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# Recent problems solved by 'nyc_function'

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 test/325883: Use slope intercept form to write the equation of the line: passing through the points (5,6) and (7,10)1 solutions Answer 233274 by nyc_function(2733)   on 2010-07-26 21:00:21 (Show Source): You can put this solution on YOUR website!First find the slope. Let m = slope m = (10 - 6)/(7 - 5) m = 4/2 m = 2 The slope is 2. We now use the point-slope formula. In the point-slope formula, we use one of the given points and the slope. y - b = m(x - a)....This is the point-slope formula. I will use (5,6), where a = 5 and b = 6. The slope is 2. y - 6 = 2(x - 5) y - 6 = 2x - 10 y = 2x - 10 + 6 y = 2x - 4 Did you follow?
 Polynomials-and-rational-expressions/325880: 3/(x+4)=2/(x)1 solutions Answer 233270 by nyc_function(2733)   on 2010-07-26 20:55:26 (Show Source): You can put this solution on YOUR website!Multiply both sides of the equation by the LCD. LCD = (x)(x + 4) [3/(x+4)] *(x)(x + 4) = (2/x) * (x)(x + 4) 3x = 2(x + 4) 3x = 2x + 8 3x - 2x = 8 x = 8 ================================================ The Proof: Let x = 8 3/(8+4)= 2/(8) 3/12 = 2/8 1/4 = 1/4...It checks!! We can now say with certainty that the right answer is x = 8.
 Quadratic-relations-and-conic-sections/325759: Find the foci of the hyperbola with the equation (y2 / 4) – (x2 / 49) = 11 solutions Answer 233224 by nyc_function(2733)   on 2010-07-26 17:29:44 (Show Source): You can put this solution on YOUR website!Your hyperbola is of the form y^2/b^2 - x^2/a^2 = 1. We need to find a and b to start with. b^2 = 4 sqrt{b^2} = sqrt{4} b = 2 a^2 = 49 sqrt{a^2} = sqrt{49} a = 7 We now know that a = 7 and b = 2. The foci will be points (-c,0) and (c,0). This means we need to find c. We can c using c = sqrt{a^2 + b^2}. c = sqrt{7^2 + 2^2} c = sqrt{49 + 4} c = sqrt{53} The foci are (-sqrt{53}, 0) and (sqrt{53}, 0). Did you follow?
 Quadratic_Equations/325777: What are the x intercepts of y + 12 = x2 + x?1 solutions Answer 233221 by nyc_function(2733)   on 2010-07-26 17:10:38 (Show Source): You can put this solution on YOUR website!To find the x-intercept, let y = 0 and solve for x. y + 12 = x^2 + x Let y = 0 0 + 12 = x^2 + x 12 = x^2 + x Subtract 12 from both sides. 0 = x^2 + x - 12 We now factor the quadratic equation. 0 = (x - 3)(x + 4) Set each factor to zero and solve for x. x - 3 = 0 x = 3 x + 4 = 0 x = -4 The x-intercepts are x = 3 and x = -4. Did you follow? ====================================== By the way, if you ever need to find the y-intercepts, let x = 0 and solve for y.
 percentage/325767: A car dealer sells a SUV for \$39,000, which represents a 25% profit over the cost. What was the cost of the SUV to the dealer?1 solutions Answer 233219 by nyc_function(2733)   on 2010-07-26 17:03:24 (Show Source): You can put this solution on YOUR website!\$31,200 is the dealer cost x is the cost of the car x+.25x = 39,000 1.25x = 39,000 39,000/1.25 x=31,200
 Systems-of-equations/325769: I am taking and online algebra II class and I do not understand how to solve this equation (y^2-9)(9y^2-9y+8) the instructions saty multiply. Would I use the foil method? This is what I came up with (y^2-9)(9y^2-9y+8) Y^2*9y^2=9y^4 y^2*-9y=-9y^3 y^2*8=8y^2 -9*9y^2=-81y^2 -9*-9y=81y^2 -9*8=72 9y^4-9y^3+8y-81y^2+81y^2-72 9y^4-9y^3+8y-y^2-72 Is this correct?1 solutions Answer 233212 by nyc_function(2733)   on 2010-07-26 16:45:08 (Show Source): You can put this solution on YOUR website!First of all, there is no equation here. You cannot have an equation without the EQUAL sign. Secondly, you must multiply every member of (y^2-9) by every member of(9y^2-9y+8). Afterwards, simplify by combining like terms. Thirdly, the first-two terms are correct. The last term is correct but terms 3 and 4 in your answer are not right. Let's do it term by term. y^2 * 9y^2 = 9y^4 y^2 * -9y = -9y^3 y^2 * 8 = 8y^2 I have completed the multiplication for the y^2 term. -9 * 9y^2 = -81y^2 -9 * -9y = 81y -9 * 8 = -72 I have completed the multiplication for the -9 term. We now have the following: 9y^4 - 9y^3 + 8y^2 - 81y^2 + 81y - 72 = We now combine like terms and that's it. 9y^4 - 9y^3 -73y^2 + 81y - 72 Did you follow?
