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jim_thompson5910 answered: 28703 problems
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Average/550626: perform the indicated operation, and if possible, simplify. please show all of your work. write your final answer exactly as a fraction in lowest terms. 3/14+2/5 1 solutions Answer 358944 by jim_thompson5910(28715)   on 2011-12-28 12:00:56 (Show Source): You can put this solution on YOUR website! Solved by pluggable solver: Fractions Solver Start with the given expression In order to add these two fractions, these fractions need to have a common denominator. In order to do that, we simply find that the LCM of 14 and 5 is 70 (note: if you need help with finding the LCM, check out this solver) Now we need to get each denominator to 70 Multiply by Multiply and to get Multiply by Multiply and to get Since both fractions have a common denominator of 70, we can now combine the fractions Combine the fractions Add the numerators So

Average/550619: translate the following phrase an algebraic expression the difference of fifteen and twice a number 1 solutions Answer 358943 by jim_thompson5910(28715)   on 2011-12-28 11:59:49 (Show Source): You can put this solution on YOUR website! "the difference of fifteen and twice a number" translates to where 'x' is the unknown number.

Distributive-associative-commutative-properties/550613: use the commutation law of multiplication to write an equivalent expression. 5(8+x) 1 solutions Answer 358942 by jim_thompson5910(28715)   on 2011-12-28 11:59:11 (Show Source): You can put this solution on YOUR website! 5(8+x) is equivalent to (8+x)5 using the commutative law of multiplication

Square-cubic-other-roots/550649: leave a non-perfect square under the radial sign: x^2+23=144. what is a non-perfect square and what is a radical sign? what I have come up with is x^2+23=144-23; x^2=121; sqrt of 121 is 11 i need to know what a perfect square is and what a radical sign is 1 solutions Answer 358940 by jim_thompson5910(28715)   on 2011-12-28 11:57:49 (Show Source): You can put this solution on YOUR website! A perfect square is a number x such that where k is some whole number. For example, 100 is a perfect square because . You can figure out if a number is a perfect square by evaluating the square root of that number. If the square root of that number is a whole number, then that number is a perfect square. So (which makes it a perfect square), but (which makes it a non-perfect square) The radical sign is just another way of saying the square root sign. Note: keep in mind that x = -11 is also a solution along with x = 11

Polynomials-and-rational-expressions/550648: i am helping my son with a worksheet from school and the answer sheet for his worksheet is saying his answer is wrong the question he is stuck on is (2xy)(3xy)(6x^8y^6) he is doing a multiplication of monomials worksheet and the answer he got is 36x^10y^6 is that right or is the worksheet right when it states the answer is 11x^10y^6 and why? 1 solutions Answer 358938 by jim_thompson5910(28715)   on 2011-12-28 11:49:24 (Show Source): You can put this solution on YOUR website! The answer is actually 36x^10y^8, so the worksheet is wrong. The final coefficient is equal to the product of the other coefficients. So the final coefficient is 2*3*6=6*6=36 Then you multiply the x terms to get x*x*x^8 = x^(1+1+8)=x^10 and then you multiply the y terms to get y*y*y^6 = y^(1+1+6) = y^8 put this all together to get 36x^10y^8

Quadratic_Equations/550612: simplify (5h^9)^6 1 solutions Answer 358937 by jim_thompson5910(28715)   on 2011-12-28 11:42:17 (Show Source): You can put this solution on YOUR website! (5h^9)^6 (5)^6(h^9)^6 15625h^(9*6) 15625h^(54) So the answer is

Geometric_formulas/550603: what is the equation of the line that passes through (9, -2) and (4,6)? 1 solutions Answer 358936 by jim_thompson5910(28715)   on 2011-12-28 11:40:59 (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 2 from both sides. Combine like terms. note: If you need help with fractions, check out this solver. So the equation that goes through the points and is

Polynomials-and-rational-expressions/550614: divide & simplify 5^13/5^3 1 solutions Answer 358935 by jim_thompson5910(28715)   on 2011-12-28 11:40:03 (Show Source): You can put this solution on YOUR website! 5^13/5^3 5^(13-3) 5^10 9765625 So 5^13/5^3 = 9765625

