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# Recent problems solved by 'algebrahouse.com'

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 �t�e�s�t/745019: The sum of two numbers is 72. One number is 12 less than the other. Find both numbers. 1 solutions Answer 453667 by algebrahouse.com(1079)   on 2013-05-04 23:20:03 (Show Source): You can put this solution on YOUR website!x = one number x - 12 = other number {one number is 12 less than the other} x + x - 12 = 72 {sum of the two numbers is 72} 2x - 12 = 72 {combined like terms} 2x = 84 {added 12 to each side} x = 42 {divided each side by 2} x - 12 = 30 {substituted 30, in for x, into x - 12} 42 and 30 are the two numbers www.algebrahouse.com
 Word_Problems_With_Coins/745011: There are 52 coins in a purse. Some of them are quarters, and some are dimes. The total value of all coins is \$7.45. how many were quarters and how many were dimes? 1 solutions Answer 453664 by algebrahouse.com(1079)   on 2013-05-04 23:00:45 (Show Source): You can put this solution on YOUR website!There are 52 coins in a purse. Some of them are quarters, and some are dimes. The total value of all coins is \$7.45. how many were quarters and how many were dimes? x = number of quarters 52 - x = number of dimes {there are 52 coins total} 0.25x + 0.1(52 - x) = 7.45 {number of coins times value of coin equals total value} 0.25x + 5.2 - 0.1x = 7.45 {used distributive property} 0.15x + 5.2 = 7.45 {combined like terms} 0.15x = 2.25 {subtracted 5.2 from each side} x = 15 {divided each side by 0.15} 52 - x = 37 {substituted 15, in for x, into 52 - x} 15 quarters and 37 dimes in the purse www.algebrahouse.com
 Equations/745010: 8x-5=35 1 solutions Answer 453662 by algebrahouse.com(1079)   on 2013-05-04 22:53:59 (Show Source): You can put this solution on YOUR website!8x - 5 = 35 8x = 40 {added 5 to each side} x = 5 {divided each side by 8} www.algebrahouse.com
 Human-and-algebraic-language/745008: A rock falls from a tower that is 127.4 m high. As it is falling, its height is given by the formula h(t)=127.4-4.9t^2. How many seconds will it take for the rock to hit the ground (h=0)?1 solutions Answer 453660 by algebrahouse.com(1079)   on 2013-05-04 22:50:53 (Show Source): You can put this solution on YOUR website!When it hits the ground, the height will be zero. h(t) = 127.4 - 4.9t² 0 = 127.4 - 4.9t² {substituted 0 in for the height, h(t)} 4.9t² = 127.4 {added 4.9t² to each side} t² = 26 {divided each side by 4.9} t ≈ 5.1 {took the square root of each side and rounded} In approximately 5.1 seconds, it will hit the ground. www.algebrahouse.com
 Polynomials-and-rational-expressions/744987: Which of the following is equivalent to x^4.yz^3/xyz^6 and explain how you got the answer. A. x^5y^2z^9 B. x^3z^3 C. x^4y/z^2 D. x^3/z^31 solutions Answer 453658 by algebrahouse.com(1079)   on 2013-05-04 22:47:23 (Show Source): You can put this solution on YOUR website!x^4yz^3 ------- xyz^6 x³ -- {when dividing same variables with exponents, think of subtract the exponents or cancel} z³ www.algebrahouse.com
 Polynomials-and-rational-expressions/745007: how do you solve the equation x+x+6=14? 1 solutions Answer 453657 by algebrahouse.com(1079)   on 2013-05-04 22:44:00 (Show Source): You can put this solution on YOUR website!x + x + 6 = 14 2x + 6 = 14 {combined like terms} 2x = 8 {subtracted 6 form each side} x = 4 {divided each side by 2} www.algebrahouse.com
 Quadratic_Equations/744996: The length of a rectangle is 1cm. more than twice its height. If the area of the rectangle is 351 sq cm, what is the perimeter of the rectangle? I already tried to solve using these L=2h+1 I got H=-1/3 P=2l+2h I don't know what to do from there...?1 solutions Answer 453655 by algebrahouse.com(1079)   on 2013-05-04 22:23:38 (Show Source): You can put this solution on YOUR website!x = height 2x + 1 = length {length is 1 more than twice its height} Area of a rectangle is length x height x(2x + 1) = 351 {multiplied length x height and set equal to area, 351} 2x² + x = 351 2x² + x - 351 = 0 2x² - 26x + 27x - 351 = 0 {split x into -26x and 27x} 2x(x - 13) + 27(x - 13) = 0 {factored 2x out of 1st two terms and 27 