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# Recent problems solved by 'mathitutor'

 Linear-equations/382860: in a tour 2 adults and 5 students paid \$77 and in other van 2 adults and 7 students paid \$95 for the same tour.find adults price and student price?1 solutions Answer 271227 by mathitutor(25)   on 2010-12-08 06:02:38 (Show Source): You can put this solution on YOUR website!Say, adults price = x and student price = y Then 2x + 5y = 77 --- (1) 2x + 7y = 95 --- (2) (2) - (1) => 7y - 5y = 95 -77 2y = 18 y = \$9 ---(3) placing y's value in (1) 2x + 45 = 77 2x = 32 x = \$16 ----(4) (3) and (4) are the answers
 Miscellaneous_Word_Problems/300237: What percent of all natural numbers from 1 to 10000 are perfect squares? A) 1% B) 1.5% C) 2% D) 2.5% E) 5%1 solutions Answer 215473 by mathitutor(25)   on 2010-05-04 05:28:41 (Show Source): You can put this solution on YOUR website!A) 1% 100^2 = 10000 Hence there are 100 perfect squares.
 Problems-with-consecutive-odd-even-integers/300236: If x denotes any negative integer number, which of the following expressions will always have the greatest value? A) x+1 B) 2x C) –2x D) 6x+2 E) x-21 solutions Answer 215472 by mathitutor(25)   on 2010-05-04 05:26:27 (Show Source): You can put this solution on YOUR website!C) -2x
 Probability-and-statistics/299678: If two events are collectively exhaustive, what is the probability that one or the other occurs? a. 0.25 b. 0.50 c. 1.00 d. Cannot be determined from the information given.1 solutions Answer 215258 by mathitutor(25)   on 2010-05-03 05:29:42 (Show Source): You can put this solution on YOUR website!B. 0.5
 Problems-with-consecutive-odd-even-integers/299701: The sum of 4 consecutive integers is 26. What is the product of the 4 numbers?1 solutions Answer 215257 by mathitutor(25)   on 2010-05-03 05:26:39 (Show Source): You can put this solution on YOUR website!Assume that the first number is x x + x + 1 + x + 2 + x + 3 = 26 => 4x + 6 = 26 => 4x = 26 - 6 => 4x = 20 => x = 20/4 => x = 5 Hence the numbers are: 5, 6, 7, 8 Product of these numbers = 5 x 6 x 7 x 8 = 1680
 Linear_Algebra/299703: If f(x) = x - 1, what is the value of x that satisfies the equality f(x) - 1 = f(x^2)- x^21 solutions Answer 215256 by mathitutor(25)   on 2010-05-03 05:23:20 (Show Source): You can put this solution on YOUR website!f(x) - 1 = f(x^2) - x^2 => x - 1 - 1 = x^2 - 1 - x^2 => x - 2 = -1 => x = -1 + 2 => x = 1
 Miscellaneous_Word_Problems/252238: The pitch of a screw is the distance between threads. With each complete rotation of the screw, it goes in or out a distance equal to its pitch. How far will a screw with a pitch of 2/45 inches go into a piece of wood when it is turned 10 complete rotations clockwise? a 1/225 in b 9/4 in c 4/9 in d 1/9 in e 9 in1 solutions Answer 184050 by mathitutor(25)   on 2009-12-25 07:09:13 (Show Source): You can put this solution on YOUR website!10 x 2/45 = 20/45 = 4/9 The answer is (C)
 Numbers_Word_Problems/250412: what is Three more than twice a number x is fifteen1 solutions Answer 182325 by mathitutor(25)   on 2009-12-15 21:05:58 (Show Source): You can put this solution on YOUR website!2x + 3 = 15 => 2x = 15 - 3 => 2x = 12 => x = 12/2 => x = 6
 Functions/250253: Please help me help my daughter solve this homework problem. For a car traveling at a constant rate of 60 mi/h, the distance traveled is a function of the time traveled. a. Express this relation as a function b Find the range of the function when the domain is [1,5,10] c What do the domain and range represent? I am thinking that the expressed function should be something like f(d) = (60m)h We can solve b. once we can figure out how to express it as a function. Thank you for your help.1 solutions Answer 182324 by mathitutor(25)   on 2009-12-15 21:01:27 (Show Source): You can put this solution on YOUR website!(a)The distance travel when something is moving at a constant speed = speed x time As the constant velocity is given = 60 mi/hr The distance travel will be varying with time and it is a function of time as given below: s(t) = 60t where t is in hours. I think this is what you are looking for. Contact me at tutor@mathitutor.com for any further help.
