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jim_thompson5910 answered: 28465 problems
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Polynomials-and-rational-expressions/145203: Simplify the expression: ( 4 x + 1 ) 2 + (2 x - 4 ) 2 Choose the correct answer from the following: 20x 2 - 8x + 17 12x 2 - 8x + 15 4x 2 + 8x - 15 1 solutions Answer 105875 by jim_thompson5910(28476)   on 2008-06-13 13:46:21 (Show Source): You can put this solution on YOUR website! First FOIL Start with the given expression Expand. Remember something like Now let's FOIL the 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 So foils and simplifies to In other words, Now let's FOIL Expand. Remember something like Now let's FOIL the 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 So foils and simplifies to In other words, So now becomes Start with the given expression Combine like terms So

Polynomials-and-rational-expressions/145202: Choose the polynominal that represents the area of the rectangle with sides (x + 6) and (x - 2): x 2 - 4x - 12 x 2 + 8x - 12 x 2 + 8x + 12 x 2 - 8x - 12 x 2 - 8x + 12 x 2 - 4x + 12 x 2 + 4x + 12 x 2 + 4x - 12 1 solutions Answer 105872 by jim_thompson5910(28476)   on 2008-06-13 13:40:08 (Show Source): You can put this solution on YOUR website! To find the area, simply multiply the given sides and Now let's FOIL the 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, So the area is

Systems-of-equations/145185: This question is from textbook Beginning Algebra I need help and lots of it LOL :)Thanks... Page 490 Number 14 5x-3y=14 2x-y=6 1 solutions Answer 105867 by jim_thompson5910(28476)   on 2008-06-13 13:01:27 (Show Source): You can put this solution on YOUR website! Do you want to use elimination/addition to solve this system? Start with the given system of equations: Now in order to solve this system by using elimination/addition, we need to solve (or isolate) one variable. I'm going to solve for y. In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for , we would have to eliminate (or vice versa). So lets eliminate . In order to do that, we need to have both coefficients that are equal in magnitude but have opposite signs (for instance 2 and -2 are equal in magnitude but have opposite signs). This way they will add to zero. By adding to zero, they can be eliminated. So to make the coefficients equal in magnitude but opposite in sign, we need to multiply both coefficients by some number to get them to an common number. So if we wanted to get and to some equal number, we could try to get them to the LCM. Since the LCM of and is , we need to multiply both sides of the top equation by and multiply both sides of the bottom equation by like this: Multiply the top equation (both sides) by Multiply the bottom equation (both sides) by Distribute and multiply Now add the equations together. In order to add 2 equations, group like terms and combine them Combine like terms and simplify Notice how the x terms cancel out Simplify Divide both sides by to isolate y Reduce Now plug this answer into the top equation to solve for x Start with the first equation Plug in Multiply Add 6 to both sides Combine like terms on the right side Divide both sides by 5 to isolate x Divide So our answer is and which also looks like Now let's graph the two equations (if you need help with graphing, check out this solver) From the graph, we can see that the two equations intersect at . This visually verifies our answer. graph of (red) and (green) and the intersection of the lines (blue circle).

Matrices-and-determiminant/145192: Could someone help me with a few system of equations problems please? These ones are to be solved by the graphing method,and I have to show how I got them when I take the test in the future,So if you could show me step by step that would be great. 1) -x + y = -1 x + y = 3 2) 3x + y = -6 x + y = -4 1 solutions Answer 105866 by jim_thompson5910(28476)   on 2008-06-13 12:57:48 (Show Source): You can put this solution on YOUR website! I'll do the first one to get you started Start with the given system of equations: In order to graph these equations, we need to solve for y for each equation. So let's solve for y on the first equation Start with the given equation Add to both sides Rearrange the equation Now lets graph (note: if you need help with graphing, check out this solver) Graph of So let's solve for y on the second equation Start with the given equation Subtract from both sides Rearrange the equation Now lets add the graph of to our first plot to get: Graph of (red) and (green) From the graph, we can see that the two lines intersect at the point (2,1)

Age_Word_Problems/145106: if 7 is subtracted from twice a number, the result is 5. find the number. 1 solutions Answer 105799 by jim_thompson5910(28476)   on 2008-06-12 13:58:57 (Show Source): You can put this solution on YOUR website! "7 is subtracted from twice a number, the result is 5" translates to Start with the given equation Add 7 to both sides Combine like terms on the right side Divide both sides by 2 to isolate x Divide -------------------------------------------------------------- Answer: So our answer is

