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nerdybill answered: 6957 problems
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Rational-functions/210900: sorry i got it off a worksheet: f(x)=x^2 + 2x + 5 i have to write each quadratic function in vertex form, give coordinates of the vertex, and the equation of the axis of symmetry. 1 solutions Answer 159314 by nerdybill(6959)   on 2009-09-03 23:20:16 (Show Source): You can put this solution on YOUR website! f(x)=x^2 + 2x + 5 . The axis of symmetry is the line x = -b/2a x = -2/2 = -1 x = -1 (equation of axis of symmetry) . f(x)=x^2 + 2x + 5 f(x)=(x^2 + 2x) + 5 f(x)=(x^2 + 2x + __ ) + 5 f(x)=(x^2 + 2x + 1 ) + 5 - 1 f(x)=(x+1)^2 + 4 f(x)=(x-(-1))^2 + 4 (vertex form) . vertex is at (-1,4)

Percentage-and-ratio-word-problems/210898: A woman earns 15% more than her husband. Together they make $69,875 per year. What is the husband's annual salary? 1 solutions Answer 159313 by nerdybill(6959)   on 2009-09-03 23:12:31 (Show Source): You can put this solution on YOUR website! A woman earns 15% more than her husband. Together they make $69,875 per year. What is the husband's annual salary? . Let x = husband's annual salary then 1.15x = wife's annual salary . x + 1.15x = 69875 2.15x = 69875 x = 69875/2.15 x = $32,500 (husband's salary)

logarithm/210892: please help me solve log(2x-1)-log(x+6)=log5 1 solutions Answer 159312 by nerdybill(6959)   on 2009-09-03 22:58:36 (Show Source): You can put this solution on YOUR website! please help me solve log(2x-1)-log(x+6)=log5 . applying log rules: log(2x-1)-log(x+6)=log5 log[(2x-1)/(x+6)]=log5 (2x-1)/(x+6) = 5 (2x-1) = 5(x+6) 2x-1 = 5x+30 -1 = 3x+30 -31 = 3x -31/3 = x . Just reviewed the answer -- when x = -31/3 it will produce a log of a NEGATIVE number -- you cannot take a log of a negative number. Either there is no solution or your original problem had a typo -- can you please check?

Miscellaneous_Word_Problems/210679: The weekly profit of a company depends on the number of employees working during the week. It is represented by the formula P = x2 + x – 10 where x is the average number of employees working on each day of the week. For what values of ‘x’ is the profit positive? 1 solutions Answer 159296 by nerdybill(6959)   on 2009-09-03 21:36:03 (Show Source): You can put this solution on YOUR website! They give you: P = x^2 + x – 10 . Set P to zero to find out when you have NO profit: 0 = x^2 + x – 10 . Solving for x will give you where it crosses the x-axis: 0 = x^2 + x – 10 Since we can't factor, we apply the quadratic equation to get: x = {2.7, -3.7} We can throw out the negative solution leaving: x = 2.7 . Values of x where P is POSITIVE: x > 2.7 . Details of quadratic to follow: 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=41 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 2.70156211871642, -3.70156211871642. Here's your graph:

Travel_Word_Problems/210876: While traveling, you notice that you traveled 65 miles in 55 minutes. If your speed does not change, how long will it take you to travel 250 miles? 1 solutions Answer 159290 by nerdybill(6959)   on 2009-09-03 21:25:26 (Show Source): You can put this solution on YOUR website! While traveling, you notice that you traveled 65 miles in 55 minutes. If your speed does not change, how long will it take you to travel 250 miles? . (55/65 * 250)/60 = (55/65 * 250)/60 = 3.526 hours or 3 hours and 32 minutes

Rational-functions/210792: This question is from textbook algebra find g of h and h of g g(x)= 4x h(x)= 2x-1 1 solutions Answer 159258 by nerdybill(6959)   on 2009-09-03 18:16:32 (Show Source): You can put this solution on YOUR website! find g of h and h of g . Given: g(x)= 4x h(x)= 2x-1 . Then g of h: g(h(x)) = 4(2x - 1) g(h(x)) = 8x - 4 . And h of g: h(g(x)) = 2(4x)-1 h(g(x)) = 8x-1

