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# Recent problems solved by 'nerdybill'

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 Radicals/165609: 3 {sqrt 3}/ {sqrt 6}1 solutions Answer 122068 by nerdybill(7008)   on 2008-11-03 18:04:53 (Show Source): You can put this solution on YOUR website! 3 {sqrt 3}/ {sqrt 6} Factor the number inside the radical: 3 {sqrt 3}/ {sqrt 2*3} ReWriting it as: 3 {sqrt 3}/[{sqrt 2}{sqrt 3}] Canceling like-terms: 3/{sqrt 2} Multiplying numerator and denominator by {sqrt 2}: 3{sqrt 2}/2 Rewriting: (3/2){sqrt 2}
 Radicals/165610: 2 {sqrt x^3} + 5x{sqrt x} - 3{sqrt x^5}1 solutions Answer 122067 by nerdybill(7008)   on 2008-11-03 18:01:36 (Show Source): You can put this solution on YOUR website! 2 {sqrt x^3} + 5x{sqrt x} - 3{sqrt x^5} You can rewrite as: 2 {sqrt x*x*x} + 5x{sqrt x} - 3{sqrt x*x*x*x*x} Now, you can "pull out" pairs: 2x {sqrt x} + 5x{sqrt x} - 3x^2{sqrt x} Factor out the sqrt x: {sqrt x}[2x + 5x - 3x^2] Combine like-terms: {sqrt x}[7x - 3x^2] Pull out the 'x': x{sqrt x}[7-3x]
 Functions/165369: Suppose you are playing a word game with seven distinct letters. How many seven-letter words can there be?1 solutions Answer 121932 by nerdybill(7008)   on 2008-11-02 20:31:43 (Show Source): You can put this solution on YOUR website!When "order" is important we refer to it as a "permutation". When "order" is NOT important we refer to it as a "combination". . nPr = (n!)/(n-r)! . In our case: n = 7 r = 7 . nPr = (n!)/(n-r)! 7_Pr_7 = (7!)/(7-7)! 7_Pr_7 = (7!)/(0)! 7_Pr_7 = (7!)/1 7_Pr_7 = (7!) 7_Pr_7 = (1*2*3*4*5*7) 7_Pr_7 = 840
 logarithm/165416: This is not from a textbook, just from a worksheet my teacher made up. The question is : 4logx = 4 I think that you can move the first 4 to make the question logx^4=4 , but that is as far as I have gotten. Thank You For Your Help!1 solutions Answer 121910 by nerdybill(7008)   on 2008-11-02 19:34:23 (Show Source): You can put this solution on YOUR website!Remembering that: log(100) = 2 or 100 = 10^2 . Looking at your problem: 4logx = 4 logx = 1 x = 10^1 x = 10
 Probability-and-statistics/165380: If the police have 7 suspects, how many different ways can they select 5 for a lineup?1 solutions Answer 121907 by nerdybill(7008)   on 2008-11-02 19:32:00 (Show Source): You can put this solution on YOUR website! If the police have 7 suspects, how many different ways can they select 5 for a lineup? . Since it doesn't matter which order the suspects line up, it is a "combination" as opposed to a "permutation". . Combination: nCr = (n!)/[r!(n-r)!] . In our case: n = 7 r = 5 . nCr = (7!)/[5!(7-5)!] nCr = (7!)/[5!(2)!] nCr = (1*2*3*4*5*6*7)/[(1*2*3*4*5)(1*2)] Canceling like-terms: nCr = (6*7)/[(1*2)] nCr = (42)/(2) nCr = 21
 percentage/165404: I am not sure if I picked the right catagory but I am having a hard time with on algebra word problem. If the formula R = -0.037t + 50.1 can be used to predict the world record in the 400 - meter dash t years after 1925, for what years will the world records be 47.6 seconds or less? If you could help me with this I would SO appreciate it! Jen1 solutions Answer 121906 by nerdybill(7008)   on 2008-11-02 19:22:04 (Show Source): You can put this solution on YOUR website!You are given: R = -0.037t + 50.1 where R is the record t is years after 1925 . So, they want to know when the record will be 47.6 seconds or less... So, just "plug it in" and solve for 't': R = -0.037t + 50.1 47.6 = -0.037t + 50.1 47.6 + 0.037t = 50.1 0.037t = 2.5 t = 2.5/0.037 t = 67.568 years after 1925 . So, 1925 + 67.568 = 1992.568 . Conclusion: 1992 and AFTER the world record will be 47.6 seconds or less
 Mixture_Word_Problems/165409: How many pounds of lima beans that cost \$.90/lb must be mixed with 16 pounds of corn that costs \$.50/lb to make a mixture of vegetables that costs \$.65/lb?1 solutions Answer 121903 by nerdybill(7008)   on 2008-11-02 19:12:49 (Show Source): You can put this solution on YOUR website!. Let x = pounds of lima beans added then .90x + .50(16) = .65(16+x) .90x + 8 = 10.40 + .65x .90x = 2.40 + .65x .25x = 2.40 x = 9.6 pounds (of lima beans)