Average/550621: evaluate 2x+7y/30 for x=15 and y=3 write your final answer exactly as a fraction in lowest terms. 1 solutions Answer 358934 by jim_thompson5910(28715)   on 2011-12-28 11:38:27 (Show Source): You can put this solution on YOUR website! (2x+7y)/30 (2*15+7*3)/30 (30+21)/30 51/30 17/10 So (2x+7y)/30 = 17/10 when x=15 and y=3

Square-cubic-other-roots/550647: leave a non-perfect square under the radical sign: 3n^2-2n^2+8=89. how do I solve something like this? 1 solutions Answer 358933 by jim_thompson5910(28715)   on 2011-12-28 11:36:42 (Show Source): You can put this solution on YOUR website! 3n^2-2n^2+8=89 3n^2-2n^2=89-8 n^2=81 n=+-sqrt(81) n=9 or n=-9

Average/550627: write a true sentence using either < or > -2.172_-2.17 1 solutions Answer 358932 by jim_thompson5910(28715)   on 2011-12-28 11:35:35 (Show Source): You can put this solution on YOUR website! -2.172 < -2.17 since -2.172 is larger in absolute value (so that places it to the left of -2.17)

Sequences-and-series/550646: 1) 3(4x-7)=2(7x+13) 2) x+6 ____ = x-12 3 1 solutions Answer 358931 by jim_thompson5910(28715)   on 2011-12-28 11:33:48 (Show Source): You can put this solution on YOUR website! I'll do the first one to get you started. # 1 Start with the given equation. Distribute. Add to 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 . Reduce. ---------------------------------------------------------------------- Answer: So the solution is

Angles/550566: can you expand this: (4z-3)^2 1 solutions Answer 358848 by jim_thompson5910(28715)   on 2011-12-27 22:33:01 (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: , , , Now add every term listed above to make a single expression. Now combine like terms. So FOILs to . In other words, .

logarithm/550554: Solve, 81^(x) = 9^(x+4). 1 solutions Answer 358840 by jim_thompson5910(28715)   on 2011-12-27 21:34:00 (Show Source): You can put this solution on YOUR website! 81^(x) = 9^(x+4) (9^2)^(x) = 9^(x+4) 9^(2x) = 9^(x+4) ------------------------------------------------------- Since the bases are equal, the exponents are equal. 2x = x+4 2x - x = 4 x = 4

Numbers_Word_Problems/550551: When 18 is subtracted from four times a certain number, the result is 5/2 the original number. What is the number? 1 solutions Answer 358839 by jim_thompson5910(28715)   on 2011-12-27 21:09:33 (Show Source): You can put this solution on YOUR website! "When 18 is subtracted from four times a certain number, the result is 5/2 the original number. " means that we have the equation . Let's solve this equation for n. Start with the given equation. Multiply both sides by the LCD to clear any fractions. Distribute and multiply. Add to both sides. Subtract from both sides. Combine like terms on the left side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is So the unknown number is 12

Linear_Equations_And_Systems_Word_Problems/550549: When 18 is subtracted from four times a certain number, the result is the original number. What is the number? 1 solutions Answer 358838 by jim_thompson5910(28715)   on 2011-12-27 21:07:01 (Show Source): You can put this solution on YOUR website! "When 18 is subtracted from four times a certain number, the result is the original number." means that we have the equation . Let's solve this equation for n. Start with the given equation. Add to both sides. Subtract from both sides. Combine like terms on the left side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is So the unknown number is 6

Word_Problems_With_Coins/550541: Find the number of possible ways using only quarters and/or nickels to make $20. 1 solutions Answer 358837 by jim_thompson5910(28715)   on 2011-12-27 21:00:33 (Show Source): You can put this solution on YOUR website! Here are all the possible ways to make $20 using only quarters and/or nickels # of Quarters | # of Nickels 0 400 1 395 2 390 3 385 4 380 5 375 6 370 7 365 8 360 9 355 10 350 11 345 12 340 13 335 14 330 15 325 16 320 17 315 18 310 19 305 20 300 21 295 22 290 23 285 24 280 25 275 26 270 27 265 28 260 29 255 30 250 31 245 32 240 33 235 34 230 35 225 36 220 37 215 38 210 39 205 40 200 41 195 42 190 43 185 44 180 45 175 46 170 47 165 48 160 49 155 50 150 51 145 52 140 53 135 54 130 55 125 56 120 57 115 58 110 59 105 60 100 61 95 62 90 63 85 64 80 65 75 66 70 67 65 68 60 69 55 70 50 71 45 72 40 73 35 74 30 75 25 76 20 77 15 78 10 79 5 80 0 There are 81 ways to make $20 using only quarters and/or nickels

