Algebra ->  Tutoring on algebra.com -> See tutors' answers!      Log On

 Tutoring Home For Students Tools for Tutors Our Tutors Register Recently Solved
 By Tutor
| By Problem Number |

Tutor:

# Recent problems solved by 'dabanfield'

Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809, >>Next

 Linear_Equations_And_Systems_Word_Problems/318939: the difference of two numbers is 6. Their sum is 30. Find the two numbers. please show all work 1 solutions Answer 228321 by dabanfield(803)   on 2010-06-30 21:33:32 (Show Source): You can put this solution on YOUR website!the difference of two numbers is 6. Their sum is 30. Find the two numbers. please show all work Let x and y be the two numbers. Then we have: 1.) x - y = 6 and 2.) x + y = 30 From 1.) we have x = y + 6. Substituting y + 6 for x in 2.) we have: (y+6) + y = 30 2y = 24 y = 12 Since x = y + 6 we have x = 12 + 6 = 18
 Linear_Algebra/318932: Find the value of k so that the line has slope m: 6x + ky = 10 and m = -2 1 solutions Answer 228320 by dabanfield(803)   on 2010-06-30 21:22:38 (Show Source): You can put this solution on YOUR website!Find the value of k so that the line has slope m: 6x + ky = 10 and m = -2 The line in slope-intercept form is: 6x + ky = 10 ky = -6x + 10 y = (-6/k)x + 10/k Since -6/k is the slope of the line we have -6/k = -2 -2k = -6 k = 3
 Linear_Algebra/318938: Can you please help me with these? Factor, if possible. (If not possible, enter PRIME.) y^4-256 and Factor, if possible. (If not possible, enter PRIME.) 3u^2-12 Andy1 solutions Answer 228319 by dabanfield(803)   on 2010-06-30 21:12:57 (Show Source): You can put this solution on YOUR website!Can you please help me with these? Factor, if possible. (If not possible, enter PRIME.) y^4-256 = (y^2 - 16)*(y^2 + 16) = (y-4)(y+4)*(y^2 + 16) and Factor, if possible. (If not possible, enter PRIME.) 3u^2-12 = 3*(u^2 - 4) = 3*(u-2)(u+2) Andy
 test/307500: Factor the expression into a product of two binomials. 5x^2(x-10)+ ( x-10)1 solutions Answer 219997 by dabanfield(803)   on 2010-05-23 09:18:37 (Show Source): You can put this solution on YOUR website!Factor the expression into a product of two binomials. 5x^2(x-10)+ ( x-10) = (5x^2 + 1)*(x-10)
 Surface-area/307169: what is the perimeter of a rectangle that has an area of 12,150 square feet? the ratio of length to width is 3:2.1 solutions Answer 219786 by dabanfield(803)   on 2010-05-21 18:13:35 (Show Source): You can put this solution on YOUR website!what is the perimeter of a rectangle that has an area of 12,150 square feet? the ratio of length to width is 3:2. Let the two sides of the rectangle be 3x and 2x respectively. Then we have: 3x*2x = 12150 6x^2 = 12150 x^2 = 2025 x = 45 The two sides then are 2*45 = 90 and 3*45 = 135
 Sequences-and-series/307192: Given these sets: A = {3, 4, 5, 6, 7} B = {6, 7, 8, 9} C = {2, 4, 6, 8} List the elements of this set C ∩ (AB) Please show steps ,Thank you1 solutions Answer 219785 by dabanfield(803)   on 2010-05-21 18:08:06 (Show Source): You can put this solution on YOUR website!Is AB the same as A U B? Please resubmit. Thanks.