Travel_Word_Problems/210749: an airplan travels 95 miles in 10 minutes. how fast is going in miles per hour? 1 solutions Answer 159211 by nerdybill(6959)   on 2009-09-03 14:19:33 (Show Source): You can put this solution on YOUR website! an airplan travels 95 miles in 10 minutes. how fast is going in miles per hour? . You are given the speed as: 95 miles per 10 minutes . When we are normally accustomed to miles per hour. So, the strategy is to "change your units" -- from minutes to hours. . Since there are 60 minutes in an hour: 95/10 * 60 = 95 *6 = 570 mph

percentage/210375: Compute the requested value. Choose the correct answer. If the selling price is $75.50 and includes the cost plus 5% of the cost, then what is the cost? 1 solutions Answer 158965 by nerdybill(6959)   on 2009-09-02 10:22:10 (Show Source): You can put this solution on YOUR website! If the selling price is $75.50 and includes the cost plus 5% of the cost, then what is the cost? . Let x = cost then x + .05x = 75.50 x(1+.05) = 75.50 x(1.05) = 75.50 x = 75.50/1.05 x = $71.90

Rectangles/210231: Find the length of the side of a square if the diagonal is 3 ft. longer than a side. 1 solutions Answer 158858 by nerdybill(6959)   on 2009-09-01 19:42:00 (Show Source): You can put this solution on YOUR website! Find the length of the side of a square if the diagonal is 3 ft. longer than a side. . Let x = length of the side of a square then from Pythagorean theorem we get: x^2 + x^2 = x+3 2x^2 = x+3 2x^2-x-3 = 0 (2x-3)(x+1) = 0 . x = {3/2, -1} We can throw out the negative solution leaving: x = 3/2 feet (or 1 and a half feet)

Triangles/210225: the area of a triangle is 152 m squared, and the height is 16 m. what us the base? 1 solutions Answer 158856 by nerdybill(6959)   on 2009-09-01 19:39:11 (Show Source): You can put this solution on YOUR website! the area of a triangle is 152 m squared, and the height is 16 m. what us the base? . Since area of any triangle is (1/2)bh we get: 152 = (1/2)bh 152 = (1/2)b(16) 152 = b(8) 19 m = b (base)

Expressions-with-variables/210020: can you help me I dont get this if there are 1024 bytes a kilobyte write an expression that describes the number of bytes in a computer chip with n kilobytes 1 solutions Answer 158728 by nerdybill(6959)   on 2009-08-31 23:54:06 (Show Source): You can put this solution on YOUR website! An example would be easier to see: Say you have a new memory chip and it has 8192 bytes then, the number of kilobytes would be 8192/1024 = 8 kilobytes . So, let's say n = number of bytes in your computer chip then n/1024 is the number of kilobytes

Miscellaneous_Word_Problems/209994: Find the exact value of each expression. log4(100) - log4(32) - log4(50) 1 solutions Answer 158703 by nerdybill(6959)   on 2009-08-31 21:51:08 (Show Source): You can put this solution on YOUR website! Find the exact value of each expression. log4(100) - log4(32) - log4(50) . log4(100) - log4(32) - log4(50) log4(100/32) - log4(50) log4(3.125) - log4(50) log4(3.125/50) log4(.0625) log(.0625)/log4 -2

Geometric_formulas/209735: Find the y- intercept -2x - y = -10 1 solutions Answer 158559 by nerdybill(6959)   on 2009-08-30 21:48:41 (Show Source): You can put this solution on YOUR website! Find the y- intercept -2x - y = -10 . Put the above equation into the "slope-intercept" form: y = mx + b where m is the slope b is the y-intercept at (0,b) . -2x = y -10 -2x + 10 = y So, m is -2 b is 10 . y-intercept is at (0,10)

logarithm/209697: ok. i have this problem ln(x-2) + ln(2x-3) = 2lnx please help me i have no understanding of this problem 1 solutions Answer 158541 by nerdybill(6959)   on 2009-08-30 19:15:39 (Show Source): You can put this solution on YOUR website! ln(x-2) + ln(2x-3) = 2lnx ln(x-2)(2x-3) = 2ln x ln(x-2)(2x-3) = ln x^2 (x-2)(2x-3) = x^2 2x^2-3x-4x+6 = x^2 2x^2-7x+6 = x^2 x^2-7x+6 = 0 (x-6)(x-1) = 0 x = {6,1}

