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# Recent problems solved by 'nyc_function'

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 Expressions-with-variables/312390: 45 is _____% of 25.1 solutions Answer 223307 by nyc_function(2733)   on 2010-06-08 07:53:13 (Show Source): You can put this solution on YOUR website!We are looking for percent. Let p = percent 45 = p times 25 This can be expressed as 45 = 25p. To find your percent, divide both sides by 25. 45/25 = p 1.8 = p The answer is 1.8% ============================================== The Proof: Going back to your original question, if we multiply 25 by 1.8, we'll get 45 proving that 1.8% is correct.
 Age_Word_Problems/312394: Adding two years to the age of a boy would make him a quartet of his father's age. Five years ago his father was one year less than ten times his son's age. Determine the age of the boy and his father1 solutions Answer 223306 by nyc_function(2733)   on 2010-06-08 07:47:29 (Show Source): You can put this solution on YOUR website!We have a system of equations in two variables expressed as an age question. Let: b = boy's age now Let f = father's age now first sentence and equation: b + 2 = f/4, f = 4b + 8 eq.1 2nd sentence and equation: 5 yrs ago, their ages were: For the boy : b - 5 for the father: f - 5 f - 5 = 10 (b-5) - 1 simplifying f = 10 b - 46 eq.2 Equate equations 1 and 2 4b + 8 = 10b - 46 b = 9 yrs. old The boy is 9 years old. f = 4(9) + 8 f = 44 yrs.old The father is 44 years old. Understand?
 Numbers_Word_Problems/312395: what are three consecutive odd numbers that add up to 357? 1 solutions Answer 223305 by nyc_function(2733)   on 2010-06-08 07:45:14 (Show Source): You can put this solution on YOUR website!Let x = first odd number Let x + 2 = second odd number Let x + 4 = third odd number Here is your equation: x + x + 2 + x + 4 = 357 3x + 6 = 357 3x = 357 - 6 3x = 351 x = 351/3 x = 117 Here are the three consecutive odd numbers: x = 117 x + 2 = 117 + 2 = 119 x + 4 = 117 + 4 = 121 They are: 117, 119, 121
 Linear-equations/312396: Write the equation in slope-intercept form of the line that has a slope of -3 and contains the point (1, 1).1 solutions Answer 223304 by nyc_function(2733)   on 2010-06-08 07:42:03 (Show Source): You can put this solution on YOUR website!They give you one point and slope. This is all you need to plug into the point-slope formula. The point-slope formula is: y - a = m(x - b). If (a,b) represents your point, then a = 1 and b = 1. If m represents your slope, then m = -3. We now plug and chug. y - 1 = -3(x - 1) y - 1 = -3x + 3 y = -3x + 3 + 1 y = -3x + 4 Done!
 Percentage-and-ratio-word-problems/312218: A transformer has a primary voltage of 480 volts and a secondary voltage of 120 volts. If the primary windings have 700 turns, how many turns are in the secondary windings? (Voltage and number of turns are directly proportional.)1 solutions Answer 223224 by nyc_function(2733)   on 2010-06-07 18:08:48 (Show Source): You can put this solution on YOUR website!Let t = number of turns in the secondary windings 480/120 = 700/t Solve for t and you will have your answer. HINT: Cross-multiply and then divide to find t.
 Quadratic_Equations/312216: Use the quadratic formula to determine the x-intercepts (if any) of the following function. Then evaluate the function for several values of x, and use the resulting points to graph the function. f(x) = -x2 + 2x - 2 1 solutions Answer 223223 by nyc_function(2733)   on 2010-06-07 18:05:19 (Show Source): You can put this solution on YOUR website!Let y = f(x) To find the x-intercepts, let y = 0 and solve for x. To evaluate the function, select different value for x, plug them into your function and do the math. You can use any number. I will give you 4 to play with. Let x = -2, -1, 0, 1. To graph the function, go to mathway.com and in the graph category, write the following: Graph y = -x^2 + 2x - 2. Is this clear?
 Quadratic_Equations/312214: Find the x- and y- intercepts. f(x) = -x^2 + 11x - 30 1 solutions Answer 223222 by nyc_function(2733)   on 2010-06-07 18:01:40 (Show Source): You can put this solution on YOUR website!Let y = f(x). To find the x-intercept, let y = 0 and solve for x. To find the y-intercept, let x = 0 and solve for y. Can you do it now?
 Circles/312210: Determine the center and the radius of the circle x^2+(y+5)^2=171 solutions Answer 223220 by nyc_function(2733)   on 2010-06-07 18:00:10 (Show Source): You can put this solution on YOUR website!The general formula for a circle not center at the origin is (x - h)^2 + (y - k)^2 = r^2 You were given x^2 +(y+5)^2 = 17. The center is (h,k). From your equation, I can see that h = 0 and k = -5. The center is (0,-5). The radius = r in the general formula for a circle. r^2 = 17 r = sqrt{17}. The center is the point (0,-5) and the radius is the square root of 17 written sqrt{17}.
