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Polynomials-and-rational-expressions/197629: please simplify (2x^2+3x-6)-(6x-5) thank you 1 solutions Answer 148193 by jim_thompson5910(28598)   on 2009-05-25 13:49:27 (Show Source): You can put this solution on YOUR website! Start with the given expression. Distribute. Group like terms. Combine like terms. So

Equations/197586: Please graph the equation y=x+3 thank you 1 solutions Answer 148170 by jim_thompson5910(28598)   on 2009-05-25 01:22:12 (Show Source): You can put this solution on YOUR website! Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is Since this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis So we have one point Now since the slope is comprised of the "rise" over the "run" this means Also, because the slope is , this means: which shows us that the rise is 1 and the run is 1. This means that to go from point to point, we can go up 1 and over 1 So starting at , go up 1 unit and to the right 1 unit to get to the next point Now draw a line through these points to graph So this is the graph of through the points and

Equations/197584: State the slope of the line given by 2x-5y=20 1 solutions Answer 148168 by jim_thompson5910(28598)   on 2009-05-24 21:49:50 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Rearrange the terms. Divide both sides by to isolate y. Break up the fraction. Reduce. So the equation is now in slope intercept form where the slope is and the y-intercept is note: the y-intercept is the point

Equations/197582: What kind of line has no slope? 1 solutions Answer 148167 by jim_thompson5910(28598)   on 2009-05-24 21:49:18 (Show Source): You can put this solution on YOUR website! Any vertical line has no slope (since the slope is undefined).

Linear-systems/197571: This question is from textbook Algebra and Trigonometry Solve the system. 2x-3y=3 5x+2y=17 1 solutions Answer 148159 by jim_thompson5910(28598)   on 2009-05-24 20:28:29 (Show Source): You can put this solution on YOUR website! Start with the given system of equations: Multiply the both sides of the first equation by 2. Distribute and multiply. Multiply the both sides of the second equation by 3. Distribute and multiply. So we have the new system of equations: Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this: Group like terms. Combine like terms. Simplify. Divide both sides by to isolate . Reduce. ------------------------------------------------------------------ Now go back to the first equation. Plug in . Multiply. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. So the solutions are and . Which form the ordered pair . This means that the system is consistent and independent. Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer. Graph of (red) and (green)

Linear-equations/197575: State the slope of the line given by 2x-5y=20 thank you 1 solutions Answer 148158 by jim_thompson5910(28598)   on 2009-05-24 20:23:25 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Rearrange the terms. Divide both sides by to isolate y. Break up the fraction. Reduce. So the equation is now in slope intercept form where the slope is and the y-intercept is note: the y-intercept is the point

Equations/197569: Write the equation of the line that passes through (5,8) and (3,2) thank you 1 solutions Answer 148153 by jim_thompson5910(28598)   on 2009-05-24 19:18:29 (Show Source): You can put this solution on YOUR website! First let's find the slope of the line through the points and Note: is the first point and is the second point . Start with the slope formula. Plug in , , , and Subtract from to get Subtract from to get Reduce So the slope of the line that goes through the points and is Now let's use the point slope formula: Start with the point slope formula Plug in , , and Distribute Multiply Add 8 to both sides. Combine like terms. Simplify So the equation that goes through the points and is Notice how the graph of goes through the points and . So this visually verifies our answer. Graph of through the points and

Bodies-in-space/197566: Does the empty space inside of a cylinder have a name besides volume? Is there a technical term to describe it? 1 solutions Answer 148150 by jim_thompson5910(28598)   on 2009-05-24 19:04:15 (Show Source): You can put this solution on YOUR website! I don't know about the technical term, but are you looking for a word such as "capacity"?

Polynomials-and-rational-expressions/197565: Solve. 1-t/9-t = 8/t-9 1 solutions Answer 148146 by jim_thompson5910(28598)   on 2009-05-24 18:02:16 (Show Source): You can put this solution on YOUR website! Start with the given equation. Take note that since this causes a division by zero. Cross multiply FOIL Distribute Get everything to one side Combine like terms. Multiply EVERY term by -1 to make the leading coefficient positive. Factor Take the square root of both sides Add 9 to both sides. So the possible solution is . However, we said earlier that , so is NOT a solution (it's not in the domain). So there are no solutions.

Polynomials-and-rational-expressions/197555: Simplify by removing factors of 1 t*2-4/t*2-4t+4 1 solutions Answer 148143 by jim_thompson5910(28598)   on 2009-05-24 17:35:33 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor to get . Factor to get . Highlight the common terms. Cancel out the common terms. Simplify. So simplifies to . In other words, where

Polynomials-and-rational-expressions/197554: Simplify by removing factors of 1 8w-56/ 7-w 1 solutions Answer 148142 by jim_thompson5910(28598)   on 2009-05-24 17:32:54 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor the numerator Factor the denominator Reduce Highlight the common terms Cancel out the common terms Simplify So where

