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Quadratic_Equations/114388: Solve the following quadratic equation. 4x squared = 13x + 12 1 solutions Answer 83605 by jim_thompson5910(28536)   on 2007-12-05 23:12:23 (Show Source): You can put this solution on YOUR website! Start with the given equation Move all of the terms to the right side Sort the terms Switch both sides (I find it easier to read if all of the terms are on the left side) Let's use the quadratic formula to solve for x: Starting with the general quadratic the general solution using the quadratic equation is: So lets solve ( notice , , and ) Plug in a=-4, b=13, and c=12 Square 13 to get 169 Multiply to get Combine like terms in the radicand (everything under the square root) Simplify the square root (note: If you need help with simplifying the square root, check out this solver) Multiply 2 and -4 to get -8 So now the expression breaks down into two parts or Lets look at the first part: Add the terms in the numerator Divide So one answer is Now lets look at the second part: Subtract the terms in the numerator Divide So another answer is So our solutions are: or Notice when we graph , we get: and we can see that the roots are and . This verifies our answer

Complex_Numbers/114760: (11x-5)^2=70 1 solutions Answer 83604 by jim_thompson5910(28536)   on 2007-12-05 23:08:49 (Show Source): You can put this solution on YOUR website! Start with the given equation Take the square root of both sides Add 5 to both sides Divide both sides by 11 to isolate x. ----------------------------------- Answer: So our solution is:

Graphs/114722: Solve. 6x – 7 = 2x + 13 1 solutions Answer 83603 by jim_thompson5910(28536)   on 2007-12-05 23:05:25 (Show Source): You can put this solution on YOUR website! Start with the given equation Add 7 to both sides Subtract 2x from both sides Combine like terms on the left side Combine like terms on the right side Divide both sides by 4 to isolate x Divide -------------------------------------------------------------- Answer: So our answer is

Functions/114811: use the horizontal line test to determine which of the following are one to one functions A) y=2x^2+5x-3 B) y= [x-2] C) y=x^-1/2 1 solutions Answer 83534 by jim_thompson5910(28536)   on 2007-12-05 16:18:44 (Show Source): You can put this solution on YOUR website! If we graph , we get which fails the horizontal line test. So the function is not one-to-one ---------------------------------------------- If we graph , we get which fails the horizontal line test. So the function is not one-to-one ---------------------------------------------- Remember, is the same as If we graph , we get which passes the horizontal line test. So the function is one-to-one

Polynomials-and-rational-expressions/114742: This question is from textbook Algebra Could you please explain in detail how you divide a Polynomial by a Binomial. Example problem:x(squared)-2x-8 divided by (x+2). Thank you 1 solutions Answer 83530 by jim_thompson5910(28536)   on 2007-12-05 15:23:17 (Show Source): You can put this solution on YOUR website! Start with the given expression Factor the numerator Cancel like terms Simplify So

Functions/114785: find f and g such that h=f*g where h(x)=(1/2x-3)^3 and the inner function g is rational 1 solutions Answer 83529 by jim_thompson5910(28536)   on 2007-12-05 15:16:01 (Show Source): You can put this solution on YOUR website! Is this a function composition, or just multiplication? If it's a composition, then... If and h(x)=f(g(x)), then simply let and . Notice if we evaluate f(g(x)), then we get So this shows that if and , then

Expressions-with-variables/114796: F(X)=2X^3 G(X)=x^3 (F + G) (X)=_______________________ (F/G) (X)=__________________________ The last one is f divided by g 1 solutions Answer 83528 by jim_thompson5910(28536)   on 2007-12-05 15:10:15 (Show Source): You can put this solution on YOUR website! So So

