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Graphs/115679: Write the equation of the line that passes through point (6,4) with a slope of 2 1 solutions Answer 84182 by jim_thompson5910(28504)   on 2007-12-09 16:22:51 (Show Source): You can put this solution on YOUR website! 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.

Linear-equations/115665: solve the system by addition 3x - y =1 3x -y = 2 1 solutions Answer 84178 by jim_thompson5910(28504)   on 2007-12-09 15:57:43 (Show Source): You can put this solution on YOUR website! Solved by pluggable solver: Solving a System of Linear Equations by Elimination/Addition Lets start with the given system of linear equations In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for y, we would have to eliminate x (or vice versa). So lets eliminate x. In order to do that, we need to have both x coefficients that are equal but have opposite signs (for instance 2 and -2 are equal but have opposite signs). This way they will add to zero. So to make the x coefficients equal but opposite, we need to multiply both x coefficients by some number to get them to an equal number. So if we wanted to get 3 and 3 to some equal number, we could try to get them to the LCM. Since the LCM of 3 and 3 is 3, we need to multiply both sides of the top equation by 1 and multiply both sides of the bottom equation by -1 like this: Multiply the top equation (both sides) by 1 Multiply the bottom equation (both sides) by -1 So after multiplying we get this: Notice how 3 and -3 and 1 and 1 add to zero (ie ) However 1 and -2 add to -1 (ie ); So we're left with which means no value of x or y value will satisfy the system of equations. So there are no solutions So this system is inconsistent

Linear-equations/115661: help me find the slope of the graph of the linear function f #42: f(2) = -3, f(-2) = 5 #44: f(-3) = -9, f(-1) = 2 #46: f(9) = -1, f(-1) = 2 #48: f(2) = 2, f(3) = 3 1 solutions Answer 84177 by jim_thompson5910(28504)   on 2007-12-09 15:56:49 (Show Source): You can put this solution on YOUR website! I'll do the first two to show you how to do these #42 If we have the statement f(2)=-3, this means we have the point (2,-3). Also if we have the statement f(-2) = 5, this means we have the point (-2,5) Now let's find the slope through (2,-3) and (-2,5) Solved by pluggable solver: Finding the slope Slope of the line through the points (2, -3) and (-2, 5) Answer: Slope is #44: If we have the statement f(-3) = -9, this means we have the point (-3,-9). Also if we have the statement f(-1) = 2, this means we have the point (-1,2) Now let's find the slope through (-3,-9) and (-1,2) Solved by pluggable solver: Finding the slope Slope of the line through the points (-3, -9) and (-1, 2) Answer: Slope is

Functions/115662: find f(-3) when f(x)=2x^2-7x+8. 1 solutions Answer 84176 by jim_thompson5910(28504)   on 2007-12-09 15:52:50 (Show Source): You can put this solution on YOUR website! Let's evaluate Start with the given function. Plug in . In other words, replace each x with -3. Evaluate to get 9. Multiply 2 and 9 to get 18 Multiply -7 and -3 to get 21 Now combine like terms

Polynomials-and-rational-expressions/115666: Factor completely. ax-ay+x squared -xy 1 solutions Answer 84175 by jim_thompson5910(28504)   on 2007-12-09 15:51:51 (Show Source): You can put this solution on YOUR website! Start with the given expression Group like terms Factor out the GCF out of the first group. Factor out the GCF out of the second group Since we have the common term , we can combine like terms So factors to

Equations/115667: rewrite the equation -8x -5y = -45 as a function of x 1 solutions Answer 84174 by jim_thompson5910(28504)   on 2007-12-09 15:49:56 (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)

