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 Exponents-negative-and-fractional/145607: 7x^-8 * 6x^31 solutions Answer 106256 by jim_thompson5910(28593)   on 2008-06-17 17:24:05 (Show Source): You can put this solution on YOUR website! Start with the given expression Multiply the coefficients 7 and 6 to get 42 When you multiply monomials, simply add the exponents Add So our answer is
 Linear-equations/145603: Megan’s verbal and math scores on the SAT was 1094. Her math score was 248 points higher than her verbal score. What were her math and verbal SAT scores? 1 solutions Answer 106254 by jim_thompson5910(28593)   on 2008-06-17 16:59:17 (Show Source): You can put this solution on YOUR website!Let x=verbal score and y=math score "Megan’s verbal and math scores on the SAT was 1094" translates to "Her math score was 248 points higher than her verbal score" translates to Start with the given system Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown. Combine like terms on the left side Subtract 248 from both sides Combine like terms on the right side Divide both sides by 2 to isolate x Divide Now that we know that , we can plug this into to find Substitute for each Simplify So our answers are and So the verbal score was 423 and the math score was 671.
 Rational-functions/145600: divide the following expression: (x^2+10x+21) / (x+7) A) x^2+3 B) x-2 C) x+5 D) x+31 solutions Answer 106253 by jim_thompson5910(28593)   on 2008-06-17 16:50:18 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor to get . Highlight the common terms. Cancel out the common terms. Simplify. So simplifies to . In other words, where
 Coordinate-system/145602: graph the following equations y=-1/3x + 4 3y-9x=301 solutions Answer 106252 by jim_thompson5910(28593)   on 2008-06-17 16:47:49 (Show Source): You can put this solution on YOUR website!# 1 Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is Since this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis So we have one point Now since the slope is comprised of the "rise" over the "run" this means Also, because the slope is , this means: which shows us that the rise is -1 and the run is 3. This means that to go from point to point, we can go down 1 and over 3 So starting at , go down 1 unit and to the right 3 units to get to the next point Now draw a line through these points to graph So this is the graph of through the points and # 2 Start with the given equation Add to both sides Rearrange the equation Divide both sides by Break up the fraction Reduce Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is Since this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis So we have one point Now since the slope is comprised of the "rise" over the "run" this means Also, because the slope is , this means: which shows us that the rise is 3 and the run is 1. This means that to go from point to point, we can go up 3 and over 1 So starting at , go up 3 units and to the right 1 unit to get to the next point Now draw a line through these points to graph So this is the graph of through the points and
 Linear-equations/145582: I need help with this math homework problem It says solve the linear equation using the substitution method: x=8-4y 3x+5y=3 1 solutions Answer 106246 by jim_thompson5910(28593)   on 2008-06-17 16:01:54 (Show Source): You can put this solution on YOUR website! Start with the given system Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown. Distribute Combine like terms on the left side Subtract 24 from both sides Combine like terms on the right side Divide both sides by -7 to isolate y Divide Now that we know that , we can plug this into to find Substitute for each Simplify So our answer is and which also looks like Notice if we graph the two equations, we can see that their intersection is at . So this verifies our answer. Graph of (red) and (green)
 Rational-functions/145589: Simplify the expression 12a^2+26a+12 / 6-5a-6a^2 A) 2(6a^2+13a+6) / -(6a^2+5a-5) B)-2 C)-2(3a+2) / (3a-2) D) 2(3a+2) / (3a-2)1 solutions Answer 106245 by jim_thompson5910(28593)   on 2008-06-17 16:00:23 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor to get . Factor to get . Highlight the common terms. Cancel out the common terms. Simplify. So simplifies to . In other words, where or So the answer is choice C
 Rational-functions/145591: Perform the indicated operations and simplify the following expression: x+6/x^2-16 * 3x-12/3x+18 A) 0 B) 3 / 3(x+4) C) 1/x+4 D) -1/x+41 solutions Answer 106244 by jim_thompson5910(28593)   on 2008-06-17 15:57:09 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor to get . Factor to get . Factor to get . Combine the fractions. Highlight the common terms. Cancel out the common terms. Simplify. So simplifies to . In other words, where ,, or So the answer choice is C