 Triangles/250392: The measure of each of the base angles of an isosceles triangle is 24 degrees less than the measure of the vertex angle. Find the measure of the vertex angle.1 solutions Answer 182322 by mathitutor(25)   on 2009-12-15 20:56:29 (Show Source): You can put this solution on YOUR website!let the vertex angle = x Hence the each of base angle = x - 24 Sum of all angles of a triangle = 180 => x + x - 24 + x - 24 = 180 => 3x - 48 = 180 => 3x = 180 + 48 => 3x = 228 => x = 76 degree.
 Rectangles/250396: The length of a rectangle is 7 centimeters less than twice its width.The perimeter of the rectangle is 34 cm. What are the demensions of the rectangle?1 solutions Answer 182318 by mathitutor(25)   on 2009-12-15 20:51:24 (Show Source): You can put this solution on YOUR website!Let the width = x Then the length = 2x - 7 Hence the perimeter = 2x + 2(2x-7) = 34 => 2x + 4x - 14 = 34 => 6x = 34 + 14 => 6x = 48 => x = 48/6 => x = 8 Hence the width = 8 cm length = 2x8 - 7 = 16 - 7 = 9 cm
 Equations/250395: 2(x+1)=3x-1 Solve for x1 solutions Answer 182314 by mathitutor(25)   on 2009-12-15 20:43:50 (Show Source): You can put this solution on YOUR website!2(x+1)=3x-1 => 2x + 2 = 3x - 1 => 3x -2x = 2 + 1 => x = 3
 Quadratic_Equations/249999: a^2-11a+28=01 solutions Answer 181984 by mathitutor(25)   on 2009-12-14 21:30:14 (Show Source): You can put this solution on YOUR website!a^2-11a+28= a^2-7a - 4a+28= a(a-7) -4(a-7)=(a-4)(a-7)=0 Hence a = 4 and 7
 Quadratic_Equations/249184: 1 solutions Answer 181546 by mathitutor(25)   on 2009-12-13 09:57:17 (Show Source): You can put this solution on YOUR website!Solve equation by factoring 9x^2+5x-11=0 (3x)^2 + 2.3x.5/6 + (5/6)^2 - 11 - (5/6)^2 = 0 [3x + 5/6]^2 - [11 + 25/36] = 0 [3x + 5/6]^2 - [421/36] = 0 [3x + 5/6]^2 - [sqrt(421)/6]^2 = 0 [3x + 5/6 + sqrt(421)/6][3x + 5/6 - sqrt(421)/6]= 0 Equate each factor to 0 and that will give you two solutions.
 Sequences-and-series/247854: Question: Find the sums of the following geometric series. 1 + 3 + 9 +...+2187. What I've tried so far... So: know:a=1 r=3 tn=2187 find:??? For this problem, wouldn't I have to find how many terms are in the sequence first? Then whatever n is, I plug that into another equation? I'm so lost...please help!1 solutions Answer 180736 by mathitutor(25)   on 2009-12-09 17:41:35 (Show Source): You can put this solution on YOUR website!This is a standard geometric progression, 3^0 + 3^1 + 3^2 + ... + 3^7 There is a standard formula for summation of terms of a geometric progression series. Use that to solve this.