Polynomials-and-rational-expressions/115668: Factor completely. m cubed - 9m squared n+ 18n squared m 1 solutions Answer 84173 by jim_thompson5910(28504)   on 2007-12-09 15:48:38 (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 18 respectively. Now multiply the first coefficient 1 and the last coefficient 18 to get 18. Now what two numbers multiply to 18 and add to the middle coefficient -9? Let's list all of the factors of 18: Factors of 18: 1,2,3,6,9,18 -1,-2,-3,-6,-9,-18 ...List the negative factors as well. This will allow us to find all possible combinations These factors pair up and multiply to 18 1*18 2*9 3*6 (-1)*(-18) (-2)*(-9) (-3)*(-6) note: remember two negative numbers multiplied together make a positive number Now which of these pairs add to -9? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -9 First Number Second Number Sum 1 18 1+18=19 2 9 2+9=11 3 6 3+6=9 -1 -18 -1+(-18)=-19 -2 -9 -2+(-9)=-11 -3 -6 -3+(-6)=-9 From this list we can see that -3 and -6 add up to -9 and multiply to 18 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 Now reintroduce the GCF ------------------------------- Answer: So factors to

Linear-equations/115675: Can someone please explain to me CLEARLY since my teacher never does step by step how to solve Linear Equations and slope intercept. I never know how to solve them and I fail all my tests and quizes. For example here is one problem from a quiz 4x+5=-12 1 solutions Answer 84172 by jim_thompson5910(28504)   on 2007-12-09 15:45:53 (Show Source): You can put this solution on YOUR website! Start with the given equation Subtract 5 from both sides Combine like terms on the right side Divide both sides by 4 to isolate x Reduce -------------------------------------------------------------- Answer: So our answer is (which is approximately in decimal form)

Polynomials-and-rational-expressions/115655: Can someone please help me with this problem. I tried to do the problem and I just keep getting very confused. We are specifically looking for how to factor polynomials when the leading coefficient is not 1. How can we find the correct way to break up the middle term to make this come out right. Can you please factor the polynomial 4x^2 + 4x - 99 Please tell us why and how you carry out each step of the process. PLEASE HELP ME!!!! 1 solutions Answer 84166 by jim_thompson5910(28504)   on 2007-12-09 14:53:54 (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 4 and -99 respectively. Now multiply the first coefficient 4 and the last coefficient -99 to get -396. Now what two numbers multiply to -396 and add to the middle coefficient 4? Let's list all of the factors of -396: Factors of -396: 1,2,3,4,6,9,11,12,18,22,33,36,44,66,99,132,198,396 -1,-2,-3,-4,-6,-9,-11,-12,-18,-22,-33,-36,-44,-66,-99,-132,-198,-396 ...List the negative factors as well. This will allow us to find all possible combinations These factors pair up and multiply to -396 (1)*(-396) (2)*(-198) (3)*(-132) (4)*(-99) (6)*(-66) (9)*(-44) (11)*(-36) (12)*(-33) (18)*(-22) (-1)*(396) (-2)*(198) (-3)*(132) (-4)*(99) (-6)*(66) (-9)*(44) (-11)*(36) (-12)*(33) (-18)*(22) note: remember, the product of a negative and a positive number is a negative number Now which of these pairs add to 4? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 4 First Number Second Number Sum 1 -396 1+(-396)=-395 2 -198 2+(-198)=-196 3 -132 3+(-132)=-129 4 -99 4+(-99)=-95 6 -66 6+(-66)=-60 9 -44 9+(-44)=-35 11 -36 11+(-36)=-25 12 -33 12+(-33)=-21 18 -22 18+(-22)=-4 -1 396 -1+396=395 -2 198 -2+198=196 -3 132 -3+132=129 -4 99 -4+99=95 -6 66 -6+66=60 -9 44 -9+44=35 -11 36 -11+36=25 -12 33 -12+33=21 -18 22 -18+22=4 From this list we can see that -18 and 22 add up to 4 and multiply to -396 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

Inequalities/115653: how to solve? -3(3X+1)<15 1 solutions Answer 84165 by jim_thompson5910(28504)   on 2007-12-09 14:50:59 (Show Source): You can put this solution on YOUR website! Start with the given inequality Distribute Add 3 to both sides Combine like terms on the right side Divide both sides by -9 to isolate x (note: Remember, dividing both sides by a negative number flips the inequality sign) Divide -------------------------------------------------------------- Answer: So our answer is