 Polynomials-and-rational-expressions/325766: 5y^6/3v^4*9v^6/25y It says to multiply and simplify But for the life of me I just can not understand it1 solutions Answer 233207 by nyc_function(2733)   on 2010-07-26 16:32:33 (Show Source): You can put this solution on YOUR website!Use the same rules that apply to regular multiplication of fractions. You must also use the rules for division of exponents. (5y^6/3v^4) * (9v^6/25y) = 25/5 = 5 y^6/y = y^5 9/3 = 3 v^6/v^4 = v^2 The left side fraction becomes (y^5/1) and the right side fraction becomes (3v^2/5). We now multiply numerator with numerator and denominator with denominator. (y^5/1) * (3v^2/5) = (3v^2y^5)/5 Did you follow?
 Mixture_Word_Problems/325046: How many bags of 5% concrete should be mixed with 7 bags of 23% concrete to get a mix of 12% concrete?1 solutions Answer 232782 by nyc_function(2733)   on 2010-07-23 18:21:32 (Show Source): You can put this solution on YOUR website!Let b = bags of concrete 0.05b + 7(0.23) = 0.12(b + 7) Can you take it from here?
 Money_Word_Problems/325051: \$20,000 is invested at 16% per year for 3 months. How much interest is earned on the investment? I've tried 16% divided by 12 = 1 4/12 *3 = 2 1/3 is that right?1 solutions Answer 232780 by nyc_function(2733)   on 2010-07-23 18:07:17 (Show Source): You can put this solution on YOUR website!I = PRT is the formula you need. NOTE: T = time (in years) 3 months = 3/12 or 1/4 years We are searching for I. I = (20,000)(0.16)(1/4) I = \$800
 Polynomials-and-rational-expressions/325052: The perimeter of a rectangular backyard is 6x +6 yards. If the width is x yards , find a binomial that represents the length.1 solutions Answer 232778 by nyc_function(2733)   on 2010-07-23 18:00:49 (Show Source): You can put this solution on YOUR website!Let p = perimeter Let L = length Let w = width p = 2L + 2w 6x + 6 = 2L + 2x 6x + 6 - 2x = 2L 4x + 6 = 2L (4x + 6)/2 = L 2x + 3 = L
 Graphs/325058: What line is perpendicular to y=3/5x+1 but contains (5,2)?1 solutions Answer 232773 by nyc_function(2733)   on 2010-07-23 17:45:55 (Show Source): You can put this solution on YOUR website!Slopes of perpendicular lines are negative reciprocals of each other. Your given slope is 3/5. The slope of the equation we want to find is -5/3. We use the point-slope formula: y - a = m(x - b), where the given point (5,2) represents the general point (b,a). NOTE: I used a and b to represent the given point but you can use any two letters of choice. Let m = -5/3 Let a = 2 Let b = 5 y - 2 = (-5/3)(x - 5) y - 2 = (-5/3)(x) + (25/3) y = (-5/3)(x) + (25/3) + 2 y = (-5/3)(x) + (31/3)
 Graphs/325060: Given the domain, find the range.{-2,-1,0,1/2} y=-3x+51 solutions Answer 232769 by nyc_function(2733)   on 2010-07-23 17:25:26 (Show Source): You can put this solution on YOUR website!STEPS: 1-replace x with each given number (one at a time) 2-simplify the function to find values for y The values for y is your range. The domain of the function are the x values. Can you take it from here?
 Mixture_Word_Problems/324878: Solution A is 25% acid and solution B is 40% acid. How much of each is needed to make 60 liters of a solution with 30% acid?1 solutions Answer 232618 by nyc_function(2733)   on 2010-07-23 00:03:46 (Show Source): You can put this solution on YOUR website!0.25x + 0.40x = 0.30(2x + 60) Can you finish?
 Parallelograms/324892: three measures of a parallelogram measure 45,135, and 135 degrees what is the measure of the fourth angle1 solutions Answer 232617 by nyc_function(2733)   on 2010-07-23 00:01:22 (Show Source): You can put this solution on YOUR website!Let a = measure of fourth angle 45 + 135 + 135 + a = 360 Can you find a?