 Square-cubic-other-roots/307168: [SQRT (8) + SQRT (16)] / [SQRT (8) + SQRT (81)]1 solutions Answer 219769 by dabanfield(803)   on 2010-05-21 17:47:19 (Show Source): You can put this solution on YOUR website![SQRT (8) + SQRT (16)] / [SQRT (8) + SQRT (81)] = (sqrt(4*2) + 4)/(sqrt(4*2) + 9) = 2*sqrt(2) + 4 / 2*sqrt(2) + 9 Multiply numerator and denominator by 2*sqrt(2) - 9: (2*sqrt(2) + 4)*(2*sqrt(2) - 9)/ (2*sqrt(2) + 9)*(2*sqrt(2) - 9)) = (4*sqrt(2)^2 - 18*sqrt(2) + 8*sqrt(2) - 36)/(4*sqrt(2)^2 - 81) = (4*2 - 10*sqrt(2) - 36)/(4*2 - 81) = (8 - 10sqrt(2) - 36)/ (8 - 81) (-10*sqrt(2) - 28)/-73 = (28 + 10 sqrt(2))/73
 Exponential-and-logarithmic-functions/307185: log(x + 4) + log(x + 3) = log 21 solutions Answer 219765 by dabanfield(803)   on 2010-05-21 17:31:41 (Show Source): You can put this solution on YOUR website!log(x + 4) + log(x + 3) = log 2 So we have: log(x+4)*(x+3) = log 2 And: (x+4)*(x+3) = 2 x^2 + 7x + 12 = 2 x^2 + 7x + 10 = 0 (x+2)*(x+5) = 0 x+2 = 0 or x+5 = 0 So x = -2 or x = -5
 Expressions-with-variables/307118: Simplify the expression. 7P2/5P41 solutions Answer 219764 by dabanfield(803)   on 2010-05-21 17:27:04 (Show Source): You can put this solution on YOUR website!7P2/5P4 = (7/5)*(p2/p4) = (7/5)*p^(2-4) = (7/5)*(p^-2) = (7/5)*(1/p^2) = 7/(5*p^2)
 Sequences-and-series/307087: What is the formula for the following sequence: 12, 42, 92, 162,...1 solutions Answer 219763 by dabanfield(803)   on 2010-05-21 17:22:02 (Show Source): You can put this solution on YOUR website!12, 42, 92, 162,... The first digit in each case is 1^2=1, 2^2=4 3^2=9 and 4^2=16. The second digit is always 2. So the next number should be 5^2 followed by 2, that is 252.
 Length-and-distance/306868: Each set of three points is collinear. Find each missing x- or y-value. Enter each answer to the nearest hundredth. (6, 10.2), (1.5, 3.45), (x, 2.85)1 solutions Answer 219554 by dabanfield(803)   on 2010-05-20 17:28:16 (Show Source): You can put this solution on YOUR website!(6, 10.2), (1.5, 3.45), (x, 2.85) The slope-intercept form of a line is: y = m*x + b where m is the slope and b is the value of y where the line crosses the x-axis (that is when x = 0 ). m = (10.2 - 3.45)/(6 - 1.5) m = 6.75/4.5 = 1.5 We have then 1.) y = 1.5*x + b. Since the line passes through the point (6,10.2) when x = 6, y = 10.2. Substituting these values in 1.) we have: 10.2 = 1.5*6 + b 10.2 = 9 + b b = 1.2 The equation of the line is then 2.) y = 1.5*x + 1.2 To find x for the third point on the line we substitute 2.85 for y in 2.): 2.85 = 1.5*x + 1.2 1.5*x = 2.85 - 1.2 1.5*x = 1.65 x = 1.65/1.5 = ?
