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Linear-systems/200813: get the value of x and y x-y=5 3x+y=3 1 solutions Answer 151054 by nerdybill(6963)   on 2009-06-22 07:23:41 (Show Source): You can put this solution on YOUR website! Applying the substitution method: x-y=5 (equation 1) 3x+y=3 (equation 2) . Solve equation 1 for x: x-y=5 x = y+5 Substitute the above into equation 2 and solve for y: 3x+y=3 3(y+5)+y=3 3y+15+y=3 4y+15=3 4y = -12 y = -3 . Substitute the above into equation 1 and solve for x: x-y=5 x-(-3)=5 x+3 = 5 x = 2 . Solution: x=2 and y=-3

Linear_Algebra/200775: Give an ordered pair (x,y) of numbers that satisfy the equations 6x + y = 4 1 solutions Answer 151014 by nerdybill(6963)   on 2009-06-21 15:31:13 (Show Source): You can put this solution on YOUR website! Give an ordered pair (x,y) of numbers that satisfy the equations 6x + y = 4 . Simply pick a value for 'x' (say 1), substitute it in and solve for y: If x = 1 6(1) + y = 4 6 + y = 4 y = -2 . Therefore, an ordered pair would be: (1, -2)

Linear-systems/200689: Find the domain of the rational function h(x)= x-80 over x to the 3rd - 2x to the 2nd - 35x 1 solutions Answer 151013 by nerdybill(6963)   on 2009-06-21 15:29:12 (Show Source): You can put this solution on YOUR website! Find the domain of the rational function h(x)= x-80 over x to the 3rd - 2x to the 2nd - 35x . Domain is all real numbers EXCEPT when 'x' makes the denominator zero. Find those exceptions by setting the denominator to zero and solving for x: x = {0, 7, -5} . Therefore, the domain is "All real numbers, except for 0, 7 and -5"

Polynomials-and-rational-expressions/200768: Please help me solve: The length of a triangle are as follows: height is 8 feet, base across is 12 feet, what is the lenght of the triangle? It looks like an isoceles triangle. Answer: a=base b=? h=height h=sqrt(b^2-1/4a^2) 8=sqrt(b^2-1/4(12^2) 8=sqrt(b^2-1/4(144) 8=sqrt(b^2-36) 8=b-6 14=b Please confirm if my answer is ccorrect? Thanks a bunch 1 solutions Answer 151004 by nerdybill(6963)   on 2009-06-21 13:06:57 (Show Source): You can put this solution on YOUR website! height is 8 feet, base across is 12 feet, what is the lenght of the triangle? It looks like an isoceles triangle. . Find the length via the Pythagorean theorem where length of triangle is the hypotenuse height is one side half the base is the other side . Let x = length of triangle 8^2 + 6^2 = x^2 64 + 36 = x^2 100 = x^2 sqrt(100) = x {-10, 10} = x Throw out negative answer: 10 feet =x

Rectangles/200752: A rectangle is 4 meters longer than it is wide. The area of the rectangle is 252 square meters. Find the length and width of the rectangle. length = ________ m width = ________ m 1 solutions Answer 151000 by nerdybill(6963)   on 2009-06-21 12:24:57 (Show Source): You can put this solution on YOUR website! A rectangle is 4 meters longer than it is wide. The area of the rectangle is 252 square meters. Find the length and width of the rectangle. . Let w = width of rectangle then w+4 = length of rectangle . w(w+4) = 252 w^2+4w = 252 w^2+4w-252 = 0 (w-14)(w+18) = 0 w = {14, -18} Throw out the negative solution leaving: w = 14 meters (width) . w+4 =14+4 = 18 meters (length)

logarithm/200763: log42(x^2-x)=1 1 solutions Answer 150992 by nerdybill(6963)   on 2009-06-21 12:08:08 (Show Source): You can put this solution on YOUR website! Assuming you mean log base 42: . {{( (x-7)(x+6) = 0}}} x = {-6, 7}

Rate-of-work-word-problems/200766: pat can read at a constant rate of 400 pages per 8 hours . how many seconds does it take pat to read one page ? 1 solutions Answer 150990 by nerdybill(6963)   on 2009-06-21 12:01:08 (Show Source): You can put this solution on YOUR website! pat can read at a constant rate of 400 pages per 8 hours . how many seconds does it take pat to read one page ? . 400 pages/ 8 hr = 1 page per .02 hr . 1 pg 1 hr 1 min -------- x ------ x ------ 8.02 hr 60 min 60 sec . = 1/72 (1 page per 72 seconds) . ans: 72 seconds