Money_Word_Problems/114793: The sophomore class at south high school raised $800 from sales tickets to a dance. tickets sold for $1.50 in advance and $ 2.00 at the door. if a total of 475 tickets were sold, what were the number of tickets sold at the door 1 solutions Answer 83527 by jim_thompson5910(28536)   on 2007-12-05 15:07:36 (Show Source): You can put this solution on YOUR website! Let x=# of advance tickets, y=# of door tickets Since there were a total of 475 tickets sold, the first equation is And since those tickets brought in $800, the next equation is Now multiply both sides by 10 to get Solved by pluggable solver: Solving a linear system of equations by subsitution Lets start with the given system of linear equations Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to choose y. Solve for y for the first equation Subtract from both sides Divide both sides by 1. Which breaks down and reduces to Now we've fully isolated y Since y equals we can substitute the expression into y of the 2nd equation. This will eliminate y so we can solve for x. Replace y with . Since this eliminates y, we can now solve for x. Distribute 20 to Multiply Reduce any fractions Subtract from both sides Combine the terms on the right side Now combine the terms on the left side. Multiply both sides by . This will cancel out and isolate x So when we multiply and (and simplify) we get <---------------------------------One answer Now that we know that , lets substitute that in for x to solve for y Plug in into the 2nd equation Multiply Subtract from both sides Combine the terms on the right side Multiply both sides by . This will cancel out 20 on the left side. Multiply the terms on the right side Reduce So this is the other answer <---------------------------------Other answer So our solution is and which can also look like (,) Notice if we graph the equations (if you need help with graphing, check out this solver) we get graph of (red) and (green) (hint: you may have to solve for y to graph these) intersecting at the blue circle. and we can see that the two equations intersect at (,). This verifies our answer. ----------------------------------------------------------------------------------------------- Check: Plug in (,) into the system of equations Let and . Now plug those values into the equation Plug in and Multiply Add Reduce. Since this equation is true the solution works. So the solution (,) satisfies Let and . Now plug those values into the equation Plug in and Multiply Add Reduce. Since this equation is true the solution works. So the solution (,) satisfies Since the solution (,) satisfies the system of equations this verifies our answer. So they sold 300 tickets in advance and 175 tickets at the door.

Reduction-of-unit-multipliers/114787: find the slope and y intercept of the line 6x-3y=36 1 solutions Answer 83524 by jim_thompson5910(28536)   on 2007-12-05 15:03:36 (Show Source): You can put this solution on YOUR website! Solved by pluggable solver: Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa) Start with the given equation Subtract from both sides Multiply both sides by Distribute Multiply Rearrange the terms Reduce any fractions So the equation is now in slope-intercept form () where (the slope) and (the y-intercept)

Quadratic_Equations/114788: Write the equation of the line passing through (–3, –5) and (3, 0). 1 solutions Answer 83523 by jim_thompson5910(28536)   on 2007-12-05 15:02:47 (Show Source): You can put this solution on YOUR website! Solved by pluggable solver: Finding the Equation of a Line First lets find the slope through the points (,) and (,) Start with the slope formula (note: (,) is the first point (,) and (,) is the second point (,)) Plug in ,,, (these are the coordinates of given points) Subtract the terms in the numerator to get . Subtract the terms in the denominator to get So the slope is ------------------------------------------------ Now let's use the point-slope formula to find the equation of the line: ------Point-Slope Formula------ where is the slope, and (,) is one of the given points So lets use the Point-Slope Formula to find the equation of the line Plug in , , and (these values are given) Rewrite as Rewrite as Distribute Multiply and to get . Now reduce to get Subtract from both sides to isolate y Combine like terms and to get (note: if you need help with combining fractions, check out this solver) ------------------------------------------------------------------------------------------------------------ Answer: So the equation of the line which goes through the points (,) and (,) is: The equation is now in form (which is slope-intercept form) where the slope is and the y-intercept is Notice if we graph the equation and plot the points (,) and (,), we get this: (note: if you need help with graphing, check out this solver) Graph of through the points (,) and (,) Notice how the two points lie on the line. This graphically verifies our answer.

