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# Recent problems solved by 'Earlsdon'

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 Exponential-and-logarithmic-functions/39666: I can not figure out for the life of me how to do this. I have tried so many times, please, HELP. Solve: 3log(5x)+4log(2x)=3 log(125x^3)+log(16x^4)=3 Have I done it right so far? For some reason it seems wrong.Please help me!!1 solutions Answer 25094 by Earlsdon(6287)   on 2006-05-28 10:35:30 (Show Source): You can put this solution on YOUR website!You are correct as far as you have gone. Now apply the "product rule" for logarthms: Simplify. Convert to exponential form. Divide both sides by 2000. Approximately.
 Percentage-and-ratio-word-problems/39677: Rose's garden is in the shape of a trapezoid. If the height of the trapezoid is 16m, one base is 20m, and the area is 224 2 m .find the lenght of the other baase. 1 solutions Answer 25093 by Earlsdon(6287)   on 2006-05-28 10:02:30 (Show Source): You can put this solution on YOUR website!Starting with the formula for the area of a trapezoid: substitute: A = 224 h = 16 b1 = 20 Solve for b2. Multiply both sides of the equation by 2. Divide both sides by h. Subtract b1 from both sides. Substitute the given values of A=224 h=16, b1=20. The other base is 8 meters.
 Polynomials-and-rational-expressions/39681: factorise 4x²- 491 solutions Answer 25092 by Earlsdon(6287)   on 2006-05-28 09:51:47 (Show Source): You can put this solution on YOUR website!Factorise: Notice that the given expression is the difference of two squares: The difference of two squares is factorable: Applying this to your expression, we have:
 Square-cubic-other-roots/39403: three-quarters times the square of a positive integer number is 3 less than fives times the integer. find the integer1 solutions Answer 24846 by Earlsdon(6287)   on 2006-05-25 11:34:31 (Show Source): You can put this solution on YOUR website!Translating the problem description into algebra: Simplify and solve for n. Mutliply through by 4 to clear the fraction. Simplify. Solve the quadratic equation by factoring. Apply the zero products principle. and/or If then and Discard this solution because you are looking for an integer. If then This is the required integer. Check: = 27 = 27
 Expressions-with-variables/39397: The length of a rectangle is 8 inches more than twice its width. If the perimeter of the rectangle is 28 inches, find the width of the rectangle.1 solutions Answer 24841 by Earlsdon(6287)   on 2006-05-25 11:22:10 (Show Source): You can put this solution on YOUR website!Start with the formula for the perimeter of a rectangle: We know that P = 28" We also know that L = 2W+8, substitute this into the formula. Simplify and solve for W. Subtract 16 from both sides of the equation. Divide both sides by 6. The width is 2 inches.
 real-numbers/39399: I am a beginner. I am stuck on correct answer: The sum of two numbers is 125 and their difference is 15. What is the larger of the two numbers? I have a choice of: 110 or 70 or 55 or 62.5. It could be 110 (if 15 were the other number) or it could be 70 if 55 was the other number. Since 70 and 55 are both listed as a solution I would pick 70. Since 110 is listed but not 15. I am thinking that 110 should not be the answer. So is it 110 or 70 ? I am not using a specific book. I am just practicing from problems someone once gave me a long time ago on paper to practice with. They forgot to include an answer key so I could check my work.1 solutions Answer 24835 by Earlsdon(6287)   on 2006-05-25 11:11:23 (Show Source): You can put this solution on YOUR website!Let x be one of the numbers and y the other number. x + y = 125 The sum of the two numbers is 125. x - y = 15 Their difference is 15. Rewrite this as: x = y+15, substitute for x in the first equation and solve for y. (y+15) + y = 125 Simplify and solve for y. 2y + 15 = 125 Subtract 15 from both sides. 2y = 110 Divide both sides by 2. y = 55 x = y+15 x = 55+15 y = 70 The larger of the two numbers is 70.
 Systems-of-equations/39331: Jill has \$3.50 in nickels and dimes. If she has 50 coins, how many of each type of coins does she have? I need to know an X and a Y. THANK YOU1 solutions Answer 24761 by Earlsdon(6287)   on 2006-05-24 20:15:01 (Show Source): You can put this solution on YOUR website!Let x = the number of dimes (\$0.10) and y = the number of nickels (\$0.05). x + y = 50 The total number of coins. Rewrite this as: x = 50-y and substitute for x in the second equation. (\$0.10)x + (\$0.05)y = \$3.50 (\$0.10)(50-y) + (\$0.05)y = \$3.50 Simplify and solve for y. 5 - 0.1y + 0.05y = 3.5 5 - 0.05y = 3.5 Subtract 5 from both sides. -0.05y = -1.5 Divide both sides by -0.05 y = 30 This is the number of nickels. x = 50-y x = 50-30 = 20 This is the number of dimes.