Graphs/145104: How many positive real soulutions are there in x^4-4x^3+6x^2-4x+1 1 solutions Answer 105796 by jim_thompson5910(28476)   on 2008-06-12 13:34:05 (Show Source): You can put this solution on YOUR website! Let's count the sign changes of From to , there is a sign change from positive to negative From to , there is a sign change from negative to positive From to , there is a sign change from positive to negative From to , there is a sign change from negative to positive So there are 4 sign changes for the expression . So there are 4, 2, or 0 positive zeros (remember to count down by 2's)

Exponents-negative-and-fractional/145102: -x Squared + 2x = 8 1 solutions Answer 105795 by jim_thompson5910(28476)   on 2008-06-12 13:10:46 (Show Source): You can put this solution on YOUR website! Start with the given equation. Get all terms to the left side. Notice we have a quadratic equation in the form of where , , and 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 . Simplify the square root (note: If you need help with simplifying square roots, check out this solver) Break up the fraction. Reduce. or Break up the expression. So our answers are or which approximate to or

Equations/145054: Can you explain how to figure this problem (6±√8)/2 and provide answer ? Thank You. 1 solutions Answer 105745 by jim_thompson5910(28476)   on 2008-06-11 20:45:11 (Show Source): You can put this solution on YOUR website! Start with the given expression Simplify to get or Break up the expression or Break up the fraction for each case or Reduce

logarithm/145032: Express both in terms of x 1. ln(x) = 2 what I thought was x = e^2 but that seemed too simple 2. tan^-1 x = 1 1 solutions Answer 105734 by jim_thompson5910(28476)   on 2008-06-11 18:53:18 (Show Source): You can put this solution on YOUR website! 1. You are correct, the answer is 2. Start with the given equation Take the tangent of both sides to eliminate the inverse tangent Simplify

Polynomials-and-rational-expressions/145030: What is the value of the discriminant of the polynomial below? 4x^2 + 7x + 4 1 solutions Answer 105732 by jim_thompson5910(28476)   on 2008-06-11 17:15:34 (Show Source): You can put this solution on YOUR website! From we can see that , , and Start with the discriminant formula Plug in , , and Square to get Multiply to get Subtract from to get So the discriminant is

Equations/145021: I need help with 2 homework problems. I can use any method (elimination, subtitution or graphical methods) the problems are 5x + 6y = 14 -3y + x = 7 I got (35/12, -7/12) next problem 2x/3 + 3y/4 = 11/12 x/3 + 7y/18 = 1/2 (I got (8/5, -3/35) 1 solutions Answer 105727 by jim_thompson5910(28476)   on 2008-06-11 15:54:35 (Show Source): You can put this solution on YOUR website! # 1 Start with the given system of equations: Multiply the top equation (both sides) by Multiply the bottom equation (both sides) by Distribute and multiply Now add the equations together. In order to add 2 equations, group like terms and combine them Combine like terms and simplify Notice how the x terms cancel out Simplify Divide both sides by to isolate y Reduce Now plug this answer into the top equation to solve for x Start with the first equation Plug in Multiply Add 6 to both sides Combine like terms on the right side Divide both sides by 5 to isolate x Divide So our answer is and which also looks like Now let's graph the two equations (if you need help with graphing, check out this solver) From the graph, we can see that the two equations intersect at . This visually verifies our answer. graph of (red) and (green) and the intersection of the lines (blue circle). # 2 Let's look at the first equation Multiply both sides of the first equation by the LCD 12 Distribute --------- Let's look at the second equation Multiply both sides of the second equation by the LCD 18 Distribute --------- So our new system of equations is: Multiply the top equation (both sides) by Multiply the bottom equation (both sides) by Distribute and multiply Now add the equations together. In order to add 2 equations, group like terms and combine them Combine like terms and simplify Notice how the x terms cancel out Simplify Divide both sides by to isolate y Reduce Now plug this answer into the top equation to solve for x Start with the first equation Plug in Multiply Subtract 27 from both sides Combine like terms on the right side Divide both sides by 8 to isolate x Divide So our answer is and which also looks like

Equations/145018: express each equation in slope-intercept form. then determin, without silving the system, whether the system of equations has exactly one solution, none, or an infinite number 4x+6y=26 -6x-9y=-39 1 solutions Answer 105724 by jim_thompson5910(28476)   on 2008-06-11 15:37:25 (Show Source): You can put this solution on YOUR website! Start with the first equation Subtract from both sides Rearrange the equation Divide both sides by Break up the fraction Reduce So the equation is now in slope-intercept form () where the slope is and the y-intercept is ---------------------------------------------- Move onto the second equation Add to both sides Rearrange the equation Divide both sides by Break up the fraction Reduce So the equation is now in slope-intercept form () where the slope is and the y-intercept is ------------------------------ Since the slope and y-intercept for both equations are the same, this means that there are an infinite number of solutions (since one equation lies on top of the other)

real-numbers/145005: How many real solutions are there to the equation shown below? x^2 + 3x + 10 = 0 1 solutions Answer 105703 by jim_thompson5910(28476)   on 2008-06-11 14:34:56 (Show Source): You can put this solution on YOUR website! From we can see that , , and Start with the discriminant formula Plug in , , and Square to get Multiply to get Subtract from to get Since the discriminant is less than zero, this means that there are two complex solutions. In other words, there are no real solutions.

