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jim_thompson5910 answered: 28465 problems
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Square-cubic-other-roots/461059: find the indicated roots. 3√-8a^6b^15 1 solutions Answer 316232 by jim_thompson5910(28476)   on 2011-06-14 19:43:02 (Show Source): You can put this solution on YOUR website! So

Equations/461000: 16-3x=-32 1 solutions Answer 316198 by jim_thompson5910(28476)   on 2011-06-14 17:01:29 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is

Trigonometry-basics/460962: If the endpoints of a diameter of a circle are (4,3)and (-3,5), what is the equation of the circle? This is my answer is this right, if not what is? Answer (5-3)^2+(-3-4)^2 =2^2+(-7)^2 =4+49 =53 radius=53/2 midpoint : (1/2, 4) equation of the circle=(x-1/2)^2+(y-4)^2=53/4 1 solutions Answer 316195 by jim_thompson5910(28476)   on 2011-06-14 16:59:56 (Show Source): You can put this solution on YOUR website! The radius is actually , which will make . You forgot to take the square root of 53 in the last step. Anyways, the equation you have is the correct one nonetheless. Good job.

Circles/460993: Can someone help me with this: Find the area of the circle, 8cm use 22/7 for tt. The area of the circle is___cm^2. Thank you 1 solutions Answer 316190 by jim_thompson5910(28476)   on 2011-06-14 16:49:11 (Show Source): You can put this solution on YOUR website! (note: this is approximate) So the area of the circle is approximately 201.142857 square cm.

Equations/460990: I need help i have no idea how to do this question 3x + 4= -2(x + 3) 1 solutions Answer 316187 by jim_thompson5910(28476)   on 2011-06-14 16:38:49 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Subtract from both sides. Add to both sides. Combine like terms on the left side. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is

test/460763: Evaluate the series. 4 ∑ (2k+1) = K=1 Thank you Remi 1 solutions Answer 316051 by jim_thompson5910(28476)   on 2011-06-13 21:57:06 (Show Source): You can put this solution on YOUR website! So

Miscellaneous_Word_Problems/460756: Please help me solve this problem: A 210 ft. long rope is cut into 3 pieces. The first piece is 3 times as long as the second piece. The third piece is 2 times as long as the second piece. What is the length of the longest piece of rope? a. 70 ft b. 90 ft c. 105 ft d. 110 ft e. 140 ft Thanks!!!! 1 solutions Answer 316048 by jim_thompson5910(28476)   on 2011-06-13 21:44:44 (Show Source): You can put this solution on YOUR website! Let x, y, and z be the lengths of the three pieces of rope. Since "The first piece is 3 times as long as the second piece", we know that . "The third piece is 2 times as long as the second piece" tells us that . Now since the three pieces were cut from a 210 ft rope, this means that Now plug in and to get Combine like terms on the left side. Divide both sides by to isolate . Reduce. This means that the second piece is 35 ft long. Now plug this into to get . So the first piece (the longest piece) is 105 ft long. ---------------------------------------------------------------------- Answer: The length of the longest piece of rope is 105 ft. So the answer is choice C)

Probability-and-statistics/460728: A bag contains 20 batteries, of which six are defective. Selecting two at random, without replacement, determine the probability that none of the batteries you select are good. >3/5 >3/10 >3/38 >9/100 please show me how you get the answer? 1 solutions Answer 316038 by jim_thompson5910(28476)   on 2011-06-13 21:01:46 (Show Source): You can put this solution on YOUR website! P(2 Defective) = P(Defective AND defective) P(2 Defective) = P(Defective) * P(Defective) P(2 Defective) = (6/20)*(5/19) P(2 Defective) = (6*5)/(20*19) P(2 Defective) = 30/380 P(2 Defective) = 3/38 So the probability that both are defective is 3/38, which means that the answer is choice C)

