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# Recent problems solved by 'nerdybill'

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 Linear_Equations_And_Systems_Word_Problems/170766: This question is from textbook Algebra 2 The equation for the cost in dollars of producing automobile tires is 2 C=0.000015x -0.03+35, where x is the number of tires produced. Find the number of tires that minimizes the cost. What is the cost for that number of tires? ***note the 2 in the second row means that 0.000015x is squared1 solutions Answer 126098 by nerdybill(6951)   on 2008-12-02 20:29:42 (Show Source): You can put this solution on YOUR website!C=0.000015x^2 -0.03x+35 . Since, the first coefficient (0.000015) is POSITIVE the equation is a parabola that opens upwards. This then says that finding the "vertex" will give you the minimum. . The vertex is then found by: x = -b/2a x = -(-0.03)/2(0.000015) x = 0.03/2(0.000015) x = 0.03/0.00003 x = 1000 (minimum number of tires) . The cost, plug it back into: C=0.000015x^2 -0.03x+35 C=0.000015(1000)^2 -0.03(1000)+35 C=15 -30+35 C=15 +5 C= \$20
 Functions/170800: Please help!!!!! Find the slope of the graph of the linear function f. f(2) = -3, f(-2) =51 solutions Answer 126097 by nerdybill(6951)   on 2008-12-02 20:19:36 (Show Source): You can put this solution on YOUR website!if they gave you: f(2) = -3, f(-2) =5 It's equivalent to giving you two points: (2,-3), (-2,5) . Now, that you have two points: m = (y2-y1)/(x2-x1) m = (5-(-3))/(-2-2) m = (5+3)/(-2-2) m = 8/(-4) m = -2 (slope)
 Angles/170785: what is one of the complementary angles is three more than two that twice the other? find the measure of each? 1 solutions Answer 126082 by nerdybill(6951)   on 2008-12-02 19:32:31 (Show Source): You can put this solution on YOUR website!what is one of the complementary angles is three more than two that twice the other? find the measure of each? . If two angles are complementary, the sum of the two angles equal 90 degrees. . Let x = one angle then 2x+3 = other angle . x + 2x+3 = 90 3x+3 = 90 3x = 87 x = 29 degrees (one angle) . Other angle: 2x+3 = 2(29)+3 = 58+3 = 61 degrees
 Equations/170781: Hi I need help with my math homework. I'm having trouble on this equation. Please help Solve for d 13d-53=9d+19 Thanks -Julie1 solutions Answer 126078 by nerdybill(6951)   on 2008-12-02 19:26:19 (Show Source): You can put this solution on YOUR website!Isolate the unknown 'd' to one side of the equation. 13d-53=9d+19 Subtracting 9d from both sides: 4d - 53 = 19 Adding 53 to both sides: 4d = 72 Finally, divide both sides by 4: d = 18
 Geometry_Word_Problems/170758: This question is from textbook The longer leg of a right triangle is 4 cm more than four times the length of the shorter leg. The hypotenuse is 1 cm longer than the longer leg. How long are the sides of the triangle?1 solutions Answer 126074 by nerdybill(6951)   on 2008-12-02 19:02:25 (Show Source): You can put this solution on YOUR website! The longer leg of a right triangle is 4 cm more than four times the length of the shorter leg. The hypotenuse is 1 cm longer than the longer leg. How long are the sides of the triangle? . Let x = length of shorter leg then 4x+4 = length of longer leg 4x+5 = length of hypotenuse . x^2 + (4x+4)^2 = (4x+5)^2 x^2 + (4x+4)(4x+4) = (4x+5)(4x+5) x^2 + 16x^2+32x+16 = 16x^2+40x+25 17x^2+32x+16 = 16x^2+40x+25 x^2+32x+16 = 40x+25 x^2-8x+16 = 25 x^2-8x-9 = 0 (x-9)(x+1) = 0 . x = {9, -1} We can toss out the negative solution leaving: x = 9 cm (shorter leg) . Longer leg: x+4 = 9+4 = 13 cm .
