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Expressions-with-variables/119604: This question is from textbook glenco mathmatics 2x- y = -4 -3x + y = -9 1 solutions Answer 87727 by jim_thompson5910(28504)   on 2008-01-11 19:13:18 (Show Source): You can put this solution on YOUR website! 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 1 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 Add to both sides Combine the terms on the right side Multiply both sides by . This will cancel out 1 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.

Complex_Numbers/119657: 2x + y = 3 with no given numbers 1 solutions Answer 87726 by jim_thompson5910(28504)   on 2008-01-11 19:11:41 (Show Source): You can put this solution on YOUR website! Do you want to graph? 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=-3 Multiply Add So here's one point (-3,9) Now lets find another point Plug in x=-2 Multiply Add So here's another point (-2,7). Add this to our graph Now draw a line through these points So this is the graph of through the points (-3,9) and (-2,7) 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 down -2 units and to the right 1 units to get to the next point), the y-intercept is (0,)and the x-intercept is (,0) ,or (,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 down 2 units and to the right 1 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 (1,1)

Linear-equations/119723: Graph each equation, 2x - 3y =12 1 solutions Answer 87723 by jim_thompson5910(28504)   on 2008-01-11 18:32:58 (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=-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) . 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 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)

Polynomials-and-rational-expressions/119700: factoring z^2+18z+45 1 solutions Answer 87711 by jim_thompson5910(28504)   on 2008-01-11 16:03:54 (Show Source): You can put this solution on YOUR website! Looking at we can see that the first term is and the last term is where the coefficients are 1 and 45 respectively. Now multiply the first coefficient 1 and the last coefficient 45 to get 45. Now what two numbers multiply to 45 and add to the middle coefficient 18? Let's list all of the factors of 45: Factors of 45: 1,3,5,9,15,45 -1,-3,-5,-9,-15,-45 ...List the negative factors as well. This will allow us to find all possible combinations These factors pair up and multiply to 45 1*45 3*15 5*9 (-1)*(-45) (-3)*(-15) (-5)*(-9) note: remember two negative numbers multiplied together make a positive number Now which of these pairs add to 18? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 18 First Number Second Number Sum 1 45 1+45=46 3 15 3+15=18 5 9 5+9=14 -1 -45 -1+(-45)=-46 -3 -15 -3+(-15)=-18 -5 -9 -5+(-9)=-14 From this list we can see that 3 and 15 add up to 18 and multiply to 45 Now looking at the expression , replace with (notice adds up to . So it is equivalent to ) Now let's factor by grouping: Group like terms Factor out the GCF of out of the first group. Factor out the GCF of out of the second group Since we have a common term of , we can combine like terms So factors to So this also means that factors to (since is equivalent to ) ------------------------------------------------------------ Answer: So factors to

Polynomials-and-rational-expressions/119704: Factor completlety 16x^2-2x-3 1 solutions Answer 87710 by jim_thompson5910(28504)   on 2008-01-11 16:02:07 (Show Source): You can put this solution on YOUR website! Looking at we can see that the first term is and the last term is where the coefficients are 16 and -3 respectively. Now multiply the first coefficient 16 and the last coefficient -3 to get -48. Now what two numbers multiply to -48 and add to the middle coefficient -2? Let's list all of the factors of -48: Factors of -48: 1,2,3,4,6,8,12,16,24,48 -1,-2,-3,-4,-6,-8,-12,-16,-24,-48 ...List the negative factors as well. This will allow us to find all possible combinations These factors pair up and multiply to -48 (1)*(-48) (2)*(-24) (3)*(-16) (4)*(-12) (6)*(-8) (-1)*(48) (-2)*(24) (-3)*(16) (-4)*(12) (-6)*(8) note: remember, the product of a negative and a positive number is a negative number 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 -48 1+(-48)=-47 2 -24 2+(-24)=-22 3 -16 3+(-16)=-13 4 -12 4+(-12)=-8 6 -8 6+(-8)=-2 -1 48 -1+48=47 -2 24 -2+24=22 -3 16 -3+16=13 -4 12 -4+12=8 -6 8 -6+8=2 From this list we can see that 6 and -8 add up to -2 and multiply to -48 Now looking at the expression , replace with (notice adds up to . So it is equivalent to ) Now let's factor by grouping: Group like terms Factor out the GCF of out of the first group. Factor out the GCF of out of the second group Since we have a common term of , we can combine like terms So factors to So this also means that factors to (since is equivalent to ) ------------------------------------------------------------ Answer: So factors to