Divisibility_and_Prime_Numbers/115654: I need help with these math problems on least common multiple. 20. 16,18 23. 4,17 26. 15,18 27. 12,14 28. 7,13 32. 3,5,12 33. 6,16,24 34. 12,18,24 1 solutions Answer 84164 by jim_thompson5910(28504)   on 2007-12-09 14:48:16 (Show Source): You can put this solution on YOUR website! I'll do a few of these to show you how to do these problems. #20 First, list the prime factorization of each number. If you need help with prime factorization, check out this solver. 16: 2*2*2*2 18: 2*3*3 Now highlight the unique factors. Remember, highlight the factors that occur most frequently 16: 2*2*2*2 18: 2*3*3 Now multiply all of the highlighted factors 2*2*2*2*3*3=144 So the LCM of 16 and 18 is 144 #23 First, list the prime factorization of each number. If you need help with prime factorization, check out this solver. 4: 2*2 17: 17 Now highlight the unique factors. Remember, highlight the factors that occur most frequently 4: 2*2 17: 17 Now multiply all of the highlighted factors 2*2*17=68 So the LCM of 4 and 17 is 68 #26 First, list the prime factorization of each number. If you need help with prime factorization, check out this solver. 15: 3*5 18: 2*3*3 Now highlight the unique factors. Remember, highlight the factors that occur most frequently 15: 3*5 18: 2*3*3 Now multiply all of the highlighted factors 2*3*3*5=90 So the LCM of 15 and 18 is 90 note: I skipped to a problem with 3 numbers #33 First, list the prime factorization of each number. If you need help with prime factorization, check out this solver. 6: 2*3 16: 2*2*2*2 24: 2*2*2*3 Now highlight the unique factors. Remember, highlight the factors that occur most frequently 6: 2*3 16: 2*2*2*2 24: 2*2*2*3 Now multiply all of the highlighted factors 2*2*2*2*3=48 So the LCM of 6, 16, and 24 is 48

Distributive-associative-commutative-properties/115652: 3x^2 + 8x + 5 how would i factor this ? 1 solutions Answer 84163 by jim_thompson5910(28504)   on 2007-12-09 14:40:54 (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 3 and 5 respectively. Now multiply the first coefficient 3 and the last coefficient 5 to get 15. Now what two numbers multiply to 15 and add to the middle coefficient 8? Let's list all of the factors of 15: Factors of 15: 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 and multiply to 15 1*15 3*5 (-1)*(-15) (-3)*(-5) note: remember two negative numbers multiplied together make a positive number Now which of these pairs add to 8? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 8 First Number Second Number Sum 1 15 1+15=16 3 5 3+5=8 -1 -15 -1+(-15)=-16 -3 -5 -3+(-5)=-8 From this list we can see that 3 and 5 add up to 8 and multiply to 15 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

Linear-equations/115649: how would I graph the line with a slope of 3 and passes through points (2,1) and (4,7). 1 solutions Answer 84162 by jim_thompson5910(28504)   on 2007-12-09 14:39:29 (Show Source): You can put this solution on YOUR website! If you only want to graph the line, simply plot the two points (2,1) and (4,7) and draw a straight line through them. ------------------------------------------- However, if you want to find the equation of the line, then... 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 Reduce 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) Distribute Multiply and to get Add to both sides to isolate y Combine like terms and to get ------------------------------------------------------------------------------------------------------------ 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.

Signed-numbers/115646: Combine like terms. 5w – 6w 1 solutions Answer 84159 by jim_thompson5910(28504)   on 2007-12-09 14:23:05 (Show Source): You can put this solution on YOUR website! Since we have a common variable "w", we can simply subtract 6 from 5 to get -1. So Which also looks like notice the 1 has been removed

Equations/115640: This question is from textbook 5n-8=11n+5 1 solutions Answer 84155 by jim_thompson5910(28504)   on 2007-12-09 13:42:51 (Show Source): You can put this solution on YOUR website! Start with the given equation Add 8 to both sides Subtract 11n from both sides Combine like terms on the left side Combine like terms on the right side Divide both sides by -6 to isolate n Reduce -------------------------------------------------------------- Answer: So our answer is (which is approximately in decimal form)

