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# Recent problems solved by 'nerdybill'

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 Surface-area/348160: How do i solve the equation s= 2(lw + hw + hl) for h?1 solutions Answer 248956 by nerdybill(6948)   on 2010-09-26 12:06:26 (Show Source): You can put this solution on YOUR website!Starting with: s= 2(lw + hw + hl) s/2 = lw + hw + hl s/2 - lw = hw + hl s/2 - lw = h(w + l) (s/2-lw)/(w+l) = h
 Geometry_Word_Problems/348137: Alfonzo' pizzeria bakes olive pieces in the outer crust of its 20 inch (diameter) pizza . there is at least one olive piece per inch of crust . how many olive pieces will you get in one slice of pizza ? assume the pizza is cut into eight slices1 solutions Answer 248949 by nerdybill(6948)   on 2010-09-26 10:49:44 (Show Source): You can put this solution on YOUR website!Alfonzo' pizzeria bakes olive pieces in the outer crust of its 20 inch (diameter) pizza . there is at least one olive piece per inch of crust . how many olive pieces will you get in one slice of pizza ? assume the pizza is cut into eight slices . Area of pizza = (pi)r^2 = (3.14)10^2 = (3.14)(100) = 314 sq inches . Area of a slice of pizza: 314/8 = 39.25 square inches . Since there is one olive per square inch: 39.25 olives per slice
 logarithm/348149: What is... 2 log x - 1/2 log y (they both have no base/the same base) Only to be simplified I think, as a fraction.1 solutions Answer 248947 by nerdybill(6948)   on 2010-09-26 10:36:55 (Show Source): You can put this solution on YOUR website! Rationalizing denominator:
 Rectangles/348138: The area of a rectangle is 30 square centimeters and its perimeter is 26 centimeters. What is the length and width of the rectangle?1 solutions Answer 248946 by nerdybill(6948)   on 2010-09-26 10:28:52 (Show Source): You can put this solution on YOUR website!The area of a rectangle is 30 square centimeters and its perimeter is 26 centimeters. What is the length and width of the rectangle? Let x = width and y = length . From:"The area of a rectangle is 30 square centimeters" (equation 1) xy = 30 . From: "perimeter is 26 centimeters" (equation 2) 26=2(x+y) . Solve equation 2 for y: 26=2(x+y) 13=x+y 13-x = y . Substitute above into equation 1 and solve for x: xy = 30 x(13-x) = 30 13x-x^2 = 30 0 = x^2-13x+30 0 = (x-15)(x+2) x = {-2, 15} We can toss out the negative solution leaving x = 15 centimeters . Substitute above into equation 1 and solve for y: xy = 30 15y = 30 y = 2 centimeters . Dimensions of rectangle: 2 by 15 centimeters
 Expressions-with-variables/348099: 1 solutions Answer 248934 by nerdybill(6948)   on 2010-09-26 09:24:58 (Show Source): You can put this solution on YOUR website!Starting with: . Multiply both sides by 12 to get rid of denominators:
 Angles/348127: what is the measure of an angle that is 48 degrees greater than its complement1 solutions Answer 248933 by nerdybill(6948)   on 2010-09-26 09:22:04 (Show Source): You can put this solution on YOUR website!what is the measure of an angle that is 48 degrees greater than its complement . Let x = measure of our angle then its complement = 90-x . We get our equation from:"measure of an angle that is 48 degrees greater than its complement" x = (90-x)-48 x = 90-x-48 x = 42-x 2x = 42 x = 21 degrees