 Exponential-and-logarithmic-functions/312209: y=log(x+6) 1 solutions Answer 223214 by nyc_function(2733)   on 2010-06-07 17:43:28 (Show Source): You can put this solution on YOUR website!What do you need to do with this log equation?
 Travel_Word_Problems/312201: My friend and I are heading to board a plane. My friend rides on an escalator while I walk along side the escalator. If my friend is travelling at 6 miles per hour while I am walking at 4 miles per hour. How far (approximately) will my friend be ahead of me after 20 minutes?1 solutions Answer 223212 by nyc_function(2733)   on 2010-06-07 17:41:59 (Show Source): You can put this solution on YOUR website!Well, if you guys walked for an hour, obviously, your friend would go six miles and you would go four. The difference is two miles. But that's for an hour. For twenty minutes, simply divide the two miles by 3 (20 minutes is one third of an hour), so your friend would be 2/3 miles (3520 feet) ahead of you.
 Trigonometry-basics/312198: Value of angles in degrees for a right triangle whose legs are 0.5' and 4.0'1 solutions Answer 223206 by nyc_function(2733)   on 2010-06-07 17:18:01 (Show Source): You can put this solution on YOUR website!Sorry about the first reply. I read your question a second time. Use the Pythagorean Theorem to find the hypotenuse. Then use the sine and cosine trig functions to find the other angles. Can you do it now? If not, write back.
 test/312199: A model rocket is shot into the air and its path is approximated by , where h is the height of the rocket above the ground in metres and t is the elapsed time in seconds. a. When will the rocket hit the ground? b. What is the maximum height of the rocket?1 solutions Answer 223205 by nyc_function(2733)   on 2010-06-07 17:12:54 (Show Source): You can put this solution on YOUR website!Were you given a formula? This type of question usually comes with a formula.
 Equations/312169: Please help me solve the equation 6+2(3j+-2)=4(1+j)1 solutions Answer 223177 by nyc_function(2733)   on 2010-06-07 15:29:16 (Show Source): You can put this solution on YOUR website! 6+ 2(3j +(-2))= 4( 1 + j) 6 + 6j - 4 = 4 + 4j 6j + 2 = 4 + 4j 2 - 4 = 4j - 6j -2 = -2j -2/-2 = j 2/2 = j 1 = j Done!
 Exponents-negative-and-fractional/311275: how do you solve(5a2/6b)(4b/a3)1 solutions Answer 222622 by nyc_function(2733)   on 2010-06-04 10:48:36 (Show Source): You can put this solution on YOUR website!Apply the same rules for regular fraction multiplication. (5a^2/6b)(4b/a^3) = 10/3a
 Trigonometry-basics/311280: the lateral surface are of a right circular cone, s, is represented by the equation, S=Pi r^2 radical((r^2+h^2)) , where r is the radius of the circular base and h is the height of the cone. if the lateral surface are of a large funnel is 236.64 square centimeters and its radius is 4.75 centimeters, find its height to the nearest hundredth of a centimeter.1 solutions Answer 222621 by nyc_function(2733)   on 2010-06-04 10:43:19 (Show Source): You can put this solution on YOUR website!Replace s with 236.64 and r with 4.75 and then solve for h. 236.64 = pi(4.75)^2 * sqrt{(4.75)^2 + h^2} I'm sure you can finish now.
 Permutations/311289: how to find the number of two letter permutations of the letter M,A,P,L,E1 solutions Answer 222619 by nyc_function(2733)   on 2010-06-04 10:37:35 (Show Source): You can put this solution on YOUR website!5P2 = 5!/(5-2)! 5P2 = 120/3! 5P2 = 120/6 5P2 = 20
 Rectangles/311283: The ratio of the measure of the larger angle to the shorter angle of a golden triangle is the golden ratio? 1 solutions Answer 222618 by nyc_function(2733)   on 2010-06-04 10:34:30 (Show Source): You can put this solution on YOUR website!Golden triangle? Perhaps you meant to type golden rectangle. Do you need to know what the goldern ratio for a golden rectangle is in short? Golden ratio = length divided by width Golden ratio = (1 + sqrt{5})/2
 Triangles/311198: Vertices of a triangle A(1,2) B(5,10) C(-7,6) Show that it is a right triangle. Find length of each side. THANK YOU ! (:1 solutions Answer 222576 by nyc_function(2733)   on 2010-06-04 00:38:42 (Show Source): You can put this solution on YOUR website!BIG HINT: Use the distance formula for points written in the form (x,y). You will use the distance formula to find the distance from A to B, from B to C and from A to C. To learn about the distance formula, copy and paste the free video clip below. If you do not understand what to do after watching the math video clip, write back. http://www.youtube.com/watch?v=YBeXhGl6pSE
 Equations/311227: (-4b-7)/(3b-12)=?1 solutions Answer 222575 by nyc_function(2733)   on 2010-06-04 00:33:58 (Show Source): You can put this solution on YOUR website!HINT: Factor your denominator. Understand?