Polynomials-and-rational-expressions/145003: What is the value of the discriminant of the polynomial below? 4x^2 + 7x + 4 1 solutions Answer 105702 by jim_thompson5910(28476)   on 2008-06-11 14:33:57 (Show Source): You can put this solution on YOUR website! From we can see that , , and Start with the discriminant formula Plug in , , and Square to get Multiply to get Subtract from to get So the discriminant is

Quadratic_Equations/145001: Use the quadratic formula to find the solutions to the quadratic equation below. Check all that apply. 3x^2 - x - 2 = 0 A. - 2/3 (both are negative) B. -1 C. 3/2 D. -4/5 (only 4 is negative) E. 1 F. 5/4 1 solutions Answer 105695 by jim_thompson5910(28476)   on 2008-06-11 14:17:48 (Show Source): You can put this solution on YOUR website! Let's use the quadratic formula to solve for x Start with the quadratic formula Plug in , , and Negate to get . Square to get . Multiply to get Rewrite as Add to 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-relations-and-conic-sections/144994: The vertex of the parabola below is at the point (1, 3) and the point (2, 6) is on the parabola. What is the equation of the parabola? i had gotten y = 6(x - 1)^2 + 3 but it came out wrong. these are the other options A. y = 3(x + 1)^2 - 3 C. y = 3(x - 1)^2 + 3 D. x = 2(y - 3)^2 + 1 1 solutions Answer 105679 by jim_thompson5910(28476)   on 2008-06-11 13:35:12 (Show Source): You can put this solution on YOUR website! Since the vertex is (1,3) this means Now plug in and Subtract Square 1 to get 1 Multiply Subtract 3 from both sides So the equation is which means that the answer is choice C)

Quadratic-relations-and-conic-sections/144993: What is the x-coordinate of the center of the ellipse with the following equation? (y+6)^2/18+(x-5)^2/4=5 1 solutions Answer 105674 by jim_thompson5910(28476)   on 2008-06-11 13:20:57 (Show Source): You can put this solution on YOUR website! Start with the given equation Rearrange the terms Divide both sides by 5 So the equation is in the form where , , , and Since the x-coordinate of the center is this means that the x-coordinate of the center is

Polynomials-and-rational-expressions/144991: The polynomial (x - 2) is a factor of the polynomial F(x) = 3x^2 - 8x + 2. True or false 1 solutions Answer 105671 by jim_thompson5910(28476)   on 2008-06-11 13:14:10 (Show Source): You can put this solution on YOUR website! First let's factor Looking at we can see that the first term is and the last term is where the coefficients are 3 and 2 respectively. Now multiply the first coefficient 3 and the last coefficient 2 to get 6. Now what two numbers multiply to 6 and add to the middle coefficient -8? 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 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 6 1+6=7 2 3 2+3=5 -1 -6 -1+(-6)=-7 -2 -3 -2+(-3)=-5 None of these pairs of factors add to -8. So the expression cannot be factored So (x - 2) is NOT a factor of So the statement is false

Functions/144988: Which of these equations represent functions? Check all that apply. A. y = (x - 2)^2 + 5 B. x^2 - 4y^2 = 1 C. y = 3x - 3 D. y = 4x^5 1 solutions Answer 105670 by jim_thompson5910(28476)   on 2008-06-11 13:12:12 (Show Source): You can put this solution on YOUR website! Choices A,C, and D are all functions. If you graph each one, you'll notice that they all pass the vertical line test

Distributive-associative-commutative-properties/144984: Not sure how to solve: 3x^2-x=0 1 solutions Answer 105665 by jim_thompson5910(28476)   on 2008-06-11 12:59:28 (Show Source): You can put this solution on YOUR website! Start with the given equation Factor the left side Now set each factor equal to zero: or or Now solve for x in each case So our answers are or Notice if we graph we can see that the roots are and . So this visually verifies our answer.