 test/348133: a certain 90-mile trip took 2 hours. exactally 1/3 of the distance traveledwas by raail, and this part of the trip took 1/5 of the travel time. what was the average rate, in miles per hour of the rail portion of the trip?1 solutions Answer 248932 by nerdybill(6948)   on 2010-09-26 09:18:31 (Show Source): You can put this solution on YOUR website!a certain 90-mile trip took 2 hours. exactally 1/3 of the distance traveledwas by raail, and this part of the trip took 1/5 of the travel time. what was the average rate, in miles per hour of the rail portion of the trip? . 1/3 of the trip is then: (1/3)(90) = 30 miles . Time it takes to travel that distance is: (1/5)(2) = 2/5 of an hour . Average rate: 30/(2/5) = 150/2 = 75 mph
 Miscellaneous_Word_Problems/348131: what would you get if you divided a half of a half of a half by a half of a fourth of a half1 solutions Answer 248931 by nerdybill(6948)   on 2010-09-26 09:15:15 (Show Source): You can put this solution on YOUR website!what would you get if you divided a half of a half of a half by a half of a fourth of a half . Translate to: [(1/2)(1/2)(1/2)]/[(1/2)(1/4)(1/2)] [1/8]/[1/16] multiplying by 16/16 we get: 16/8 which reduces to: 2
 Travel_Word_Problems/348134: Two boats leave the dock at 12:00 noon, one of them moving northward at 6 miles per hour, and the other moving westward at 8 mph. How far apart are the boats after 2hours? A. 20 miles B. 28 miles C. 10 miles D. 14 miles1 solutions Answer 248930 by nerdybill(6948)   on 2010-09-26 09:05:38 (Show Source): You can put this solution on YOUR website!Two boats leave the dock at 12:00 noon, one of them moving northward at 6 miles per hour, and the other moving westward at 8 mph. How far apart are the boats after 2hours? A. 20 miles B. 28 miles C. 10 miles D. 14 miles . After two hours: northward boat travels: 2*6 = 12 miles westward boat travels: 2*8 = 16 miles . To find distance apart, apply Pythagorean theorem: Let d = distance apart then d^2 = 12^2 + 16^2 d^2 = 144 + 256 d^2 = 400 d = 20 miles
 logarithm/348073: What is the value of the given expression: log AB^2 a. 2 log A log B b. 2 log A+log B c. log A + log B + log 2 d. log A + 2 log B Thanks1 solutions Answer 248883 by nerdybill(6948)   on 2010-09-26 00:35:48 (Show Source): You can put this solution on YOUR website!log AB^2 log A + log B^2 log A + 2log B
 Numbers_Word_Problems/348019: The perimeter of a rectangle equals one and a half times its area. Express the length of the rectangle in terms of the width (use variable "w" for width). 1 solutions Answer 248839 by nerdybill(6948)   on 2010-09-25 20:50:03 (Show Source): You can put this solution on YOUR website!The perimeter of a rectangle equals one and a half times its area. Express the length of the rectangle in terms of the width (use variable "w" for width) . Area of any rectangle = width * length Perimeter of any rectangle = 2(width+length) . Let w = width and temporarily x = length . From the problem, perimeter is: 1.5wx . But, Perimeter = 2(w+x) So, then we have 1.5wx = 2(w+x) Solving for x: 1.5wx = 2(w+x) 1.5wx = 2w+2x 1.5wx-2x = 2w factoring the left: x(1.5w-2) = 2w x = 2w/(1.5w-2) . So, your answer would be length is equal to: 2w/(1.5w-2)
 Geometry_Word_Problems/347999: Tom wants to build a fence around his rectangular swimming pool. The dimensions of the pool are 18 feet by 22feet. He wants the border around the pool to be of uniform width. If he has 60 yards of fencing, find the width of the border.1 solutions Answer 248811 by nerdybill(6948)   on 2010-09-25 18:40:51 (Show Source): You can put this solution on YOUR website!Tom wants to build a fence around his rectangular swimming pool. The dimensions of the pool are 18 feet by 22feet. He wants the border around the pool to be of uniform width. If he has 60 yards of fencing, find the width of the border. . Convert 60 yards to feet: 60 * 3 = 180 feet . Let x = width of border then 18+2x = width of fence 22+2x = length of fence . perimeter = 2(width+length) 180 = 2(18+2x + 22+2x) 180 = 2(40+4x) 90 = 40+4x 50 = 4x 12.5 feet = x