 Equations/311205: Please multiply by 1 to find an expression equivalent to 16 ___ 11 with a denominator of 331 solutions Answer 222574 by nyc_function(2733)   on 2010-06-04 00:32:18 (Show Source): You can put this solution on YOUR website!Are you trying to divide 16 by the fraction 11/33?
 Quadratic_Equations/311225: how do i work out x+11=y and 7x-49=y? (two differwnt equations) 1 solutions Answer 222573 by nyc_function(2733)   on 2010-06-04 00:29:30 (Show Source): You can put this solution on YOUR website!Solve for x in x + 11 = y. x + 11 = y x = y - 11 Now plug that into the other equation to find the value of y. 7x - 49 = y 7(y - 11) - 49 = y 7y - 77 - 49 = y -126 = -7y + y -126 = -6y -126/-6 = y 21 = y We lastly replace y with 21 in EITHER of the equations given to you to find x. I will use x + 11 = y but you could use 7x-49 = y if you want to. x + 11 = y x + 11 = 21 x = 21 - 11 x = 10 Done!
 Numbers_Word_Problems/311226: The sum of a two-digit number is 6. If the digits are reversed, the new number is 18 less than the original number. Find the original number.1 solutions Answer 222572 by nyc_function(2733)   on 2010-06-04 00:22:39 (Show Source): You can put this solution on YOUR website!Let a = original number Let b = the other digit a + b = 6 b + a = a - 18 You have two equations in two unknowns. Can you continue?
 Trigonometry-basics/311224: The truck of a leaning tree makes an angle of 12 degrees with the vertical. To prevent the tree from falling over, a 35.0 m rope is attached to the top of the tree and is pegged into level ground some distance away. If the tree is 20.0m from its base to its top, calculate the angle the rope makes with the ground to the nearest degree.1 solutions Answer 222571 by nyc_function(2733)   on 2010-06-04 00:16:43 (Show Source): You can put this solution on YOUR website!Di you try drawing this stuff? Try sinx = 20.0/35 Enter 20.0 into calculator and then divide by 35. After that, press the sine inverse key to find your angle represented here by the letter x. Can you continue?
 Expressions-with-variables/311222: (xyz+2x)(xz-10x)1 solutions Answer 222568 by nyc_function(2733)   on 2010-06-03 23:59:13 (Show Source): You can put this solution on YOUR website!(xyz+2x)(xz-10x) = USE FOIL (xyz+2x)(xz-10x) = x^2y(z^2) - 10(x^2)yz + 2(x^2)z - 20x^2
 Polynomials-and-rational-expressions/311201: Factor Completely: 25x^2-161 solutions Answer 222567 by nyc_function(2733)   on 2010-06-03 23:33:48 (Show Source): You can put this solution on YOUR website!25x^2 - 16 = (5x - 4) (5x + 4)
 Trigonometry-basics/311216: What is the exact value of cos(-240)?1 solutions Answer 222565 by nyc_function(2733)   on 2010-06-03 23:23:49 (Show Source): You can put this solution on YOUR website!The answer is -1/2. Memorize the unit circle and you'll fly through trigonometry.
 Linear-equations/311213: Solve -5x-2=-26+x1 solutions Answer 222564 by nyc_function(2733)   on 2010-06-03 23:21:28 (Show Source): You can put this solution on YOUR website!-5x-2=-26+x -5x - x = -26 + 2 -6x = -24 x = -24/-6 x = 4
 Triangles/311215: Which of the following are measurements of the sides of a right triangle? A.3, 4, 5 B.28, 26, 12 C.17, 14, 61 solutions Answer 222563 by nyc_function(2733)   on 2010-06-03 23:20:12 (Show Source): You can put this solution on YOUR website!3^2 + 4^2 = 5^2 9 + 16 = 25 25 = 25 The answer is choice A.
 Angles/311214: The ratio of the measures of two complementary angles is 5:13. What are the measures of the angles? 1 solutions Answer 222561 by nyc_function(2733)   on 2010-06-03 23:17:51 (Show Source): You can put this solution on YOUR website!Let 5x = smaller angle Let 13x = bigger angle 5x + 13x = 90 Can you continue?