Polynomials-and-rational-expressions/114758: Use the ac test to determine which of the following trinomials can be factored. Find the values of m and n for each trinomial that can be factored. x squared - x + 2 1 solutions Answer 83499 by jim_thompson5910(28536)   on 2007-12-05 12:39:43 (Show Source): You can put this solution on YOUR website! Solved by pluggable solver: Factoring using the AC method (Factor by Grouping) In order to factor , first multiply the leading coefficient 1 and the last term 2 to get 2. Now we need to ask ourselves: What two numbers multiply to 2 and add to -1? Lets find out by listing all of the possible factors of 2 Factors: 1,2, -1,-2, List the negative factors as well. This will allow us to find all possible combinations These factors pair up to multiply to 2. 1*2=2 (-1)*(-2)=2 note: remember two negative numbers multiplied together make a positive number Now which of these pairs add to -1? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -1 || First Number | Second Number | Sum 1 | 2 | 1+2=3 -1 | -2 | -1+(-2)=-3 None of these factors add to -1. So the quadratic cannot be factored.

Polynomials-and-rational-expressions/114757: Use the ac test to determine which of the following trinomials can be factored. Find the values of m and n for each trinomial that can be factored. x squared + 2x - 15 1 solutions Answer 83498 by jim_thompson5910(28536)   on 2007-12-05 12:38:18 (Show Source): You can put this solution on YOUR website! Solved by pluggable solver: Factoring using the AC method (Factor by Grouping) In order to factor , first multiply the leading coefficient 1 and the last term -15 to get -15. Now we need to ask ourselves: What two numbers multiply to -15 and add to 2? Lets find out by listing all of the possible factors of -15 Factors: 1,3,5,15, -1,-3,-5,-15, List the negative factors as well. This will allow us to find all possible combinations These factors pair up to multiply to -15. (-1)*(15)=-15 (-3)*(5)=-15 Now which of these pairs add to 2? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 2 |||| First Number | Second Number | Sum 1 | -15 | 1+(-15)=-14 3 | -5 | 3+(-5)=-2 -1 | 15 | (-1)+15=14 -3 | 5 | (-3)+5=2 We can see from the table that -3 and 5 add to 2. So the two numbers that multiply to -15 and add to 2 are: -3 and 5 So the original quadratic breaks down to this (just replace with the two numbers that multiply to -15 and add to 2, which are: -3 and 5) Replace with Group the first two terms together and the last two terms together like this: Factor a 1x out of the first group and factor a 5 out of the second group. Now since we have a common term we can combine the two terms. Combine like terms. ============================================================================== Answer: So the quadratic factors to Notice how foils back to our original problem . This verifies our answer.

Radicals/114754: Can some one help me please. Solve by completing the square x^2 + 8x + 13 = 0 Thank you inadavance. 1 solutions Answer 83497 by jim_thompson5910(28536)   on 2007-12-05 12:29:41 (Show Source): You can put this solution on YOUR website! Start with the given equation Subtract 13 from both sides Take half of the x coefficient 8 to get 4 (ie ) Now square 4 to get 16 (ie ) Add this result (16) to both sides. Now the expression is a perfect square trinomial. Factor into (note: if you need help with factoring, check out this solver) Combine like terms on the right side Take the square root of both sides Subtract 4 from both sides to isolate x. So the expression breaks down to or So our answer is approximately or Here is visual proof graph of When we use the root finder feature on a calculator, we would find that the x-intercepts are and , so this verifies our answer.

Distributive-associative-commutative-properties/114751: (11x + 3y) (x + 4y) = 1 solutions Answer 83496 by jim_thompson5910(28536)   on 2007-12-05 12:12:20 (Show Source): You can put this solution on YOUR website! Start with the given expression Remember, when you FOIL an expression, you follow this procedure: Multiply the First terms: Multiply the Outer terms: Multiply the Inner terms: Multiply the Last terms: Now collect every term to make a single expression Now combine like terms --------------------- Answer: So foils and simplifies to In other words,