 Mixture_Word_Problems/347991: How many pints of a 10% cleaning solution must be mixed with 6 pints of an 8% cleaning solution to give a 9% solution? 1 solutions Answer 248807 by nerdybill(6948)   on 2010-09-25 18:36:57 (Show Source): You can put this solution on YOUR website!How many pints of a 10% cleaning solution must be mixed with 6 pints of an 8% cleaning solution to give a 9% solution? . Let x = pints of 10% solution added then .10x + .08(6) = .09(6 + x) .10x + .48 = .54 + .09x .01x + .48 = .54 .01x = .06 x = .06/.01 x = 6 pints
 Numeric_Fractions/347945: simplify the ratio 9.6 to 6.81 solutions Answer 248784 by nerdybill(6948)   on 2010-09-25 16:16:31 (Show Source): You can put this solution on YOUR website!9.6 to 6.8 multiplying both sides by 10: 96 to 68 dividing both sides by 4: 24 to 17
 expressions/347948: Showing my work, how do I evaluate this problem? 3.03+(-2.05)-(-9.25)+|-10|1 solutions Answer 248767 by nerdybill(6948)   on 2010-09-25 15:34:49 (Show Source): You can put this solution on YOUR website!I'm correcting my "absolute" conversion... 3.03+(-2.05)-(-9.25)+|-10| 3.03+(-2.05)-(-9.25)+10 3.03-2.05+9.25+10 0.985+9.25+10 10.23+10 20.23
 Numbers_Word_Problems/347962: 5 times the sum of a number and -1 is the same as 6 times the number.1 solutions Answer 248765 by nerdybill(6948)   on 2010-09-25 15:32:19 (Show Source): You can put this solution on YOUR website!5 times the sum of a number and -1 is the same as 6 times the number. . Let x = the number then 5(x+(-1)) = 6x 5(x-1) = 6x 5x-5 = 6x -5 = x . Answer: the "number" is -5
 Rectangles/347961: A rectangular garden is 40 ft wide. If its area is 3800 ft2, what is the length of the garden? 1 solutions Answer 248764 by nerdybill(6948)   on 2010-09-25 15:30:40 (Show Source): You can put this solution on YOUR website!A rectangular garden is 40 ft wide. If its area is 3800 ft2, what is the length of the garden? . Let x = length then since width*length=area we have: 40x = 3800 x = 3800/40 x = 380/4 x = 95 feet (length)
 test/347893: P=a+b+c solve for b 1 solutions Answer 248761 by nerdybill(6948)   on 2010-09-25 15:28:03 (Show Source): You can put this solution on YOUR website!P=a+b+c solve for b . Starting with: P=a+b+c subtract 'a' from both sides: P-a=a+b+c-a P-a=b+c subtract 'c' from both sides: P-a-c=b+c-c P-a-c=b
 Equations/347930: in the equations y= -2x-4 the slope is1 solutions Answer 248760 by nerdybill(6948)   on 2010-09-25 15:25:23 (Show Source): You can put this solution on YOUR website!in the equations y= -2x-4 the slope is . the equation is given in the "slope-intercept" form of: y=mx+b where m is the slope . So, the slope, by inspection, is -2
 Miscellaneous_Word_Problems/347882: A planet orbiting the sun 42,000 miles from the center of the sun. It makes 1 revolution in 3 days. Find the speed of the planet in miles per hour.1 solutions Answer 248727 by nerdybill(6948)   on 2010-09-25 09:27:50 (Show Source): You can put this solution on YOUR website!A planet orbiting the sun 42,000 miles from the center of the sun. It makes 1 revolution in 3 days. Find the speed of the planet in miles per hour. . circumference is (pi)d where d is diameter . circumference = (3.14)(2)42000 = 263760 miles . 3 days = 3(24) = 72 hours . Speed = 263760/72 = 3663.33 mph
