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# Recent problems solved by 'nerdybill'

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 Quadratic_Equations/343956: Solve: -3x + 14 - x < 56 + 3x Gracias!1 solutions Answer 246065 by nerdybill(6948)   on 2010-09-16 10:49:33 (Show Source): You can put this solution on YOUR website!-3x + 14 - x < 56 + 3x -4x + 14 < 56 + 3x 14 < 56 + 7x -42 < 7x -6 < x x > -6
 Triangles/343290: I do not know how to set up this problem. Can anyone help me? Two frames are needed with the same outside perimeter: one frame in the shape of a square and one in the shape of an equilateral triangle. Each side of the triangle is 6 centimeters longer than each side of the square. Find the dimensions of each frame.1 solutions Answer 245620 by nerdybill(6948)   on 2010-09-14 22:31:38 (Show Source): You can put this solution on YOUR website!Two frames are needed with the same outside perimeter: one frame in the shape of a square and one in the shape of an equilateral triangle. Each side of the triangle is 6 centimeters longer than each side of the square. Find the dimensions of each frame. . Let x = length of one side of the square (in cm) then x+6 = length of one side of the triangle . Perimeter of square is 4x perimeter of triangle is 3(x+6) . So: 4x = 3(x+6) 4x = 3x+18 x = 18 centimeters and Length of one side of triangle: x+6 = 18+6 = 24 centimeters . Dimensions of square: 18 by 18 by 18 by 18 (centimeters) Dimensions of triangle: 24 by 24 by 24 (centimeters)
 Human-and-algebraic-language/342861: Hotels collect 4 percent sale tax on all sales. If the total sales including tax are 1058.30 find the portion that is the tax.1 solutions Answer 245420 by nerdybill(6948)   on 2010-09-14 11:31:12 (Show Source): You can put this solution on YOUR website!Hotels collect 4 percent sale tax on all sales. If the total sales including tax are 1058.30 find the portion that is the tax. . Let x = hotel bill then .04x = tax portion . x + .04x = 1058.30 x(1 + .04) = 1058.30 x(1.04) = 1058.30 x = 1017.60 . tax portion: .04x = .04(1017.60) = \$40.70
 Rectangles/342879: if a rectangle has width of 5 and diagonal with lenght of 13, what is the area of the rectangle?1 solutions Answer 245418 by nerdybill(6948)   on 2010-09-14 11:28:00 (Show Source): You can put this solution on YOUR website!if a rectangle has width of 5 and diagonal with lenght of 13, what is the area of the rectangle? . find the length by applying Pythagorean theorem: Let x = length then x^2 + 5^2 = 13^2 x^2 = 13^2 - 5^2 x^2 = 169 - 25 x^2 = 144 x = 12 . area = 5*12 = 60 square units
 Trigonometry-basics/341312: let's assume a right triangle ABC. A is the angle theta but we don't know the degree. So a=5 that is the opposite side of theta, b=adjacent side that is unknown, and c=29 representing the hypothenus. Determine the value of B. Round to two decimal places.1 solutions Answer 244433 by nerdybill(6948)   on 2010-09-10 09:38:51 (Show Source): You can put this solution on YOUR website!let's assume a right triangle ABC. A is the angle theta but we don't know the degree. So a=5 that is the opposite side of theta, b=adjacent side that is unknown, and c=29 representing the hypothenus. Determine the value of B. Round to two decimal places. . Since you have a "right triangle", you can apply Pythagorean theorem: a^2 + b^2 = c^2 5^2 + b^2 = 29^2 b^2 = 29^2 - 5^2 b^2 = 841 - 25 b^2 = 816 b = 28.57
 Exponential-and-logarithmic-functions/341314: Hello I need a little help with my homework. I started trying to work it out but I am not sure if it is the correct solution. Please help! Question: Population growth. The exponential growth rate of the population of United Arab Emirates is 4.4% per year (one of the highest in the world). What is the doubling time? Sources: Based on data from U.S. Census Bureau; International Data Base 2007 My Answer: I changed 4.4% to .044^2. My result was .001936 or round to 0.002%. Is this correct? Should I be using the P(t) = P0e^kt? If so how should I go by doing so? Thanks for your help in advance!1 solutions Answer 244432 by nerdybill(6948)   on 2010-09-10 09:34:29 (Show Source): You can put this solution on YOUR website!Population growth. The exponential growth rate of the population of United Arab Emirates is 4.4% per year (one of the highest in the world). What is the doubling time? Sources: Based on data from U.S. Census Bureau; International Data Base 2007 My Answer: I changed 4.4% to .044^2. My result was .001936 or round to 0.002%. Is this correct? Should I be using the P(t) = P0e^kt? If so how should I go by doing so? . Yes, you should be using P(t) = P0e^kt . From the problem you are given: k = 4.4% = .044 . Let x = Po (initial population) then 2x = population doubles . So, instead of: P(t) = P0e^kt We now have: 2x = xe^(.044t) . Now, we solve for t: 2x = xe^(.044t) dividing both sides by x: 2 = e^(.044t) take ln of both sides: ln(2) = .044t ln(2)/.044 = t 15.75 years = t (doubling time)
 Systems-of-equations/341349: Trying to help my daughter solve the following..... 7.5 (a - 3) and it says to use the distributive property (?) and expand like terms when possible. I havent done math in forEVER..'dist.prop' and 'like terms' are mysteries to me!1 solutions Answer 244426 by nerdybill(6948)   on 2010-09-10 09:26:59 (Show Source): You can put this solution on YOUR website!Given: 7.5 (a - 3) This says "7.5 times the quantity a minus 3". . To "distribute" the 7.5, we multiply each term inside the parenthesis by 7.5. . The distributive property simply states that given expression is the same as the following: 7.5 (a - 3) = 7.5(a) - 7.5(3) = 7.5a - 22.5
