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jim_thompson5910 answered: 28586 problems
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Graphs/135510: Solve 1 solutions Answer 99291 by jim_thompson5910(28598)   on 2008-04-06 17:12:25 (Show Source): You can put this solution on YOUR website! Start with the given equation Add to both sides Add to both sides Square both sides Foil the right side Combine like terms Subtract 2x from both sides. Subtract 2 from both sides. Combine like terms Square both sides Foil the left side Distribute Subtract 8x from both sides. Subtract 4 from both sides. Combine like terms 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

Graphs/135472: Solve 1 solutions Answer 99273 by jim_thompson5910(28598)   on 2008-04-06 14:43:55 (Show Source): You can put this solution on YOUR website! Start with the given equation Cube both sides Expand the left side Subtract 12x from both sides. Subtract 2 from both sides. Combine like terms So from a graphing calculator, we find that the solution to is

Graphs/135458: Solve 1 solutions Answer 99260 by jim_thompson5910(28598)   on 2008-04-06 14:17:44 (Show Source): You can put this solution on YOUR website! Let's graph So we can see that everything to the right of is in the solution set. So part of our solution is Start with the given inequality Set the numerator equal to zero 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 the critical values are or Now plot the critical values on a number line So let's evaluate a point that is to the left of (which is the left most endpoint). Let's evaluate the value Start with the given inequality Plug in Evaluate and simplify Since is true, this means that one part of the solution in interval notation is ----------------------------------------------- Now let's test a point that is in between the critical values and Start with the given inequality Plug in Evaluate and simplify Since is false, this means that the interval does not work. So that means that this interval is not in the solution set and can be ignored. ----------------------------------------------- So let's evaluate a point that is to the right of (which is the right most endpoint). Let's evaluate the value Start with the given inequality Plug in Evaluate and simplify Since is true, this means that one part of the solution in interval notation is ----------------------------------------------- So the answer in interval notation is

Graphs/135456: Solve 1 solutions Answer 99258 by jim_thompson5910(28598)   on 2008-04-06 14:09:17 (Show Source): You can put this solution on YOUR website! Start with the given inequality Factor the left side Set the left side equal to zero Solve for x in each case So this means that the critical values are Now plot the critical values on a number line So let's evaluate a point that is to the left of (which is the left most endpoint). Let's evaluate the value Start with the given inequality Plug in Evaluate and simplify Since is false, this means that the interval does not work. So that means that this interval is not in the solution set and can be ignored. ----------------------------------------------- Now let's test a point that is in between the critical values and Start with the given inequality Plug in Evaluate and simplify Since is true, this means that one part of the solution in interval notation is ----------------------------------------------- So let's evaluate a point that is to the right of (which is the right most endpoint). Let's evaluate the value Start with the given inequality Plug in Evaluate and simplify Since is false, this means that the interval does not work. So that means that this interval is not in the solution set and can be ignored. ----------------------------------------------- So the answer in interval notation is

Graphs/135454: Solve 1 solutions Answer 99257 by jim_thompson5910(28598)   on 2008-04-06 14:02:59 (Show Source): You can put this solution on YOUR website! Start with the given inequality Factor the left side Set the left side equal to zero Solve for x in each case So this means that the critical values are Now plot the critical values on a number line So let's evaluate a point that is to the left of (which is the left most endpoint). Let's evaluate the value Start with the given inequality Plug in Evaluate and simplify Since is true, this means that one part of the solution in interval notation is (] ----------------------------------------------- Now let's test a point that is in between the critical values and Start with the given inequality Plug in Evaluate and simplify Since is false, this means that the interval does not work. So that means that this interval is not in the solution set and can be ignored. ----------------------------------------------- So let's evaluate a point that is to the right of (which is the right most endpoint). Let's evaluate the value Start with the given inequality Plug in Evaluate and simplify Since is true, this means that one part of the solution in interval notation is [) ----------------------------------------------- Answer: So the answer in interval notation is (] [)

Graphs/135451: Solve 1 solutions Answer 99254 by jim_thompson5910(28598)   on 2008-04-06 13:57:19 (Show Source): You can put this solution on YOUR website! First, let's find the vertical asymptotes Stet the denominator equal to zero 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 the vertical asymptotes are or This means that the critical values are and So let's test a value that is to the left of Start with the given inequality Plug in Simplify Since is false, this means that the interval does not work ------------------------------------ So let's test a value that is in between and Start with the given inequality Plug in Simplify Since is true, this means that the part of the solution set is [] ------------------------------- Finally, let's test a point that is to the right of Start with the given inequality Plug in Simplify Since is false, this means that the interval does not work ---------------------------------------- Answer: So the solution in interval notation is []