expressions/119708: How do I factor this? X^2-12x+36 1 solutions Answer 87709 by jim_thompson5910(28504)   on 2008-01-11 16:01:02 (Show Source): You can put this solution on YOUR website! Looking at we can see that the first term is and the last term is where the coefficients are 1 and 36 respectively. Now multiply the first coefficient 1 and the last coefficient 36 to get 36. Now what two numbers multiply to 36 and add to the middle coefficient -12? Let's list all of the factors of 36: Factors of 36: 1,2,3,4,6,9,12,18 -1,-2,-3,-4,-6,-9,-12,-18 ...List the negative factors as well. This will allow us to find all possible combinations These factors pair up and multiply to 36 1*36 2*18 3*12 4*9 6*6 (-1)*(-36) (-2)*(-18) (-3)*(-12) (-4)*(-9) (-6)*(-6) note: remember two negative numbers multiplied together make a positive number Now which of these pairs add to -12? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -12 First Number Second Number Sum 1 36 1+36=37 2 18 2+18=20 3 12 3+12=15 4 9 4+9=13 6 6 6+6=12 -1 -36 -1+(-36)=-37 -2 -18 -2+(-18)=-20 -3 -12 -3+(-12)=-15 -4 -9 -4+(-9)=-13 -6 -6 -6+(-6)=-12 From this list we can see that -6 and -6 add up to -12 and multiply to 36 Now looking at the expression , replace with (notice adds up to . So it is equivalent to ) Now let's factor by grouping: Group like terms Factor out the GCF of out of the first group. Factor out the GCF of out of the second group Since we have a common term of , we can combine like terms So factors to So this also means that factors to (since is equivalent to ) note: is equivalent to since the term occurs twice. So also factors to ------------------------------------------------------------ Answer: So factors to

expressions/119714: Is this the right factoring x^2-5x-6 (x-2)(x-3) 1 solutions Answer 87708 by jim_thompson5910(28504)   on 2008-01-11 16:00:04 (Show Source): You can put this solution on YOUR website! No it is not. If you foil you'll get Looking at we can see that the first term is and the last term is where the coefficients are 1 and -6 respectively. Now multiply the first coefficient 1 and the last coefficient -6 to get -6. Now what two numbers multiply to -6 and add to the middle coefficient -5? Let's list all of the factors of -6: Factors of -6: 1,2,3,6 -1,-2,-3,-6 ...List the negative factors as well. This will allow us to find all possible combinations These factors pair up and multiply to -6 (1)*(-6) (2)*(-3) (-1)*(6) (-2)*(3) note: remember, the product of a negative and a positive number is a negative number Now which of these pairs add to -5? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -5 First Number Second Number Sum 1 -6 1+(-6)=-5 2 -3 2+(-3)=-1 -1 6 -1+6=5 -2 3 -2+3=1 From this list we can see that 1 and -6 add up to -5 and multiply to -6 Now looking at the expression , replace with (notice adds up to . So it is equivalent to ) Now let's factor by grouping: Group like terms Factor out the GCF of out of the first group. Factor out the GCF of out of the second group Since we have a common term of , we can combine like terms So factors to So this also means that factors to (since is equivalent to ) ------------------------------------------------------------ Answer: So factors to

expressions/119713: Was I able to factor this correctly? 4x^2-15x-25 =(2x+5)(2x+5) 1 solutions Answer 87707 by jim_thompson5910(28504)   on 2008-01-11 15:56:22 (Show Source): You can put this solution on YOUR website! Looking at we can see that the first term is and the last term is where the coefficients are 4 and -25 respectively. Now multiply the first coefficient 4 and the last coefficient -25 to get -100. Now what two numbers multiply to -100 and add to the middle coefficient -15? Let's list all of the factors of -100: Factors of -100: 1,2,4,5,10,20,25,50 -1,-2,-4,-5,-10,-20,-25,-50 ...List the negative factors as well. This will allow us to find all possible combinations These factors pair up and multiply to -100 (1)*(-100) (2)*(-50) (4)*(-25) (5)*(-20) (-1)*(100) (-2)*(50) (-4)*(25) (-5)*(20) note: remember, the product of a negative and a positive number is a negative number Now which of these pairs add to -15? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -15 First Number Second Number Sum 1 -100 1+(-100)=-99 2 -50 2+(-50)=-48 4 -25 4+(-25)=-21 5 -20 5+(-20)=-15 -1 100 -1+100=99 -2 50 -2+50=48 -4 25 -4+25=21 -5 20 -5+20=15 From this list we can see that 5 and -20 add up to -15 and multiply to -100 Now looking at the expression , replace with (notice adds up to . So it is equivalent to ) Now let's factor by grouping: Group like terms Factor out the GCF of out of the first group. Factor out the GCF of out of the second group Since we have a common term of , we can combine like terms So factors to So this also means that factors to (since is equivalent to ) So factors to