Graphs/200735: This question is from textbook Beginning and Intermediate Algebra How do you find the X and Y intercepts and then graph the line 1 solutions Answer 150954 by nerdybill(6963)   on 2009-06-20 23:04:09 (Show Source): You can put this solution on YOUR website! How do you find the X and Y intercepts and then graph the line . Given your equation... . 1. to find the x-intercept, set 'y'=0 and solve for x Your x-intercept will then be at ("value found", 0) . 2. to find the y-intercept, set 'x'=0 and solve for y Your y-intercept will then be at (0, "value found") . 3. plot the two points found above in an x-y graph and draw a line through the two points -- that's it, you're done.

Rational-functions/200675: 3x^2-18x-48= 1 solutions Answer 150927 by nerdybill(6963)   on 2009-06-20 09:03:23 (Show Source): You can put this solution on YOUR website! I presume you'd like to factor this: 3x^2-18x-48 . 3(x^2-6x-16) 3(x-8)(x+2)

Miscellaneous_Word_Problems/200679: two angles are complementary if the sum of their measures 90 degrees. Themeasure of the first angle is 5 degrees less than 4 times the second angle. What is the measure of the first angle. 1 solutions Answer 150925 by nerdybill(6963)   on 2009-06-20 08:57:06 (Show Source): You can put this solution on YOUR website! two angles are complementary if the sum of their measures 90 degrees. Themeasure of the first angle is 5 degrees less than 4 times the second angle. What is the measure of the first angle. . Let x = second angle then 4x-5 = first angle . x + 4x-5 = 90 x + 4x = 95 5x = 90 x = 18 degrees (second angle) . First angle: 4x-5 = 4(18)-5 = 72-5 = 67 degrees (first angle)

Mixture_Word_Problems/200681: Please I need help with this. Find x if shaded area is 90.the (whole rectangle is shaded except for the holes) By developing and solving by factoring quadratic equation. The rectangle width is 2x-2, length is 3x, and there are 3 holes cut out with the width of x and length of x-1. I know l*w=A but how do you take out the hole squares? 1 solutions Answer 150924 by nerdybill(6963)   on 2009-06-20 08:53:47 (Show Source): You can put this solution on YOUR website! Please I need help with this. Find x if shaded area is 90.the (whole rectangle is shaded except for the holes) By developing and solving by factoring quadratic equation. The rectangle width is 2x-2, length is 3x, and there are 3 holes cut out with the width of x and length of x-1. I know l*w=A but how do you take out the hole squares? . Area of rectangle = (3x)(2x-2) . Area of one hole = x(x-1) Three holes would then be 3x(x-1) . "Shaded area" = "area of rectangle" - "area of holes" 90 = (3x)(2x-2) - 3x(x-1) On the right side, distribute: 90 = (6x^2-6x) - (3x^2-3x) 90 = 6x^2-6x - 3x^2+3x 90 = 3x^2-3x 0 = 3x^2-3x-90 0 = x^2-x-30 Factoring: 0 = (x-6)(x+5) x = {-5, 6} Throwing out the negative solution we get: x = 6

Functions/200612: h(x)= x-3/x^3-4x What is the domain of the function 1 solutions Answer 150860 by nerdybill(6963)   on 2009-06-19 12:32:10 (Show Source): You can put this solution on YOUR website! . Domain specifies the values 'x' can take. The only thing we have to worry about is if the denominator goes to zero. . So, set the denominator to zero and solve for x: x^3-4x = 0 x(x^2-4) = 0 . So, the denominator goes to zero if: x=0 or x^2-4=0 . Therefore, x = all real numbers EXCEPT: x=0, x=-2, x=2

Miscellaneous_Word_Problems/200610: The amount of an investment of P dollars for t years at simple interest rate r is given by A = P + prt Rewrite this formula by factoring out the greatest common factor on the right-hand side. 1 solutions Answer 150859 by nerdybill(6963)   on 2009-06-19 12:28:21 (Show Source): You can put this solution on YOUR website! A = p + prt The 'p' can be factored: A = p(1 + rt) . That's all there is to it...