Graphs/135447: Solve by graphing 1 solutions Answer 99250 by jim_thompson5910(28598)   on 2008-04-06 13:33:05 (Show Source): You can put this solution on YOUR website! Here's the graph for Here's the graph for And here's the graph of the two equations together From the graph, we can see that the intersections are (0,2) and (5,7)

Graphs/135446: Solve by substitution 1 solutions Answer 99249 by jim_thompson5910(28598)   on 2008-04-06 13:28:03 (Show Source): You can put this solution on YOUR website! Start with the given system Isolate for the second equation Plug in into the first equation Subtract 16 from both sides Combine like terms 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 y in each case So our y values are or Start with the given equation Plug in Simplify Take the square root of both sides So our first ordered pair is (0,-4) --------------------------- Start with the given equation Plug in Simplify Take the square root of both sides or So our next ordered pairs are (,2) or (,2) -------------------------- Answer: So the solutions are (0,-4), (,2), or (,2)

Graphs/135444: Graph the system and find the intersection(s) 1 solutions Answer 99247 by jim_thompson5910(28598)   on 2008-04-06 13:17:38 (Show Source): You can put this solution on YOUR website! Here is the graph of Here is the graph of Graphed together they look like And we can see that they intersect at the points (-4,-2) and (2,4)

Graphs/135442: Solve the system 1 solutions Answer 99246 by jim_thompson5910(28598)   on 2008-04-06 13:14:26 (Show Source): You can put this solution on YOUR website! Start with the given system Set the two equations equal to one another Subtract 12x from both sides. Add 19 to both sides. Combine like terms 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 x values are or Start with the first equation Plug in Simplify So the first ordered pair is (4,29) ------------- Start with the first equation Plug in Simplify So the second ordered pair is (3,17) ------------ Answer: So the solutions are (4,29) or (3,17)

Graphs/135440: Solve and give answer in interval notation 1 solutions Answer 99245 by jim_thompson5910(28598)   on 2008-04-06 13:09:15 (Show Source): You can put this solution on YOUR website! First, let's find the vertical asymptote Set the denominator equal to 0 Solve for x So the vertical asymptote is . If we graph, we can see that the vertical asymptote is a critical value. So from the graph, we can see that anything to the left of is not in the interval. So this means that one part of the solution is Start with the given inequality Multiply both sides by Distribute Subtract 3x from both sides Add 5 to both sides So another part of the solution is Answer: So the answer in interval notation is

Graphs/135439: Solve and give answer in interval notation 1 solutions Answer 99243 by jim_thompson5910(28598)   on 2008-04-06 13:01:11 (Show Source): You can put this solution on YOUR website! Start with the given inequality Move all terms to the left side Factor the left side Set the left side equal to zero Solve for x in each case So this means that the critical values are Now plot the critical values on a number line So let's evaluate a point that is to the left of (which is the left most endpoint). Let's evaluate the value Start with the given inequality Plug in Evaluate and simplify Since is true, this means that one part of the solution in interval notation is (] ----------------------------------------------- Now let's test a point that is in between the critical values and Start with the given inequality Plug in Evaluate and simplify Since is false, this means that the interval does not work. So that means that this interval is not in the solution set and can be ignored. ----------------------------------------------- So let's evaluate a point that is to the right of (which is the right most endpoint). Let's evaluate the value Start with the given inequality Plug in Evaluate and simplify Since is true, this means that one part of the solution in interval notation is [) ----------------------------------------------- Answer: So the answer in interval notation is (][)

Graphs/135438: Solve and give answer in interval notation 1 solutions Answer 99242 by jim_thompson5910(28598)   on 2008-04-06 12:53:58 (Show Source): You can put this solution on YOUR website! Start with the given inequality Factor the left side Set the left side equal to zero Solve for x in each case So this means that the critical values are Now plot the critical values on a number line So let's evaluate a point that is to the left of (which is the left most endpoint). Let's evaluate the value Start with the given inequality Plug in Evaluate and simplify Since is false, this means that the interval does not work. So that means that this interval is not in the solution set and can be ignored. ----------------------------------------------- Now let's test a point that is in between the critical values and Start with the given inequality Plug in Evaluate and simplify So the graph now looks like Since is true, this means that one part of the solution in interval notation is [] ----------------------------------------------- So let's evaluate a point that is to the right of (which is the right most endpoint). Let's evaluate the value Start with the given inequality Plug in Evaluate and simplify Since is false, this means that the interval does not work. So that means that this interval is not in the solution set and can be ignored. ----------------------------------------------- Answer: So the solution in interval notation is []