 test/165398: 114.) Area of a Triangle. Find the exact area of a triangle with a base of sqrt(30)meters and a height of sqrt (6) meters.1 solutions Answer 121892 by nerdybill(7008)   on 2008-11-02 18:10:11 (Show Source): You can put this solution on YOUR website!Area of a Triangle. Find the exact area of a triangle with a base of sqrt(30)meters and a height of sqrt (6) meters. . Since the area of any triangle is (1/2)bh where b is base h is height . Plugging in our numbers: (1/2)bh (1/2)(sqrt(30))(sqrt(6)) (1/2)(sqrt(30*6)) (1/2)(sqrt(6*30)) (1/2)(sqrt(2*2*3*3*5)) Pulling out pairs: (1/2)(2)(3)(sqrt(5)) 3(sqrt(5))
 Money_Word_Problems/165348: Hi, I can't seem to find a solution to this word problem: "A man invests a certain sum of money at 14% and twice that amount at 15%. If his total interest earnings are \$660 per year, how much has he invested at 14% and how much at 15%?" I don't even know where to begin. Word problems are one of my weakest topics. Thanks, Jane 1 solutions Answer 121883 by nerdybill(7008)   on 2008-11-02 16:17:45 (Show Source): You can put this solution on YOUR website!"A man invests a certain sum of money at 14% and twice that amount at 15%. If his total interest earnings are \$660 per year, how much has he invested at 14% and how much at 15%?" . Let x = amount invested at 14% then 2x = amount invested at 15% . .14x + .15(2x) = 660 .14x + .30x = 660 .44x = 660 x = 660/.44 x = \$1500 (amount invested at 14% . Amount invested at 15%: 2x = 2(1500) = \$3000 (amount invested at 15%)
 Functions/165333: can you help me i have to find the domain and do not understand the equation on how to do it. g(x)= (7x+4)/(x+4)1 solutions Answer 121876 by nerdybill(7008)   on 2008-11-02 15:27:05 (Show Source): You can put this solution on YOUR website!Domain is simply "the range" of values 'x' can take. . For your equation: g(x)= (7x+4)/(x+4) The ONLY values of x where it will be undefined is when the DENOMINATOR (x+4) is zero. So, set it to zero and solve for x: (x+4) = 0 x = -4 . So, the domain is ALL real numbers EXCEPT for -4.
 Miscellaneous_Word_Problems/165320: Two trains started fromt he same station at the same time and traveled in opposite directions. After traveling 10 hours, they were 1,400 miles apart. The rate of the fast train exceeded the rate if the slow train by 5 miles per hour. Find the rate of each train. Can you please help me solve this equation? Thank you.1 solutions Answer 121875 by nerdybill(7008)   on 2008-11-02 15:17:10 (Show Source): You can put this solution on YOUR website!Two trains started fromt he same station at the same time and traveled in opposite directions. After traveling 10 hours, they were 1,400 miles apart. The rate of the fast train exceeded the rate if the slow train by 5 miles per hour. Find the rate of each train. . Let x = speed of slow train then x+5 = speed of fast train . Using the "distance formula": d = rt where d is distance r is speed or rate t is time . 10x + 10(x+5) = 1400 10x + 10x + 50 = 1400 20x + 50 = 1400 20x = 1350 x = 67.5 mph (slow train) . Fast train: x+5 = 67.5+5 = 72.5 mph
 expressions/165325: Multiply: (4x + 1)(2x2 + 5x + 1) 1 solutions Answer 121874 by nerdybill(7008)   on 2008-11-02 15:11:02 (Show Source): You can put this solution on YOUR website!(4x + 1)(2x^2 + 5x + 1) Using the "distributive property" : (4x)(2x^2 + 5x + 1) + (1)(2x^2 + 5x + 1) Expanding: (8x^3 + 20x^2 + 4x) + (2x^2 + 5x + 1) 8x^3 + 20x^2 + 4x + 2x^2 + 5x + 1 8x^3 + 22x^2 + 9x + 1
 Miscellaneous_Word_Problems/165328: Professor Counts his midterms as 2/3 of the grade and his final as 1/3of the grade. If Wendy scored 48 on the midterm, What range of scores on the final exam would put Wendy’s average between 70-79 inclusive? Not from a book or ISBN# 1 solutions Answer 121870 by nerdybill(7008)   on 2008-11-02 14:49:05 (Show Source): You can put this solution on YOUR website!Let x = final grade . The inequality looks like this: 70 <= (2/3)(48) + (1/3)x <= 79 70 <= (2)(16) + x/3 <= 79 70 <= 32 + x/3 <= 79 . Looking at the left inequality first: 70 <= 32 + x/3 210 <= 96 + x 114 <= x . Looking at the right inequality: 32 + x/3 <= 79 96 + x <= 237 x <= 141 . Putting it all together: 114 <= x <= 141 This means Wendy has to score between 114 and 141 on her final exam.