 Expressions-with-variables/170673: A long distance telephone calling card charges \$0.05 per minute, but adds on a \$0.75 charge for each call dialed. Using 'C' for the number of calls made and 'I' for the time spent talking, create an expression that will keep track of the cost of using the card. answer- C=.75 I/.05 ? Using the expression created calculate the remaining value on a \$20.00 phone card after 5 calls that lasted a total of 26 minutes. answer is \$14.95 but don't know how to use an expression to find answer. I did .75 * 5=3.75 26*.05= 1.30 3.75+1.30=5.05 20.00-5.05= 14.95 Any help would be appreciated as this is my first math course in over 20 years. 1 solutions Answer 126006 by nerdybill(6951)   on 2008-12-02 10:05:09 (Show Source): You can put this solution on YOUR website!A long distance telephone calling card charges \$0.05 per minute, but adds on a \$0.75 charge for each call dialed. Using 'C' for the number of calls made and 'I' for the time spent talking, create an expression that will keep track of the cost of using the card. "cost of using card" = "total dialing charges" + "total minutes called" "cost of using card" = .75C + .05I . Using the expression created calculate the remaining value on a \$20.00 phone card after 5 calls that lasted a total of 26 minutes. "remaining cost" = "current value" - "cost" "remaining cost" = 20 - (.75C + .05I) "remaining cost" = 20 - (.75(5) + .05(26)) "remaining cost" = 20 - (3.75 + .1.3) "remaining cost" = 20 - 5.05 "remaining cost" = \$14.95
 logarithm/170597: ln (y^2-1)= ln(y-1) + ln51 solutions Answer 125929 by nerdybill(6951)   on 2008-12-01 20:08:23 (Show Source): You can put this solution on YOUR website!Using "log rules": ln (y^2-1)= ln(y-1) + ln5 ln (y^2-1)= ln(5(y-1)) ln (y^2-1)= ln(5y-5) y^2-1= 5y-5 y^2-5y-1= -5 y^2-5y+4= 0 Factoring: (y-4)(y-1)= 0 y = {1,4} You have to toss out 1 as a possible solution since ln(0) is undefined. . Therefore: y = 4
 Graphs/170579: how do you change -2x=2y+5 into slope-intercept form?1 solutions Answer 125924 by nerdybill(6951)   on 2008-12-01 18:27:38 (Show Source): You can put this solution on YOUR website!The "slope-intercept" form is: y = mx + b where m is slope b is y-intercept . -2x=2y+5 -2y-2x = 5 -2y = 2x + 5 y = (2/-2)x + (5/-2) y = -x + (-5/2)
 Rectangles/170574: Express the area (A) of a rectangle with perimeter 100 feet as a function of the length (L) of one of its sides.1 solutions Answer 125922 by nerdybill(6951)   on 2008-12-01 18:25:07 (Show Source): You can put this solution on YOUR website! Express the area (A) of a rectangle with perimeter 100 feet as a function of the length (L) of one of its sides. . Normally, for a rectangle, if you had a "length" and "width" the perimeter would be: "length" + "width" + "length" + "width" or 2("length" + "width") . Area would be: (length)(width) . So, if: L = length the width = (100-2L)/2 = 50-L . Therefore, if A=Area then A = L(50-L) A = 50L-L^2 or A = -L^2+50L
 Travel_Word_Problems/170448: Hi, I am having trouble finding the right equation to use in solving the following word problem from my GRE math test prep worksheet. Can you please advise me on how to start? Two cars started from the same point and traveled on a straight course in opposite directions for exactly 2 hours, at which time they were 208 miles apart. If one car traveled, on average, 8 mph faster than the other car, what was the average speed for each car for the 2-hour trip? Thanks, Julie1 solutions Answer 125848 by nerdybill(6951)   on 2008-12-01 07:01:00 (Show Source): You can put this solution on YOUR website!Two cars started from the same point and traveled on a straight course in opposite directions for exactly 2 hours, at which time they were 208 miles apart. If one car traveled, on average, 8 mph faster than the other car, what was the average speed for each car for the 2-hour trip? . Let x = speed of one car then because "one car traveled, on average, 8 mph faster than the other car" x+8 = speed of second car . Applying "distance formula": d = rt where d is distance r is rate or speed t is time . "distance traveled by car one" + "distance traveled by car two" = 208 2x + 2(x+8) = 208 2x + 2x + 16 = 208 4x + 16 = 208 4x = 192 x = 48 mph (speed of one car) . Second car: x+8 = 48+8 = 56 mph (speed of second car)