logarithm/209694: I had 10 problems on this. i was able to complete all except 2. e^2x - 3e^x + 2 = 0 i believe i am supposed to move the 2 to the other side. but im not quite sure how to solve this problem id greatly appreciate ur help 1 solutions Answer 158535 by nerdybill(6959)   on 2009-08-30 18:30:30 (Show Source): You can put this solution on YOUR website! Apply log rules: . Assuming the 2x is both part of the exponent then, e^2x - 3e^x + 2 = 0 e^2x - e^x^3 + 2 = 0 e^2x - e^x^3 = -2 e^(2x/x^3) = -2 2x/x^3 = e^(-2) 2/x^2 = e^(-2) 2 = e^(-2)x^2 2/e^(-2) = x^2 14.778 = x^2 3.844 = x

Angles/209580: This question is from textbook Geometry The measure of angle 1 is five less than four times the measure of angle 2. If angle 1 and angle 2 form a linear pair, what are their measurements? 1 solutions Answer 158531 by nerdybill(6959)   on 2009-08-30 18:09:03 (Show Source): You can put this solution on YOUR website! The measure of angle 1 is five less than four times the measure of angle 2. If angle 1 and angle 2 form a linear pair, what are their measurements? . Let x = measure of angle 2 then 4x-5 = measure of angle 1 . If the angles are linear, this means the sum of the two angles is 180 degs: x + (4x-5) = 180 5x-5 = 180 5x = 185 x = 37 degrees (angle 2) . angle 1: 4x-5 = 4(37)-5 = 148-5 = 143 degrees (angle 1)

Miscellaneous_Word_Problems/209689: kate and chris are training for a marathon. kate can run 3.5 mph while chris runs 6mph. if chris gives kate a 1 mile head start, when will he pass her? 1 solutions Answer 158529 by nerdybill(6959)   on 2009-08-30 18:05:01 (Show Source): You can put this solution on YOUR website! kate and chris are training for a marathon. kate can run 3.5 mph while chris runs 6mph. if chris gives kate a 1 mile head start, when will he pass her? . You will need to apply the distance formula: d = rt where d is distance r is rate or speed t is time . Let t = time Chris passes Kate then 6t = 3.5t + 1 2.5t = 1 t = 1/2.5 t = .4 hours or, in terms of minutes: .4*60 = 24 minutes

Quadratic_Equations/209614: This question is from textbook Help please! Let f(x) = x2 - 8x + 16. Find x so that f(x) = 22 1 solutions Answer 158510 by nerdybill(6959)   on 2009-08-30 16:56:28 (Show Source): You can put this solution on YOUR website! Let f(x) = x2 - 8x + 16. Find x so that f(x) = 22 . Plug in the given value and solve for x: 22 = x^2 - 8x + 16 0 = x^2 - 8x - 6 Use the quadratic equation to solve for x. Doing so, yields: x = {8.69, -0.69} . 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=88 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 8.69041575982343, -0.69041575982343. Here's your graph:

Signed-numbers/209662: what is the expression of two fifths the cube of a number? 1 solutions Answer 158507 by nerdybill(6959)   on 2009-08-30 16:39:00 (Show Source): You can put this solution on YOUR website! what is the expression of two fifths the cube of a number? . "cube of a number" is: x^3 . "two fifths" then is: (2/5)x^3 . Or, 2x^3/5

Polynomials-and-rational-expressions/209557: factor: 2x^5 + x^4 - 8x^3 - 4x^2 1 solutions Answer 158441 by nerdybill(6959)   on 2009-08-30 09:28:06 (Show Source): You can put this solution on YOUR website! factor: 2x^5 + x^4 - 8x^3 - 4x^2 . Begin by factoring out what is common among all terms: x[2x^4 + x^3 - 8x^2 - 4x] . Group terms: x[(2x^4 + x^3) - (8x^2 + 4x)] . Factor expressions inside parentheses: x[x^3(2x + 1) - 4x(2x + 1)] x[(2x + 1)(x^3- 4x)] x(2x + 1)(x^3- 4x)