 Miscellaneous_Word_Problems/347857: A bakery sells single layer mini-cakes that are 3 inches in diameter for \$4 each. They also have a 9-inch cake for \$15. If both cakes are the same thickness, which option gives you more cake for the money, nine mini-cakes or one 9-inch cake? 1 solutions Answer 248726 by nerdybill(6948)   on 2010-09-25 09:22:28 (Show Source): You can put this solution on YOUR website!A bakery sells single layer mini-cakes that are 3 inches in diameter for \$4 each. They also have a 9-inch cake for \$15. If both cakes are the same thickness, which option gives you more cake for the money, nine mini-cakes or one 9-inch cake? . Volume of cake = r^2(pi) Let t = thickness volume of mini-cake = (1.5)^2(3.14)t = 7.065t Since there are nine mini-cake, total volume is: 9(7.065t) = 63.585t . volume of 9-inch cake = 3^2(3.14)t = 28.26t . Relate volume per cost: mini-cake:63.585t/12 = 5.29875t (vol per dollar) 9-inch cake: 28.26t/15 = 1.884t (vol per dollar) . Answer:mini-cake gives MORE volume per dollar
 Rectangles/347872: the length of a rectangle is 4 more than seven times the width. write an expression for the area a of the rectangle.1 solutions Answer 248724 by nerdybill(6948)   on 2010-09-25 09:13:08 (Show Source): You can put this solution on YOUR website!the length of a rectangle is 4 more than seven times the width. write an expression for the area a of the rectangle. . Let w = width then from "length of a rectangle is 4 more than seven times the width" we have 7w+4 = length . since area=width*length:
 Travel_Word_Problems/347743: Car 1 leaves Miami and travels at a speed of 47mph. Car 2 leaves 2 hours later and travels at 58mph. How long will it take for car 2 to catch up to car 1.1 solutions Answer 248620 by nerdybill(6948)   on 2010-09-24 18:56:02 (Show Source): You can put this solution on YOUR website!Car 1 leaves Miami and travels at a speed of 47mph. Car 2 leaves 2 hours later and travels at 58mph. How long will it take for car 2 to catch up to car 1. . Apply distance formula: d=rt . Let x = time (hours) to catch up then 47x = 58(x-2) 47x = 58x-116 -11x = -116 x = 116/11 x = 10.55 hours or x = 10 hours and 33 minutes
 expressions/347724: Showing my work, how do I evaluate -23-(-24)/-11-(-17) + |-22|1 solutions Answer 248618 by nerdybill(6948)   on 2010-09-24 18:47:35 (Show Source): You can put this solution on YOUR website!apply "order of operations": (PEMDAS) . Starting with: -23-(-24)/-11-(-17) + |-22| eliminate the absolute value: -23-(-24)/-11-(-17) + 22 eliminate the double negatives: -23+24/-11+17 + 22 perform division: -23-2.182+17 + 22 -25.182+17 + 22 -8.182 + 22 13.182
 Linear-equations/347339: Put the equation of a line into slope-intercept form. 3x + 2y = 10 1 solutions Answer 248359 by nerdybill(6948)   on 2010-09-23 18:33:13 (Show Source): You can put this solution on YOUR website!Put the equation of a line into slope-intercept form. 3x + 2y = 10 . Starting with: 3x + 2y = 10 Subtract 3x from both sides: 2y = -3x + 10 Divide both sides by 2: y = (-3/2)x + 5 (this is what they're looking for) . slope-intercept form: y = mx + b where m is the slope b is the y-intercept
 Mixture_Word_Problems/346723: Hello theres one question on my alegebra that i just cannot figure it's: How many liters of water must be added to 30liters of a 20% alcohol solution to dilute it to a 15% solution?1 solutions Answer 247923 by nerdybill(6948)   on 2010-09-22 15:58:31 (Show Source): You can put this solution on YOUR website!How many liters of water must be added to 30liters of a 20% alcohol solution to dilute it to a 15% solution? . Let x = liters of water to add then "amt of alcohol at start" = "amt of alcohol at end" .20(30) = .15(30+x) 6 = 4.5+.15x 1.5 = .15x 1.5/.15 = x 10 liters = x