Polynomials-and-rational-expressions/119703: factor completely -3t^3+3t^2-6t 1 solutions Answer 87705 by jim_thompson5910(28504)   on 2008-01-11 15:30:53 (Show Source): You can put this solution on YOUR website! Start with the given expression Factor out the GCF Now let's focus on the inner expression ------------------------------------------------------------ Looking at we can see that the first term is and the last term is where the coefficients are 1 and 2 respectively. Now multiply the first coefficient 1 and the last coefficient 2 to get 2. Now what two numbers multiply to 2 and add to the middle coefficient -1? Let's list all of the factors of 2: Factors of 2: 1,2 -1,-2 ...List the negative factors as well. This will allow us to find all possible combinations These factors pair up and multiply to 2 1*2 (-1)*(-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 pairs of factors add to -1. So the expression cannot be factored ------------------------------------------------------------ Answer: So factors to

Equations/119697: Can you help me with this equation? Calculate the total rent paid on an apartment for n months if the rent is $565 a month 1 solutions Answer 87689 by jim_thompson5910(28504)   on 2008-01-11 13:56:00 (Show Source): You can put this solution on YOUR website! To find the total rent after 2 months, just multiply 2 and 565 to get . To find the total rent after 3 months, just multiply 3 and 565 to get . This pattern continues... So to find the total rent after n months, just multiply n and 565 to get . So the total rent due after n months is 565n

Linear-equations/119694: graph equation y=3\4x+2 1 solutions Answer 87687 by jim_thompson5910(28504)   on 2008-01-11 13:38:53 (Show Source): You can put this solution on YOUR website! 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=-8 Multiply Add Reduce So here's one point (-8,-4) Now lets find another point Plug in x=-4 Multiply Add Reduce So here's another point (-4,-1). Add this to our graph Now draw a line through these points So this is the graph of through the points (-8,-4) and (-4,-1) 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 3 units and to the right 4 units to get to the next point) the y-intercept is (0,)and the x-intercept is (,0) ,or (,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 3 units and to the right 4 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 (0,2) and (4,5)

Linear-equations/119695: graph equation using intercept method 2x+3y=6 2x-3y=12 1 solutions Answer 87686 by jim_thompson5910(28504)   on 2008-01-11 13:37:29 (Show Source): You can put this solution on YOUR website! #1 Start with the given equation Let's find the x-intercept To find the x-intercept, let y=0 and solve for x: Plug in Simplify Divide both sides by 2 Reduce So the x-intercept is (note: the x-intercept will always have a y-coordinate equal to zero) ------------------ Start with the given equation Now let's find the y-intercept To find the y-intercept, let x=0 and solve for y: Plug in Simplify Divide both sides by 3 Reduce So the y-intercept is (note: the y-intercept will always have a x-coordinate equal to zero) ------------------------------------------ So we have these intercepts: x-intercept: y-intercept: Now plot the two points and Now draw a line through the two points to graph graph of through the points and #2 Start with the given equation Let's find the x-intercept To find the x-intercept, let y=0 and solve for x: Plug in Simplify Divide both sides by 2 Reduce So the x-intercept is (note: the x-intercept will always have a y-coordinate equal to zero) ------------------ Start with the given equation Now let's find the y-intercept To find the y-intercept, let x=0 and solve for y: Plug in Simplify Divide both sides by -3 Reduce So the y-intercept is (note: the y-intercept will always have a x-coordinate equal to zero) ------------------------------------------ So we have these intercepts: x-intercept: y-intercept: Now plot the two points and Now draw a line through the two points to graph graph of through the points and