Graphs/135437: Solve and give answer in interval notation 1 solutions Answer 99241 by jim_thompson5910(28598)   on 2008-04-06 12:52:01 (Show Source): You can put this solution on YOUR website! Start with the given inequality Factor the left side Set the left side equal to zero Solve for x in each case So this means that the critical values are Now plot the critical values on a number line So let's evaluate a point that is to the left of (which is the left most endpoint). Let's evaluate the value Start with the given inequality Plug in Evaluate and simplify Since is false, this means that the interval does not work. So that means that this interval is not in the solution set and can be ignored. ----------------------------------------------- Now let's test a point that is in between the critical values and Start with the given inequality Plug in Evaluate and simplify So the graph now looks like Since is true, this means that one part of the solution in interval notation is [] ----------------------------------------------- So let's evaluate a point that is to the right of (which is the right most endpoint). Let's evaluate the value Start with the given inequality Plug in Evaluate and simplify Since is false, this means that the interval does not work. So that means that this interval is not in the solution set and can be ignored. ----------------------------------------------- Answer: So the solution in interval notation is []

Graphs/135369: Solve and give answer in interval notation 1 solutions Answer 99175 by jim_thompson5910(28598)   on 2008-04-05 17:57:18 (Show Source): You can put this solution on YOUR website! Start with the given inequality Set the left side equal to zero Solve for x in each case So this means that the critical values are Now plot the critical values on a number line So let's evaluate a point that is to the left of (which is the left most endpoint). Let's evaluate the value Start with the given inequality Plug in Evaluate and simplify Since is true, this means that everything to the left of is in the solution set. So the graph looks like this So one part of the solution in interval notation is ----------------------------------------------- Now let's test a point that is in between the critical values and Start with the given inequality Plug in Evaluate and simplify Since is false, this means that the interval does not work. So that means that this interval is not in the solution set and can be ignored. ----------------------------------------------- So let's evaluate a point that is to the right of (which is the right most endpoint). Let's evaluate the value Start with the given inequality Plug in Evaluate and simplify So everything to the right of is in the solution set. So our graph now looks like Since is true, this means that one part of the solution in interval notation is ----------------------------------------------- Answer: So the solution in interval notation is

Graphs/134953: 1 solutions Answer 98810 by jim_thompson5910(28598)   on 2008-04-02 19:47:23 (Show Source): You can put this solution on YOUR website! Start with the given equation Cube both sides. This will eliminate the denominator 3 from the exponent Take the square root of both sides Subtract 4 from both sides Combine like terms on the right side -------------------------------------------------------------- Answer: So our answer is

Graphs/134952: 1 solutions Answer 98809 by jim_thompson5910(28598)   on 2008-04-02 19:44:29 (Show Source): You can put this solution on YOUR website! Start with the given equation Cube both sides Subtract 5x from both sides. Add 11 to both sides. Combine like terms Take the square root of both sides So our answer is or

Graphs/134950: sqrt(5-x)=x-3 1 solutions Answer 98807 by jim_thompson5910(28598)   on 2008-04-02 19:38:00 (Show Source): You can put this solution on YOUR website! Start with the given equation Square both sides Foil the right side Subtract 5 from both sides. Add x to both sides. Combine like terms Factor the right 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 possible answers are or However, if you plug in , you'll notice that the equation is not equal. So this shows use that is not a solution ---------------------- Answer: So our only solution is

Graphs/134949: sqrt(4x-3)=sqrt(x+9) 1 solutions Answer 98806 by jim_thompson5910(28598)   on 2008-04-02 19:33:13 (Show Source): You can put this solution on YOUR website! Start with the given equation Square both sides Add 3 to both sides Subtract x from both sides Combine like terms on the left side Combine like terms on the right side Divide both sides by 3 to isolate x Divide -------------------------------------------------------------- Answer: So our answer is

Graphs/134947: Solve: 1 solutions Answer 98805 by jim_thompson5910(28598)   on 2008-04-02 19:30:16 (Show Source): You can put this solution on YOUR website! Start with the given equation Square both sides Subtract 7 from both sides So answer is

Graphs/134946: Solve: 1 solutions Answer 98802 by jim_thompson5910(28598)   on 2008-04-02 19:27:18 (Show Source): You can put this solution on YOUR website! Start with the given equation 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 Now set each factor equal to zero: or Now solve for x for each factor: , or

Graphs/134945: Solve: 1 solutions Answer 98801 by jim_thompson5910(28598)   on 2008-04-02 19:23:08 (Show Source): You can put this solution on YOUR website! Start with the given equation 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

Graphs/134943: Solve: 1 solutions Answer 98800 by jim_thompson5910(28598)   on 2008-04-02 19:21:31 (Show Source): You can put this solution on YOUR website! Start with the given equation Factor the left side (note: if you need help with factoring, check out this solver) Factor by use of the difference of squares to get . Factor by use of the difference of squares to get Now set each factor equal to zero: , , or Now solve for x for each factor: , , or So our answer is , , or