Polynomials-and-rational-expressions/197552: 8/11x*2-11x - 7/11x-11 This problem is eight over eleven x squared minus eleven x SUBTRACT seven over eleven x minus elevin 1 solutions Answer 148140 by jim_thompson5910(28598)   on 2009-05-24 17:24:29 (Show Source): You can put this solution on YOUR website! Start with the given expression. Multiply the second fraction by Distribute Now that the denominators are equal, we can subtract the fractions. So where or

sets-and-operations/197527: Given U = {All letters of the alphabet}, A = {c, d, e, f}, and B = {e, f, g, h, k}. List the elements of set (a) A U B (b) A ∩ B (c) A′ ∩ B′ (d) A′ U B′ (e) A U B′ (f) (A U B′) ∩ B (g) (A U B) ∩ (A U B′) 1 solutions Answer 148136 by jim_thompson5910(28598)   on 2009-05-24 17:13:59 (Show Source): You can put this solution on YOUR website! I'll do the first five to get you going in the right direction... Start with the given sets: Find their respective complement sets (eg, the complement of A is everything in U, but NOT in A): ------------------------------------------------------------------------- a) Simply combine the two sets A and B (remember to remove any duplicates) to find the union: ------------------------------------------------------------------------- b) Now form a new set of the common elements of sets A and B: Use the same logic to complete the rest (but this time we're using different sets in different combinations) c) ------------------------------------------------------------------ d) ------------------------------------------------------------------ e)

Linear-equations/197547: write an equation in slope intercept form of the line passing through each pair of points: (6,-2) and (3,-4) 1 solutions Answer 148133 by jim_thompson5910(28598)   on 2009-05-24 17:03:09 (Show Source): You can put this solution on YOUR website! First let's find the slope of the line through the points and Note: is the first point and is the second point . Start with the slope formula. Plug in , , , and Subtract from to get Subtract from to get Reduce So the slope of the line that goes through the points and is Now let's use the point slope formula: Start with the point slope formula Plug in , , and Rewrite as Distribute Multiply Subtract 2 from both sides. Combine like terms. So the equation that goes through the points and is Notice how the graph of goes through the points and . So this visually verifies our answer. Graph of through the points and

Graphs/197525: Which statement is true of the graph of the equation x=4? 1) It has a slope of 1. 2) It has a slope -4. 3) It is parallel to the x-axis. 4) It is parallel to the y-axis. 1 solutions Answer 148129 by jim_thompson5910(28598)   on 2009-05-24 16:55:09 (Show Source): You can put this solution on YOUR website! The graph of is a vertical line. So what does that tell you about the slope? Remember, ALL vertical lines have undefined slopes. So we can easily rule out choices 1) and 2). So we're only left with choices 3) and 4). Since is a vertical line, and all vertical lines are parallel to the y-axis, this tells us that is parallel to the y-axis.

Linear-equations/197548: write an equation in slope intercept form of the line passing through each pair of points: (-8,2) and (0,6) 1 solutions Answer 148128 by jim_thompson5910(28598)   on 2009-05-24 16:50:36 (Show Source): You can put this solution on YOUR website! First let's find the slope of the line through the points and Note: is the first point and is the second point . Start with the slope formula. Plug in , , , and Subtract from to get Subtract from to get Reduce So the slope of the line that goes through the points and is Now let's use the point slope formula: Start with the point slope formula Plug in , , and Rewrite as Distribute Multiply Add 2 to both sides. Combine like terms. Simplify So the equation that goes through the points and is Notice how the graph of goes through the points and . So this visually verifies our answer. Graph of through the points and

Distributive-associative-commutative-properties/197529: What would be an illustration of the distributive property of multiplication over addition? 1 solutions Answer 148125 by jim_thompson5910(28598)   on 2009-05-24 16:41:33 (Show Source): You can put this solution on YOUR website! Here's an example: Take note that and which shows us that is true.

Miscellaneous_Word_Problems/197530: Write the following in roster form: Set N is the set of natural numbers between two and nine. 1 solutions Answer 148124 by jim_thompson5910(28598)   on 2009-05-24 16:38:04 (Show Source): You can put this solution on YOUR website! Simply write EVERY natural (counting) number from 2 to 9 like this:

absolute-value/197537: Find the absolute value of -5 minus -3. 1 solutions Answer 148121 by jim_thompson5910(28598)   on 2009-05-24 16:36:13 (Show Source): You can put this solution on YOUR website!

Exponents/197538: Find the product of -3x² and 11x to the 4th power. 1 solutions Answer 148120 by jim_thompson5910(28598)   on 2009-05-24 16:34:49 (Show Source): You can put this solution on YOUR website! Start with the given expression. Rearrange the terms Multiply -3 and 11 to get -33 Add the exponents. Add So

Polynomials-and-rational-expressions/197542: ok I am a bit stuck on what to do here I tried the solvers but it keeps telling me an error of some sort. The only direction I have for this problem is to multiply can some one please help me. Thanks – 4x5(– 3x5 + 2x2 – 4) 1 solutions Answer 148119 by jim_thompson5910(28598)   on 2009-05-24 16:33:00 (Show Source): You can put this solution on YOUR website! Start with the given expression. Distribute Multiply. Note: when you multiply common variables, you add the exponents. So