Polynomials-and-rational-expressions/460669: solve the polynomial 12x^2-5x-3 1 solutions Answer 315985 by jim_thompson5910(28476)   on 2011-06-13 17:51:12 (Show Source): You can put this solution on YOUR website! I'm assuming you mean factor it. 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 : 1,2,3,4,6,9,12,18,36 -1,-2,-3,-4,-6,-9,-12,-18,-36 Note: list the negative of each factor. This will allow us to find all possible combinations. These factors pair up and multiply to . 1*(-36) = -36 2*(-18) = -36 3*(-12) = -36 4*(-9) = -36 6*(-6) = -36 (-1)*(36) = -36 (-2)*(18) = -36 (-3)*(12) = -36 (-4)*(9) = -36 (-6)*(6) = -36 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 -36 1+(-36)=-35 2 -18 2+(-18)=-16 3 -12 3+(-12)=-9 4 -9 4+(-9)=-5 6 -6 6+(-6)=0 -1 36 -1+36=35 -2 18 -2+18=16 -3 12 -3+12=9 -4 9 -4+9=5 -6 6 -6+6=0 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 . In other words, . Note: you can check the answer by expanding to get or by graphing the original expression and the answer (the two graphs should be identical).

Numeric_Fractions/460662: 8c-19=37 1 solutions Answer 315980 by jim_thompson5910(28476)   on 2011-06-13 17:34:57 (Show Source): You can put this solution on YOUR website! Start with the given equation. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is

logarithm/460653: simplify log base 2 of 8 - log base 2 of 4 1 solutions Answer 315975 by jim_thompson5910(28476)   on 2011-06-13 17:14:26 (Show Source): You can put this solution on YOUR website! So

Rational-functions/460116: Rewrite with positive exponents. Assume that even roots are of nonnegative quantities and that all denominators are nonzero (x^-3/x^-2) 1 solutions Answer 315579 by jim_thompson5910(28476)   on 2011-06-12 00:51:38 (Show Source): You can put this solution on YOUR website! So

expressions/460110: 3x^2 + 4y^2 - ( 5x^2 - 7y^2 - 1) how do I solve this? I am way lost! 1 solutions Answer 315576 by jim_thompson5910(28476)   on 2011-06-11 23:33:54 (Show Source): You can put this solution on YOUR website! 3x^2 + 4y^2 - ( 5x^2 - 7y^2 - 1) 3x^2 + 4y^2 - 5x^2 + 7y^2 + 1 (3x^2 - 5x^2) + (4y^2 + 7y^2) + 1 -2x^2 + 11y^2 + 1 So 3x^2 + 4y^2 - ( 5x^2 - 7y^2 - 1) = -2x^2 + 11y^2 + 1

Quadratic_Equations/460108: Hi, I am new to this site, can someone help me. I have not had math in years and I am terrible at it. My question is: Find the quadratic equations that fits the following set of data points. ((-1,5),(-4,59),(-3,37)) Thank you 1 solutions Answer 315574 by jim_thompson5910(28476)   on 2011-06-11 23:31:10 (Show Source): You can put this solution on YOUR website! Since we're forcing a parabola to go through these three points, this means that when we plug in each 'x' into the general formula , we'll get 'y'. So essentially, we're plugging in corresponding values of 'x' and 'y' and forming equations, which we'll use to solve for 'a', 'b', and 'c'. So for instance, if we plug in x=-1, then we'll get the output of y=-5. This means that which simplifies to Do the same with the second point to get the second equation Finally, do the same with the third point to get the third equation ---------------------------------------------- After doing all that, we have the system which translates into this augmented matrix Row reduce this matrix (see this image for full steps on how to do that) to get Note: alternatively you can use a calculator to do the row reduction. The last column represents the values of 'a', 'b', and 'c' respectively. So , and So the quadratic equation that goes through the three given points is As a check, if we plug in x = -1, then.... So plugging in x = -1 gives us y = 5, meaning that the point (-1,5) lies on the parabola. This partially verifies our answer. Do the same with the other two points to verify this equation actually works. Let me know if this helps.

Quadratic_Equations/460102: Use the discriminant to determine whether the following equations have solutions that are: two different rational solutions; two different irrational solutions; exactly one rational solution; or two different imaginary solutions 8x^2 + 7x + 3 = 0 1 solutions Answer 315572 by jim_thompson5910(28476)   on 2011-06-11 23:20:02 (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 Since the discriminant is less than zero, this means that there are two complex solutions. In other words, there are no real solutions.