 Angles/165301: Find an angle such that 3 times the complement of the angle is 50 degrees greater than the supplement of the angle.1 solutions Answer 121852 by nerdybill(7008)   on 2008-11-02 11:41:11 (Show Source): You can put this solution on YOUR website! Find an angle such that 3 times the complement of the angle is 50 degrees greater than the supplement of the angle. . Two things you need to know: If two angles are supplementary, the sum of the two angles = 180. If two angles are complementary, the sum of the two angles = 90. . Let x = the angle then 90-x = complement of angle 180-x = supplement of angle . 3(90-x) = (180-x) + 50 270-3x = 180-x+50 270-3x = 230-x 270 = 230+2x 40 = 2x 20 degrees = x
 Polynomials-and-rational-expressions/165295: This question is from textbook Alebra Structure and Method Book 1 What would be the answer to s=vt + 16tsquared; solve for v1 solutions Answer 121850 by nerdybill(7008)   on 2008-11-02 11:17:27 (Show Source): You can put this solution on YOUR website!s = vt + 16t^2 subtract vt from both sides: s - vt = 16t^2 subtract s from both sides: -vt = 16t^2 - s multiply both sides by -1: vt = s - 16t^2 finally divide both sides by t: v = s/t - 16t
 Equations/165296: How do you solve an eqation like this? 4x-5(3x+10)=1261 solutions Answer 121849 by nerdybill(7008)   on 2008-11-02 11:14:13 (Show Source): You can put this solution on YOUR website!4x-5(3x+10)=126 First, distribute the -5 to terms inside the parenthesis: 4x-15x-50 = 126 combine like-terms: -11x-50 = 126 add 50 to both sides: -11x = 176 finally, divide both sides by 11 x = -176/11 x = -16
 Rational-functions/165298: P(x)/(x-2)=2x^2+x-2+-5/(x-2). Find P(x). Please help me out, I have no idea what to do!!!1 solutions Answer 121848 by nerdybill(7008)   on 2008-11-02 11:01:25 (Show Source): You can put this solution on YOUR website!The problem gives you: P(x)/(x-2) = 2x^2+x-2+-5/(x-2) P(x)/(x-2) = 2x^2+x-2 + -5/(x-2) . If you multiply BOTH sides by (x-2), the (x-2) cancels from both sides leaving you with your answer: P(x) = (x-2)(2x^2+x-2) + -5 . At this point, you should "expand" the left term: P(x) = (2x^3+x^2-2x)-(4x^2+2x-4) + -5 P(x) = 2x^3+x^2-2x-4x^2-2x+4 + -5 P(x) = 2x^3-3x^2-4x+4 + -5 P(x) = 2x^3-3x^2-4x-1
 Money_Word_Problems/165280: Mr. Smith invested \$18,000 part at 8% and the rest at 10%. The annual income from the 10% investment is \$360 more than the annual income from the 8% investment. Find the amount invested at each rate.1 solutions Answer 121843 by nerdybill(7008)   on 2008-11-02 10:11:00 (Show Source): You can put this solution on YOUR website!Let x = amount invested at 8% then because "total invested was 18000" 18000-x = amount invested at 10% . .10(18000-x) = .08x + 360 1800 - .10x = .08x + 360 1800 = .18x + 360 1440 = .18x 1440/.18 = x \$8000 = x (amount invested at 8%) . Amount invested at 10%: 18000-x = 18000-8000 = \$10000 (amount invested at 10%)
 Linear_Equations_And_Systems_Word_Problems/165274: 1. what is the approximate weight of oil in a container 3 feet high and 9 inches in diameter? (oil weighs approximately 55 pounds per cubic foot). 2. find the area of a rectange which measures 12 feet, 3 inches by 3 feet, 9 inches. The correct answer expressed in square feet is? 3.the diameter of a circle is 6 feet, 3 inches. what is the circumference of the circle? NOTE: to convert decimal fractions to inches in this problem, multiply by 12.1 solutions Answer 121842 by nerdybill(7008)   on 2008-11-02 10:05:24 (Show Source): You can put this solution on YOUR website!1. what is the approximate weight of oil in a container 3 feet high and 9 inches in diameter? (oil weighs approximately 55 pounds per cubic foot). volume of container = (pi)r^2 * height radius = 1/3(diameter) = 4.5 inches Convert that into feet: 4.5 / 12 = 0.375 feet . volume of container = (pi)r^2 * height volume of container = (3.14)(0.375)^2 * 3 = 1.3246875 cubic feet . "volume" * 55 = 1.3246875 * 55 = 72.86 pounds . 