Graphs/134942: Solve: 1 solutions Answer 98799 by jim_thompson5910(28598)   on 2008-04-02 19:21:19 (Show Source): You can put this solution on YOUR website! Start with the given equation Factor the left side (note: if you need help with factoring, check out this solver) Factor by use of the difference of squares to get . Factor by use of the difference of squares to get Now set each factor equal to zero: , , or Now solve for x for each factor: , , or So our answer is , , or

Graphs/134941: Solve: 1 solutions Answer 98798 by jim_thompson5910(28598)   on 2008-04-02 19:16:24 (Show Source): You can put this solution on YOUR website! Start with the given equation 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

Graphs/134939: Solve: 1 solutions Answer 98797 by jim_thompson5910(28598)   on 2008-04-02 19:14:15 (Show Source): You can put this solution on YOUR website! Start with the given equation Subtract 4x from both sides. 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

Linear-equations/134833: Graph 3x-4y=8 using the slope and y-intercept 1 solutions Answer 98681 by jim_thompson5910(28598)   on 2008-04-02 00:51:34 (Show Source): You can put this solution on YOUR website! Start with the given equation Subtract from both sides Rearrange the equation Divide both sides by 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 4. This means that to go from point to point, we can go up 3 and over 4 So starting at , go up 3 units and to the right 4 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

Complex_Numbers/134721: The Fundamental Theorem of Algebra Use the given zero to find the remaining zeros of each polynomial function. P(x)=x^4-6x^3+71x^2-146x+530; 2+7i x intercepts = 2+7i & 2-7i x=2-7i =x-2+7i=0=(x-(2-7i))=0 (x-(2-7i))(x-(2+7i))= x^2-x(2+7i)-x(2-7i)+(2+7i)(2-7i)= x^2-2x-7xi-2x+7xi+53= x^2-4x+53= x^4-6x^3+71x^2-146x+530/x^2-4x+53= x^2-2x+10= (x^2-4x+53)(x^2-2x+10) Now I'm stuck. Could really use some help Thanks so much 1 solutions Answer 98551 by jim_thompson5910(28598)   on 2008-04-01 11:32:06 (Show Source): You can put this solution on YOUR website! You have the correct steps. All that you need to do is solve for x in Let's use the quadratic formula to solve for x: Starting with the general quadratic the general solution using the quadratic equation is: So lets solve ( notice , , and ) Plug in a=1, b=-2, and c=10 Negate -2 to get 2 Square -2 to get 4 (note: remember when you square -2, you must square the negative as well. This is because .) Multiply to get Combine like terms in the radicand (everything under the square root) Simplify the square root (note: If you need help with simplifying the square root, check out this solver) Multiply 2 and 1 to get 2 After simplifying, the quadratic has roots of or So the remaining zeros are or

Equations/134494: -3(4x+3)+4(6x+1)=43 1 solutions Answer 98379 by jim_thompson5910(28598)   on 2008-03-30 23:29:59 (Show Source): You can put this solution on YOUR website! Start with the given equation Distribute Combine like terms on the left side Add 5 to both sides Combine like terms on the right side Divide both sides by 12 to isolate x Divide -------------------------------------------------------------- Answer: So our answer is

Equations/134477: Can you show me all the steps to solve equations like 2x-3=5x+4 1 solutions Answer 98375 by jim_thompson5910(28598)   on 2008-03-30 22:41:12 (Show Source): You can put this solution on YOUR website! Start with the given equation Add 3 to both sides Subtract 5x 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 Reduce -------------------------------------------------------------- Answer: So our answer is (which is approximately in decimal form)

Polynomials-and-rational-expressions/134492: factoring completely: 14xSquared-53x+14. 1 solutions Answer 98374 by jim_thompson5910(28598)   on 2008-03-30 22:39:26 (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 14 and 14 respectively. Now multiply the first coefficient 14 and the last coefficient 14 to get 196. Now what two numbers multiply to 196 and add to the middle coefficient -53? Let's list all of the factors of 196: Factors of 196: 1,2,4,7,14,28,49,98 -1,-2,-4,-7,-14,-28,-49,-98 ...List the negative factors as well. This will allow us to find all possible combinations These factors pair up and multiply to 196 1*196 2*98 4*49 7*28 14*14 (-1)*(-196) (-2)*(-98) (-4)*(-49) (-7)*(-28) (-14)*(-14) note: remember two negative numbers multiplied together make a positive number Now which of these pairs add to -53? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -53 First Number Second Number Sum 1 196 1+196=197 2 98 2+98=100 4 49 4+49=53 7 28 7+28=35 14 14 14+14=28 -1 -196 -1+(-196)=-197 -2 -98 -2+(-98)=-100 -4 -49 -4+(-49)=-53 -7 -28 -7+(-28)=-35 -14 -14 -14+(-14)=-28 From this list we can see that -4 and -49 add up to -53 and multiply to 196 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