 Matrices-and-determiminant/145533: This question is from textbook finite mathematics Use the Gauss-Jordan method to solve each system of equations. 3x-6y+3z=11 2x-y+z=-9 5x-5y+2z=18 I know how to change it into matrix form but then what?1 solutions Answer 106217 by jim_thompson5910(28593)   on 2008-06-17 12:54:38 (Show Source): You can put this solution on YOUR website!This solution was generated from the linear algebra toolkit So , and
 Polynomials-and-rational-expressions/145526: Using Rational Zero Theorem- Find all rational zeros of the polynomial 8x^3-10x^2-17x+101 solutions Answer 106175 by jim_thompson5910(28593)   on 2008-06-16 20:43:17 (Show Source): You can put this solution on YOUR website!Any rational zero can be found through this equation where p and q are the factors of the last and first coefficients So let's list the factors of 10 (the last coefficient): Now let's list the factors of 8 (the first coefficient): Now let's divide each factor of the last coefficient by each factor of the first coefficient Now simplify These are all the distinct rational zeros of the function that could occur
 Linear_Algebra/145524: I am working with Inverse functions and need help find (f(g))(x) and (g(f))(x) given f(x)=log(2)x g(x)=2 to x power sorry if that is written confusing.. on paper the 2 after log is lowered 1 solutions Answer 106173 by jim_thompson5910(28593)   on 2008-06-16 20:36:00 (Show Source): You can put this solution on YOUR website!Let's evaluate f(g(x)) Start with the first function Plug in Rewrite the right side using the identity Take the log base 2 of 2 to get 1. Note: Multiply ------------------------ Let's evaluate g(f(x)) Start with the second function Plug in Let . So this means that by use of the property ====> Replace with "y" Now replace with "x" So both f(g(x)) and g(f(x)) equal x.
 Rational-functions/145523: I need help when asked to find asymptotes of a rational function. For example: f(x)=x+2 ------ x sqrd-5x+61 solutions Answer 106171 by jim_thompson5910(28593)   on 2008-06-16 20:22:03 (Show Source): You can put this solution on YOUR website! Start with the given function Looking at the numerator , we can see that the degree is since the highest exponent of the numerator is . For the denominator , we can see that the degree is since the highest exponent of the denominator is . Horizontal Asymptote: Since the degree of the numerator (which is ) is less than the degree of the denominator (which is ), the horizontal asymptote is always So the horizontal asymptote is -------------------------------------------------- Vertical Asymptote: To find the vertical asymptote, just set the denominator equal to zero and solve for x Set the denominator equal to zero Now let's use the quadratic formula to solve for x. If you need help with the quadratic formula, check out this solver. After using the quadratic formula, we get the solutions or So this means the vertical asymptotes are or Notice if we graph , we can visually verify our answers: Graph of with the horizontal asymptote (blue line) and the vertical asymptotes and (green lines)
 Quadratic_Equations/145522: x^2+7x+10=0 3x^2-6x=01 solutions Answer 106168 by jim_thompson5910(28593)   on 2008-06-16 20:09:27 (Show Source): You can put this solution on YOUR website!I'm assuming you want to solve for x. I'll solve the first one to get you started. # 1 Start with the given equation. Let's use the quadratic formula to solve for x Start with the quadratic formula Plug in , , and Square to get . Multiply to get Subtract from to get Multiply and to get . Take the square root of to get . or Break up the expression. or Combine like terms. or Simplify. So our answers are or
 Quadratic_Equations/145521: If f(x)=2x^2-7x+3 find f(2) and find f(-3)1 solutions Answer 106167 by jim_thompson5910(28593)   on 2008-06-16 20:08:21 (Show Source): You can put this solution on YOUR website!# 1 Start with the given function Plug in Raise 2 to the 2nd power to get 4 Multiply 2 and 4 to get 8 Multiply 7 and 2 to get 14 Subtract 14 from 8 to get -6 Add -6 and 3 to get -3 ---------------------------------------------------------------------- # 2 Start with the given function Plug in Raise -3 to the 2nd power to get 9 Multiply 2 and 9 to get 18 Multiply 7 and -3 to get -21 Subtract -21 from 18 to get 39 Add 39 and 3 to get 42
 Equations/145507: solve for y: 2/3y+k=j1 solutions Answer 106155 by jim_thompson5910(28593)   on 2008-06-16 17:38:51 (Show Source): You can put this solution on YOUR website! Start with the given equation Subtract k from both sides Multiply both sides by So our answer is
 Expressions-with-variables/145505: 16 2(x-4) --- + ------ x2-16 x+4 Adding Rational Expressions 1 solutions Answer 106153 by jim_thompson5910(28593)   on 2008-06-16 17:36:57 (Show Source): You can put this solution on YOUR website! Start with the given expression Factor to get . So the LCD is Multiply the second fraction by Combine the fractions Foil to get Foil to get Distribute Since the two fractions have the same denominator, this means we can combine them. Combine like terms So simplifies to . In other words, where or