 Miscellaneous_Word_Problems/306765: The sum of the digits of a two digit counting number is 10. If the digits are reversed, the new number is two less than three times the original number. What is the original number?1 solutions Answer 219552 by dabanfield(803)   on 2010-05-20 17:07:58 (Show Source): You can put this solution on YOUR website!The sum of the digits of a two digit counting number is 10. If the digits are reversed, the new number is two less than three times the original number. What is the original number? Let x be the tens digit and y the units digit. The original number then is 10*x + y. The new number is 10*y + x. We have then: 1.) x + y = 10 and 2.) 3*(10*x + y) - 2 = 10*y + x From 1.) we have x = 10 - y. Substituting 10 - y for x in 2.) we have: 3*(10*(10-y) + y) - 2 = 10*y + (10 - y) 3*(100 - 10y + y) - 2 = 10*y + (10 - y) 3*(100 - 9*y) - 2 = 10*y + (10 - y) 300 - 27*y - 2 = 10*y + 10 - y 298 - 27*y = 9*y + 10 36*y = 288 y = 8 Substituting 8 for y in 1.) above we have: x + y = 10 x + 8 = 10 x = 2 The original number then is 28.
 Radicals/306864: how do you work out 4 times the square root of 2 plus 6 times the sqaure root of 50 ??1 solutions Answer 219550 by dabanfield(803)   on 2010-05-20 16:50:07 (Show Source): You can put this solution on YOUR website!how do you work out 4 times the square root of 2 plus 6 times the sqaure root of 50 ?? 4*sqrt(2) + 6*sqrt(50) = 4*sqrt(2) + 6*sqrt(25*2) = 4*sqrt(2) + 6*sqrt(25)*sqrt(2)= 4*sqrt(2) + 6*5*sqrt(2) = 4*sqrt(2) + 30*sqrt(2) = 34*sqrt(2)
 Travel_Word_Problems/306764: I dont even know where to start with this problem. The boat can travel 112 miles downstream in 4 hours but requires 6 hours to travel 48 miles upstream. What is the speed of the boat in still water, and what is the speed of the current?1 solutions Answer 219471 by dabanfield(803)   on 2010-05-20 10:47:59 (Show Source): You can put this solution on YOUR website!I dont even know where to start with this problem. The boat can travel 112 miles downstream in 4 hours but requires 6 hours to travel 48 miles upstream. What is the speed of the boat in still water, and what is the speed of the current? We will need to use the formula distance = speed*time (d=s*t). Let c be the speed of the current and b the speed the speed the boat can travel in still water. The speed going downstream (with the current) is b+c and the speed going upstream (against the current ) is b-c. We have two equations: Upstream: d = s*t 48 = (b-c)* 6 Divide both sides above by 6: 8 = b - c 1.) b = 8 + c Downstream: d = s*t 112 = (b+c) * 4 Divide both sides above by 4: 2.) 28 = b + c Substituting 8 + c for b (from 1.) in equation 2.) we have: 28 = (8 + c) + c 28 = 8 + 2*c 2*c = 20 c = 10 Sustituting 10 for c in 1.) we have b = 8 + 10 = 18.
 Angles/306767: The measure of one angle is seven less than twice the measure of the other angle.what are the measures of both angles.1 solutions Answer 219469 by dabanfield(803)   on 2010-05-20 10:25:43 (Show Source): You can put this solution on YOUR website!The measure of one angle is seven less than twice the measure of the other angle.what are the measures of both angles. More information is needed. Are the angles complementary? Supplementary?
 Polynomials-and-rational-expressions/306759: I am trying to figure out how to start this problem. I saw it and I immediately was confused. Please help me solve this equation: 1 solutions Answer 219468 by dabanfield(803)   on 2010-05-20 10:16:57 (Show Source): You can put this solution on YOUR website![((x+1)/(x-1)+1)/((x+1)/(x-1)-1)]^5 Let's look at the expression that is being raised to the 5th power. A common denominator for the terms is x-1. Rewriting 1 as (x-1)/(x-1): ((x+1)/(x-1)) + (x-1)/(x-1) / ((x+1)/(x-1) - (x-1)/(x-1)) Combining terms we have: (((x+1) + (x+1))/(x-1)) / (((x+1) - (x-1))/(x-1)) = ((2x+2)/(x-1)) / (2/(x-1)) Multiplying numerator and denominator above by (x-1) gives: (2x+2)/2 = 2*(x+1)/2 = x+1 So the original problem reduces to (x+1)^5 You could expand out (x+1)^5.