2. find the area of a rectange which measures 12 feet, 3 inches by 3 feet, 9 inches. The correct answer expressed in square feet is? . convert 12 feet 3 inches to feet: 12 + 3/12 = 12 + 1/4 = 48/4 + 1/4 = 49/4 feet . convert 3 feet, 9 inches: 3 + 9/12 = 3 + 3/4 = 12/4 + 3/4 = 15/4 . Area then is: (49/4)(15/4) = 735/16 = 45.94 square feet . 3.the diameter of a circle is 6 feet, 3 inches. what is the circumference of the circle? NOTE: to convert decimal fractions to inches in this problem, multiply by 12. Circumference = (pi)d where pi is 3.14 d is diameter . Convert 6 feet, 3 inches to feet: 6 + 3/12 = 6 + 1/4 = 24/4 + 1/4 = 25/4 feet . Circumference = (pi)d = (3.14)(25/4) = 78.5/4 = 19.625 feet or in inches: 19.625 * 12 = 235.5 inches
 Rectangles/165223: Find the perimeter and the area of the shaded region use 3.14 for pie. A retangle shaded with a half circle on one end. The width is 25 ft. the height is 20 ft. I have the answers but I need to know how to work the problem. Answer: Perimeter = 101.4 ft Area = 343 ft2 Can someone please help by showing me how to work the problem?1 solutions Answer 121835 by nerdybill(7008)   on 2008-11-02 08:54:49 (Show Source): You can put this solution on YOUR website!area of rectangle: width*height 25*20 = 500 square feet . area of half circle: area for a full circle = (pi)r^2 half circle would be half of the above: (1/2)(pi)r^2 plugging in our values: (1/2)(3.14)10^2 (1/2)(3.14)100 (3.14)50 157 square feet . Area of shaded region is: "area of rectangle" - "area of half circle" 500 - 157 = 343 square feet . Perimeter: Edge along the rectangle: height + 2(width) 20 + 2(25) 20 + 50 70 feet . Edge along the half-circle: "circumference of a full circle" is (pi)(d) we only want half of that so: (1/2)(pi)(d) (1/2)(3.14)(20) (3.14)(10) 31.4 feet . Perimeter then is: 70 + 31.4 = 101.4 feet
 Geometry_Word_Problems/165257: The width of a rectangle is 3 feet less than its length. If the perimeter is 22 feet, what is the width? (Pre-Algebra) By Charles P. Mckeague, fifth addition. 1 solutions Answer 121815 by nerdybill(7008)   on 2008-11-01 22:20:15 (Show Source): You can put this solution on YOUR website!Let x = length then from "width of a rectangle is 3 feet less than its length" we have x-3 = width . Perimeter = 2(length+width) 22 = 2(x + x-3) 22 = 2(2x-3) 22 = 4x-6 28 = 4x 7 feet = x (length) . width: x-3 = 7-3 = 4 feet (width)
 Human-and-algebraic-language/165256: One number is four more than a second number. Two times the first number is 12 more than four times the second number.1 solutions Answer 121814 by nerdybill(7008)   on 2008-11-01 22:15:09 (Show Source): You can put this solution on YOUR website! One number is four more than a second number. Two times the first number is 12 more than four times the second number. . Let x = second number then from "One number is four more than a second number" x+4 = first number . From "Two times the first number is 12 more than four times the second number" we get our equation: 2(x+4) = 12 + 4x 2x+8 = 12 + 4x 8 = 12 + 2x -4 = 2x -2 = x (second number) . First number: x+4 = -2+4 = 2 (first number)
 test/165186: 7.)Solve by completeing the square. 2x^2+x-6=01 solutions Answer 121809 by nerdybill(7008)   on 2008-11-01 21:29:50 (Show Source): You can put this solution on YOUR website!2x^2+x-6=0 Group terms first: (2x^2+x)-6=0 (2x^2+x) = 6 2(x^2 + (1/2)x) = 6 (x^2 + (1/2)x) = 3 (x^2 + (1/2)x + 1/16) - 1/16 = 3 (x^2 + (1/2)x + 1/16) = 3 + 1/16 (x^2 + (1/2)x + 1/16) = 48/16 + 1/16 (x + 1/4)^2 = 49/16 Taking the square root of both sides: x + 1/4 = (+-)7/4 x = -1/4 + (+-)7/4 . Two possible solutions then are: x = -1/4 + 7/4 = 6/4 = 1.5 or x = -1/4 - 7/4 = -8/4 = -2
logarithm/165215: This question is from textbook
log(base 3)(x+8) + log(base 3)(x) = 2
I'm not for sure if I am sitting this up right.