Quadratic_Equations/119661: What is the value of k if one root of (3k+1)x^2-2kx=-5 is 1? 1 solutions Answer 87685 by jim_thompson5910(28504)   on 2008-01-11 13:24:35 (Show Source): You can put this solution on YOUR website! If 1 is a root, then . Start with the given equation Add 5 to both sides Plug in Simplify Combine like terms on the left side Subtract 6 from both sides -------------------------------------------------------------- Answer: So our answer is

Equations/119692: WRITE THE EQUATION IN STANDARD FORM WITH INTEGER COEFFICIENTS 4x-y-7=0 1 solutions Answer 87684 by jim_thompson5910(28504)   on 2008-01-11 13:18:15 (Show Source): You can put this solution on YOUR website! Start with the given equation Add 7 to both sides So the equation is now in standard form where , , and

Expressions-with-variables/119691: Solve each system by substitution. check your answer. y=x-2 y=4x+1 1 solutions Answer 87683 by jim_thompson5910(28504)   on 2008-01-11 13:15:22 (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. Subtract 1 from 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 3 to isolate x Divide Now that we know that , we can plug this into to find Substitute for each Simplify So our answer is and

Human-and-algebraic-language/119644: Ifentify the variables, coefficients,and constants in the algebraic -6x -xy +60 1 solutions Answer 87682 by jim_thompson5910(28504)   on 2008-01-11 13:13:10 (Show Source): You can put this solution on YOUR website! Variables: x and y Coefficients (ie the numbers in front of the variables): -6 and -1 Constants: 60

Quadratic_Equations/119662: One root of x^2-4x+4a=0 is 2-4i. What is the value of a ? 1 solutions Answer 87681 by jim_thompson5910(28504)   on 2008-01-11 12:53:13 (Show Source): You can put this solution on YOUR website! If 2-4i is a root, then when , the entire left side will equal zero. Start with the given equation Plug in Foil and distribute Replace with Multiply Combine like terms Add 20 to both sides Combine like terms on the right side Divide both sides by 4 to isolate a Divide -------------------------------------------------------------- Answer: So our answer is Note: you can check this answer by using the quadratic formula

Rational-functions/119617: Hey, I need help with identities in chapter 6 lesson 6 of my book entitled Rational Expressions and Equations it says as follows: Equations that are true for all acceptable replacements of the variable are identities. Determine which equations areidenties. problem as follows: xsquared + 6x - 16/ x-2 = x + 8 I also need help with solving rational expressions. This is algebra 2 Thank you so much I can realy use the help I need to bring up my grade cause I am realy worried about my G.P.A. because I want to get into a very good college. Thanks again 1 solutions Answer 87619 by jim_thompson5910(28504)   on 2008-01-10 20:29:22 (Show Source): You can put this solution on YOUR website! Start with the given equation. Note: since since that will make the denominator equal to zero Factor to get Combine the fractions Cancel like terms Simplify Subtract 8 from both sides Subtract x from both sides Combine like terms on the left side Combine like terms on the right side Simplify Since this equation is always true for any x value, this means is an identity and x can equal any number except 2.

Complex_Numbers/119571: This question is from textbook Algebra and Trigonometry Structure and Method Book 2 1 solutions Answer 87605 by jim_thompson5910(28504)   on 2008-01-10 18:32:23 (Show Source): You can put this solution on YOUR website! Start with the given expression. Note: since and we cannot take the square root of a negative number, we must make the restriction Combine the square roots. Factor -20 into Cancel like terms Simplify Multiply Take the square root of 4 to get 2

logarithm/119567: can you please explain this to me step by step so i can understand it. log(3-2x) - log (x+9)=0 i hope you can help me understand this thank you julie 1 solutions Answer 87603 by jim_thompson5910(28504)   on 2008-01-10 18:23:43 (Show Source): You can put this solution on YOUR website! Start with the given equation. Note: Since you did not specify a base, this means that we're going to use the default base 10. Combine the logs using the identity Rewrite the equation using the property: ====> Evaluate to get Multiply both sides by Subtract 9 from both sides Add 2x to both sides Combine like terms on the left side Combine like terms on the right side Divide both sides by 3 to isolate x Divide -------------------------------------------------------------- Answer: So our answer is