 Permutations/306621: in how many ways can 2 co-chairs be selected from a club of 20 students?1 solutions Answer 219466 by dabanfield(803)   on 2010-05-20 09:58:20 (Show Source): You can put this solution on YOUR website!C(20,2) = 20!/((20-2)!*2!) = 20!/(18!*2!)
 Proportions/306545: solve for x in the following 3:80 x 150.1 solutions Answer 219384 by dabanfield(803)   on 2010-05-19 21:03:27 (Show Source): You can put this solution on YOUR website!Question is unclear. Please resubmit.
 Trigonometry-basics/306522: which expression is equivalent to log(7)2401 - log(3)243 1) log(4)2158 2) 7 log 2401 - log 243 3) -log(4) 2401/243 4) -11 solutions Answer 219383 by dabanfield(803)   on 2010-05-19 21:01:50 (Show Source): You can put this solution on YOUR website!which expression is equivalent to log(7)2401 - log(3)243 Since 7*7*7*7 = 7^4 = 2401, log(7)2401 = 4 Also 3*3*3*3*3 = 3^5 = 243, so log(3)243 = 5 The expression above then reduces to 4 - 5 = -1
 Linear-systems/306509: A chemist has one solution that is 40% alcohol and another that is 55% alcohol. How much of each must she use to make 15 liters of solution that is 50% alcohol?1 solutions Answer 219381 by dabanfield(803)   on 2010-05-19 20:44:07 (Show Source): You can put this solution on YOUR website!A chemist has one solution that is 40% alcohol and another that is 55% alcohol. How much of each must she use to make 15 liters of solution that is 50% alcohol? Let x be the amount of 40% alcohol and y the amount of 55% alcohol. Then we have: 1.) x + y = 15 and 2.) .40x + .55y = .50*15 From 1.) we know that x = 15-y. Substituting 15-y for x in 2.) gives us: .40*(15-y) + .55*y = 7.5 6 - .4y + .55y = 7.5 .15y = 1.5 y = 10 Substituting 10 for y in equation 1.) we have x + 10 = 15, so x =5.
 Linear-equations/306246: Which answer choice is the set of all solutions to the inequality square root ofx < 4? A. There are no solutions. B. x < 16 C. x > 16 D. All real numbers. 1 solutions Answer 219196 by dabanfield(803)   on 2010-05-19 09:18:13 (Show Source): You can put this solution on YOUR website!sqrt(x) < 4 Squaring both sides we have: x < 16 Note that sqrt(x) is not defined for x < 0 so the answer is actually: 0 <= x < 16
 Trigonometry-basics/306193: your aircraft uses 10 gallons of fuel per hour, how much will you use in 2 hours?1 solutions Answer 219194 by dabanfield(803)   on 2010-05-19 09:12:57 (Show Source): You can put this solution on YOUR website!amount used equals the rate of use multiplied by the time so: amount = 10*2 = 20 gallons.
 Equations/306197: Please help: Solve for (x) (x-1) (x-3)=-41 solutions Answer 219192 by dabanfield(803)   on 2010-05-19 09:10:31 (Show Source): You can put this solution on YOUR website!(x-1) (x-3)=-4 x^2 - 4x + 3 = -4 x^2 - 4x + 7 = 0 This is a quadratic equation with a = 1, b = -4 and c = 7. Use the quadratic formula to find the solutions.