Linear-equations/115635: 28-2(10x-0.365)=7x+0.035 1 solutions Answer 84151 by jim_thompson5910(28504)   on 2007-12-09 13:08:36 (Show Source): You can put this solution on YOUR website! Start with the given equation Distribute Multiply both sides by 1000 to move the decimal on each number 3 times. This will make every number a whole number. Distribute and multiply Combine like terms on the left side Subtract 28730 from both sides Subtract 7000x from both sides Combine like terms on the left side Combine like terms on the right side Divide both sides by -27000 to isolate x Reduce -------------------------------------------------------------- Answer: So our answer is (which is approximately in decimal form)

Polynomials-and-rational-expressions/115569: I cant figure out how to solve ... (x+4)/3x + (x+8)/5x = 2 1 solutions Answer 84150 by jim_thompson5910(28504)   on 2007-12-09 13:04:16 (Show Source): You can put this solution on YOUR website! Start with the given expression Now multiply both sides by the LCD to eliminate every fraction Distribute. Since the fractions are gone, we have to keep in mind that Distribute again Combine like terms on the left side Subtract 44 from both sides Subtract 30x from both sides Combine like terms on the left side Divide both sides by -22 to isolate x Divide -------------------------------------------------------------- Answer: So our answer is

Graphs/115626: Please help. Graph the following inequality x-y≤2 Thanks JMS 1 solutions Answer 84149 by jim_thompson5910(28504)   on 2007-12-09 13:00:42 (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 (note: if you need help with graphing, check out this solver) 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 true, we simply shade the entire region that contains (0,0) Graph of with the boundary (which is the line in red) and the shaded region (in green)

Linear-equations/115633: how do I calculate the slope of the line that pases through the following points: (-5,-9) and (7,-9) 1 solutions Answer 84147 by jim_thompson5910(28504)   on 2007-12-09 12:59:30 (Show Source): You can put this solution on YOUR website! Solved by pluggable solver: Finding the slope Slope of the line through the points (-5, -9) and (7, -9) Answer: Slope is

Linear-equations/115632: Are these two lines perpendicular? Line 1: y=x+3 Line 2: x-y=13 1 solutions Answer 84146 by jim_thompson5910(28504)   on 2007-12-09 12:58:42 (Show Source): You can put this solution on YOUR website! Let's solve for y in the second equation Start with the given equation Subtract x from both sides Multiply both sides by -1 to isolate y. This will change the sign of all of the terms on the right Now since the slope of the first line is and the slope of the second line is also , these two lines are parallel. So they cannot be perpendicular.

Functions/115630: Please help. Given f(x)=4x+2 find f(a+2) I came up with the answer of 4a+10. Is this correct? Thanks JMS 1 solutions Answer 84143 by jim_thompson5910(28504)   on 2007-12-09 12:53:37 (Show Source): You can put this solution on YOUR website! You are correct. After substitution, you should get which then becomes

Linear-equations/115622: What is the slope and y intercept of the following y = -x 1 solutions Answer 84142 by jim_thompson5910(28504)   on 2007-12-09 12:41:37 (Show Source): You can put this solution on YOUR website! Let's use the general equation where m is the slope and b is the y-intercept From , we can see that and (Remember really looks like ) So the slope is and the y-intercept is

Linear-systems/115597: 2x/3 - 2< or equal to 8 - x 1 solutions Answer 84141 by jim_thompson5910(28504)   on 2007-12-09 12:18:24 (Show Source): You can put this solution on YOUR website! Start with the given inequality Multiply both sides by the LCM of 3. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver) Distribute and multiply the LCM to each side Add 6 to both sides Add 3x to both sides Combine like terms on the left side Combine like terms on the right side Divide both sides by 5 to isolate x Divide -------------------------------------------------------------- Answer: So our answer is

Equations/115590: 3/5x - (2-x) = -10 1 solutions Answer 84140 by jim_thompson5910(28504)   on 2007-12-09 12:16:44 (Show Source): You can put this solution on YOUR website! Start with the given equation Multiply both sides by the LCM of 5. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver) Distribute and multiply the LCM to each side Distribute Combine like terms on the left side Add 10 to both sides Combine like terms on the right side Divide both sides by 8 to isolate x Divide -------------------------------------------------------------- Answer: So our answer is