Quadratic_Equations/114734: Graph the inequality. y is equal to or greater then 1 1 solutions Answer 83493 by jim_thompson5910(28536)   on 2007-12-05 11:44:53 (Show Source): You can put this solution on YOUR website! In order to graph , we need to graph the equation (just replace the inequality sign with an equal sign). So lets graph the line (simply draw a horizontal line through ) graph of Now lets pick a test point, say (0,0). Any point will work, (just make sure the point doesn't lie on the line) but this point is the easiest to work with. Now evaluate the inequality with the test point Substitute (0,0) into the inequality Plug in and Simplify (note: for some reason, some of the following images do not display correctly in Internet Explorer. So I recommend the use of Firefox to see these images.) Since this inequality is not true, we do not shade the entire region that contains (0,0). So this means we shade the region that is on the opposite side of the line Graph of with the boundary (which is the line in red) and the shaded region (in green)

Quadratic_Equations/114744: Graph by first solving for y. x – 3y = 9 1 solutions Answer 83492 by jim_thompson5910(28536)   on 2007-12-05 11:42:12 (Show Source): You can put this solution on YOUR website! Solved by pluggable solver: Graphing Linear Equations Start with the given equation Subtract from both sides Multiply both sides by Distribute Multiply Rearrange the terms Reduce any fractions So the equation is now in slope-intercept form () where (the slope) and (the y-intercept) So to graph this equation lets plug in some points Plug in x=-9 Multiply Add Reduce So here's one point (-9,-6) Now lets find another point Plug in x=-6 Multiply Add Reduce So here's another point (-6,-5). Add this to our graph Now draw a line through these points So this is the graph of through the points (-9,-6) and (-6,-5) So from the graph we can see that the slope is (which tells us that in order to go from point to point we have to start at one point and go up 1 units and to the right 3 units to get to the next point) the y-intercept is (0,)and the x-intercept is (,0) . So all of this information verifies our graph. We could graph this equation another way. Since this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,). So we have one point (0,) Now since the slope is , this means that in order to go from point to point we can use the slope to do so. So starting at (0,), we can go up 1 units and to the right 3 units to get to our next point Now draw a line through those points to graph So this is the graph of through the points (0,-3) and (3,-2)

Graphs/114728: Which property of the real numbers is illustrated by the following statement? 15 • (2 + 18) = 15 • 2 + 15 • 18 1 solutions Answer 83491 by jim_thompson5910(28536)   on 2007-12-05 11:21:44 (Show Source): You can put this solution on YOUR website! The distribution property is being used here. The distributive property states:

Quadratic_Equations/114663: 7x – 5 + 3x = 6 + x – 10 1 solutions Answer 83440 by jim_thompson5910(28536)   on 2007-12-04 22:28:27 (Show Source): You can put this solution on YOUR website! Start with the given equation Combine like terms on the left side Combine like terms on the right side Add 5 to both sides Subtract x from both sides Combine like terms on the left side Combine like terms on the right side Divide both sides by 9 to isolate x Reduce -------------------------------------------------------------- Answer: So our answer is (which is approximately in decimal form)

Quadratic_Equations/114666: 10(–x – 7) + 20 = –5(2x + 4) 1 solutions Answer 83438 by jim_thompson5910(28536)   on 2007-12-04 22:26:50 (Show Source): You can put this solution on YOUR website! Start with the given equation Distribute Combine like terms on the left side Add 50 to both sides Add 10x to both sides Combine like terms on the left side Combine like terms on the right side Simplify Since this equation is never true for any x value, this means there are no solutions.

Equations/114668: 2(x-3)-3(x+5)=3(x-2)-7 1 solutions Answer 83436 by jim_thompson5910(28536)   on 2007-12-04 22:24:51 (Show Source): You can put this solution on YOUR website! Start with the given equation Distribute Combine like terms on the left side Combine like terms on the right side Add 21 to both sides Subtract 3x from both sides Combine like terms on the left side Combine like terms on the right side Divide both sides by -4 to isolate x Divide -------------------------------------------------------------- Answer: So our answer is

Equations/114680: 2(x-2)=x+3 1 solutions Answer 83435 by jim_thompson5910(28536)   on 2007-12-04 22:23:36 (Show Source): You can put this solution on YOUR website! Start with the given equation Distribute Add 4 to both sides Subtract x from both sides Combine like terms on the left side Combine like terms on the right side -------------------------------------------------------------- Answer: So our answer is