 Graphs/145490: What is the domain and range for the following equations: y=1-x y=|1-x| y=1-x^2 1 solutions Answer 106148 by jim_thompson5910(28593)   on 2008-06-16 16:52:59 (Show Source): You can put this solution on YOUR website!# 1 D: all real numbers R: all real numbers # 2 D: all real numbers R: # 3 D: all real numbers R:
 Exponential-and-logarithmic-functions/145504: How do you Plot the graphs of the following functions 1. (x)=6x 2. f(x)=3x - 2 3. f(x)=(1/2)x 4. f(x)= log2x 1 solutions Answer 106146 by jim_thompson5910(28593)   on 2008-06-16 16:50:45 (Show Source): You can put this solution on YOUR website!I'll do the first two to get you started # 1 Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is note: really looks like Since this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis So we have one point Now since the slope is comprised of the "rise" over the "run" this means Also, because the slope is , this means: which shows us that the rise is 6 and the run is 1. This means that to go from point to point, we can go up 6 and over 1 So starting at , go up 6 units and to the right 1 unit to get to the next point Now draw a line through these points to graph So this is the graph of through the points and # 2 Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is Since this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis So we have one point Now since the slope is comprised of the "rise" over the "run" this means Also, because the slope is , this means: which shows us that the rise is 3 and the run is 1. This means that to go from point to point, we can go up 3 and over 1 So starting at , go up 3 units and to the right 1 unit to get to the next point Now draw a line through these points to graph So this is the graph of through the points and
 Graphs/145489: This question is from textbook graph the inequality y<3x+1.1 solutions Answer 106143 by jim_thompson5910(28593)   on 2008-06-16 15:13:21 (Show Source): You can put this solution on YOUR website! Start with the 1st inequality Replace the inequality sign with an equals sign So in order to plot , we need to plot the equation first Graph of Now plug in a test point (0,0) into the inequality Plug in and Evaluate and simplify Since the inequality is true, this means that we shade the entire region that contains the point (0,0). So this means that we shade everything below the line . Note: Since the inequality is a "less than" sign, this means that the line should be a dotted line. Graph of with the shaded region in green
 Equations/145491: I can't seem to figure out this problem, can someone please help me? 1-2/x ----- x-4/x1 solutions Answer 106142 by jim_thompson5910(28593)   on 2008-06-16 15:09:32 (Show Source): You can put this solution on YOUR website! Start with the given expression Multiply both the numerator and the denominator by the LCD Distribute. Notice how the inner denominators cancel Simplify Factor to get . Highlight the common terms. Cancel out the common terms. Simplify. So simplifies to . In other words, where , , or
 Inequalities/145493: Can anyone please Solve the inequality 4x <12 than sketch the solution set on the real number line. Thank You 1 solutions Answer 106141 by jim_thompson5910(28593)   on 2008-06-16 15:03:18 (Show Source): You can put this solution on YOUR website! Start with the given inequality Divide both sides by 4 to isolate x Divide -------------------------------------------------------------- Answer: So our answer is Here's the graph of the solution set Note: at there is a open circle (which means this point is excluded)
 Equations/145492: Any solutions to this problem? Thank You Graph the following (< =means≤,less than or equal to) -2 < =x <11 solutions Answer 106140 by jim_thompson5910(28593)   on 2008-06-16 15:01:47 (Show Source): You can put this solution on YOUR website!Graph of Note: at there is a closed circle (which means this point is included) and at there is a open circle (which means this point is excluded)
 Graphs/145488: This question is from textbook solve the inequality 4<-z-4<11. Give the result in set notation and graph it.1 solutions Answer 106139 by jim_thompson5910(28593)   on 2008-06-16 14:58:46 (Show Source): You can put this solution on YOUR website! Start with the given inequality Add 4 to all sides Divide every side by -1 to isolate z. Remember, dividing every side of an inequality by a negative number flips the inequality signs Rearrange the inequality. So the solution in interval notation is: (-15,-8) The solution in set notation is Now let's graph the solution set Note: at there is a open circle (which means this point is excluded) and at there is a open circle (which means this point is excluded)
 Radicals/145409: 30√11-6√111 solutions Answer 106084 by jim_thompson5910(28593)   on 2008-06-15 20:02:24 (Show Source): You can put this solution on YOUR website! Start with the given expression Factor out the GCF Subtract Rearrange the terms