Rational-functions/200602: dap5654@aol.com. I am in intermediate algebra. I am having trouble with equations with rational expressions. Could you help me solve this equation? ? I think the answer is 3,4. 1 solutions Answer 150851 by nerdybill(6963)   on 2009-06-19 11:40:29 (Show Source): You can put this solution on YOUR website! Cross multiplying we get: Factoring: x = {-4,3}

Square-cubic-other-roots/200603: sqrt 2 (sqrt 50 + sqrt 10) 1 solutions Answer 150850 by nerdybill(6963)   on 2009-06-19 11:38:12 (Show Source): You can put this solution on YOUR website! Distributing the to terms inside the ():

Linear-equations/200484: Find the slope of the line 4x-5y=2 1 solutions Answer 150735 by nerdybill(6963)   on 2009-06-18 08:09:20 (Show Source): You can put this solution on YOUR website! Put 4x-5y=2 into the "slope-point" form of y = mx + b where m is the slope b is the y-intercept . 4x-5y=2 -5y = -4x+2 5y = 4x-2 y = (4/5)x - 2/5 . Therefore, the slope is 4/5

Travel_Word_Problems/200494: This question is from textbook Elementary and Intermediate Algebra Avoiding a collision. A car is traveling on a road that is perpendicular to a railroad track. When the car is 30 meters from the crossing, the car’s new collision detector warns the driver that there is a train 50 meters from the car and heading toward the same crossing. How far is the train from the crossing? 1 solutions Answer 150734 by nerdybill(6963)   on 2009-06-18 08:04:48 (Show Source): You can put this solution on YOUR website! Avoiding a collision. A car is traveling on a road that is perpendicular to a railroad track. When the car is 30 meters from the crossing, the car’s new collision detector warns the driver that there is a train 50 meters from the car and heading toward the same crossing. How far is the train from the crossing? . Applying Pythagorean theorem: Let x = train's distance from crossing then x^2 + 30^2 = 50^2 x^2 = 50^2 - 30^2 x^2 = 2500 - 900 x^2 = 1600 x = x = 40 meters

logarithm/200476: 1 solutions Answer 150727 by nerdybill(6963)   on 2009-06-17 23:34:24 (Show Source): You can put this solution on YOUR website! Applying log rules: Solving for x using the quadratic equation yields: x = {6.162, -0.162} We can throw out the negative solution leaving: x = 6.162 . Details of quadratic follows: 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=40 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 6.16227766016838, -0.16227766016838. Here's your graph:

logarithm/200475: 1 solutions Answer 150725 by nerdybill(6963)   on 2009-06-17 23:27:18 (Show Source): You can put this solution on YOUR website! Apply log rules: log (x) + log ( x + 3 ) = 1 log [(x)(x+3)] = 1 (x)(x+3) = 10^1 x^2 + 3x = 10 x^2 + 3x - 10 = 0 (x+5)(x-2) = 0 x = {-5, 2} Throwing out the negative solution we are left with: x = 2

Polynomials-and-rational-expressions/200431: 9a^2-64b^2= 1 solutions Answer 150693 by nerdybill(6963)   on 2009-06-17 15:55:35 (Show Source): You can put this solution on YOUR website! I presume you want to factor it... . 9a^2-64b^2 can be written as: (3a)^2-(8b)^2 now you can consider it as a difference of squares: (3a+8b)(3a-8b)

Unit_Conversion_Word_Problems/200434: A bowling ball weighs 16 pounds. How many kilograms does it weigh? 1 solutions Answer 150692 by nerdybill(6963)   on 2009-06-17 15:53:34 (Show Source): You can put this solution on YOUR website! Since 1 pound = 0.45359237 kilograms . 16 * 0.45359237 = 7.26 kilograms

Miscellaneous_Word_Problems/200371: Amount of an investment. The amount of an investment of P dollars for t years at simple interest rate r is given by A = P + Prt. a) Rewrite this formula by factoring out the greatest common factor on the right-hand side. b) Find A if $8300 is invested for 3 years at a simple interest rate of 15%. 1 solutions Answer 150670 by nerdybill(6963)   on 2009-06-17 11:15:41 (Show Source): You can put this solution on YOUR website! Amount of an investment. The amount of an investment of P dollars for t years at simple interest rate r is given by A = P + Prt. a) Rewrite this formula by factoring out the greatest common factor on the right-hand side. A = P + Prt Factoring out a P: A = P(1 + rt) . b) Find A if $8300 is invested for 3 years at a simple interest rate of 15%. A = P(1 + rt) A = 8300(1 + .15(3)) A = 8300(1 + .45) A = 8300(1.45) A = $12035