Quadratic_Equations/114678: Solve by using the quadratic formula: 9z squared + 12z + 4 = 0 1 solutions Answer 83434 by jim_thompson5910(28536)   on 2007-12-04 22:22:50 (Show Source): You can put this solution on YOUR website! Let's use the quadratic formula to solve for z: Starting with the general quadratic the general solution using the quadratic equation is: So lets solve ( notice , , and ) Plug in a=9, b=12, and c=4 Square 12 to get 144 Multiply to get Combine like terms in the radicand (everything under the square root) Simplify the square root (note: If you need help with simplifying the square root, check out this solver) Multiply 2 and 9 to get 18 So now the expression breaks down into two parts or Lets look at the first part: Add the terms in the numerator Divide So one answer is Now lets look at the second part: Subtract the terms in the numerator Divide So another answer is So our only solution is: Notice when we graph (just replace z with x), we get: and we can see that the roots is . This verifies our answer

Quadratic_Equations/114676: Solve by using the quadratic formula: Z squared + 4z + 1 = 0 1 solutions Answer 83433 by jim_thompson5910(28536)   on 2007-12-04 22:20:56 (Show Source): You can put this solution on YOUR website! Let's use the quadratic formula to solve for z: Starting with the general quadratic the general solution using the quadratic equation is: So lets solve ( notice , , and ) Plug in a=1, b=4, and c=1 Square 4 to get 16 Multiply to get Combine like terms in the radicand (everything under the square root) Simplify the square root (note: If you need help with simplifying the square root, check out this solver) Multiply 2 and 1 to get 2 So now the expression breaks down into two parts or Now break up the fraction or Simplify or So these expressions approximate to or So our solutions are: or Notice when we graph (just replace z with x), we get: when we use the root finder feature on a calculator, we find that and .So this verifies our answer

Linear-equations/114651: Solve for y then graph. 2x-3y=12 (2x-3y)+(-2x)=12+(-2x) 2x-3y-2x=-2x+12 2x-2x-3y=-2x+12 -3y=-2x+12 -3y=-2x+12 My question is this: Am I correct on this equation so far and I am not sure how to graph this I have been working on this all afternoon. Thank you for your help, Barb Neely 1 solutions Answer 83421 by jim_thompson5910(28536)   on 2007-12-04 21:03:42 (Show Source): You can put this solution on YOUR website! You are correct so far Start with the given equation Divide both sides by -3 Break up the fraction Reduce Solved by pluggable solver: Graphing Linear Equations In order to graph we only need to plug in two points to draw the line So lets plug in some points Plug in x=-6 Multiply Add Reduce So here's one point (-6,-8) Now lets find another point Plug in x=-3 Multiply Add Reduce So here's another point (-3,-6). Add this to our graph Now draw a line through these points So this is the graph of through the points (-6,-8) and (-3,-6) So from the graph we can see that the slope is (which tells us that in order to go from point to point we have to start at one point and go up 2 units and to the right 3 units to get to the next point) the y-intercept is (0,)and the x-intercept is (,0) We could graph this equation another way. Since this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,). So we have one point (0,) Now since the slope is , this means that in order to go from point to point we can use the slope to do so. So starting at (0,), we can go up 2 units and to the right 3 units to get to our next point Now draw a line through those points to graph So this is the graph of through the points (0,-4) and (3,-2)

Inequalities/114648: -x-4>3x-2 1 solutions Answer 83416 by jim_thompson5910(28536)   on 2007-12-04 20:54:52 (Show Source): You can put this solution on YOUR website! Start with the given inequality Add 4 to both sides Subtract 3x from both sides Combine like terms on the left side Combine like terms on the right side Divide both sides by -4 to isolate x (note: Remember, dividing both sides by a negative number flips the inequality sign) Reduce -------------------------------------------------------------- Answer: So our answer is (which is approximately in decimal form)