Inequalities/115595: 2 - 3x< or equal to 8 1 solutions Answer 84139 by jim_thompson5910(28504)   on 2007-12-09 12:14:22 (Show Source): You can put this solution on YOUR website! Start with the given inequality Subtract 2 from both sides Combine like terms on the right side Divide both sides by -3 to isolate x (note: Remember, dividing both sides by a negative number flips the inequality sign) Divide -------------------------------------------------------------- Answer: So our answer is

Polynomials-and-rational-expressions/115563: Factor using AC Method. 9x^2-15x-6 1 solutions Answer 84115 by jim_thompson5910(28504)   on 2007-12-08 23:57:03 (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 9 and -6 respectively. Now multiply the first coefficient 9 and the last coefficient -6 to get -54. Now what two numbers multiply to -54 and add to the middle coefficient -15? Let's list all of the factors of -54: Factors of -54: 1,2,3,6,9,18,27,54 -1,-2,-3,-6,-9,-18,-27,-54 ...List the negative factors as well. This will allow us to find all possible combinations These factors pair up and multiply to -54 (1)*(-54) (2)*(-27) (3)*(-18) (6)*(-9) (-1)*(54) (-2)*(27) (-3)*(18) (-6)*(9) 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 -54 1+(-54)=-53 2 -27 2+(-27)=-25 3 -18 3+(-18)=-15 6 -9 6+(-9)=-3 -1 54 -1+54=53 -2 27 -2+27=25 -3 18 -3+18=15 -6 9 -6+9=3 From this list we can see that 3 and -18 add up to -15 and multiply to -54 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

Miscellaneous_Word_Problems/115562: This question is from textbook Solve each of quadriatic equations. Round to two decimal places if possible. It is not clear how to do this step by step. could someone help please. x^2=25 1 solutions Answer 84113 by jim_thompson5910(28504)   on 2007-12-08 23:23:39 (Show Source): You can put this solution on YOUR website! Start with the given equation Move all of the terms to the left side Factor the left side (note: if you need help with factoring, check out this solver) Now set each factor equal to zero: or or Now solve for x in each case So our answer is or Notice if we graph we can see that the roots are and . So this visually verifies our answer.

Functions/115559: let f(x)=sqrt x+1 and g(x)=1/x+1 and evaluate (f*g) (x) 1 solutions Answer 84112 by jim_thompson5910(28504)   on 2007-12-08 23:18:58 (Show Source): You can put this solution on YOUR website! Do you want to do a function composition? If you do, then... Start with the given composition Plug in This means you replace each x of f(x) with

Miscellaneous_Word_Problems/115557: The area of a square is 625 mm^2. Find its side length? 1 solutions Answer 84111 by jim_thompson5910(28504)   on 2007-12-08 23:08:48 (Show Source): You can put this solution on YOUR website! Remember, the area of a square is where A is the area and s is the side length of the square. So in this case A=625 Plug in A=625 Take the square root of both sides Simplify So the length of the side is 25 mm Does this make sense?

Miscellaneous_Word_Problems/115556: The area of square is 625 mm^2. Find its side length? 1 solutions Answer 84110 by jim_thompson5910(28504)   on 2007-12-08 23:05:57 (Show Source): You can put this solution on YOUR website! Remember, the area of a square is where A is the area and s is the side length of the square. So in this case A=625 Plug in A=625 Take the square root of both sides Simplify So the length of the side is 25 mm

real-numbers/115555: I really need help with this problem. The problem says to find two consecutive intergers whose product is 90, it must be solved algebraically. Thank You. 1 solutions Answer 84109 by jim_thompson5910(28504)   on 2007-12-08 23:00:48 (Show Source): You can put this solution on YOUR website! Remember, consecutive integers follow the pattern , , etc. So if their product is 90, then Distribute Move all of the terms to the left side Factor the left side (note: if you need help with factoring, check out this solver) Now set each factor equal to zero: or or Now solve for x in each case So our answer is or So our two numbers are either 9,10 or -10,-9