 Trigonometry-basics/247896: write the standard form of the equation of the circle that passes through the point (0,1) with its center at the origin.1 solutions Answer 180734 by mathitutor(25)   on 2009-12-09 17:34:47 (Show Source): You can put this solution on YOUR website!radius = a = sqrt[(0-0)^2 + (1-0)^2] = 1 the equation of the circle is x^2 + y^2 = 1^2 x^2 + y^2 = 1
 Linear-systems/247895: 180=7x-151 solutions Answer 180733 by mathitutor(25)   on 2009-12-09 17:32:37 (Show Source): You can put this solution on YOUR website!180 = 7x -15 Add 15 to both side 180 + 15 = 7x -15 + 15 195 = 7x x = 195/7
 Linear_Algebra/245999: x + y=8 over x - y =-10 1 solutions Answer 179686 by mathitutor(25)   on 2009-12-04 21:38:36 (Show Source): You can put this solution on YOUR website!x + y = 8 ---(1) x - y = -10 ---(2) (1) + (2) gives, 2x = -2 => x = -1 put the value of x in 1, -1 + y = 8 => y = 8 + 1 = 9
 Quadratic_Equations/244008: What is the quadratic equation of 4x^2-8x-9=0 (simplifiy your answer. type an exact answer using radicals as needed. Use integers or fractions for any number in the expression. Express complex numbers in the form of i.)1 solutions Answer 178631 by mathitutor(25)   on 2009-11-30 12:49:26 (Show Source): You can put this solution on YOUR website!4x^2-8x-9=0 => (2x)^2 - 2.2x.2 + 2^2 -9 -4 = 0 => (2x -2)^2 = 13 => 2x - 2 = +sqrt(13) or -sqrt(13) => 2x = 2 +sqrt(13) or 2-sqrt(13) x = 1 + sqrt(13)/2 or 1 - sqrt(13)/2
 Quadratic_Equations/244009: What is the quadratic equation of 4x^2-8x-9=0 (simplifiy your answer. type an exact answer using radicals as needed. Use integers or fractions for any number in the expression. Express complex numbers in the form of i.)1 solutions Answer 178629 by mathitutor(25)   on 2009-11-30 12:46:25 (Show Source): You can put this solution on YOUR website!4x^2-8x-9=0 => (2x)^2 - 2.2x.2 + 2^2 -9 -4 = 0 => (2x -2)^2 = 13 => 2x - 2 = +sqrt(13) or -sqrt(13) => 2x = 2 +sqrt(13) or 2-sqrt(13) x = 1 + sqrt(13)/2 or 1 - sqrt(13)/2
 Graphs/243976: Find an equation of the line meeting the specified conditions. Write your final answer in slope-intercept form. Containing the point (0, 4) and parallel to y = 7x - 6 1 solutions Answer 178627 by mathitutor(25)   on 2009-11-30 12:39:57 (Show Source): You can put this solution on YOUR website!slope = m = dy/dx = 7 y = 7x + c put x =0, y = 4 to calculate c 4 = c Hence the equation is y = 7x + 4
 logarithm/243984: Factorise: 25^2-64y^21 solutions Answer 178625 by mathitutor(25)   on 2009-11-30 12:37:50 (Show Source): You can put this solution on YOUR website!25^2-64y^2 = (5)^2 - (8y)^2 = (5+8y)(5-8y)
 Rectangles/243971: The sum of 2numbers is 15. 1 less than 3 times the smaller is equal to the larger. Find the 2 numbers.1 solutions Answer 178624 by mathitutor(25)   on 2009-11-30 12:34:10 (Show Source): You can put this solution on YOUR website!assume that the numbers are x and 15-x. 3x - 1 = 15 -x => 4x = 16 => x = 4 The numbers are 4 and 11.
 Age_Word_Problems/244005: If I add four times my age four years from now to five times my age five years from now, I get ten times my current age. How old will I be five years from now?1 solutions Answer 178623 by mathitutor(25)   on 2009-11-30 12:31:30 (Show Source): You can put this solution on YOUR website!Assume my current age = x 4(x+4) + 5(x+5) = 10x => 4x + 16 + 5x + 25 = 10x => 9x + 41 = 10x => 10x-9x = 41 => x = 41
 Polynomials-and-rational-expressions/244006: What is the root of 49x^2-25=0?1 solutions Answer 178622 by mathitutor(25)   on 2009-11-30 12:28:30 (Show Source): You can put this solution on YOUR website!49x^2-25=0 => (7x)^2 - 5^2 = 0 => (7x + 5)(7x-5) = 0 => x = 5/7 and -5/7