Inequalities/119564: how do you solve and graph the absolute value 2x > 6? 1 solutions Answer 87601 by jim_thompson5910(28504)   on 2008-01-10 18:16:47 (Show Source): You can put this solution on YOUR website! Start with the given inequality Break up the absolute value (remember, if you have , then or ) or Break up the absolute value inequality using the given rule Now lets focus on the first inequality Start with the given inequality Divide both sides by 2 to isolate x Divide Now lets focus on the second inequality Start with the given inequality Divide both sides by 2 to isolate x Divide ---------------------------------------------------- Answer: So our answer is or which looks like this in interval notation if you wanted to graph the solution set, you would get Graph of the solution set in blue and the excluded values represented by open circles

logarithm/119561: can you please explain this to me in step by step form so hopefully i can understand this. log x 9/4 =2 please help me thank you julie 1 solutions Answer 87599 by jim_thompson5910(28504)   on 2008-01-10 18:11:14 (Show Source): You can put this solution on YOUR website! Does this say: "log base x of 9/4 equals 2"? If it does, then... Start with the given equation. Rewrite the equation using the property: ====> Take the square root of both sides. Since you cannot take the log of a negative number, I'm going to exclude the negative answer. Break up the square root Simplify to get Simplify to get So our answer is

Triangles/119555: In a quadrilateral JKLM, measure angle J=x,measure angle K=2x, measure angle L=2x+10,and measure angle M=3x-5. Find the measure of the angle. 1 solutions Answer 87598 by jim_thompson5910(28504)   on 2008-01-10 18:05:23 (Show Source): You can put this solution on YOUR website! For any quadrilateral, the sum of the 4 angles is 360 degrees. So in this case, Start with the given equation Plug in , , ,and Combine like terms on the left side Subtract 5 from both sides Combine like terms on the right side Divide both sides by 8 to isolate x Reduce Since (which is in decimal form), our first angle is Since , we can plug this into to get So our second angle is Since , we can plug this into to get So our third angle is Since , we can plug this into to get So our fourth angle is -------------------------------------------------------------- Answer: So the measures of the four angles are: , , , and Check: Start with the given equation Plug in , , , and Add. Since the two sides of the equation are equal, this verifies our answer.

Polynomials-and-rational-expressions/119550: hi i really dont understand what to do for this equation please help me out. thanks i apreciate it. (16x) over (25x^2-5) times ( 2x^2-x-1) over(8x) 1 solutions Answer 87596 by jim_thompson5910(28504)   on 2008-01-10 17:54:17 (Show Source): You can put this solution on YOUR website! Start with the given expression Factor to get Factor to get Factor to get Factor to get Combine the fractions Cancel like terms Divide and simplify So simplifies to In other words,

Quadratic_Equations/119529: This question is from textbook determine whether the equation has 2 solutions, 1 solution, or no solution. SHOW WORK! PUT IN STANDARD FORM! 22)x^2-3x+2=0 24)-3x^2+5x-1=0 26)x^2-2x+4=0 28)3x^2-6x+3=0 30)-5x^2+6x-6=0 1 solutions Answer 87595 by jim_thompson5910(28504)   on 2008-01-10 17:46:15 (Show Source): You can put this solution on YOUR website! I'll do the first two to help you get started #22 From the quadratic formula the discriminant consists of all of the terms in the square root. So the discriminant is the discriminant tells us how many solutions (and what type of solutions) we can expect for any quadratic. Now let's find the discriminant for : Plug in a=1, b=-3, c=2 Square -3 to get 9 Multiply -4*1*2 to get -8 Combine 9 and -8 to get 1 Since the discriminant equals 1 (which is greater than zero) , this means there are two real solutions. Remember if the discriminant is greater than zero, then the quadratic will have two real solutions. #24 From the quadratic formula the discriminant consists of all of the terms in the square root. So the discriminant is the discriminant tells us how many solutions (and what type of solutions) we can expect for any quadratic. Now let's find the discriminant for : Plug in a=-3, b=5, c=-1 Square 5 to get 25 Multiply -4*-3*-1 to get -12 Combine 25 and -12 to get 13 Since the discriminant equals 13 (which is greater than zero) , this means there are two real solutions. Remember if the discriminant is greater than zero, then the quadratic will have two real solutions.

test/119540: This question is from textbook Algebra II I really really need help and I've been searching over the internet for the best source to hepl me unfortunately my school exam on this is tomorrow. But it would really help to know how to do the problems. My main problem is in Chapter 3 of my book , on Solving Linear Systems Alegraically. I don't understand anything about it, it just confuses me . such as 3x + 4y equals -4 x + 2y equals 2 and in the book it says to solve the linear system using the substituion method. I'm having problems on problems like that and on graphing in section 3.3 of my book on Graphing and Solving Systems of Linear inequalities. on pages 159 and 148 mostly those pages THanks! 1 solutions Answer 87594 by jim_thompson5910(28504)   on 2008-01-10 17:35:57 (Show Source): You can put this solution on YOUR website! 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 4. 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 2 to Multiply Reduce any fractions Add to both sides Combine the terms on the right side Make 1 into a fraction with a denominator of 2 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 Add to both sides Combine the terms on the right side Multiply both sides by . This will cancel out 2 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.