Expressions-with-variables/200374: Hello, I need some help. I keep trying the following problem and am not sure what I am doing wrong. I am not sure if I am changing the signs in the right places. The problem and what I have so far are as follows: Perform the indicated operations: (x^2 - 4x + 1) - (-8x^2 + 2x - 6) - (x^2 + 3x + 3/5) x^2 - 8x^2 - x^2 - 4x + 2x + 3x + 1 - 6 + 3/5 Can you please help. Thank you in advance. 1 solutions Answer 150662 by nerdybill(6963)   on 2009-06-17 06:47:29 (Show Source): You can put this solution on YOUR website! (x^2 - 4x + 1) - (-8x^2 + 2x - 6) - (x^2 + 3x + 3/5) x^2 - 8x^2 - x^2 - 4x + 2x + 3x + 1 - 6 + 3/5 (Error!!) . You MUST distribute the negative sign to ALL terms within the (): (x^2 - 4x + 1) - (-8x^2 + 2x - 6) - (x^2 + 3x + 3/5) Distributing negative to terms in second (): (x^2 - 4x + 1) + 8x^2 - 2x + 6 - (x^2 + 3x + 3/5) Distributing negative to terms in last (): (x^2 - 4x + 1) + 8x^2 - 2x + 6 - x^2 - 3x - 3/5 x^2 - 4x + 1 + 8x^2 - 2x + 6 - x^2 - 3x - 3/5 Grouping terms: x^2 + 8x^2 - x^2 - 4x - 2x - 3x + 1 + 6 - 3/5 8x^2 - 9x + 1 + 6 - 3/5 8x^2 - 9x + 5/5 + 30/5 - 3/5 8x^2 - 9x + 35/5 - 3/5 8x^2 - 9x + 32/5

Miscellaneous_Word_Problems/200373: Area of a painting. A rectangular painting with a width of x centimeters has an area of x^2 +50x square centimeters. Find a binomial that represents the length. See the accompanying figure. 1 solutions Answer 150661 by nerdybill(6963)   on 2009-06-17 06:38:34 (Show Source): You can put this solution on YOUR website! Area of a painting. A rectangular painting with a width of x centimeters has an area of x^2 +50x square centimeters. Find a binomial that represents the length. See the accompanying figure. . Since, length*width = area . Given: width = x area = x^2 + 50x . Plug in what was given: length(x) = x^2 + 50x dividing both sides by x: length = x + 50 (this is what they're looking for)

Expressions-with-variables/200377: (5/u)-2 = (15/U)+4 1 solutions Answer 150660 by nerdybill(6963)   on 2009-06-17 06:34:56 (Show Source): You can put this solution on YOUR website! (5/u)-2 = (15/U)+4 . I'm assuming both u's are the same... . (5/u)-2 = (15/u)+4 Multiplying both sides by u, we get: 5-2u = 15+4u Adding 2u to both sides: 5 = 15+6u -10 = 6u -10/6 = u -5/3 = u

Pythagorean-theorem/200344: A wagon wheel is placed against a wall. One point on the edge of the wheel is 5 inches from the ground and 10 inches from the wall. What is the radius of the wheel? 1 solutions Answer 150655 by nerdybill(6963)   on 2009-06-17 00:05:11 (Show Source): You can put this solution on YOUR website! A wagon wheel is placed against a wall. One point on the edge of the wheel is 5 inches from the ground and 10 inches from the wall. What is the radius of the wheel? . Think Pythagorean theorem. . Draw a diagram -- the wheel is the hypotenuse while the wall and the floor forms the two sides of a right triangle. . Let d = diameter of wheel then d^2 = 5^2 + 10^2 d^2 = 25 + 100 d^2 = 125 d = d = d = . Radius is half the diameter: radius = = 5.59 inches