Vectors/460103: Solve the solution -5 < x + 3 < 11 1 solutions Answer 315570 by jim_thompson5910(28476)   on 2011-06-11 23:19:06 (Show Source): You can put this solution on YOUR website! Start with the given compound inequality. Subtract from all sides. Combine like terms on the left side. Combine like terms on the right side. So our answer is

Quadratic_Equations/460095: Solve quad equation 2x^2-4x=-2x 1 solutions Answer 315564 by jim_thompson5910(28476)   on 2011-06-11 22:59:06 (Show Source): You can put this solution on YOUR website! Start with the given equation. Get every term to the left side. Combine like terms. Notice that the quadratic is 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 the solutions are or

Quadratic_Equations/460093: solve using the square root property. 3(x+9)^2-81=0 1 solutions Answer 315563 by jim_thompson5910(28476)   on 2011-06-11 22:54:17 (Show Source): You can put this solution on YOUR website! 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 Simplify the square root. or Subtract from both sides. -------------------------------------- Answer: So the solutions are or .

Triangles/460090: can a right triangle have a side bigger than its hypotenuse? 1 solutions Answer 315561 by jim_thompson5910(28476)   on 2011-06-11 22:49:21 (Show Source): You can put this solution on YOUR website! No, the hypotenuse of a right triangle is ALWAYS the longest side.

Inequalities/460091: Can someone help me with solving the inequality? -14 ≤ 4x - 7≤ -2 1 solutions Answer 315560 by jim_thompson5910(28476)   on 2011-06-11 22:48:56 (Show Source): You can put this solution on YOUR website! Start with the given compound inequality. Add to all sides. Combine like terms on the left side. Combine like terms on the right side. Divide all sides by 4. So the answer is

Inequalities/460087: Can someone help me solve and graph this inequality problem? -21 ≤ 4x +3 and 4x +3 < 23 1 solutions Answer 315557 by jim_thompson5910(28476)   on 2011-06-11 22:39:43 (Show Source): You can put this solution on YOUR website! First, solve the inequalities separately. Let's solve the first inequality Start with the given inequality. Add to both sides. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . note: Remember, the inequality sign flips when we divide both sides by a negative number. Reduce. So the solution to the first inequality is ----------------------------------------------- Now let's solve the second inequality Start with the given inequality. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. So the solution to the second inequality is =============================================================== So the two solutions are AND So the question is now: what number(s) fall are BOTH greater than -6 AND less than 5? The answer is any number that satisfies the compound inequality . Basically, I combined the two inequalities above to form the final compound inequality. So the answer is

Inequalities/460086: Can someone help me solve this inequality problem? 0.6x +3 ≤ 1.4x-8 what is the solution? {x x __ __} 1 solutions Answer 315555 by jim_thompson5910(28476)   on 2011-06-11 22:31:29 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Multiply both sides by 10 to clear out the decimals. Distribute and multiply. Subtract from both sides. Subtract from both sides. Combine like terms on the left side. Combine like terms on the right side. Divide both sides by to isolate . note: Remember, the inequality sign flips when we divide both sides by a negative number. Reduce. ---------------------------------------------------------------------- Answer: So the solution is So the answer in set-builder notation is

Parallelograms/460082: the area of a parallelogram is 80sq.cm and one side is 20cm .Find the corresponding altitude? 1 solutions Answer 315552 by jim_thompson5910(28476)   on 2011-06-11 22:06:23 (Show Source): You can put this solution on YOUR website! Hint: The area of a parallelogram is where b is the base and h is the height (or altitude).

Equations/460081: Hello, I have a problem that I am working on but I have two answers. Can someone tell me what I am doing wrong. The problem is: solve by x: x^2+14x+4=0 my first answer is: 7sqrt 5, 7-sqrt 5 my second answer is: -7-3 sqrt 5, 3 sqrt 7 I am so lost, please help. Thanks 1 solutions Answer 315550 by jim_thompson5910(28476)   on 2011-06-11 21:55:08 (Show Source): You can put this solution on YOUR website! Start with the given equation. Notice that the quadratic is 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 the solutions are or

Quadratic_Equations/460080: write a quadratic equation in the variable x having the given numbers as solutions. type in standard form, ax^2+bx+c=o soultion :10, only solution 1 solutions Answer 315549 by jim_thompson5910(28476)   on 2011-06-11 21:54:05 (Show Source): You can put this solution on YOUR website! or (note: since there's one solution, but the polynomial is of degree 2, this means there's a double root) or So the equation is