out of last two terms - factoring by grouping} (2x + 27)(x - 13) = 0 {factored (x - 13) out of the two terms} 2x + 27 = 0 or x - 13 = 0 {set each factor equal to 0} 2x = -27 or x = 13 {subtracted 27 in 1st and added 13 in 2nd} x = -13.5 or x = 13 {solved each equation for x} x = 13 {height of a rectangle cannot be negative} 2x + 1 = 27 {substituted 13, in for x, into 2x + 1} height is 13 cm and length is 27 cm Perimeter of a rectangle is 2(height) + 2(length) P = 2(13) + 2(27) {substituted 13 for height and 27 for length, into perimeter formula} = 26 + 54 {multiplied} = 80 {added} Perimeter of rectangle is 81 cm www.algebrahouse.com
 Exponents/744995: please help me solve (-0.4)^31 solutions Answer 453651 by algebrahouse.com(1079)   on 2013-05-04 22:12:04 (Show Source): You can put this solution on YOUR website!(-0.4)³ = (-0.4)(-0.4)(-0.4) {took (-0.4) to the third power} = -0.064 {multiplied} www.algebrahouse.com
 Numbers_Word_Problems/744978: find three consecutive odd intergers so that 3 times their sum is 5 more than 8 times the middle one1 solutions Answer 453648 by algebrahouse.com(1079)   on 2013-05-04 21:56:58 (Show Source): You can put this solution on YOUR website!Find three consecutive odd integers, so that 3 times their sum is 5 more than 8 times the middle one. x = 1st odd integer x + 2 = 2nd odd integer x + 4 = 3rd odd integer {odd and also even integers increase by 2} 3(x + x + 2 + x + 4) = 8(x + 2) + 5 {sum is equal to 5 more than 8 times the middle one} 3(3x + 6) = 8x + 16 + 5 {combined like terms on left, used distributive property on right} 9x + 18 = 8x + 21 {combined like terms} x = 3 {subtracted 8x and subtracted 18 from each side} x + 2 = 5 {substituted 3, in for x, into x + 2} x + 4 = 7 {substituted 3, in for x, into x + 4} 3,5, and 7 are the three consecutive odd integers www.algebrahouse.com
 Polynomials-and-rational-expressions/744977: determine the domain of f(x)=x^2+2x+11 solutions Answer 453646 by algebrahouse.com(1079)   on 2013-05-04 21:52:13 (Show Source): You can put this solution on YOUR website!Domain is the set of x-values {the input} The graph of the function f(x) = x² + 2x + 1 is a parabola {u-shaped graph} opening upward The domain is the set of all real numbers. www.algebrahouse.com
 Rational-functions/744983: what is the diagonal, in feet, of a square with each side measuring 6 radical 2 feet1 solutions Answer 453643 by algebrahouse.com(1079)   on 2013-05-04 21:48:15 (Show Source): You can put this solution on YOUR website!A right triangle is formed with two legs of 6√2 ft and the diagonal as the hypotenuse. a² + b² = c² {the Pythagorean Theorem} (6√2)² + (6√2)² = c² {substituted 6√2 in for the legs, a and b} 36(2) + 36(2) = c² {evaluated the exponents} 72 + 72 = c² {multiplied} 144 = c² {added} c = 12 {took the square root of each side} www.algebrahouse.com
 Age_Word_Problems/726644: George is 5 years older than Mary. The sum of their ages is 43 years. How old are George and Mary?1 solutions Answer 444701 by algebrahouse.com(1079)   on 2013-03-15 22:18:01 (Show Source): You can put this solution on YOUR website!x = Mary's age x + 5 = George's age x + x + 5 = 43 {sum of ages is 43} 2x + 5 = 43 {combined like terms} 2x = 38 {subtracted 5 from each side} x = 19 {divided each side by 2} x + 5 = 24 {substituted 19, in for x, into x + 5} Mary is 19 George is 24 www.algebrahouse.com
 Complex_Numbers/726643: Please help me understand: "Express in terms of i" (-)sqrt of (-98). 1 solutions Answer 444700 by algebrahouse.com(1079)   on 2013-03-15 22:15:31 (Show Source): You can put this solution on YOUR website!-√-98 = -√-1 √49 √2 {factored -98 into -1, 49, and 2} = -7i√2 {when working with complex numbers, √-1 is represented by i} www.algebrahouse.com
 Rectangles/724034: A rectangular lot is four times as long as it is wide. It's perimeter is 100m. Find its length.1 solutions Answer 443542 by algebrahouse.com(1079)   on 2013-03-09 20:14:51 (Show Source): You can put this solution on YOUR website!x = width 4x = length {it is four times as long as it is wide} Perimeter of a rectangle = 2(width) + 2(length) 2(x) + 2(4x) = 100 {substituted into perimeter formula} 2x + 8x = 100 {multiplied} 10x = 100 {combined like terms} x = 10 {divided each side by 10} 4x = 40 {substituted 10, in for x, into 4x} length = 40 m www.algebrahouse.com