Polynomials-and-rational-expressions/209556: solve x^4 + 3x^3 -10x^2 = 0 1 solutions Answer 158439 by nerdybill(6959)   on 2009-08-30 09:23:41 (Show Source): You can put this solution on YOUR website! solve x^4 + 3x^3 -10x^2 = 0 . Begin by factoring out x^2: x^2(x^2 + 3x -10) = 0 . Now, factor expression inside parenthesis: x^2(x+5)(x-2) = 0 setting each term on the left to zero we get: x = {-5, 0, 2}

Functions/209391: Let and be two functions defined by F(x)=x^2+x-12 g(x)=x^2-7x-8. Find all values of x that are NOT in the domain of the function f/g.? 1 solutions Answer 158308 by nerdybill(6959)   on 2009-08-29 01:37:38 (Show Source): You can put this solution on YOUR website! Domain specifies the "values" 'x' can take. . F(x)=x^2+x-12 g(x)=x^2-7x-8. Find all values of x that are NOT in the domain of the function f/g.? . f/g is therefore: (x^2+x-12)/(x^2-7x-8) The ONLY values x CAN'T take are values that make the denominator go to zero. Look for those by setting the denominator to zero and solving for x: x^2-7x-8 = 0 (x-8)(x+1) = 0 x = {-1, 8} So, the ONLY two values 'x' can't take is -1 and 8. Therefore, the domain is: (-oo, -1) U (-1, 8) U (8,+oo) OR, you could say: x: x all real numbers except -1 and 8

Polynomials-and-rational-expressions/209386: solve for the variable x^2 - 3x - 28 = 0 1 solutions Answer 158307 by nerdybill(6959)   on 2009-08-29 01:31:46 (Show Source): You can put this solution on YOUR website! x^2 - 3x - 28 = 0 Strategy, attempt to factor first, failing that, resort to the quadratic equation. . In this case, it can be factored: (x-7)(x+4) = 0 therefore, x = {-4, 7}

Miscellaneous_Word_Problems/209373: If a ball is thrown downwards from a height of 128 feet with an initial velocity of 32 feet per second and its height above the ground is given by the formula S = - 16t2 – 32 t + 128. How long will it take the ball to reach the ground? 1 solutions Answer 158297 by nerdybill(6959)   on 2009-08-28 22:55:25 (Show Source): You can put this solution on YOUR website! Since 'S' is the "height above the ground", set it to zero and solve for t: S = - 16t^2 – 32 t + 128 0 = - 16t^2 – 32 t + 128 Divide both sides by -16: 0 = t^2 + 2t - 8 Factoring the right: 0 = (t+4)(t-2) t = {-4, 2} We can throw out the negative solution leaving: t = 2 seconds

Mixture_Word_Problems/209248: two cyclists start from the same point and ride in opposite directions. One cyclist rides twice as fast as the other. In 3 h, they are 81 mi apart. Find the rate of each cyclist. 1 solutions Answer 158168 by nerdybill(6959)   on 2009-08-28 08:33:26 (Show Source): You can put this solution on YOUR website! two cyclists start from the same point and ride in opposite directions. One cyclist rides twice as fast as the other. In 3 h, they are 81 mi apart. Find the rate of each cyclist. . You will be applying the distance formula: d = rt where d is distance r is rate or speed t is time . Let x = speed of slower cyclist then 2x = speed of faster cyclist . 3(x + 2x) = 81 (x + 2x) = 27 3X = 27 X = 9 mph (slower cyclist) . faster cyclist: 2x = 2(9) = 18 mph (faster cyclist)