Equations/197448: Find the slope of the line that passes through (-3,7) and (5,-5) thank you 1 solutions Answer 148060 by jim_thompson5910(28598)   on 2009-05-23 18:35:01 (Show Source): You can put this solution on YOUR website! First let's find the slope of the line through the points and Note: is the first point and is the second point . Start with the slope formula. Plug in , , , and Subtract from to get Subtract from to get Reduce So the slope of the line that goes through the points and is Now let's use the point slope formula: Start with the point slope formula Plug in , , and Rewrite as Distribute Multiply Add 7 to both sides. Combine like terms. So the equation that goes through the points and is

Equations/197447: Find the x-intercept of 3x-4y=24 thank you 1 solutions Answer 148059 by jim_thompson5910(28598)   on 2009-05-23 18:25:59 (Show Source): You can put this solution on YOUR website! x-intercept To find the x-intercept, plug in and solve for x Start with the given equation. Plug in . Multiply and 0 to get 0. Simplify. Divide both sides by to isolate . Reduce. So the x-intercept is .

Quadratic_Equations/197444: Hi! Can you help me with changing an equation 52=4x-4y into ax+by=c? I am very confused! Thanks in advance! Lynne 1 solutions Answer 148058 by jim_thompson5910(28598)   on 2009-05-23 18:25:16 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract 52 from both sides. Subtract 4x from both sides. Add 4y to both sides. Multiply EVERY term by -1 to make the x coefficient positive Now the equation is in the form where , and Note: you could have simply flipped the equation to get

Graphs/197445: Please show me step by step to graph 3x+2y=6 thank you 1 solutions Answer 148057 by jim_thompson5910(28598)   on 2009-05-23 18:18:03 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Rearrange the terms. Divide both sides by to isolate y. Break up the fraction. Reduce. Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is Since this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis So we have one point Now since the slope is comprised of the "rise" over the "run" this means Also, because the slope is , this means: which shows us that the rise is -3 and the run is 2. This means that to go from point to point, we can go down 3 and over 2 So starting at , go down 3 units and to the right 2 units to get to the next point Now draw a line through these points to graph So this is the graph of through the points and

Polynomials-and-rational-expressions/197405: Multiply. 1 solutions Answer 148051 by jim_thompson5910(28598)   on 2009-05-23 16:58:35 (Show Source): You can put this solution on YOUR website! Start with the given expression. Expand. Distribute. Multiply. Now combine like terms. So expands to . In other words, .

Graphs/197441: Please show mw step by step how to graph this. Such as what point to start on...start 3 and go up 3 over 2..something like that the equation is y= 2 over 5x +1 thank you 1 solutions Answer 148050 by jim_thompson5910(28598)   on 2009-05-23 16:57:07 (Show Source): You can put this solution on YOUR website! Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is Since this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis So we have one point Now since the slope is comprised of the "rise" over the "run" this means Also, because the slope is , this means: which shows us that the rise is 2 and the run is 5. This means that to go from point to point, we can go up 2 and over 5 So starting at , go up 2 units and to the right 5 units to get to the next point Now draw a line through these points to graph So this is the graph of through the points and

Linear-systems/197443: Hi! I am having trouble putting the following equation into proper form. My assignment was to create two equations that would fit the intergers 4,9. I chose for my first equation: 2x+3y=35. The other equation and the one I am having trouble with is 52=4x-4y. I thought when I put the second equation into the form ax+by=c my answer would be 4x+4y=52. I am wrong. Can you please help me? Thank you in advance. Lynne 1 solutions Answer 148049 by jim_thompson5910(28598)   on 2009-05-23 16:56:01 (Show Source): You can put this solution on YOUR website! If you are looking for a system of equations that has the solution (4,9), then the system has the solution (4,9). So you are correct. Note: this is NOT the only system that has this solution. Another system would be

Polynomials-and-rational-expressions/197440: using FOIL method How would I solve the following equation (2x + 1) (x + 4) 1 solutions Answer 148046 by jim_thompson5910(28598)   on 2009-05-23 16:35:14 (Show Source): You can put this solution on YOUR website! Start with the given expression. 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:. --------------------------------------------------- So we have the terms: , , , Now add every term listed above to make a single expression. Now combine like terms. So FOILs to . In other words, .

Radicals/197400: Simplify by factoring. Assume that all expressions under radicals represent nonnegative numbers. 1 solutions Answer 148030 by jim_thompson5910(28598)   on 2009-05-22 23:42:26 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor into Break up the square root using the identity . Take the square root of to get . Take the square root of to get . Rearrange and multiply. ================================================== Answer: So simplifies to In other words, where every variable is non-negative.

Polynomials-and-rational-expressions/197366: Perform the indicated operations and simplify. I got as an answer but do not think this is correct. 1 solutions Answer 147991 by jim_thompson5910(28598)   on 2009-05-22 16:06:36 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor the last denominator. Take note that the LCD is . In order to add/subtract these fractions, we need to get EVERY denominator equal to the LCD. Multiply the first fraction by FOIL Multiply the second fraction by FOIL Now that every denominator is equal, we can add/subtract the fractions. Combine the fractions. Distribute Combine like terms. Factor Highlight the common terms. Cancel out the common terms. Simplify. So simplifies to In other words,