Linear-equations/119522: a line with slope 305and y-intercept (0,4) 9 1 solutions Answer 87568 by jim_thompson5910(28504)   on 2008-01-10 16:00:01 (Show Source): You can put this solution on YOUR website! Is the slope supposed to say "3/5"? If you want to find the equation of line with a given a slope of which goes through the point (,), you can simply use the point-slope formula to find the equation: ---Point-Slope Formula--- where is the slope, and is the given point So lets use the Point-Slope Formula to find the equation of the line Plug in , , and (these values are given) Distribute Multiply and to get Add 4 to both sides to isolate y Combine like terms and to get ------------------------------------------------------------------------------------------------------------ Answer: So the equation of the line with a slope of which goes through the point (,) is: which is now in form where the slope is and the y-intercept is Notice if we graph the equation and plot the point (,), we get (note: if you need help with graphing, check out this solver) Graph of through the point (,) and we can see that the point lies on the line. Since we know the equation has a slope of and goes through the point (,), this verifies our answer.

Inequalities/119513: how would you solve this -3 > 7y-3 > -24 1 solutions Answer 87565 by jim_thompson5910(28504)   on 2008-01-10 15:39:30 (Show Source): You can put this solution on YOUR website! Start with the given compound inequality Reverse the compound inequality by switching the outer sides and reversing the inequality signs Add 3 to all sides Divide every side by 7 to isolate y. So the solution in interval notation is: (-3,0) 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)

expressions/119518: I really need help with these questions. Evaluate each function for x= -2,0,and 5. 1.) y = 9 + x 2.) y = x^2 - 1 Please help me because I need to get this to my teacher tommorrow. 1 solutions Answer 87562 by jim_thompson5910(28504)   on 2008-01-10 15:34:29 (Show Source): You can put this solution on YOUR website! #1 Let's evaluate Start with the given function. Plug in . In other words, replace each x with -2. Multiply 1 and -2 to get -2 Now combine like terms -----------Now let's evaluate another value--------- Let's evaluate Start with the given function. Plug in . In other words, replace each x with 0. Multiply 1 and 0 to get 0 Now combine like terms -----------Now let's evaluate another value--------- Let's evaluate Start with the given function. Plug in . In other words, replace each x with 5. Multiply 1 and 5 to get 5 Now combine like terms #2 Let's evaluate Start with the given function. Plug in . In other words, replace each x with -2. Evaluate to get 4. Now combine like terms -----------Now let's evaluate another value--------- Let's evaluate Start with the given function. Plug in . In other words, replace each x with 0. Evaluate to get 0. Now combine like terms -----------Now let's evaluate another value--------- Let's evaluate Start with the given function. Plug in . In other words, replace each x with 5. Evaluate to get 25. Now combine like terms

Linear-equations/119501: Find the slope and y-intercept. -4x + 5y = 25 1 solutions Answer 87549 by jim_thompson5910(28504)   on 2008-01-10 13:17:02 (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 Add to 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)

Radicals/119510: Find the distance between each pair of points. 1. (0,8)and(0,-4) 2. (2,6)and(-3,4) I'm lost on where to start on this type of problem. 1 solutions Answer 87548 by jim_thompson5910(28504)   on 2008-01-10 13:15:12 (Show Source): You can put this solution on YOUR website! #1 Start with the given distance formula where is the first point and is the second point Plug in , , , Evaluate to get 0. Evaluate to get 12. Square each value Add Simplify the square root (note: If you need help with simplifying the square root, check out this solver) So the distance between (0,8) and (0,-4) is 12 units #2 Start with the given distance formula where is the first point and is the second point Plug in , , , Evaluate to get 5. Evaluate to get 2. Square each value Add So the distance approximates to which rounds to 5.39 So the distance between (2,6) and (-3,4) is approximately 5.39 units