005-12-07 19:36:07 (Show Source): You can put this solution on YOUR website!If your line is (-7, 2) ; (-7, -2) then the line is a vertical line (straight up-and-down) rather than a horizontal line (flat, side-to-side). The equation of this line would be: x = -7 and, you are right, there is no y-intercept, only an x-intercept (x = -7), so the slope-intercept form has no meaning for such a line. Since the y-coordinate of this line can take on any value you please, the coordinate of any point on this line can be written: (-7, a), where a is any real number. A vertical line has an undefined slope (m) and no y-intercept (b) so it cannot be represented by the slope-intercept form of the equation. Also, the equation: y = x represents a line that is at 45 degrees to the axes and passes through the origin. Here's the graph of y=x:
 Polynomials-and-rational-expressions/21799: Hi, Can anyone help with this? I believe I have to divide but am not positive: If a spacecraft is traveling 3x10(20) miles per hour, how long does it take the spacecraft to travel 9.3x10(23) miles? Express answer in Scientific Notation. Please note that the (20) and (23) are exponents. Thanks for your help!!1 solutions Answer 10517 by Earlsdon(6291)   on 2005-12-06 11:29:32 (Show Source): You can put this solution on YOUR website!When you are not sure of whether or not you have to divide, do a little dimensional analysis on the problem. Your answer will be in number of hours. The distance is in miles. The speed is in miles/hour. So, if you try: miles divided by miles/hour and simplify this you'll get hours because the miles will cancel. You need to divide the distance (miles) by the speed (miles/hour) to get the time of travel(hours). hours.
 Exponential-and-logarithmic-functions/21784: log(2+x)-log(x)=log 11 could you help explain how to do this1 solutions Answer 10514 by Earlsdon(6291)   on 2005-12-06 11:19:59 (Show Source): You can put this solution on YOUR website!Solve for x: Apply the Quotient rule for logarithms to the left side. If log a = log b, then a = b Multiply both sides by x. Subtract x from both sides. Divide both sides by 10. Check: Use your calculator or a table of logarithms to find the values of the logs.
 Polynomials-and-rational-expressions/21699: Solve the polynomial equation by factoring and then using the zero product principle. 3x to the 4th power minus 75x to the second power = 0.1 solutions Answer 10467 by Earlsdon(6291)   on 2005-12-05 18:19:10 (Show Source): You can put this solution on YOUR website!Solve by factoring: Factor out 3x^2 Apply the zero product principle. and/or If then, x = 0 If then, and x = +5 or x = -5 The roots are: x = 0 A double root. x = 5 x = -5 Here's what the graph looks like.
 Exponential-and-logarithmic-functions/21665: log base3 x +log base3 (x-4) +16=181 solutions Answer 10450 by Earlsdon(6291)   on 2005-12-05 11:22:23 (Show Source): You can put this solution on YOUR website!Solve for x: log(x)+log(x-4)+16 = 18 Subtract 16 from both sides. log(x)+log(x-4) = 2 Apply the product rule for logarithms:LogM+logN = log(MN) log(x)+log(x-4) = log(x^2-4x) = 2 Rewrite in exponential form: logx = y means so: log(x^2-4x) = 2 means Subtract 3^2 = 9 from both sides. Solve using the quadratic formula: = The roots are:
 Radicals/21593: HELP ME SIMPLIFY PLEASE A TO THE NEGATIVE 3RD POWER AND B TO THE 2ND POWER IT SHOULD LOOK LIKE THIS A-3B2 THANKS SOO MUCH!! 1 solutions Answer 10432 by Earlsdon(6291)   on 2005-12-04 18:57:35 (Show Source): You can put this solution on YOUR website!Simplify:
 Radicals/21594: WRITE IN EXPONENTIAL FORM: SQUARE ROOT OF X THANK YOU SOO MUCH I LOVE YOU GUYS!!1 solutions Answer 10431 by Earlsdon(6291)   on 2005-12-04 18:54:56 (Show Source): You can put this solution on YOUR website!Roots are written as the denominator of a fractional exponent.