 Polynomials-and-rational-expressions/39267: Can you help me factor x^2-3x-2? 1 solutions Answer 24710 by Earlsdon(6287)   on 2006-05-24 14:41:01 (Show Source): You can put this solution on YOUR website!Factor: Try this! You are looking for two binomials of the form: where: and Let's see what we can find. If m = 1 and n = -2, then (This is ok) and (but this won't do it). Try m = -1 and n = 2, then (This is ok)and (but this won't do either). As you can see, we've exhausted the possibilities of the restriction on m and n, so the conclusion is that the expression: is not factorable, therefore, it is prime.
 Square-cubic-other-roots/39247: can you please show me and explain EACH step in setting up and solving the following application problems. Give answers to the nearest thousandth if rounding is needed. c. The length of a rectangle is 2 cm longer than its width. If the diagonal of the rectangle is 10cm. What are the dimensions (length and width) of the rectangle? 1 solutions Answer 24671 by Earlsdon(6287)   on 2006-05-24 10:19:06 (Show Source): You can put this solution on YOUR website!Start with the Pythagorean theorem. The diagonal (D) of a rectangle is the hypotenuse of a right triangle whose legs are the rectangle's length (L) and width (W). So we can write: But we are also given that the length (L) is 2 cm longer than its width (W), so we can write: L = W+2 Substituting this into the above equation, we have: and we know that D = 10 cm, so... Simplify and solve for W. Subtract 100 from both sides of the equation. Divide both sides by 2 to simplify. Factor the quadratic equation. Apply the zero products principle. and/or If then If then Discard this solution as the width must be a positive number. The width is 6 cm. The length is width + 2 cm = 6 + 2 = 8 cm.
 test/38945: This question is from textbook Basic Technical Mathematics I have been trying to figure out this problem and I keep coming up with the wrong answer. I believe I am doing the formula right but even my husband can't come up with the right answer. Please help and Thank you. cindy1 solutions Answer 24388 by Earlsdon(6287)   on 2006-05-22 15:29:26 (Show Source): You can put this solution on YOUR website!Solve for x: Simplify. Collect like-terms. Subtract x from both sides of the equation. Add 8 to both sides. Divide both sides by 8. Answer:
 Trigonometry-basics/38934: a sector of a circle has area 8.1pi cm squared and central angle 36 degrees. find its radius and arc length.1 solutions Answer 24387 by Earlsdon(6287)   on 2006-05-22 15:24:41 (Show Source): You can put this solution on YOUR website!If the sector has a central angle of 36 degrees, then its area is:, we can write: Simplify and solve for the radius, r. cm. The arc length will be of the circumference or: Simplify. =
 Age_Word_Problems/38940: Allen is 3 times as old as Betty. Catherine is 5 yrs younger than Allen. 3 yrs ago sum of all ages is 56. What is each of their present age?1 solutions Answer 24386 by Earlsdon(6287)   on 2006-05-22 15:00:23 (Show Source): You can put this solution on YOUR website!Start by letting: A = Allen's present age. B = Betty's present age. C = Catherine's present age. From the problem desciption: 1) A = 3B (Allen is 3 times as old as Betty) 2) C = A-5 (Catherine is 5 years younger than Allen). 3) (A-3)+(B-3)+(C-3) = 56 (Three years ago, the sum of their ages was 56). Simplify equation 3) A+B+C-9 = 56 Add 9 to both sides. A+B+C = 65 Substitute equation 1) for A. 3B+B+C = 65 Rewrite equation 2 as: C = 3B-5 and substitute for C. 3B+B+3B-5 = 65 Simplify. 7B-5 = 65 Add 5 to both sides 7B = 70 Divide both sides by 7. B = 10 This is Betty's age. A = 3B = 3(10) = 30 This is Allen's age. C = A-5 = 30-5 = 25 This is Catherine's age.
 Polynomials-and-rational-expressions/38880: factor completely with respect to the integers 2x^4-14x^2+241 solutions Answer 24340 by Earlsdon(6287)   on 2006-05-21 22:37:11 (Show Source): You can put this solution on YOUR website!Factor: Factor out a 2. Factor the parentheses. Factor the parentheses.