Linear_Equations_And_Systems_Word_Problems/200360: A jazz concert brought in $191,000 on the sale of 7400 tickets, if tickets were sold for $20 and $30 each, how many of each type of ticket were sold? 1 solutions Answer 150654 by nerdybill(6963)   on 2009-06-16 23:58:01 (Show Source): You can put this solution on YOUR website! A jazz concert brought in $191,000 on the sale of 7400 tickets, if tickets were sold for $20 and $30 each, how many of each type of ticket were sold? . Let x = number of $20 tickets sold then 7400-x = number of $30 tickets sold . 20x + 30(7400-x) = 191000 20x + 222000 - 30x = 191000 20x - 30x = -31000 -10x = -31000 x = 3100 ($20 tickets) . $30 tickets: 7400-x = 7400-3100 = 4300 ($30 tickets)

Graphs/200358: HI everyone, Im trying to finish the following problems but I am struggling a bit. I have to show full working and comment on the outcomes. I dont expect answers to all 3, but if someone can show me one of each type that would be super. Question 1. Find the equation of the line that passes through the point (-2,5) and parallel to the y axis. Question 2. Find the equation of the line passing through (1,3) and parallel to the line y = 3/2 x - 1/2. Question 3. A line with the gradient passes through the point (1,3). Find the equation of the line. Thanks for your help. -Nick. 1 solutions Answer 150653 by nerdybill(6963)   on 2009-06-16 23:54:10 (Show Source): You can put this solution on YOUR website! Question 1. Find the equation of the line that passes through the point (-2,5) and parallel to the y axis. x = -2 . Question 2. Find the equation of the line passing through (1,3) and parallel to the line y = 3/2 x - 1/2. If a two lines are parallel, the slopes are the same. Our line has a slope of 3/2 crossing (1,3) plug into point-slope form y-y1 = m(x-x1) y-3 = (3/2)(x-1) y-3 = (3/2)x - 3/2 y = (3/2)x - 3/2 + 3 y = (3/2)x - 3/2 + 6/2 y = (3/2)x + 3/2 . Question 3. A line with the gradient 2 passes through the point (1,3). Find the equation of the line. Gradient is equivalent to the slope So m = 2 and it crosses (1,3) plug into point-slope form y-y1 = m(x-x1) y-3 = 2(x-1) y-3 = 2x-2 y = 2x + 1

Linear-equations/200311: A student has earned scores of 87, 81, and 88 on the first 3 of 4 tests. If the student wants an average (arithmetic mean) of exactly 87, what score must she earn on the fourth test? 1 solutions Answer 150584 by nerdybill(6963)   on 2009-06-16 14:44:20 (Show Source): You can put this solution on YOUR website! A student has earned scores of 87, 81, and 88 on the first 3 of 4 tests. If the student wants an average (arithmetic mean) of exactly 87, what score must she earn on the fourth test? . Let x = score on fourth test then (x+87+81+88)/4 = 87 (x+256)/4 = 87 Multiplying both sides by 4: (x+256) = 87*4 (x+256) = 348 x = 348-256 x = 92 (score for fourth test)

Rational-functions/200114: A community water tank can be filled in 10 hours by the town office well alone and in 16 hours by the high school well alone. How long will it take to fill the tank if both wells are working together? 1 solutions Answer 150437 by nerdybill(6963)   on 2009-06-15 08:52:08 (Show Source): You can put this solution on YOUR website! A community water tank can be filled in 10 hours by the town office well alone and in 16 hours by the high school well alone. How long will it take to fill the tank if both wells are working together? . Rate of town office well: 1 tank per 10 hours : 1/10 Rate of high school well: 1 tank per 16 hours : 1/16 . Let x = number of hours required for both wells then x(1/10 + 1/16) = 1 x/10 + x/16) = 1 Multiplying both sides by 160 (common denominator): 16x + 10x = 160 26x = 160 x = 160/26 x = 6.154 hours

Geometry_Word_Problems/200118: Cheyenne will drive 3,000 miles across Interstate 90. She plans to drive 7 hours each day averaging 60 miles per hour. What is the least number of days the trip will take? 1 solutions Answer 150436 by nerdybill(6963)   on 2009-06-15 08:45:28 (Show Source): You can put this solution on YOUR website! Cheyenne will drive 3,000 miles across Interstate 90. She plans to drive 7 hours each day averaging 60 miles per hour. What is the least number of days the trip will take? . Applying the distance formula: d = rt where d is distance traveled r is rate or speed t is time . Each day Cheyenne travels: 7*60 = 420 miles . Number of days, then, to travel 3000 miles: 3000/420 = 7.143 Since she takes MORE than 7 days, the "least" number of days then is 8 days (answer)