 test/718516: Maria bought seven boxes and ate half of them by the end of the week later half if all her boxes were destroyed in a fire. There are now only 22 boxes left.with how many did she start? Show your work.1 solutions Answer 440921 by algebrahouse.com(1079)   on 2013-02-24 22:41:30 (Show Source): You can put this solution on YOUR website!x = starting number of boxes x + 7 ------ = 22 {half of all boxes is 22} 2 x + 7 = 44 {multiplied each side by 2} x = 37 {subtracted 7 from each side} She started with 37 boxes www.algebrahouse.com
 test/718515: Maria bought seven boxes. A week later half if all her boxes were destroyed in a fire. There are now only 22a boxes left. With how many did she start? Show your work 1 solutions Answer 440918 by algebrahouse.com(1079)   on 2013-02-24 22:38:46 (Show Source): You can put this solution on YOUR website!x = starting number of boxes x + 7 ------ = 22 {half of all boxes is 22} 2 x + 7 = 44 {multiplied each side by 2} x = 37 {subtracted 7 from each side} She started with 37 boxes www.algebrahouse.com
 Square-cubic-other-roots/718405: what is the square root of 49x^3? 1 solutions Answer 440895 by algebrahouse.com(1079)   on 2013-02-24 20:30:51 (Show Source): You can put this solution on YOUR website!√(49x)³ = √49x² √x {grouped the perfect squares under the first square root sign} = 7x √x {evaluated the square root of 49x²} www.algebrahouse.com
 Polynomials-and-rational-expressions/718440: Simplify (7B)^-21 solutions Answer 440894 by algebrahouse.com(1079)   on 2013-02-24 20:28:07 (Show Source): You can put this solution on YOUR website!(7B)^-2 1 ----- {to make a negative exponent positive, move the term up or down, opposite of where it currently is} (7B)² 1 ----- {took everything in parentheses to the 2nd power} 49B² www.algebrahouse.com
 Equations/718420: 4(2x+3)+2(x+5)=7 show work please!1 solutions Answer 440892 by algebrahouse.com(1079)   on 2013-02-24 20:25:32 (Show Source): You can put this solution on YOUR website!4(2x + 3) + 2(x + 5) = 7 8x + 12 + 2x + 10 = 7 {used distributive property} 10x + 22 = 7 {combined like terms} 10x = -15 {subtracted 22 from each side} x = -15/10 {divided each side by 10} x = -3/2 {reduced} www.algebrahouse.com
 Linear-systems/718421: I need help solving 3c+2d=2 D=4 By substitution1 solutions Answer 440891 by algebrahouse.com(1079)   on 2013-02-24 20:23:58 (Show Source): You can put this solution on YOUR website!3c + 2d = 2 d = 4 3c + 2(4) = 2 {substituted 4 for d} 3c + 8 = 2 {multiplied} 3c = -6 {subtracted 8 from each side} c = -2 {divided each side by 3} c = -2 and d = 4 www.algebrahouse.com
 Numbers_Word_Problems/718425: one more than a number times one less than a number is 24. Find the number Please !1 solutions Answer 440889 by algebrahouse.com(1079)   on 2013-02-24 20:21:19 (Show Source): You can put this solution on YOUR website!x = the number (x + 1)(x - 1) = 24 {one more than a number times one less than a number is 24} x² - 1 = 25 {used foil method} x² = 25 {added 1 to each side} x = 5 or -5 {took the square root of each side} the number could be 5 or -5 www.algebrahouse.com
 pythagorean/718430: hypotenuse c =17, leg a= 8 what is leg b1 solutions Answer 440888 by algebrahouse.com(1079)   on 2013-02-24 20:19:01 (Show Source): You can put this solution on YOUR website!Pythagorean Theorem a² + b² = c² {c is the hypotenuse, a and b are the legs} 8² + b² = 17² {substituted given values into Pythagorean Theorem} 64 + b² = 289 {evaluated exponents} b² = 225 {subtracted 64 from each side} b = 15 {took the square root of each side} www.algebrahouse.com
 Polynomials-and-rational-expressions/718433: mulitply and write the answer without exponents. (2x10^4)x(3x10^6)1 solutions Answer 440887 by algebrahouse.com(1079)   on 2013-02-24 20:16:29 (Show Source): You can put this solution on YOUR website!(2 x 10^4) x (3 x 10^6) = (2 x 3) x (10^4 x 10^6) {grouped terms together} = 6 x 10^10 {multiplied and added exponents on same base, when multiplying} = 60,000,000,000 {moved decimal point to the right 10 places} www.algebrahouse.com