Quadratic_Equations/460073: I am having a hard time with quadratic equations, can someone help me. Find the quadratic equaton that fits the following set of data points ((-1,-5),(-4,59),(-3,37)) Thank you 1 solutions Answer 315548 by jim_thompson5910(28476)   on 2011-06-11 21:47:55 (Show Source): You can put this solution on YOUR website! Since we're forcing a parabola to go through these three points, this means that when we plug in each 'x' into the general formula , we'll get 'y'. So essentially, we're plugging in corresponding values of 'x' and 'y' and forming equations, which we'll use to solve for 'a', 'b', and 'c'. So for instance, if we plug in x=-1, then we'll get the output of y=-5. This means that which simplifies to Do the same with the second point to get the second equation Finally, do the same with the third point to get the third equation ---------------------------------------------- After doing all that, we have the system which translates into this augmented matrix Row reduce this matrix (see this image for full steps on how to do that) to get Note: alternatively you can use a calculator to do the row reduction. The last column represents the values of 'a', 'b', and 'c' respectively. So , and So the quadratic equation that goes through the three given points is As a check, if we plug in x = -1, then.... So plugging in x = -1 gives us y = -5, meaning that the point (-1,-5) lies on the parabola. This partially verifies our answer. Do the same with the other two points to verify this equation actually works.

Finance/460015: I need help on how to plug in the information into the formula and the steps in which I work it. ROUND EACH STEP TO AT LEAST 5 PLACES AND ONLY ROUND TO THE NEAREST CENT AT THE END OF THE CALCULATION. Financed amount 18,500 Term of lean 48 months Annual rate of interest 11% I need to use this formula to calculte the monthly payments: P=A[1-(1+i)^-n/i]^-1 Where P represents your payment, A is the financed amount, i is the monthly interest rate in decimal form (i = annual rate/12), and n is the duration of the loan in months. vv 1 solutions Answer 315543 by jim_thompson5910(28476)   on 2011-06-11 20:31:29 (Show Source): You can put this solution on YOUR website! ... Start with the given formula. In this case, A = 18500 (the total amount financed, ie loaned out), i = 0.11/12 = 0.00916666666666667 (the monthly interest rate), and n = 48 (number of payments) ... Plug in the given values shown above ... Add ... Raise 1.00916666666667 to the negative 48th power to get 0.645328639529821 ... Subtract ... Divide ... Raise 38.6914211422014 to the negative first power to get 0.0258455226114526 ... Multiply So the monthly payment is $478.14 (rounded to the nearest cent).

logarithm/460058: I was given an equation and the book explained for to solve it using a graphing calculator but I would like to understand how it's done algebraically. e^(0.5x)-7.3= 2.08x + 6.2 This is how far I got before I drew a blank. Any help would be awesome. e^(0.5x)= 2.08x+13.5 1 solutions Answer 315541 by jim_thompson5910(28476)   on 2011-06-11 20:23:37 (Show Source): You can put this solution on YOUR website! There's no way to solve this equation algebraically because the variable we're solving for is located in the exponent on the left side and it's not located in the exponent on the right side. Basically, if the variable is located in the exponent, then EVERY copy of that variable must also be an exponent as well. To solve this, we would use the lambert W function, but that's beyond the scope of most courses. So you're going to have to settle to find the approximate solution. In this case, your book is having you use your graphing calculator to find these approximate solutions.

Linear-equations/459987: write the slope-intercept equation for the line that passes through (2, -7) and (4, -13) please show all work 1 solutions Answer 315504 by jim_thompson5910(28476)   on 2011-06-11 17:27:14 (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 . So this means that and . Also, is the second point . So this means that and . 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 7 from both sides. Combine like terms. So the equation that goes through the points and is

Probability-and-statistics/460024: If the class average is 195 and the SD is 30, what would be the score 1 SD above and below the mean? 1 solutions Answer 315503 by jim_thompson5910(28476)   on 2011-06-11 17:21:55 (Show Source): You can put this solution on YOUR website! Score 1 SD Above the mean = mean + 1*SD = 195+1*30 = 225 Score 1 SD Below the mean = mean - 1*SD = 195-1*30 = 165

Travel_Word_Problems/459898: is it possible to travel a great distance without any displacement? prove the answer. 1 solutions Answer 315395 by jim_thompson5910(28476)   on 2011-06-11 06:45:18 (Show Source): You can put this solution on YOUR website! Yes it is. Consider running around in circles (say around a track) 500 times, but at the end of the run, you end up exactly where you started. Doing so will mean you've traveled quite a distance, but you've gone nowhere (hence zero displacement).