 Expressions-with-variables/170456: This question is from textbook Introductory Algebra Between what two consecutive integers is √78 ?1 solutions Answer 125846 by nerdybill(6951)   on 2008-12-01 06:55:42 (Show Source): You can put this solution on YOUR website!Since: 8*8 = 64 and 9*9 = 81 . √78 is between 8 and 9
 Expressions-with-variables/170464: This question is from textbook Introductory Algebra A 10-m ladder is leaning against a building. The bottom of the ladder is 5 m from the building. How high is the top of the ladder?1 solutions Answer 125845 by nerdybill(6951)   on 2008-12-01 06:54:08 (Show Source): You can put this solution on YOUR website!A 10-m ladder is leaning against a building. The bottom of the ladder is 5 m from the building. How high is the top of the ladder? . Apply Pythagorean's theorem: Let H = height of top of ladder . H^2 + 5^2 = 10^2 H^2 + 25 = 100 H^2 = 75 H = sqrt(75) H = 8.66 m
 Linear_Equations_And_Systems_Word_Problems/170454: Hi, Here's my fourth and final GRE math prep word problem of the day: If 3 time's Jane's age, in years, is equal to 8 times Beth's age, in years, and the difference between their ages is 15 years, how old are Jane and Beth? Thank you, Julie1 solutions Answer 125844 by nerdybill(6951)   on 2008-12-01 06:48:15 (Show Source): You can put this solution on YOUR website!Let J = Jane's age and B = Beth's age . From: "3 time's Jane's age, in years, is equal to 8 times Beth's age" 3J = 8B (equation 1) . From: "difference between their ages is 15 years" J-B = 15 (equation 2) . Solving equation 2 for J: J-B = 15 J = 15+B . Plug the above into equation 1 and solve for B: 3J = 8B 3(15+B) = 8B 45+3B = 8B 45 = 5B 9 = B (Beth's Age) . Plug the above into equation 2 and solve for J: J-B = 15 J-9 = 15 J = 24 (Jane's Age)
 logarithm/170403: Solve the following equation. Show all your work. logx(10-3x)=21 solutions Answer 125805 by nerdybill(6951)   on 2008-11-30 21:37:31 (Show Source): You can put this solution on YOUR website!logx(10-3x)=2 . If you meant "log base x" then: logx(10-3x)=2 10-3x=x^2 0 = x^2+3x-10 0 = (x+5)(x-2) . x = {-5, 2}
 Expressions-with-variables/170288: This question is from textbook We have to solve using the eliminaiton or substitution method. I am really struggling with this class so I'm not sure where to start. 2(x-y)=3+x which is 2x - 2y =3+x x = 3y + 41 solutions Answer 125710 by nerdybill(6951)   on 2008-11-30 14:38:44 (Show Source): You can put this solution on YOUR website!First order of business, put all the x's and y's to one side: 2x - 2y =3+x x = 3y + 4 . Rearranging then, we have: x - 2y =3 x - 3y =4 . Now, using the "elimination method", subtract the second equation from the first: x - 2y = 3 -x + 3y = -4 --------------- y = -1 . Now, use the above definition of 'y' and substitute it into equation 2: x = 3y + 4 x = 3(-1) + 4 x = -3 + 4 x = 1 . Solution: (x,y) = (1, -1)
Quadratic_Equations/170286: I need help with this word problem I have tried and so has a tutor at school.
Malikka takes a paddleboat 1km upriver against a 4km/hr current then returns downriver with the current, back to starting point. Her whole trip takes 2 hours, write a quadratic equation describing this situation. The unknown is the speed, v, that Mallika would paddle with no current present. Solve. What speed (in km/hr) would Mallika paddle by herself with no current present?
1 solutions

Answer 125702 by nerdybill(6951)   on 2008-11-30 14:02:07 (Show Source):
You can put this solution on YOUR website!
Let v = speed of paddleboat w/no current
.
Applying "distance formula":
d = rt
where
d is distance
r is rate or speed
t is time
.
Let t = time traveling upriver
then
2-t = time traveling downstream
.
We have two unknowns (v and t) so we'll need two equations:
t(v-4) = 1 (equation 1)
(2-t)(v+5) = 1 (equation 2)
.
Solving equation 1 for 't':
t(v-4) = 1
t = 1/(v-4)
.
Substitute the above into equation 2 and solve for v:
(2-(1/(v-4)))(v+5) = 1
multiply both sides by (v-4):
(2(v-4) - 1)(v+5) = 1
(2v-8 - 1)(v+5) = 1
(2v-9)(v+5) = 1
Applying FOIL:
2v^2 + 10v - 9v -45 = 1
2v^2 + v -45 = 1
2v^2 + v -46 = 0
.