 Travel_Word_Problems/324885: If John and Mary drive the same time: one hour. John drive 60 mile per hour. Mary drive 30 miles per hour. What will be the equation? 1 solutions Answer 232616 by nyc_function(2733)   on 2010-07-23 00:00:05 (Show Source): You can put this solution on YOUR website!You need an equation for what? Do you mean the distance formula? If so, it is D = rate * times
 Circles/324859: if the circumference of a circle is 64 cm, what is the lenth of an arc that measures 45 degrees?1 solutions Answer 232615 by nyc_function(2733)   on 2010-07-22 23:58:01 (Show Source): You can put this solution on YOUR website!C = 2pir 64 = 2pir 64/2pi = r 32/pi = r ========== ach length = 45*(32/pi)(pi/180) Can you finish? Just multiply the right side of the equation.
 Linear-equations/324894: Find a linear equation whose graph has the indicated slope and passes through the given point. slope -2, point (2,1)1 solutions Answer 232614 by nyc_function(2733)   on 2010-07-22 23:47:34 (Show Source): You can put this solution on YOUR website!Use the point-slope formula. y - a = m(x - b) (2,1) = (b,a) y - 1 = -2(x - 2) y - 1 = -2x + 4 y = -2x + 4 + 1 y = -2x + 5
 Radicals/324333: Add. simplify by collecting like radical terms if possible, assuming that all expressions under radicals represent nonnegative numbers. √7a+ 2√(175a^3) 1 solutions Answer 232228 by nyc_function(2733)   on 2010-07-21 16:36:42 (Show Source): You can put this solution on YOUR website!sqrt{7a} + 2(sqrt{175a^3}) = sqrt{7a} + 2*sqrt{25}*sqrt{7}*sqrt{a^2}*sqrt{a} = sqrt{7a} + 10a*sqrt{7a} Both radicals cannot be added because although both have the same radicand, one has 10a and the other does not. Final answer: sqrt{7a} + 10a*sqrt{7a}
 Signed-numbers/324464: if + and - canceles each other out then does + and + cancel each other out too?1 solutions Answer 232227 by nyc_function(2733)   on 2010-07-21 16:29:30 (Show Source): You can put this solution on YOUR website!No, positive and positive do not cancel each other out. When + and - are placed together, they cancel each other out because by being together, they becomes zero everytime. ======================================= If + and + do not cancel, what happens in terms of which math operation? Do you understand? Your question is not complete. Are you talking about addition, subtraction, multiplication oor division?
 logarithm/324458: Solve for: 25^(2x-1) = 5^(5x+1)1 solutions Answer 232225 by nyc_function(2733)   on 2010-07-21 16:25:08 (Show Source): You can put this solution on YOUR website!Rewrite 25 s 5^2. (5^2)^(2x - 1) = 5^(5x + 1) 5^(4x - 2) = 5^(5x + 1) Since we now have the same base 5 on both sides, we simply bring down the exponents and solve for x. 4x - 2 = 5x + 1 Can you find x now?
 Linear_Equations_And_Systems_Word_Problems/324436: Jen Butler had been pricing speed-pass train fares for a group trip to new york. three adults and four children must pay \$121. two adults and three children must pay \$86. find the price of the adults tickets and the children's tickets. 1 solutions Answer 232224 by nyc_function(2733)   on 2010-07-21 16:21:44 (Show Source): You can put this solution on YOUR website!You have a system of linear equations in two varables. I will set it up and you can work out the math. Let a = adult ticket price Let c = children ticket price 3a + 4c = 121 2a + 3c = 86 Can you take it from here?
 Radicals/324453: solve for the value of h in D=1.2h and h is inside of the square symbol. Also how far can you see at a distance of 14,255 in elevation. 1 solutions Answer 232222 by nyc_function(2733)   on 2010-07-21 16:18:18 (Show Source): You can put this solution on YOUR website!Do you mean D = 1.2? If so, D = distance and h = height Divide both sides by 1.2. D/1.2 = Square both sides to find h. (D/1.2)^2 = []^2 D^2/1.44 = h ============================= To find how far a person can see, replace h with 14255 in the original equation and solve for D. D = 1.2 D = 143.27 feet
 Money_Word_Problems/324251: what monthly payment is required at 18% intrest to yield 5000.00 in three years1 solutions Answer 232098 by nyc_function(2733)   on 2010-07-21 00:38:35 (Show Source): You can put this solution on YOUR website!R= monthly instalment i =18/(100x12)= 0.015 n = 3x12 = 36 months use the formula A = R[(1+i)^n -1]/i 5000 = R[(1.015)^36 - 1]/ 0.015 R = {5000x0.015}/ [(1.015)^36 -1} use calculator R = \$105.76
 Surface-area/324288: A CYLINDER has a circular base with a diameter of 14ft and a height of 8ft. what is the surface area?1 solutions Answer 232097 by nyc_function(2733)   on 2010-07-21 00:34:01 (Show Source): You can put this solution on YOUR website!Did you try searching for the surface area of a cylinder with a circular base online? Let A = surface area of cylinder with circular base Let r = 7 Why 7? If the diameter is 14, the radius is 1/2 of the diameter length and so 14 times 1/2 = 7. Let h = 14 Let pi = 3.14 The formula to use is A = 2pi(r^2) + 2pirh. Just plug and chug. Here is the set up and you can do the math to find A. A = 2(3.14)(7)^2 + 2(3.14)(7)(14) Can you finish? Just use your calculator to find A.