 test/38869: = x+3 is it right?1 solutions Answer 24339 by Earlsdon(6287)   on 2006-05-21 22:28:59 (Show Source): You can put this solution on YOUR website!Simplify: Factor the denominator and rearrange the numerator. Cancel the common factor (x-3)
 Coordinate-system/38647: A general equation of the family of lines perpendicular to 2x-5y=7 is... THE ANSWER IS: 5x+2y=k (BUT HOW DO U GET THIS?) please tell me how and why this is the answer YOUR HELP IS MOST APPRECIATED, THANK YOU SO MUCH 1 solutions Answer 24209 by Earlsdon(6287)   on 2006-05-20 16:42:32 (Show Source): You can put this solution on YOUR website!Start by putting the given equation in the slope-intercept form: --> You can see that the slope, m, of the given line is Now you want the family of lines that are perpendicular to this line, and as you know, perpendicular lines will have a slope that is the negative reciprocal of the given line...so the slope of the perpendicular lines will be the negative reciprocal of or Since you are looking for the family of lines, you don't really care where these lines intercept the y-axis, so the y-intercept, b, can be any real number. So now we have, in the slope-intercept form, the equation for the family of lines perpendicular to the given line: Where b, the y-intercept is any real number. Now if you rearrange this equation: Multiply both sides by 2 to clear the fraction. Add 5x to both sides. But since b is any real number, so 2b is any real number so you can let 2b = k, so finally you have: .
 logarithm/38623: Express 4^3 = 64 in logaritnmic form Please show your working out, and thank you in advance for your help1 solutions Answer 24176 by Earlsdon(6287)   on 2006-05-20 11:02:27 (Show Source): You can put this solution on YOUR website!Exponential form: Logarithmic form: b = base Applying this to your problem: Exponential form: Logarithmic form: 4 = base
 logarithm/38624: Simplify the expression log9 - (log12 - log4) Please show your working out, and thanks in advance for your help1 solutions Answer 24175 by Earlsdon(6287)   on 2006-05-20 10:52:38 (Show Source): You can put this solution on YOUR website!Simplify: Applying the "quotient rule for logarithms": Simplify and apply the quotient rule again. Simplify. Done!
 Money_Word_Problems/38631: Find the final amount of the investment. \$10,000 invested at 6% compounded quarterly for 5 1/2 years. (end of problem) I've put this in my TI-83 calculator 20 times... and it still comes out 58,374.99. What am I doing wrong? I know the formula is A=P(1+r/t)^rt Can you help?1 solutions Answer 24174 by Earlsdon(6287)   on 2006-05-20 10:42:48 (Show Source): You can put this solution on YOUR website!The formula for interest compounded q times per year is: Where: P = Present value. A = The amount invested (\$10,000.00) i = The rate of interest, as a decimal (0.06) q = The number of compounding periods (4) n = The number of years invested (5.5) Substituting the above into the formula: The final amount is: \$13,875.66
 Expressions-with-variables/38533: V = C(Ro – R)R^2 where C > 0 is a constant based on individual body characteristics, Ro is the radius of the windpipe before the cough, and R is the radius of the windpipe during the cough. Find the value of R that maximizes the velocity, and state the resulting maximum velocity. I just want to confirm that I am on the right track? V = C(Ro – R)R^2 = C Ro R^2 - CR^3 V'(R)= 0 CR(2Ro - 3R) = 0, R = 0 or 2/3. I think the elgebra may not be right? Can someone please tell me if this is the right idea. Thankyou. 1 solutions Answer 24059 by Earlsdon(6287)   on 2006-05-19 11:24:06 (Show Source): You can put this solution on YOUR website!Well, Your initial steps are OK but I think that your final statement lost an Ro. Setting Solve for R. Factor CR. Apply the zero products principle. and/or If then Since If then and
 Linear-equations/38449: Find the slope of the line whose equation is 3x + 2y = 51 solutions Answer 23962 by Earlsdon(6287)   on 2006-05-18 18:10:27 (Show Source): You can put this solution on YOUR website!To find the slope (m) solve the equation for y then it will be in the "slope-intercept" form:, then you just read the slope which is the coefficient of x. Subtract 3x from both sides of the equation. Divide both sides by 2. Compare this with: You can see that
 Systems-of-equations/38317: what is the answer to y=3x+3 3x+2y=-12 I tried to figure it out and got an answer can you tell me if its right1 solutions Answer 23826 by Earlsdon(6287)   on 2006-05-17 23:12:09 (Show Source): You can put this solution on YOUR website!Solve the system of equations: Substitute this for y in the second equation and solve for x. Solve for x. Simplify. Subtract 6 from both sides. Divide both sides by 9. Substitute this for x in the first equation and solve for y. Solution: (-2, -3)
 Polynomials-and-rational-expressions/38330: 3x over 4x-1 = 1 over x1 solutions Answer 23816 by Earlsdon(6287)   on 2006-05-17 22:41:28 (Show Source): You can put this solution on YOUR website!Solve: Cross-multiply. Subtract (4x-1) from both sides. Factor. Apply the zero products principle. and/or If then and If then Roots are:
 Angles/38150: How do you figure out that a angle is supplementary?1 solutions Answer 23646 by Earlsdon(6287)   on 2006-05-16 21:47:28 (Show Source): You can put this solution on YOUR website!Two angles are supplementary if their sum is 180 degrees.