 Polynomials-and-rational-expressions/21586: Could you please help me with this problem Evaluate: 1 solutions Answer 10430 by Earlsdon(6291)   on 2005-12-04 18:51:44 (Show Source): You can put this solution on YOUR website!Perhaps I'm being a little picky buy you can't "evaluate" (calculate the numerical value of) this expression without knowing the value of x. You can, however, simplify the expression by performing the indicated multiplication. Now we have the English out of the way, let's do the math. Simplify: Multiply the 1st term of the first term (3x^2) in the 1st set of parenthese by every term in the 2nd set of parentheses. Then, multiply the 2nd term (-2) of the 1st set of parentheses by every term in the 2nd set of parentheses. Finally, combine like-terms and simplify where possible. = =
 Geometric_formulas/21574: I need to come up with an equation (I am in algebra) and then compute the following: The length of a rectangular table top is 8 feet shorter than 5 times the width. If the area of the table top is 48 square feet, find the dimensions of the table? I am so confused. Can someone help!!1 solutions Answer 10429 by Earlsdon(6291)   on 2005-12-04 18:23:43 (Show Source): You can put this solution on YOUR website!Let the length of the table top be L and its width W. L = 5W-8 The area of a rectangle is: Substitute L = 5W-8 But A = 48 sq.ft. Subtract 48 from both sides. Solve by factoring. Apply the zero product principle. and/or If and Discard this solution as the width can only be positive. If then, The width is 4 feet. The length, L, is 5(4)-8 = 20 - 8 = 12 feet. Check: A = L*W A = 12*4 A = 48 sq.ft.
 Radicals/21575: Hey could you help me solve this problem?? X/5 - X+2/3 = 1/15 SO FAR I HAVE: 15(X/5 - X+2/3) = 15(1/15) 15 (X/5) - 15 (X+2/3) =??? 3X - 5(X+2) = ??? 3X -5X-10=??? I DONT KNOW HOW TO FINISH IT PLEASE SOMEONE HELP ME U guys are the best i appreciate all ur help!! Without you id never get algebra THANKS1 solutions Answer 10424 by Earlsdon(6291)   on 2005-12-04 18:03:27 (Show Source): You can put this solution on YOUR website!Solve: Multiply both sides by 15 to clear the fractions. Combine the x terms. Subtract 10 from both sides. Divide both sides by -12.
 Triangles/21529: I have a yard that is a triangle. My sides measure 110 ft by 120 ft by 150 ft. If 1 bag of fertilizer covers 1200 square ft. how many bags will I need to cover the yard?1 solutions Answer 10411 by Earlsdon(6291)   on 2005-12-04 12:52:17 (Show Source): You can put this solution on YOUR website!Use Heron's formula to find the area of your triangular yard. where: S = semi-perimeter of the triangle S=190 ft) and a, b, & c are the lengths of the sides of the triangle. square feet. Divide this by 1200 sq.ft. per bag. You will need 6 bags of fertilizer
 logarithm/21525: I need help solving this logarithmic equation: log (x+9)=1-log x 1 solutions Answer 10409 by Earlsdon(6291)   on 2005-12-04 12:06:08 (Show Source): You can put this solution on YOUR website!Solve for x: Add logx to both sides. Simplify the left side. (loga+logb = log(ab)) Substitute log10 = 1 If loga = logb then a = b. Subtract 10 from both sides. Solve by factoring. Apply the zero product principle. and/or If then, If then, You can check the solutions by substitution.
 Quadratic-relations-and-conic-sections/21481: Could you please help me with this problem: Solve for x: 1 solutions Answer 10408 by Earlsdon(6291)   on 2005-12-04 11:42:08 (Show Source): You can put this solution on YOUR website!Solve for x: Factor out a 2. Factor the parentheses. Factor the parentheses again. Apply the zero product principle. and/or and/or and/or The roots are: x = -2 x = 2 x = -3 x = 3