 test/341139: if sarah can pain a fence in 4 hours and tim can paint the same fence in 8 hours how much would it take them to paint the fence toguether1 solutions Answer 244253 by nerdybill(6948)   on 2010-09-09 18:43:56 (Show Source): You can put this solution on YOUR website!if sarah can pain a fence in 4 hours and tim can paint the same fence in 8 hours how much would it take them to paint the fence toguether . Let x = time it takes for both to paint fence together then x(1/4 + 1/8) = 1 multiplying both sides by 8: x(2 + 1) = 8 x(3) = 8 x = 8/3 hours or x = 2 and 2/3 hours or x = 2 hours and 40 minutes
 Geometry_Word_Problems/341054: The base of a triangle is 2 in. longer than the height. The area is 12in^2 . Find the height and the base. How would I write this equation?1 solutions Answer 244223 by nerdybill(6948)   on 2010-09-09 16:42:46 (Show Source): You can put this solution on YOUR website!The base of a triangle is 2 in. longer than the height. The area is 12in^2 . Find the height and the base. . area for any triangle is: (1/2)bh where b is base h is height . Let h = height then because "The base of a triangle is 2 in" we have h+2 = base . The formula is: (1/2)(h+2)h = 12 . Solving, we start by multiplying both sides by 2 to get: (h+2)h = 24 h^2 + 2h = 24 h^2 + 2h - 24 = 0 (h+6)(h-4) = 0 . h = {-6, 4} we can toss out the negative value leaving: h = 4 inches (height) . Base: h+2 = 4+2 = 6 inches
 Numbers_Word_Problems/341040: one less than twice the square of a number1 solutions Answer 244219 by nerdybill(6948)   on 2010-09-09 16:26:27 (Show Source): You can put this solution on YOUR website! Let x = the number then "one less than twice the square of a number" is expressed as:
 Exponential-and-logarithmic-functions/341031: 3(5-7)^4 what is the best way the simplify this problem1 solutions Answer 244216 by nerdybill(6948)   on 2010-09-09 16:23:38 (Show Source): You can put this solution on YOUR website! Simplify expression inside parenthesis:
 Equations/340980: Factor Completely. 5x^2y + 5xy - 60y Please help!1 solutions Answer 244203 by nerdybill(6948)   on 2010-09-09 14:20:54 (Show Source): You can put this solution on YOUR website!5x^2y + 5xy - 60y Factor out what is common among all three terms: 5y(x^2 + x - 12) Next, factor the expression inside the parenthesis: 5(x+4)(x-3)
 Travel_Word_Problems/340963: Your word problem on the first page was changed from "A freight train leaves the station traveling (50) miles an hour and a passenger train leaves the station 30 minutes later traveling (70) miles per hour. How long will it take for the passenger train to catch up with the freight train?" to a totally different word problem no matter what tab I clicked. This was not helpful to me. Please show me how to set up a formula to solve this problem.1 solutions Answer 244202 by nerdybill(6948)   on 2010-09-09 14:18:55 (Show Source): You can put this solution on YOUR website!A freight train leaves the station traveling (50) miles an hour and a passenger train leaves the station 30 minutes later traveling (70) miles per hour. How long will it take for the passenger train to catch up with the freight train? . Apply the distance formula of: d = rt where d is distance (miles) r is rate or speed t is time (hours) . Realize that 30 minutes = .5 hours . Let x = hours traveled by the freight train then x - .5 = hours traveled by the passenger train . "distance traveled by freight train" = "distance traveled by passenger train" 50x = 70(x-.5) 50x = 70x-35 -20x = -35 x = 1.75 hours or x = 1 hour and 45 minutes
 Sequences-and-series/340937: Solve the equation for x. If necessary, round your answer to two decimal places. 5^x= 241 solutions Answer 244194 by nerdybill(6948)   on 2010-09-09 13:17:10 (Show Source): You can put this solution on YOUR website! Take log base 5 of both sides to give you: Apply "change of base":
 test/340940: Hi story problems are not favorite and seem to get confused with them. Can you please help me with this one. Jack usually mows his lawn in 3 hours. Marilyn can mow the same yard in 7 hours, how much time would it take for them to mow the lawn together? Thanks :o)1 solutions Answer 244192 by nerdybill(6948)   on 2010-09-09 13:14:57 (Show Source): You can put this solution on YOUR website!Jack usually mows his lawn in 3 hours. Marilyn can mow the same yard in 7 hours, how much time would it take for them to mow the lawn together? . Let x = hous it takes for both to mow lawn then x(1/3 + 1/7) = 1 Multiplying both sides by 21: x(7 + 3) = 21 x(10) = 21 x = 2.1 hours or x = 2 hours and 6 minutes
 Equations/340931: B-9[B-8(4-B)]=608 I'm getting 64.9, I think I'm doing a step wrong?1 solutions Answer 244188 by nerdybill(6948)   on 2010-09-09 12:56:13 (Show Source): You can put this solution on YOUR website!You must apply the "order of operations" (PEMDAS): B-9[B-8(4-B)]=608 Distribute the -8 to terms inside parenthesis: B-9[B-32+8B]=608 Combining like-terms inside brackets: B-9[9B-32]=608 Distribute the -9 to terms inside brackets: B-81B+288=608 Combining like-terms: -80B+288=608 Subtracting 288 from both sides -80B=608-288 -80B=320 Dividing both sides by -80 B = -4
 Triangles/340929: the hypotenuse of a right triangle is twice as long as the height. determine the height as a function of the base b.1 solutions Answer 244185 by nerdybill(6948)   on 2010-09-09 12:51:53 (Show Source): You can put this solution on YOUR website!the hypotenuse of a right triangle is twice as long as the height. determine the height as a function of the base b. . Because it is a "right triangle" we can apply Pythagorean theorem: Let h = height of triangle then 2h = hypotenuse .