 Rational-functions/38016: Rationalize the denominator I know to times both sides by and I get then im lost, i know the answer is 1 solutions Answer 23521 by Earlsdon(6287)   on 2006-05-16 00:51:37 (Show Source): You can put this solution on YOUR website!Rationalise the denominator: Your first step, multiplying top and bottom by was the right move! Simplify. Cancel the 2's which is the same as
 logarithm/38014: Evaluate the 3 is supposed to be over the check, where the invisible 2 usually goes. I got ln 1/e^1/3 whcich then equals -1/3, but I think I'm missing a step.1 solutions Answer 23520 by Earlsdon(6287)   on 2006-05-16 00:36:01 (Show Source): You can put this solution on YOUR website!Your answer is correct: You can write the problem as: But , so:
 Polynomials-and-rational-expressions/37924: factor the following sums or differences of two cubes b^3-81 solutions Answer 23467 by Earlsdon(6287)   on 2006-05-15 21:33:50 (Show Source): You can put this solution on YOUR website!The general form for factoring the difference of two cubes is: In your problem: can be written as: so that A = b and B = 2 Simplify.
 Geometry_proofs/37916: Hi, I am having trouble trying to figure out how to do this problem. I am in 9th grade geometry but we are do a review of Algebra/Coordinate Proof. The question is: Position and label a right isosceles triangle on the coordinate plane. Then prove that the segment joining the midpoint of the two legs of the right triangle is parallel to the hypotenuse. Thanks so much for your help- Will1 solutions Answer 23466 by Earlsdon(6287)   on 2006-05-15 21:21:35 (Show Source): You can put this solution on YOUR website!Probably the easiest way to see this is to draw the right isosceles triangle with the right angle at the origin of your coordinate axes. Then draw the horizontal leg a distance of a-units along the positive x-axis and the vertical leg a distance of a-units along the positive y-axis. Connect the ends of the x-axis leg and the y-axis leg to form the hypotenuse. You can label the triangle with A at the right-angle vertex, B at the end of the x-axis leg, and C at the end of the y-axis leg. With this labeling, the hypotenuse is segment CB, the x-axis leg is AB, and the y-axis leg is AC. Now, place a point (E) on the x-axis leg at a distance of a/2 from the origin (this point bisects the segment AB) and another point (F) on the y-axis leg at a distance of a/2 from the origin (this point bisects the segment AC), then connect these two points. The proof: Using the fact that parallel lines have identical slopes, find the slope of the hypotenuse. Slope is rise over run and for the hypotenuse, the rise is distance a and the run is distance a so the slope is a/a = 1 (it's really a negative slope). The slope of the line connecting the midpoints of the two legs is (a/2)/(a/2) = 1 (again, this is really a negative slope) Since the slopes of the two lines are equal, the lines are parallel. QED
 Graphs/37981: This question is from textbook Algebra and trigonometry with analytic geometry From a square piece of cardboard with width x inches, a square of width x-3 inches is removed from the center. Write the area of the remaining piece as a function of x. I'm having some difficulty with functions. Thank you for your time. 1 solutions Answer 23464 by Earlsdon(6287)   on 2006-05-15 20:53:29 (Show Source): You can put this solution on YOUR website!The area of a square with sides equal to x is given by: Now if you remove a square of sides (x-3), the area of the removed square is given by: a = (x-3)^2, so the remaining area is: Let's call this area A1. Simplify. This is the remaining area as a function of x.
 Quadratic_Equations/37968: Solve the quadratic equation by factoring and applying the property "ab=0 if and only if a=0 or b=0" (x^2)+3kx-(10k^2)=01 solutions Answer 23463 by Earlsdon(6287)   on 2006-05-15 20:45:38 (Show Source): You can put this solution on YOUR website!Solve by factoring: Apply the "zero products principle" (ab = 0, iff a = 0 and/or b=0) and/or If then If then P.S. iff means "if and only if"
 Polynomials-and-rational-expressions/37919: 1. what is 9s squared - 6x - 1? im on perfect squares and factoring. in the glencoe math book for algebra 1. section 9-61 solutions Answer 23445 by Earlsdon(6287)   on 2006-05-15 18:59:23 (Show Source): You can put this solution on YOUR website!Factor: You most likely have a typo...9s squared...did you mean 9x squared? This is not factorable, so it's prime. If you had: then this would factor as a perfect square!
 Equations/37922: How do you find the answer to this word problem: The perimeter of a rectangular garden is 40ft. The width is 2ft. more than one-half the length. Find the length and width. 1 solutions Answer 23444 by Earlsdon(6287)   on 2006-05-15 18:50:51 (Show Source): You can put this solution on YOUR website!Start with the formula for the perimeter of a rectangle: In your problem, P = 40ft. Substitute these into the basic formula above: Simplify and solve for L Subtract 4 from both sides of the equation. Divide both sides by 3. The length is 12ft. The width is = 8ft. Check: It checks!