Equations/114595: Solve the porportion 13. 12/54 = 8/w Any help with this equation would be Greatly appreciated. 1 solutions Answer 83407 by jim_thompson5910(28536)   on 2007-12-04 20:27:19 (Show Source): You can put this solution on YOUR website! Start with the given ratio Multiply both sides by w Multiply both sides by 54 Multiply Divide both sides by 12 Simplify So our answer is

Equations/114597: Solve the porportion 15. 27/45 = z/15 Any help with this equation would be Greatly appreciated. 1 solutions Answer 83406 by jim_thompson5910(28536)   on 2007-12-04 20:26:23 (Show Source): You can put this solution on YOUR website! Start with the given ratio Multiply both sides by 15 Multiply Simplify So our answer is

Equations/114592: Solve the porportion 4/5 = 64/c Any help with this equation would be Greatly appreciated. 1 solutions Answer 83368 by jim_thompson5910(28536)   on 2007-12-04 17:33:34 (Show Source): You can put this solution on YOUR website! Start with the given equation Multiply both sides by c Multiply both sides by 5 Multiply Divide both sides by 4 to isolate c

Functions/114591: Consider the function f(x) = x^2 +6x - 2 Find h, the x-coordinate of the vertex of this parabola 1 solutions Answer 83366 by jim_thompson5910(28536)   on 2007-12-04 17:25:47 (Show Source): You can put this solution on YOUR website! To find the x-coordinate, simply use this formula: So in this case, a=1 and b=6. Now plug them into the formula Multiply Reduce So the x-coordinate, or h, is -3 Check: Notice if we graph , we can see that the x-coordinate of the vertex is -3. So this verifies our answer.

Coordinate-system/114588: Find the equation, in standard form, with all interger coeffecients, of the line perpendicular to 3x - 6y = 9 and passing through (-2,-1) 1 solutions Answer 83361 by jim_thompson5910(28536)   on 2007-12-04 17:05:58 (Show Source): You can put this solution on YOUR website! First convert 3x - 6y = 9 to slope intercept form Solved by pluggable solver: Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa) Start with the given equation Subtract from both sides Multiply both sides by Distribute Multiply Rearrange the terms Reduce any fractions So the equation is now in slope-intercept form () where (the slope) and (the y-intercept) Now let's find the equation of the line through points (-2,-1) that is perpendicular to Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line Remember, any two perpendicular lines are negative reciprocals of each other. So if you're given the slope of , you can find the perpendicular slope by this formula: where is the perpendicular slope So plug in the given slope to find the perpendicular slope When you divide fractions, you multiply the first fraction (which is really ) by the reciprocal of the second Multiply the fractions. So the perpendicular slope is So now we know the slope of the unknown line is (its the negative reciprocal of from the line ). Also since the unknown line goes through (-2,-1), we can find the equation by plugging in this info into the point-slope formula Point-Slope Formula: where m is the slope and (,) is the given point Plug in , , and Distribute Multiply Subtract from both sides to isolate y Combine like terms So the equation of the line that is perpendicular to and goes through (,) is So here are the graphs of the equations and graph of the given equation (red) and graph of the line (green) that is perpendicular to the given graph and goes through (,)

Age_Word_Problems/114581: This question is from textbook This is the closest subject I could find, so, here goes.The real subject is digit problems. ::A number between 300 and 400 is forty times the sum of its digits. The tens digit is 6 more than the units digit. Find the number. 1 solutions Answer 83360 by jim_thompson5910(28536)   on 2007-12-04 17:01:52 (Show Source): You can put this solution on YOUR website! Let x=tens digit, y=units digit Since "The tens digit is 6 more than the units digit" we get Since the number is between 300 and 400, we know that the number must be of the form and since the number is 40 times the sum of the digits, we then have the equation Distribute Now plug in Distribute again Combine like terms Subtract 11y from both sides Subtract 360 from both sides Combine like terms Divide both sides by 91 So the units digit is 0 This means the tens digit is: So we have: tens digit: 6 , ones digit: 0 ----------------------------------------- Answer: So our number is 360 Check: Notice if we add the digits of 360, we get 3+6+0=9 Now multiply the sum by 40 9*40=360 which is our number. So our answer is verified