 Miscellaneous_Word_Problems/324275: The number N of aluminum cans used each year varies directly as the number of people P using the cans. If 56 people use 18,088 cans in one year, how many cans are used in a city which has a population of 1,965,000? 1 solutions Answer 232096 by nyc_function(2733)   on 2010-07-21 00:27:03 (Show Source): You can put this solution on YOUR website!N = Pk We need to find k (the constant of proportionality) as step one. 18,088 = 56k 18,088/56 = k 323 = k ================================================================ We now let k = 323 and P = 1,965,000. We need to find N in the equation N = Pk N = (1,965,000)(323) N = 634,695,000 Did you follow? This is a direct variation word problem.
 Mixture_Word_Problems/324285: A contractor mixes concrete from bags of pre-mix for small jobs. How many bags with 10% cement should he mix with 8 bags of 12.5% cement to produce a mix containing 11% cement.1 solutions Answer 232094 by nyc_function(2733)   on 2010-07-21 00:10:26 (Show Source): You can put this solution on YOUR website!Let b = bags of cement 0.10b + 8(0.125) = 0.11(b + 8) Can you take it from here? I gave you the equation that you'll need to find the answer.
 Linear_Equations_And_Systems_Word_Problems/324280: According to a census, the population of a country was about 151 million in 1936 and 249 million in 1976. Find the slope of the line representing this equation. 1 solutions Answer 232093 by nyc_function(2733)   on 2010-07-21 00:05:39 (Show Source): You can put this solution on YOUR website!Let m = slope m = (249 - 151)/(1976 - 1936) Can you do the math and find the slope?
 Rectangles/323901: A parking lot has a rectangular area of 40,000 yds(squared). the length is 200yd more than twice the witdt. what are the dimensions of the lot/?1 solutions Answer 231792 by nyc_function(2733)   on 2010-07-20 00:07:20 (Show Source): You can put this solution on YOUR website!Use A = L*W Let A = 40,000 Let L = 2x + 200 Let W = x 40,000 = (2x + 200)(x) Can you take it from here?
 Probability-and-statistics/323885: Find the outcome of the roulette bets: You bet \$30 on 1-12 and also bet \$15 on number 10. a. The ball lands on 18 b. The ball lands on 9 c. The ball lands on 101 solutions Answer 231790 by nyc_function(2733)   on 2010-07-20 00:03:24 (Show Source): You can put this solution on YOUR website!Let P = probability There are only 12 numbers listed as 1-12. PART (A) P(18) = what? It must be zero because the highest number on the list is 12. P(18) = 0 PART B: P(9) = 9/12 or 3/4 PART C: P(10) = 10/12 or 5/6 I hope this helps.
 Rectangles/323889: the Length of a rectangle is four times its width. If the area of the rectangle is 324 yd^2, find its perimeter1 solutions Answer 231785 by nyc_function(2733)   on 2010-07-19 23:56:57 (Show Source): You can put this solution on YOUR website!Length = 4x Width = x Area = 324 324 = (4x)(x) 324 = 4x^2 324/4 = x^2 81 = x^2 sqrt[81] = sqrt[x^2] 9 = x We find the perimter using P = 2L + 2W. P = 2(4x) + 2(x) P = 2(4*9) + 2(9) P = 2(36) + 18 P = 72 + 18 P = 90 yards
 Angles/323897: The measure of an angle is six more than twice the measure of its complement. Find the measures of both angles.1 solutions Answer 231783 by nyc_function(2733)   on 2010-07-19 23:52:08 (Show Source): You can put this solution on YOUR website!Let A = angle Let (90 - A) = the complement of the angle A = 2(90 - A) Can you take it from here?