Can't factor so use the quadratic formula. Doing so will yield:
v = {4.552, -5.052}
.
We can toss out the negative solution leaving us with:
v = 4.552 km/hr
.
 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=369 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 4.55234317807464, -5.05234317807464. Here's your graph:

 Permutations/170259: A baseball player with a batting average of .300 comes to bat. What are the odds in favor of the ball player getting a hit.1 solutions Answer 125689 by nerdybill(6951)   on 2008-11-30 12:30:26 (Show Source): You can put this solution on YOUR website!odds = P(E)/(1-P(E)) . Since P(E) = .30 odds = .30/(1-.30) odds = .30/.70 odds = 1/2.33 odds = 1:2.33
 Quadratic_Equations/170246: find the quadratic function whose vertex is (-1,5) and passing through the point (2,7) and graph the function. need answer before 12/1/08 1 solutions Answer 125686 by nerdybill(6951)   on 2008-11-30 11:40:05 (Show Source): You can put this solution on YOUR website!Reviewing vertex formula: http://www.mathwarehouse.com/geometry/parabola/standard-and-vertex-form.php . Standard "vertex form": y= a(x-h)^2+k where (h,k) is the vertex . The problem gives you: (h,k) = (-1,5) (x,y) = (2,7) . Plug the above into: y= a(x-h)^2+k 7= a(2-(-1))^2+5 Solve for 'a': 7= a(2+1)^2+5 7= a(3)^2+5 7= 9a+5 2 = 9a 2/9 = a . Therefore: y= a(x-h)^2+k y= (2/9)(x-(-1))^2+5 y= (2/9)(x+1)^2+5 y= (2/9)(x^2+2x+1)+5 9y= 2(x^2+2x+1)+45 9y= 2x^2+4x+2+45 9y= 2x^2+4x+47 y = (2/9)x^2 + (4/9)x + (47/9)
 Human-and-algebraic-language/170232: 1. A triangular window of height 15 inches and base 21 inches is to be laminated with a sunblock coating that costs \$1.22 per square inch to apply. What is the total cost of coating the window, to the nearest cent? (Hint: Area of Triangle: A = base*height/2)1 solutions Answer 125673 by nerdybill(6951)   on 2008-11-30 09:38:26 (Show Source): You can put this solution on YOUR website! Using the hint provided: Area of Triangle: A = base*height/2 . From the problem it gave us: base = 21 height = 15 . Plugging it into: A = base*height/2 A = 21*15/2 A = 315/2 A = 157.5 square inches . Since sunblock costs: \$1.22 per square inch 1.22 * 157.5 = \$192.15
 Inequalities/170214: The length of a rectangle is three times its width. If the perimeter is at most 112 centimeters, what is the greatest possible value for the width? Write an inequality to model the problem. 1 solutions Answer 125653 by nerdybill(6951)   on 2008-11-30 05:06:20 (Show Source): You can put this solution on YOUR website!Since the perimeter of any rectangle is: width + width + length + length 2(width) + 2(length) 2(width + length) . Let w = width of rectangle then because "length of a rectangle is three times its width" 3w = length of rectangle . 2(width + length) <= 112 plugging in our variables above: 2(w + 3w) <= 112 2(4w) <= 112 8w <= 112 w <= 112/8 w <= 14 centimeters (width) . Solution: greatest possible width is 14 centimeters
 Travel_Word_Problems/170217: Trains A and B are travelling in the same direction on parallel tracks. train A is traveling at 40mph and train b is travelling at44mph. Train A passes a station at 9:10 pm and Train B passes the same station @9:40. At what time will train b cath up with train?1 solutions Answer 125651 by nerdybill(6951)   on 2008-11-30 04:56:37 (Show Source): You can put this solution on YOUR website!Let x = time (in hours) it takes for train B to catch up to train A Because of the difference in time the two trains passes a station we have: x + (1/2) = time train A traveled . We use the "distance formula" d = rt where d is distance traveled r is rate or speed t is time . For train B to catch up: "distance traveled by train A" = "distance traveled by train B" 40(x + (1/2)) = 44x multiplying both sides by 2: 40(2x + 1) = 88x 80x + 40 = 88x 40 = 8x 5 hours = x . But wait, the problem wanted "clock" time: 9:40 PM + 5 hours = 2:40 AM