Quadratic_Equations/144981: The sum of two numbers is 8. The sum of the squares of the two numbers is 34. Find the numbers. I know they are 3 and 5, but how do I show I arrived at that answer 1 solutions Answer 105655 by jim_thompson5910(28476)   on 2008-06-11 12:26:08 (Show Source): You can put this solution on YOUR website! "The sum of two numbers is 8" translates to "The sum of the squares of the two numbers is 34" translates to Start with the first equation Subtract x from both sides to isolate y Move onto the second equation Plug in Foil Get all terms to the left side. Combine like terms. Notice we have a quadratic equation in the form of where , , and Let's use the quadratic formula to solve for x Start with the quadratic formula Plug in , , and Negate to get . 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

Polynomials-and-rational-expressions/144979: Which term prevents the following expression from being considered polynomial? F(x)= 1/√2 x^4-1/√5 x^3-7x^-2+1.4x+21 A. -7x-2 B. 1/√2 x^4 C. -1/√5 x^3 D. 1.4x E. 21 1 solutions Answer 105654 by jim_thompson5910(28476)   on 2008-06-11 12:11:40 (Show Source): You can put this solution on YOUR website! Notice how . Since there is a division by a variable, this means that the expression is not a polynomial. So the answer is A)

Distributive-associative-commutative-properties/144978: This question is from textbook Elementary and Intermediate Algebra for College Students how do you solve? 4x^2-16=0 1 solutions Answer 105653 by jim_thompson5910(28476)   on 2008-06-11 12:10:20 (Show Source): You can put this solution on YOUR website! Start with the given equation Factor out the GCF 4 Factor the left side using the difference of squares formula Now set each factor equal to zero: or or Now solve for x in each case So our answers are or Notice if we graph we can see that the roots are and . So this visually verifies our answer.

Distributive-associative-commutative-properties/144977: This question is from textbook Elementary and Intermediate Algebra for College Students how do you solve? 4x^2-16=0 1 solutions Answer 105652 by jim_thompson5910(28476)   on 2008-06-11 12:09:19 (Show Source): You can put this solution on YOUR website! Start with the given equation Factor out the GCF 4 Factor the left side using the difference of squares formula Now set each factor equal to zero: or or Now solve for x in each case So our answers are or Notice if we graph we can see that the roots are and . So this visually verifies our answer.

Distributive-associative-commutative-properties/144974: This question is from textbook Elementary and Intermediate Algebra for college students How do i solve this: Factor: a^2+a+3a+3 1 solutions Answer 105651 by jim_thompson5910(28476)   on 2008-06-11 11:49:41 (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

Polynomials-and-rational-expressions/144973: For the polynomial below, find F(4). F(x) = 2x^3 - x^2 - 4x + 9 1 solutions Answer 105650 by jim_thompson5910(28476)   on 2008-06-11 11:48:12 (Show Source): You can put this solution on YOUR website! Start with the given function Plug in Raise 4 to the 3rd power to get 64 Multiply 2 and 64 to get 128 Raise 4 to the 2nd power to get 16 Subtract 16 from 128 to get 112 Multiply 4 and 4 to get 16 Subtract 16 from 112 to get 96 Add 96 and 9 to get 105

Systems-of-equations/144943: Hi I am having a problem solving this any help would be appreciated thank you in advance. I have to find the solution to the system of equations by the substitution method. this is my problem: #2 x=4- 4y -x +2y = 2 1 solutions Answer 105647 by jim_thompson5910(28476)   on 2008-06-11 11:27:36 (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 Add 4 to both sides Combine like terms on the right side Divide both sides by 6 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)

Systems-of-equations/144944: This question is from textbook Toby Slater beginning Algebra Hi I am having a problem solving this any help would be appreciated thank you in advance. I have to find the solution to the system of equations by the substitution method. this is my problem: #2 x=4- 4y -x +2y = 2 1 solutions Answer 105646 by jim_thompson5910(28476)   on 2008-06-11 11:26:07 (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 Add 4 to both sides Combine like terms on the right side Divide both sides by 6 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)

Sequences-and-series/144841: The sum of the first 6 multiples of 8 , starting with 8 ,is 1 solutions Answer 105537 by jim_thompson5910(28476)   on 2008-06-10 14:03:47 (Show Source): You can put this solution on YOUR website! 8+16+24+32+40+48=168

Equations/144834: Simplify the expression.Write the answer in scientific notation. (1.9 x 10^5)^3 1 solutions Answer 105534 by jim_thompson5910(28476)   on 2008-06-10 14:00:53 (Show Source): You can put this solution on YOUR website!

Linear_Algebra/144840: Hello name is susan, will you help me understand this problem solve for k, t=3k +3u 1 solutions Answer 105532 by jim_thompson5910(28476)   on 2008-06-10 13:58:15 (Show Source): You can put this solution on YOUR website! Start with the given equation Subtract t from both sides Subtract 3k from both sides Divide both sides by -3 to isolate k Simplify -------------------------------------------------------------- Answer: So our answer is