 Equations/306201: a force of 72 n acting upon a given object results in an acceleration of 8 m/s squared. if the magnitude of the force acting upon the same object is changed to 63 n, what will the objects acceleration become? would it be 7 m/s squared 1 solutions Answer 219190 by dabanfield(803)   on 2010-05-19 09:06:15 (Show Source): You can put this solution on YOUR website!a force of 72 n acting upon a given object results in an acceleration of 8 m/s squared. if the magnitude of the force acting upon the same object is changed to 63 n, what will the objects acceleration become? would it be 7 m/s squared Force = mass * acceleration (F = m*a) Let m be the mass of the object. We know that 72 = m*8 so m = 72/8 = 9. If the acceleration is 63 then we have: 63 = m*a 63 = 9*a a = 63/9 = 7 m/s sq
 Numbers_Word_Problems/306199: can the total of 5 odd numbers would be 321 solutions Answer 219187 by dabanfield(803)   on 2010-05-19 09:00:44 (Show Source): You can put this solution on YOUR website!Each odd number can be written as 2*k + 1 for some value of k. Let's say the five numbers are: 2*k1 + 1 2*k2 + 1 2*k3 + 1 2*k4 + 1 2*k5 + 1 The sum of these then is 2*(k1+k2+k3+k4+k5) + 5 = 2*(k1+k2+k3+k4+k5+2) + 1 which is an odd number so can't be 32 (which is even)
 absolute-value/306196: How do you calculate the value of the following expression:11/6 + 5/16 = 88/48 +15/48 = 103/481 solutions Answer 219186 by dabanfield(803)   on 2010-05-19 08:53:37 (Show Source): You can put this solution on YOUR website!How do you calculate the value of the following expression:11/6 + 5/16 = 88/48 +15/48 = 103/48 11/6 + 5/16 = 88/48 + 15/48 = 103/48 is correct :)
 Linear-equations/306252: What is the y-intercept of x = y + 6? A. y = 6 B. y = -6 C. y = 0 D. y = 3 1 solutions Answer 219185 by dabanfield(803)   on 2010-05-19 08:48:52 (Show Source): You can put this solution on YOUR website!What is the y-intercept of x = y + 6? The y-intercept is the value of y when x is zero so: 0 = y + 6 y = -6
 Square-cubic-other-roots/305085: How do I complete the square? 1 solutions Answer 218485 by dabanfield(803)   on 2010-05-16 18:44:58 (Show Source): You can put this solution on YOUR website!x^2 + 6x + 23 = 0 Rewrie the above as: x^2 + 6x = -23 To complete the square on the loeft side we need to divide the coefficient on the x term by 2, square it and add the result to both sides: The coefficient on the x term is 6, so we have (6/2)^2 = 3^2 = 9. Adding 9 to both sides we have: x^2 + 6x + 9 = -23 + 9 x^2 + 6x + 9 = -14 (x+3)*(x+3) = -14 (x+3)^2 = -14 Taking the square root of both sides: (x+3)= +sqrt(-14) and (x+3)= -sqrt(-14) Note that sqrt(-14) is a complex number, namely i*sqrt(14). We have then: x+3 = i*sqrt(14) x = -3 + i*sqrt914) and x+3 = -i*sqrt(14) x = -3 - i*sqrt(14)
 Quadratic_Equations/305086: It says: Solve by completing the square equation: m^2-25/2x=5/2 the 25/2 is a fraction and the "x" is on the side, and the 5/2 is a fraction as well. This is what I've tried so far: I moved the "5/2" to the other side of the equal sign to where it looks like this: m^2-25/2x-5/2=0 then I've tried to figure out how to square it 1 solutions Answer 218481 by dabanfield(803)   on 2010-05-16 18:24:49 (Show Source): You can put this solution on YOUR website!Are you sure there are two variables, m AND x?
 Functions/305139: f(x)=4x h(x)=-7x-5 find h(f(3)) please tell me what i did wrong this is how i tried to solve the above problem 4(3)(-7(3)-5)1 solutions Answer 218480 by dabanfield(803)   on 2010-05-16 18:21:24 (Show Source): You can put this solution on YOUR website!f(x)=4x h(x)=-7x-5 find h(f(3)) please tell me what i did wrong this is how i tried to solve the above problem 4(3)(-7(3)-5) f(3) = 4*3 = 12 h(f(3)) = h(12) = (-7*12) - 5 = -84 - 5 = -89