 Linear_Equations_And_Systems_Word_Problems/718042: The weight of two pieces of baggage is 38 kg. If the weight of one is 7 kg less than twice the weight of the other. What is the weight of each piece of baggage?1 solutions Answer 440695 by algebrahouse.com(1079)   on 2013-02-23 22:57:28 (Show Source): You can put this solution on YOUR website!x = one weight 2x - 7 = other weight {one is 7 less than twice the other} x + 2x - 7 = 38 {the combined weight of the two is 38} 3x - 7 = 38 {combined like terms} 3x = 45 {added 7 to each side} x = 15 {divided each side by 3} 2x - 7 = 23 {substituted 23, in for x, into 2x - 7} 15 kg and 23 kg are the weights of each piece www.algebrahouse.com
 Numbers_Word_Problems/718037: The difference between 36 and 24 is twice the square root of a number. What is the number?1 solutions Answer 440694 by algebrahouse.com(1079)   on 2013-02-23 22:49:14 (Show Source): You can put this solution on YOUR website!Difference between 36 and 24 is 12 12 is twice 6 6 is the square root of 36 36 is the number www.algebrahouse.com
 Age_Word_Problems/718036: Tom's age is twice as that of Jerry's. If N represents Jerry's age. What is Tom's age?1 solutions Answer 440693 by algebrahouse.com(1079)   on 2013-02-23 22:46:03 (Show Source): You can put this solution on YOUR website!N is Jerry's age 2N = Tom's age {Tom is equal to two times Jerry's age} www.algebrahouse.com
 test/718033: How do i solve 4a squared -12a-16??????1 solutions Answer 440690 by algebrahouse.com(1079)   on 2013-02-23 22:36:43 (Show Source): You can put this solution on YOUR website!4a² - 12a - 16 = 0 {I assume you meant equal to 0} 4(a² - 3a - 4) = 0 {factored 4 out} 4(a - 4)(a + 1) = 0 {factored into two binomials} a - 4 = 0 or a + 1 = 0 {set each factor equal to 0, excluding the 4} a = 4 or a = -1 {solved each equation for a} www.algebrahouse.com
 Geometry_Word_Problems/718027: Find the dimension of a rectangle. The area is 238cm^ and the perimeter is 62cm?1 solutions Answer 440688 by algebrahouse.com(1079)   on 2013-02-23 22:24:42 (Show Source): You can put this solution on YOUR website!2x + 2y = 62 {perimeter is 2 times width + 2 times length} xy = 238 {area is width times length} x + y = 31 {divided each side of top equation by 2} x = -y + 31 {subtracted y from each side} y(-y + 31) = 238 {substituted -y + 31, in for x, into x(y) = 238} -y² + 31y = 238 {used distributive property} y² - 31y + 238 = 0 {added y² and subtracted 31y from each side} (y - 17)(y - 14) = 0 {factored into two binomials} y - 17 = 0 or y - 14 = 0 {set each factor equal to 0} y = 17 or y = 14 {solved each equation for x} width is 14 cm and length is 17 cm www.algebrahouse.com
 Rational-functions/718024: x-7 divided by x+2=1/41 solutions Answer 440686 by algebrahouse.com(1079)   on 2013-02-23 22:13:35 (Show Source): You can put this solution on YOUR website!x - 7 ------ = 1/4 x + 2 4(x - 7) = 1(x + 2) {cross-multiplied} 4x - 28 = x + 2 {used distributive property} 3x = 30 {subtracted x and added 28 to each side} x = 10 {divided each side by 3} www.algebrahouse.com
 Linear-equations/718005: Parallel to x - y = 4 and passing through (-3,2) Express in standard form1 solutions Answer 440685 by algebrahouse.com(1079)   on 2013-02-23 22:09:10 (Show Source): You can put this solution on YOUR website!Parallel lines have equal slopes Slope-intercept form is y = mx + b m is the slope b is the y-intercept x - y = 4 -y = -x + 4 {subtracted x from each side} y = x - 4 {divided each side by -1} slope is 1 point is (-3,2) slope is 1 y - y1 = m(x - x1) {point-slope form} y - 2 = 1[x - (-3)] {substituted into point-slope form} y - 2 = x + 3 {simplified} -x + y = 5 {put into standard form} www.algebrahouse.com
 Travel_Word_Problems/718022: A bus travels 216 km in 3hours find its average speed in m/s1 solutions Answer 440684 by algebrahouse.com(1079)   on 2013-02-23 22:04:50 (Show Source): You can put this solution on YOUR website!216 km is 216,000 meters {1 km is 1,000 m} 3 hrs is 10,800 s {1 hour is 3,600 seconds} 216,000 -------- {divided meters by seconds} 10,800 = 20 m/s {divided} www.algebrahouse.com