Linear-systems/550539: HELP PLEASE????? solve using substitution method 3x + 9y = 57 -7x + y = 65 type an ordered pair 1 solutions Answer 358835 by jim_thompson5910(28715)   on 2011-12-27 20:40:25 (Show Source): You can put this solution on YOUR website! Start with the given system of equations: Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y. So let's isolate y in the second equation Start with the second equation Add to both sides Rearrange the equation --------------------- Since , we can now replace each in the first equation with to solve for Plug in into the second equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown. Distribute to Multiply Combine like terms on the left side Subtract 585 from both sides Combine like terms on the right side Divide both sides by 66 to isolate x Divide -----------------First Answer------------------------------ So the first part of our answer is: Since we know that we can plug it into the equation (remember we previously solved for in the first equation). Start with the equation where was previously isolated. Plug in Multiply Combine like terms -----------------Second Answer------------------------------ So the second part of our answer is: -----------------Summary------------------------------ So our answers are: and which form the point 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).

Numeric_Fractions/550536: 2x^2 - 12x __________ x - 6 1 solutions Answer 358834 by jim_thompson5910(28715)   on 2011-12-27 20:07:26 (Show Source): You can put this solution on YOUR website! (2x^2 - 12x)/(x-6) (2x(x - 6))/(x-6) 2x So (2x^2 - 12x)/(x-6) = 2x

Expressions-with-variables/550535: what is the speed in meters per secound of a paper airplaine that flies 24 meters in 6 secound 1 solutions Answer 358833 by jim_thompson5910(28715)   on 2011-12-27 20:01:07 (Show Source): You can put this solution on YOUR website! The speed is 24/6 = 4 meters per second

Expressions-with-variables/550534: solve for x 3 over 5(x+2)=x-4 1 solutions Answer 358832 by jim_thompson5910(28715)   on 2011-12-27 19:57:35 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Multiply both sides by the LCD to clear any fractions. 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 . Reduce. ---------------------------------------------------------------------- Answer: So the solution is

Expressions-with-variables/550533: if a+ar=b+r the value of a in terms of b and r can be expressed as 1 solutions Answer 358831 by jim_thompson5910(28715)   on 2011-12-27 19:53:59 (Show Source): You can put this solution on YOUR website! a+ar=b+r a(1+r)=b+r a=(b+r)/(1+r)

Polynomials-and-rational-expressions/550525: Factor completely, if prime, state this 5tˆ3 – 21tˆ2 + 18t 1 solutions Answer 358827 by jim_thompson5910(28715)   on 2011-12-27 19:23:15 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor out the GCF . Now let's try to factor the inner expression --------------------------------------------------------------- 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 : 1,2,3,5,6,9,10,15,18,30,45,90 -1,-2,-3,-5,-6,-9,-10,-15,-18,-30,-45,-90 Note: list the negative of each factor. This will allow us to find all possible combinations. These factors pair up and multiply to . 1*90 = 90 2*45 = 90 3*30 = 90 5*18 = 90 6*15 = 90 9*10 = 90 (-1)*(-90) = 90 (-2)*(-45) = 90 (-3)*(-30) = 90 (-5)*(-18) = 90 (-6)*(-15) = 90 (-9)*(-10) = 90 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 90 1+90=91 2 45 2+45=47 3 30 3+30=33 5 18 5+18=23 6 15 6+15=21 9 10 9+10=19 -1 -90 -1+(-90)=-91 -2 -45 -2+(-45)=-47 -3 -30 -3+(-30)=-33 -5 -18 -5+(-18)=-23 -6 -15 -6+(-15)=-21 -9 -10 -9+(-10)=-19 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 -------------------------------------------------- So then factors further to =============================================================== Answer: So completely 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).