 Mixture_Word_Problems/340917: how much water should be added to 1 gallon of pure antifreeze to obtain a solution that is 65% antifreeze?1 solutions Answer 244180 by nerdybill(6948)   on 2010-09-09 12:31:51 (Show Source): You can put this solution on YOUR website!how much water should be added to 1 gallon of pure antifreeze to obtain a solution that is 65% antifreeze? . Let x = gallons of water added then 0x + 1(1) = .65(1 + x) 1 = .65(1 + x) 1 = .65 + .65x .35 = .65x .35/.65 = x .54 gallons = x
Expressions-with-variables/340910: (x-2)^2 +4 =10
1 solutions

Answer 244172 by nerdybill(6948)   on 2010-09-09 11:42:56 (Show Source):
You can put this solution on YOUR website!
(x-2)^2 +4 =10
(x-2)(x-2) +4 =10
x^2-2x-2x+4 +4 =10
x^2-4x+8 =10
x^2-4x-2 = 0
Solve by applying the quadratic formula to get:
x = {4.449, -0.449}
.
.
 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=24 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 4.44948974278318, -0.449489742783178. Here's your graph:

 Proportions/340535: Determine how you could use a 5-unit jar and a 7-unit jar to measure and hold 8 units.1 solutions Answer 244022 by nerdybill(6948)   on 2010-09-08 17:41:58 (Show Source): You can put this solution on YOUR website!Determine how you could use a 5-unit jar and a 7-unit jar to measure and hold 8 units. . First: fill 5-unit jar and pour contents into 7-unit jar (2-unit empty) Second: refill 5-unit jar and fill balance of 7-unit jar (now, 5-unit jar has 3-units) Third: empty 7-unit jar Fourth: pour the 3-units left in 5-unit jar into 7-unit jar (it now holds 3-units) Fifth: refill 5-unit jar . Contents of both jars now contains 8-units.
 Numeric_Fractions/340355: This is a question about "Scientific Notation" I couldn't find a tab for it! Write 0.000036 in scientific notation? Write 4.78 times 10 to the power of eight in standard notation?1 solutions Answer 243862 by nerdybill(6948)   on 2010-09-08 10:40:13 (Show Source): You can put this solution on YOUR website!Write 0.000036 in scientific notation? that's 3.6 x 10^(-5) . Write 4.78 times 10 to the power of eight in standard notation? 478,000,000
 Quadratic_Equations/340339: Hi, I need help with: Evaluate the discriminant b^2 - 4ac. Then use the answer to state how many real-number solutions exist for the equation: y = x^2 + 8x + 16 Thanks!1 solutions Answer 243860 by nerdybill(6948)   on 2010-09-08 10:34:35 (Show Source): You can put this solution on YOUR website!This site explains it quite well: http://www.mathwarehouse.com/quadratic/discriminant-in-quadratic-equation.php . A "quadratic" is in the form of: y = ax^2 + bx + c . Given: y = x^2 + 8x + 16 we now have: a is 1 b is 8 c is 16 . Plug into: b^2 - 4ac 8^2 - 4(1)(16) 64 - 64 0 . Since "discriminant" is zero Conclusion:"ONE real solution"
What is y = x^2 + 4x - 1
find the x-intercepts
Thanks!
1 solutions

Answer 243858 by nerdybill(6948)   on 2010-09-08 10:30:15 (Show Source):
You can put this solution on YOUR website!
What is y = x^2 + 4x - 1
.
To find the x-intercepts, set y=0 and solve for x:
0 = x^2 + 4x - 1
.
Applying the quadratic formula gives you:
x = {0.236, -4.236}
(0.236,0) and (-4.236,0)
.