So far I have:
log(base 3)( x+8/x ) = 2 Should I multiply or divide since its a +?
Any help appreciated.

1 solutions

Answer 121773 by nerdybill(7008)   on 2008-11-01 15:41:07 (Show Source):
You can put this solution on YOUR website!
For log rules see:
http://www.purplemath.com/modules/logrules.htm
.
log(base 3)(x+8) + log(base 3)(x) = 2
.
Applying log rule: logb(mn) = logb(m) + logb(n)
log(base 3)(x^2+8x) = 2
.
Applying log rule: logb(m) = n =>> m = b^n
x^2+8x = 3^2
.
x^2+8x = 8
x^2+8x-8 = 0
.
Since we can't factor, use the quadratic equation. Doing so will yield:
x = {0.899, -8.899}
.
 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=96 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 0.898979485566356, -8.89897948556636. Here's your graph:
= 0

 test/165194: 22.) Find he exact solution. The height in feet for a ball thrown upward at 48 feet per second is given by s(t)= - 16r^2 + 48t. Where t is the time in seconds after the ball is tossed. What is the maximum height that the ball will reach?1 solutions Answer 121770 by nerdybill(7008)   on 2008-11-01 15:30:55 (Show Source): You can put this solution on YOUR website!s(t)= - 16t^2 + 48t . The idea is that the equation describes a parabola. If the coefficient 'a' is negative, the parabola opens downward. Thus the vertex will give you the "maximum". . The vertex form of a parabola is: y= a(x-h)^2+k . The idea is to convert the given equation into the above form. s(t)= - 16t^2 + 48t s(t)= -16(t^2 - 4t) Completing the square, we have: s(t)= -16(t^2 - 4t + 4) + 64 s(t)= -16(t-2)^2 + 64 . We now "see" that the vertex is at: (h,k) = (2, 64) . Which says, that at 2 seconds, the ball will reach the maximum height of 64 feet.
 Graphs/165160: how do you graph y=51 solutions Answer 121745 by nerdybill(7008)   on 2008-11-01 10:29:43 (Show Source): You can put this solution on YOUR website!Difficult to explain in words, but, here goes... . Given that you drew two axes -- where the vertical axis is the y-axis and the horizontal axis is the x-axis then: . y=5 is represented by a HORIZONTAL line (that is parallel to the x-axis) AND crosses the y-axis at +5. .
Travel_Word_Problems/165121: 1. A rectangular garden has dimensions of 18 feet by 13 feet. A gravel path of uniform width is to be built around the garden. How wide can the path be if there is enough gravel for 516 square feet?

1 solutions

Answer 121728 by nerdybill(7008)   on 2008-11-01 05:51:42 (Show Source):
You can put this solution on YOUR website!
Draw a diagram of the problem -- it'll help you see how to solve it.
.
If you do, the "inner rectangle" represents the garden while the "outer rectangle" (bordered by the outside edge of the gravel path).
.
"outer rectangle" - "inner rectangle" = "area of gravel path"
.
Let x = width of gravel path
.
"outer rectangle" then is:
(2x+18)(2x+13)
= 4x^2 + 26x + 36x + 234
= 4x^2 + 62x + 234
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"Inner rectangle" is:
18 * 13 = 234
.
"outer rectangle" - "inner rectangle" = "area of gravel path"
we have:
(4x^2 + 62x + 234) - 234 = 516
4x^2 + 62x = 516
4x^2 + 62x - 516 = 0
2x^2 + 31x - 258 = 0
Since, it is difficult to factor, use the quadratic equation. It will yield:
x = {6, -21.5}
.
Since the negative solution does not make sense, throw it out leaving:
x = 6 feet (width of gravel path)
.