Polynomials-and-rational-expressions/550524: Factor completely. Remember to look first for a common factor. If a polynomial is prime, state this. 6p^2 − 6q^2 1 solutions Answer 358826 by jim_thompson5910(28715)   on 2011-12-27 19:15:06 (Show Source): You can put this solution on YOUR website! 6p^2-6q^2 6(p^2-q^2) 6(p-q)(p+q)

Polynomials-and-rational-expressions/550523: Factor completely. If a polynomial is prime, state this. 6x2 + 19x + 10 1 solutions Answer 358825 by jim_thompson5910(28715)   on 2011-12-27 19:01:40 (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 : 1,2,3,4,5,6,10,12,15,20,30,60 -1,-2,-3,-4,-5,-6,-10,-12,-15,-20,-30,-60 Note: list the negative of each factor. This will allow us to find all possible combinations. These factors pair up and multiply to . 1*60 = 60 2*30 = 60 3*20 = 60 4*15 = 60 5*12 = 60 6*10 = 60 (-1)*(-60) = 60 (-2)*(-30) = 60 (-3)*(-20) = 60 (-4)*(-15) = 60 (-5)*(-12) = 60 (-6)*(-10) = 60 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 60 1+60=61 2 30 2+30=32 3 20 3+20=23 4 15 4+15=19 5 12 5+12=17 6 10 6+10=16 -1 -60 -1+(-60)=-61 -2 -30 -2+(-30)=-32 -3 -20 -3+(-20)=-23 -4 -15 -4+(-15)=-19 -5 -12 -5+(-12)=-17 -6 -10 -6+(-10)=-16 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).

Linear-systems/550512: -2x – 8y = -42 -4x + 6y = -18 1 solutions Answer 358822 by jim_thompson5910(28715)   on 2011-12-27 18:30:54 (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. 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-systems/550506: HELP!!!!! PLEASE........solve using substitution method.... 8x + 2y = 0 -7x + y = 22 type an ordered pair 1 solutions Answer 358816 by jim_thompson5910(28715)   on 2011-12-27 18:12:09 (Show Source): You can put this solution on YOUR website! Start with the given system of equations: Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y. So let's isolate y in the second equation Start with the second equation Add to both sides Rearrange the equation --------------------- Since , we can now replace each in the first equation with to solve for 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 to Multiply Combine like terms on the left side Subtract 44 from both sides Combine like terms on the right side Divide both sides by 22 to isolate x Divide -----------------First Answer------------------------------ So the first part of our answer is: Since we know that we can plug it into the equation (remember we previously solved for in the first equation). Start with the equation where was previously isolated. Plug in Multiply Combine like terms -----------------Second Answer------------------------------ So the second part of our answer is: -----------------Summary------------------------------ So our answers are: and which form the point 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).

Conjunction/550503: Use De Morgan’s laws to determine whether the two statements are equivalent. Show your work. ∼(p ∨ ∼q), ∼p ∧ q 1 solutions Answer 358814 by jim_thompson5910(28715)   on 2011-12-27 17:59:47 (Show Source): You can put this solution on YOUR website! ~(p V ~q) ~(p) ^ ~(~q) ~p ^ q So the two expressions are equivalent

Linear-equations/550501: 9x + 11y = 86 9x – 2y = -5 1 solutions Answer 358809 by jim_thompson5910(28715)   on 2011-12-27 17:55:00 (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 -1. 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. Add to 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)

Geometric_formulas/550500: what is the next term in the sequence? 729, -243, 81, -27 1 solutions Answer 358805 by jim_thompson5910(28715)   on 2011-12-27 17:46:08 (Show Source): You can put this solution on YOUR website! You're dividing by -3 each time, so the next term is -27/(-3) = 9

Geometric_formulas/550496: if the complement of an angle measures 22 degrees, what is the measure of its supplement? 1 solutions Answer 358804 by jim_thompson5910(28715)   on 2011-12-27 17:45:14 (Show Source): You can put this solution on YOUR website! Let x = the unknown angle The complement of angle x is 90-x and because the complement is 22 degrees, we know that 90-x = 22 Solve for x to get -x = 22-90 ---> -x = -68 ---> x = 68 So the original angle is 68 degrees and the supplement of 68 degrees is 180 - 68 = 112 degrees