Human-and-algebraic-language/209211: Julie and Eric row their boat (at a constant speed) 45 miles downstream for 5 hours, helped by the current. Rowing at the same rate, the trip back against the current takes 9 hours. Find the rate of the current. 1 solutions Answer 158155 by nerdybill(6959)   on 2009-08-28 00:25:04 (Show Source): You can put this solution on YOUR website! Julie and Eric row their boat (at a constant speed) 45 miles downstream for 5 hours, helped by the current. Rowing at the same rate, the trip back against the current takes 9 hours. Find the rate of the current. . You will need to apply the "distance formula": d = rt where d is distance r is rate or speed t is time . Let x = rate of the current and y = rate Julie and Eric can row . Since we have two variables, we'll need two equations: Downstream: 5(y+x) = 45 (equation 1) Upstream: 9(y-x) = 45 (equation 2) . Solve equation 2 for y: 9(y-x) = 45 y-x = 5 y = 5+x . Substitute the above into equation 1 and solve for x: 5(y+x) = 45 5(5+x+x) = 45 5+x+x = 9 2x = 4 x = 2 mph (rate of the current)

Travel_Word_Problems/209146: If a car travels at 45 miles/hr, what is its speed in feet/min? 1 solutions Answer 158129 by nerdybill(6959)   on 2009-08-27 21:42:09 (Show Source): You can put this solution on YOUR website! If a car travels at 45 miles/hr, what is its speed in feet/min? . 45 miles/hr * 1 hr/60 min * 5280 ft/mile = 45 * (1/60) * 5280 = 3960 feet/min

Geometry_Word_Problems/209166: This question is from textbook Prentice Hall Mathematics Algebra 2 the measures of an angle and its complement differ by twenty-two degrees. find the measures of the angles. 1 solutions Answer 158127 by nerdybill(6959)   on 2009-08-27 21:39:05 (Show Source): You can put this solution on YOUR website! the measures of an angle and its complement differ by twenty-two degrees. find the measures of the angles. . If two angles are complementary, the sum of the two angles equals 90 degrees. . Let x = lesser of two angles then x+22 = greater of two angles . x + (x+22) = 90 2x + 22 = 90 2x = 68 x = 34 degrees . Other angle: x+22 = 34+22 = 56 degrees . The measure of the two angles are 34 and 56 degrees.

Linear-equations/209062: 2y=x+4 need the slope and intersection 1 solutions Answer 158023 by nerdybill(6959)   on 2009-08-27 13:51:19 (Show Source): You can put this solution on YOUR website! 2y=x+4 need the slope and intersection . To determine the "slope" and the "y-intercept", you can manipulate the given equation into the "slope-intercept" form of a straight line: y = mx + b where m is the slope b is the y-intercept at (0,b) . To get it in the above form, simply divide both sides of the given equation by 2: 2y=x+4 y = (1/2)x + 2 This means: m (slope) is 1/2 and (0,2) is the y-intercept . To find the x-intercept, set y=0 and solve for 'x': 2y=x+4 2(0)=x+4 0=x+4 -4 = x therefore, (-4,0) is the x-intercept

Equations/208959: One of the first mixtures of metals, called amalgams, used by dentists for tooth fillings consisted of 26.0 grams of silver, 10.8 grams of tin, 2.4 grams of copper, and 0.8 grams of zinc. How much silver is in a 25.0 gram sample of this analgam? thank you 1 solutions Answer 157985 by nerdybill(6959)   on 2009-08-26 23:34:19 (Show Source): You can put this solution on YOUR website! 26.0 grams of silver, 10.8 grams of tin, 2.4 grams of copper, and 0.8 grams of zinc . Total weight = 26.0 + 10.8 + 2.4 + 0.8 = 40 grams . Of the total weight, 26 grams is made up of silver Or 26/40 * 100 = 65% . So, if you have 25 grams of analgam, 65% would be silver: .65 * 25 = 16.25 grams

logarithm/208905: Solve the equation for x. e^(ax) = Ce^(bx), where a is not equal to b 1 solutions Answer 157960 by nerdybill(6959)   on 2009-08-26 19:57:27 (Show Source): You can put this solution on YOUR website! Solve the equation for x. e^(ax) = Ce^(bx), where a is not equal to b . Applying "log rules": e^(ax) = Ce^(bx) Divide both sides by e^(bx): e^(ax)/e^(bx) = C Rewriting the left side: e^(ax-bx) = C Take the ln of both sides: ax-bx = ln(C) Factor the left: x(a-b) = ln(C) Dividing we get: x = ln(C)/(a-b)