 Quadratic_Equations/170210: find three consecutive odd integers such that the squar of the thid integer plus the product of the other two integers is 268.1 solutions Answer 125648 by nerdybill(6951)   on 2008-11-30 00:36:00 (Show Source): You can put this solution on YOUR website!find three consecutive odd integers such that the squar of the thid integer plus the product of the other two integers is 268. . Let x = first consecutive odd integer then x+2 = second consecutive odd integer x+4 = third consecutive odd integer . From:"the square of the third integer plus the product of the other two integers is 268" we get: (x+4)^2 + x(x+2) = 268 x^2+8x+16 + x^2+2x = 268 2x^2 + 10x + 16 = 268 x^2 + 5x + 8 = 134 x^2 + 5x - 126 = 0 (x-9)(x+14) = 0 . x = {9, -14} . We can toss out the -14, leaving us with: x=9 . Solution: 9, 11, 13
 Linear_Equations_And_Systems_Word_Problems/170192: Can someone help? A lion eats one sheep in 4 hours, a leopard eats one sheep in 5 hours, and a bear eats one sheep in 6 hours. How long would it take the three animals together to eat one sheep?1 solutions Answer 125640 by nerdybill(6951)   on 2008-11-29 22:32:55 (Show Source): You can put this solution on YOUR website!. Let x = time (in hours) it takes all three to eat one sheep . x/4 + x/5 + x/6 = 1 30x + 24x + 20x = 120 74x = 120 x = 120/74 x = 1.622 hours or 1 hour 37 minutes and 18 seconds
 Age_Word_Problems/170191: HELP! I am totally lost!!! A man will be 3 times as old as his son will be in 9 years. If he is 6 times as old as his son now, how old is the son?1 solutions Answer 125639 by nerdybill(6951)   on 2008-11-29 22:23:42 (Show Source): You can put this solution on YOUR website!A man will be 3 times as old as his son will be in 9 years. If he is 6 times as old as his son now, how old is the son? . Let x = son's age then from "he is 6 times as old as his son now" 6x = man's age . From: "A man will be 3 times as old as his son will be in 9 years." we get our equation: 6x+9 = 3(x+9) 6x+9 = 3x+27 3x+9 = 27 3x = 18 x = 6 years old (son's age)
 Quadratic_Equations/170116: I messed up on my last question, can you please show how to solve this quadratic equation by completing the square not sq. rt prop. m^2 = 8m + 31 solutions Answer 125548 by nerdybill(6951)   on 2008-11-29 11:46:36 (Show Source): You can put this solution on YOUR website!m^2 = 8m + 3 Move all the 'm' terms to one side: m^2 - 8m = 3 Take half of b (-8) and square it (16). Add to both sides: m^2 - 8m + 16 = 3 + 16 Factoring the left side: (m-4)(m-4) = 19 (m-4)^2 = 19 Take the square root of both sides m-4 = sqrt(19) m = 4+sqrt(19) or m = {8.3589, -0.3589}
 Square-cubic-other-roots/170090: This question is from textbook a circle has a radius of 10 inch. Find the increase in area that occurs when the radius is increased by 2 inches. Round to the nearest hundredths?1 solutions Answer 125540 by nerdybill(6951)   on 2008-11-29 10:12:27 (Show Source): You can put this solution on YOUR website! a circle has a radius of 10 inch. Find the increase in area that occurs when the radius is increased by 2 inches. Round to the nearest hundredths? . Area of a circle is (pi)r^2 . "area of increased radius circle" - "area of original circle" . (pi)(10+2)^2 - (pi)(10)^2 (pi)(12)^2 - (pi)(10)^2 pi ((12)^2 - (10)^2) pi (144 - 100) pi (44) (3.14)(44) 138.16 sq inches
 Money_Word_Problems/170067: A factory worer earns \$1.25 for each electric razor completed. Find the wages for the worker if she had completed 120 razors.1 solutions Answer 125518 by nerdybill(6951)   on 2008-11-29 05:37:57 (Show Source): You can put this solution on YOUR website!That would be: 1.25 * 120 = \$150.00
 Polynomials-and-rational-expressions/170076: reduce 5x-x^2/x^2-10x+251 solutions Answer 125517 by nerdybill(6951)   on 2008-11-29 05:35:39 (Show Source): You can put this solution on YOUR website! Factoring numerator and denominator: Factor out a -1 from the denominator: Now, we can cancel like-terms: Distributing the -1: