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Recent problems solved by 'jim_thompson5910'

jim_thompson5910 answered: 28493 problems
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Complex_Numbers/195737: Multiply: (1/6 – i)^2 1 solutions Answer 146787 by jim_thompson5910(28504)   on 2009-05-10 22:55:58 (Show Source): You can put this solution on YOUR website! 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:. --------------------------------------------------- So we have the terms: , , , and Now add every term listed above to make a single expression. Now combine like terms. So FOILs to . In other words, .

Complex_Numbers/195738: Divide: (6 + 3i)/6 – 3i) 1 solutions Answer 146786 by jim_thompson5910(28504)   on 2009-05-10 22:52:16 (Show Source): You can put this solution on YOUR website! Start with the given expression. Multiply the fraction by . Combine the fractions. FOIL the numerator. FOIL the denominator. Multiply. Combine like terms. Break up the fraction. Reduce. So . So the expression is now in standard form where and

Polynomials-and-rational-expressions/195739: what is 4s+s-4 + 3s-5s + 2 equals 1 solutions Answer 146785 by jim_thompson5910(28504)   on 2009-05-10 22:50:57 (Show Source): You can put this solution on YOUR website! Start with the given expression Group like terms Combine like terms So

Quadratic_Equations/195740: Solve by factoring: 25x^2 + 2x + 1 = 12x 1 solutions Answer 146784 by jim_thompson5910(28504)   on 2009-05-10 22:49:52 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract 12x from both sides. Combine like terms. Factor Take the square root of both sides Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . ---------------------------------------------------------------------- Answer: So the answer is which in decimal form is .

Exponential-and-logarithmic-functions/195736: These are problemsusing expotential equations. Any help you could offer would be greatly appreciated because I am struggling with these. Thank you. 1. The volume of a cubical bin is 27 cubic feet. What are the length, width, and height? 2. The formual for nth term b of a geo series is b=ar to the n-1 Find n when b=1024 a=16 4-2 3. If a set has three elements, how many subsets does it have? 1 solutions Answer 146783 by jim_thompson5910(28504)   on 2009-05-10 22:47:20 (Show Source): You can put this solution on YOUR website! 1) The volume of a cube is simply equal to the side length cubed. So take the cube root of 27 to get 3. So the width, length, and height are 3 feet. Note: all sides of a cube are equal. ------------------------------------ 2) I'm not sure what you mean by a=16 4-2 ??? ------------------------------------ 3) To find the number of subsets of any set, simply raise the number of elements of that set as a power of 2 like so: So there are 8 subsets Proof: Here are the 8 subsets of set {a,b,c} {a,b,c}, {a,b}, {a,c}, {b,c} {a}, {b}, {c} {}

Polynomials-and-rational-expressions/195735: what is 3c+4 + 5c+2 equal 1 solutions Answer 146782 by jim_thompson5910(28504)   on 2009-05-10 22:23:18 (Show Source): You can put this solution on YOUR website! Start with the given expression Group like terms Combine like terms So

Miscellaneous_Word_Problems/195733: Building a pool in the shape of an ellipse. The equation for the pool is x^2/324 + y^2/196 = 1 Find the longest distance and shortest distance across the pool. I'm not sure where to start? y^2=1-x^2/324 and then square both sides? 1 solutions Answer 146778 by jim_thompson5910(28504)   on 2009-05-10 21:56:03 (Show Source): You can put this solution on YOUR website! Start with the given equation. Rewrite as Rewrite as So the equation is now in the form (which is the general equation of an ellipse) where , , and The longest distance between any two points along a line on the ellipse falls on the major axis. The length of the semi major axis simply turns out to be the larger value of "a" or "b" Since "a" is larger, this means that the length of the semi major axis is 18 units. Double this value to get 36 units. So the the longest distance across the pool is 36 units. For the shortest distance, just use the smaller value 14 and double it to 28. So the the shortest distance across the pool is 28 units.

Polynomials-and-rational-expressions/195729: factor the trinomial a^2+10a+21 1 solutions Answer 146772 by jim_thompson5910(28504)   on 2009-05-10 21:39:29 (Show Source): You can put this solution on YOUR website! Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is . Now multiply the first coefficient by the last term to get . Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ? To find these two numbers, we need to list all of the factors of (the previous product). Factors of : 1,3,7,21 -1,-3,-7,-21 Note: list the negative of each factor. This will allow us to find all possible combinations. These factors pair up and multiply to . 1*21 3*7 (-1)*(-21) (-3)*(-7) Now let's add up each pair of factors to see if one pair adds to the middle coefficient : First Number Second Number Sum 1 21 1+21=22 3 7 3+7=10 -1 -21 -1+(-21)=-22 -3 -7 -3+(-7)=-10 From the table, we can see that the two numbers and add to (the middle coefficient). So the two numbers and both multiply to and add to Now replace the middle term with . Remember, and add to . So this shows us that . Replace the second term with . Group the terms into two pairs. Factor out the GCF from the first group. Factor out from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis. Combine like terms. Or factor out the common term --------------------------------------------- Answer: So factors to .

Polynomials-and-rational-expressions/195730: factor by grouping 7x^3-7x^2-x+1 1 solutions Answer 146771 by jim_thompson5910(28504)   on 2009-05-10 21:38:56 (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/195731: multiply and simplify (6t)*2(6t)*4 1 solutions Answer 146770 by jim_thompson5910(28504)   on 2009-05-10 21:37:59 (Show Source): You can put this solution on YOUR website! So

Polynomials-and-rational-expressions/195713: Hello, Not sure if I chose the right catorgory but I need help with the following problem. The area of a rectangle is 55 square meters. Find the length and width of the rectangle if its length is 6 meters greater than its width. Use an equation and the formula for area of a rectangle A = l × w Thank you! 1 solutions Answer 146769 by jim_thompson5910(28504)   on 2009-05-10 21:36:16 (Show Source): You can put this solution on YOUR website! First, we'll use the area of a rectangle formula . Also, since "its length is 6 meters greater than its width", this means that Start with the given equation. Plug in Rearrange the terms. Distribute Subtract 55 from both sides. Notice we have a quadratic equation in the form of where , , and Let's use the quadratic formula to solve for W Start with the quadratic formula Plug in , , and 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 the possible answers are or However, a negative width doesn't make much sense. So this means we'll ignore So the solution is which makes the width 5 meters. Go back to the second equation Plug in Add So the length is 11 meters.

Equations/195714: I need to solve this, but no idea how, help please is homework for tomorrow 3 (-4b) -2 (a-b-c)= 1 solutions Answer 146767 by jim_thompson5910(28504)   on 2009-05-10 21:29:55 (Show Source): You can put this solution on YOUR website! Start with the given expression. Distribute Multiply Combine like terms. So

Polynomials-and-rational-expressions/195727: divide & check 48x*3y*2 ---------------- 8x*7y*2 1 solutions Answer 146766 by jim_thompson5910(28504)   on 2009-05-10 21:28:13 (Show Source): You can put this solution on YOUR website! Start with the given expression. Expand. Note: and Highlight the common terms. Cancel out the common terms. Simplify. Multiply. So simplifies to . In other words, where every variable is non zero

Polynomials-and-rational-expressions/195726: divide & check 56x*7-64x*6+56x*4 ------------------- 8x*4 1 solutions Answer 146765 by jim_thompson5910(28504)   on 2009-05-10 21:25:31 (Show Source): You can put this solution on YOUR website! Note: use ^ for exponent instead of * Start with the given expression. Factor out the GCF from the numerator Highlight the common terms. Cancel out the common terms. Simplify So where Note: you can use a graph to verify your answer.

Polynomials-and-rational-expressions/195725: factor complety 5a*2-26a+5 1 solutions Answer 146764 by jim_thompson5910(28504)   on 2009-05-10 21:22:17 (Show Source): You can put this solution on YOUR website! Note: use ^ for exponent instead of * Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is . Now multiply the first coefficient by the last term to get . Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ? To find these two numbers, we need to list all of the factors of (the previous product). Factors of : 1,5,25 -1,-5,-25 Note: list the negative of each factor. This will allow us to find all possible combinations. These factors pair up and multiply to . 1*25 5*5 (-1)*(-25) (-5)*(-5) Now let's add up each pair of factors to see if one pair adds to the middle coefficient : First Number Second Number Sum 1 25 1+25=26 5 5 5+5=10 -1 -25 -1+(-25)=-26 -5 -5 -5+(-5)=-10 From the table, we can see that the two numbers and add to (the middle coefficient). So the two numbers and both multiply to and add to Now replace the middle term with . Remember, and add to . So this shows us that . Replace the second term with . Group the terms into two pairs. Factor out the GCF from the first group. Factor out from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis. Combine like terms. Or factor out the common term --------------------------------------------- Answer: So factors to .

Polynomials-and-rational-expressions/195720: subtract (xy-ab-8)-(xy-3ab-1) 1 solutions Answer 146763 by jim_thompson5910(28504)   on 2009-05-10 21:20:50 (Show Source): You can put this solution on YOUR website! Start with the given expression. Distribute Group like terms. Combine like terms. Simplify. So

Quadratic_Equations/195697: 7x^2-16x-28=0 11x^2=8 1 solutions Answer 146762 by jim_thompson5910(28504)   on 2009-05-10 21:18:41 (Show Source): You can put this solution on YOUR website! # 1 Start with the given equation. 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 Rewrite as Add to to get Multiply and to get . Simplify the square root (note: If you need help with simplifying square roots, check out this solver) or Break up the expression. or Reduce So the answers are or which approximate to or # 2 Start with the given equation. Divide both sides by . Take the square root of both sides. or Break up the "plus/minus" to form two equations. or Simplify the square root. -------------------------------------- Answer: So the solutions are or .

Polynomials-and-rational-expressions/195721: multiply (x5+7x)(x5-7x) 1 solutions Answer 146761 by jim_thompson5910(28504)   on 2009-05-10 21:14:27 (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: , , , and Now add every term listed above to make a single expression. Now combine like terms. So FOILs to . In other words, .

Polynomials-and-rational-expressions/195719: solve b2-7b+12=0 1 solutions Answer 146760 by jim_thompson5910(28504)   on 2009-05-10 21:13:33 (Show Source): You can put this solution on YOUR website! Start with the given equation. Notice we have a quadratic equation in the form of where , , and Let's use the quadratic formula to solve for b 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 the answers are or

Rational-functions/195715: I hope i picked the right section to put this problem in. alright here is the problem, i am totally lost on how to do this: (x/x+4) - (2/x-1) = (20/x^2+3x-4) HELP! 1 solutions Answer 146759 by jim_thompson5910(28504)   on 2009-05-10 21:11:57 (Show Source): You can put this solution on YOUR website! Start with the given equation. Factor. Take note that or as these values cause a division by zero. Multiply every term on both sides by the LCD . Doing this will eliminate all of the fractions. Cancel out and simplify Rearrange the terms. Distribute. Subtract 20 from both sides. 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 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 the possible answers are or However, we stated earlier that or (they cause a division by zero). So we must ignore the possible solution (it is not in the domain) ============================================================ Answer: So the only solution is

Square-cubic-other-roots/195716: Simplify square roots: i.e. Simplify the square root of 36x^4y^5 or square root of 121x^5 divided by 9 1 solutions Answer 146756 by jim_thompson5910(28504)   on 2009-05-10 21:05:18 (Show Source): You can put this solution on YOUR website! # 1 Start with the given expression. Factor into Factor into Break up the square root using the identity . Take the square root of to get . Take the square root of to get . Take the square root of to get . Multiply. ================================================== Answer: So simplifies to In other words, where every variable is non-negative. # 2 Start with the given expression. Break up the root. Take the square root of 9 to get 3. 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 the terms. ================================================== Answer: So simplifies to In other words, where

Travel_Word_Problems/195718: A baseball player has hit a ball. The height, y, of the ball x seconds after it is hit is given by y= -16x^2 + 80x + 3. At what time will the ball reach its maximum height? I used the quadratic formula and my answer was 2.04 What is the maximum height of the ball? I used the original formula.My answer was 232.78 When will the ball hit the ground? My answer was 4.08 Is this right?? thanks 1 solutions Answer 146754 by jim_thompson5910(28504)   on 2009-05-10 21:00:16 (Show Source): You can put this solution on YOUR website! At what time will the ball reach its maximum height? What is the maximum height of the ball? First, we need the vertex. The vertex will tell us what the max height will be: In order to find the vertex, we first need to find the x-coordinate of the vertex. To find the x-coordinate of the vertex, use this formula: . Start with the given formula. From , we can see that , , and . Plug in and . Multiply 2 and to get . Reduce. So the x-coordinate of the vertex is . Note: this means that the axis of symmetry is also . Now that we know the x-coordinate of the vertex, we can use it to find the y-coordinate of the vertex. Start with the given equation. Plug in . Square to get . Multiply and to get . Multiply and to get . Combine like terms. So the y-coordinate of the vertex is . So the vertex is . which in decimal form is . So this means that at 2.5 seconds, the ball will be at the max height of 103. When will the ball hit the ground? Start with the given equation. Plug in 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 Rewrite as Add to to get Multiply and to get . Simplify the square root (note: If you need help with simplifying square roots, check out this solver) or Break up the expression. So the possible answers are or which approximate to or Since a negative time doesn't make sense, this means that the only solution is So it will take about 5.037 seconds for the ball to hit the ground.

logarithm/195711: log(small)4(x+3) + log(small)4 (x-3)=2 the fours are small in the bottom corner so that's why i put small. 1 solutions Answer 146753 by jim_thompson5910(28504)   on 2009-05-10 20:53:36 (Show Source): You can put this solution on YOUR website! Start with the given equation. Combine the logs using the identity Rewrite the equation using the property: ====> Square 4 to get 16 FOIL Add 9 to both sides. Combine like terms. Take the square root of both sides. or Break up the "plus/minus" or Take the square root of 25 to get 5 So the possible solutions are or However since you cannot take the log of a negative number, this rules out as a solution (since plugging this value in results in a negative argument) ================================================ Answer: So the only solution is

Quadratic_Equations/195679: A rocket is launched from atop a 101-foot cliff with an initial velocity of 116ft/s. a. Substitute the values into the vertical motion formula h=-16t^2+vt+c. Let h=0 b.Use the quadratic formula find out how long the rocket will take to hit the ground after it is launched Round to the nearest tenth of a second 1 solutions Answer 146742 by jim_thompson5910(28504)   on 2009-05-10 15:13:49 (Show Source): You can put this solution on YOUR website! a) Start with the given equation. Plug in and b) Start with the given equation. Plug in Notice we have a quadratic equation in the form of where , , and Let's use the quadratic formula to solve for t Start with the quadratic formula Plug in , , and Square to get . Multiply to get Rewrite as Add to to get Multiply and to get . Simplify the square root (note: If you need help with simplifying square roots, check out this solver) or Break up the expression. or Reduce So the answers are or which approximate to or Since a negative time doesn't make sense, the only answer is So it takes about 7.305 seconds for the rocket to hit the ground.

Quadratic_Equations/195677: Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth. 2a^2-46a+252=0 1 solutions Answer 146740 by jim_thompson5910(28504)   on 2009-05-10 15:02:18 (Show Source): You can put this solution on YOUR website! Start with the given equation. Notice we have a quadratic equation in the form of where , , and Let's use the quadratic formula to solve for "a" 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 the solutions are or

Linear_Equations_And_Systems_Word_Problems/195674: Hi, I am having a problem with the following question. On a test containing 120 questions, the final score is based on 1 point for each correct answer and 1/4 of a point subtracted for each incorrect answer. Allan answered all of the questions and received a final score of 100 points. How many questions did Allan answer correctly? Thank you for your help! Melissa 1 solutions Answer 146739 by jim_thompson5910(28504)   on 2009-05-10 14:59:45 (Show Source): You can put this solution on YOUR website! Let x = number of correct answers y = number of incorrect answers Since there are 120 questions and you can only get a correct or incorrect answer, this means that Also, since "the final score is based on 1 point for each correct answer and 1/4 of a point subtracted for each incorrect answer" and Allan "received a final score of 100 points", this means that Start with the first equation. Subtract x from both sides. Move onto the second equation Plug in Distribute Multiply Reduce Multiply EVERY term by the LCD to clear any fractions. Multiply and simplify Combine like terms on the left side. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. So this means that Allan answered 104 questions correctly.

Quadratic_Equations/195673: Solve the equation by completing the square. Round to the nearest hundredth if necessary. 3x^2-6x-24=0 1 solutions Answer 146738 by jim_thompson5910(28504)   on 2009-05-10 14:52:00 (Show Source): You can put this solution on YOUR website! Start with the left side of the given equation. Factor out the coefficient . This step is very important: the coefficient must be equal to 1. Take half of the coefficient to get . In other words, . Now square to get . In other words, Now add and subtract inside the parenthesis. Make sure to place this after the "x" term. Notice how . So the expression is not changed. Group the first three terms. Factor to get . Combine like terms. Distribute. Multiply. So after completing the square, transforms to . So . So is equivalent to . -------------------------------------------------------------- Now let's solve Start with the given equation. Add to both sides. Combine like terms. Divide both sides by . Reduce. Take the square root of both sides. or Break up the "plus/minus" to form two equations. or Take the square root of to get . or Add to both sides. or Combine like terms. -------------------------------------- Answer: So the solutions are or .

Quadratic-relations-and-conic-sections/195669: I have a "conic invasion" worksheet. I have to tell by the equation the type of figure and the specific info needed to graph the equation. PLEASE HELP ME! im not asking for the answers or anything (unless youre feeling generous :) just how to get these started im totally lost. 1.y^2+9(x+13)^2=9 2.x^2+y^2=144 for 10>or=y>or=-12 3.x^2+y^2+10x-10y+46=0 4.y+1=0 for 2>or=x>or=-2 5.2x^2-49y+392=0 for y 6.(y^2)/9 + [(x-13)^2]/1=1 7.3x+2y=4 for 2>or=x>or=0 8.2x^2-49y=294 for y 9.15x+7y=175 for 7>or=x>or=-2 10.5x^2-49y=441 for y 11.15x-7y+175=0 for 0>or=x>or=-2 12.3x-2y+4=0 for 0>or=x>or=-2 13.(x-5)^2+(y-5)^2=4 1 solutions Answer 146737 by jim_thompson5910(28504)   on 2009-05-10 14:49:19 (Show Source): You can put this solution on YOUR website! Method # 1 Simply get each equation into the form and use the following properties: If , and , then the equation is a circle If and , then the equation is an ellipse If , then the equation is a parabola If , then the equation is a hyperbola Method # 2: Try to get each equation into one of the following forms: Circle: Ellipse: Hyperbola: (parabolas open in x-direction) Hyperbola: (parabolas open in y-direction) Parabola (vertex form): , or Parabola (vertex form): (standard form)

Polynomials-and-rational-expressions/195667: Solve (5-x)/(2-x)-(3-2x)/(2x)=1 1 solutions Answer 146736 by jim_thompson5910(28504)   on 2009-05-10 14:30:36 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply every term on both sides by the LCD . Doing this will eliminate all of the fractions. Cancel out and simplify Multiply FOIL Distribute 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 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 the answers are or

Probability-and-statistics/195663: two cards are drawn from a deck of 7 cards numbered 1 through 7. once a card is drawn, it is not replaced. find the probability of drawing a 4 and then a 6. 1 solutions Answer 146735 by jim_thompson5910(28504)   on 2009-05-10 14:14:58 (Show Source): You can put this solution on YOUR website! P(drawing a 4) = 1/7 once a 4 is drawn (and not put back), there are 6 cards left. So P(drawing a 6 next) = 1/6 So ... P(drawing a 4 then a 6) = P(drawing a 4) * P(drawing a 6 next) = (1/7)*(1/6) = (1*1)/(7*6) = 1/42

Probability-and-statistics/195661: If a number cube is rolled two times, what is the probability of rolling a 1 both times? 1 solutions Answer 146733 by jim_thompson5910(28504)   on 2009-05-10 14:07:35 (Show Source): You can put this solution on YOUR website! P(rolling 1 twice) = P(rolling a 1 AND rolling a 1) = P(rolling a 1) * P(rolling a 1) = (1/6)*(1/6) = (1*1)/(6*6) = 1/36