 Geometry_Word_Problems/346677: Angle A and angle B are supplementary angles. If the measure of angle B is 6 degrees greater twice the measure of angle A, find the measure of each angle.1 solutions Answer 247877 by nerdybill(6948)   on 2010-09-22 13:30:15 (Show Source): You can put this solution on YOUR website!Angle A and angle B are supplementary angles. If the measure of angle B is 6 degrees greater twice the measure of angle A, find the measure of each angle. . By definition of "supplementary angles" we have: A + B = 180 . Then, from: "angle B is 6 degrees greater twice the measure of angle A" we have B = 2A+6 . Substitute the above into: A + B = 180 A + 2A+6 = 180 3A+6 = 180 3A = 174 A = 58 degrees . Substitute above into the following to find B: A + B = 180 58 + B = 180 B = 122 degrees
 Systems-of-equations/346645: Write a system of two equations using x and y to represent the following problem. A chemist is mixing two solutions together. The chemist wants 100 gallons when complete. He is mixing a 24% solution with a 50% solution to get a 36% solution. How many gallons of each will he use? 1 solutions Answer 247850 by nerdybill(6948)   on 2010-09-22 11:09:36 (Show Source): You can put this solution on YOUR website!Write a system of two equations using x and y to represent the following problem. A chemist is mixing two solutions together. The chemist wants 100 gallons when complete. He is mixing a 24% solution with a 50% solution to get a 36% solution. How many gallons of each will he use? . Let x = amount of 24% solution and y = amount of 50% solution . From: "The chemist wants 100 gallons when complete." we get equation 1: x+y = 100 From: "He is mixing a 24% solution with a 50% solution to get a 36% solution." we get equation 2: .24x + .50y = .36(100) . Solve equation 1 for y: x+y = 100 y = 100-x . Substitute the above into equation 2: .24x + .50y = .36(100) .24x + .50(100-x) = .36(100) .24x + 50-.50x = 36 50-.26x = 36 -.26x = -14 x = 53.85 gallons (of 24% solution) . to find 50% solution substitute above into equation 1: x+y = 100 53.85+y = 100 y = 46.15 gallons
 Money_Word_Problems/346618: Part of \$18,000 is invested at 8% annual interest, and the rest is invested at 6%. After one year, the accounts paid \$1,220 in interest. How much was invested at the lower rate? (Give your answer correct to the nearest cent.) 1 solutions Answer 247819 by nerdybill(6948)   on 2010-09-22 10:17:27 (Show Source): You can put this solution on YOUR website!Part of \$18,000 is invested at 8% annual interest, and the rest is invested at 6%. After one year, the accounts paid \$1,220 in interest. How much was invested at the lower rate? (Give your answer correct to the nearest cent.) . Let x = amount invested at lower rate of 6% then 18000-x = amount invested at 8% . Our equation: .06x + .08(18000-x) = 1220 .06x + 1440 - .08x = 1220 1440 - .02x = 1220 -.02x = -220 x = \$11,000.00
 logarithm/346617: Simplify giving your answer as a fraction in lowest terms (i.e. cancel any common factors). -2log9(9^3)+2log9(9^5) could you give me a walkthrough of how to solve the probem cheers Peter1 solutions Answer 247817 by nerdybill(6948)   on 2010-09-22 10:11:12 (Show Source): You can put this solution on YOUR website!Starting with: reduces to:
 test/346325: Solve for x tx-ux=3t1 solutions Answer 247651 by nerdybill(6948)   on 2010-09-21 18:01:34 (Show Source): You can put this solution on YOUR website!Solve for x tx-ux=3t factoring the left: x(t-u) = 3t dividing both sides by (t-u): x = 3t/(t-u)