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Geometry_proofs/188693: Prove that if and x<0, then x=-2 is true. 1 solutions Answer 141506 by jim_thompson5910(28476)   on 2009-03-28 14:20:56 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract 18 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 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 answers are or However, since , this means that "x" is negative. So this means that is the only solution (if the inequality restriction is applied).

Equations/188660: This question is from textbook saxon algebra 2 The formula for the area of a trapezoid is A=1/2(b1+b2)h. Solve the formula for b1. The numbers next to the b's are supposed to drop down. Like the opposite of an exponent. 1 solutions Answer 141473 by jim_thompson5910(28476)   on 2009-03-27 22:39:35 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply both sides by 2. Rearrange the terms. Divide both sides by "h". Subtract from both sides. Multiply by Combine the fractions. So the solution is

Complex_Numbers/188659: This question is from textbook saxon algebra 2 Solve the equation. Write the solutions in the form a+bi. x^2+10x+30=0 1 solutions Answer 141471 by jim_thompson5910(28476)   on 2009-03-27 22:31:22 (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 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 answers are or So the solutions are in the form where (for both solutions), for the first solution, and for the second solution.

Polynomials-and-rational-expressions/188658: I do not know where to begin? 4x^4-10x^3+8x^2/2x I am supposed to express in the lowest term. 1 solutions Answer 141469 by jim_thompson5910(28476)   on 2009-03-27 22:29:27 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor out the GCF from the numerator Factor to get Highlight the common terms. Cancel out the common terms. Simplify Distribute So where

Rational-functions/188592: Divide. State any restrictions on the variable. y^2+5y+4/y^2-49 divide by 2y^2+5y-12/y^2+9y+14 1 solutions Answer 141468 by jim_thompson5910(28476)   on 2009-03-27 21:57:31 (Show Source): You can put this solution on YOUR website! Start with the given expression. Multiply the first fraction by the reciprocal of the second fraction . Factor to get . Factor to get . Factor to get . Factor to get . Combine the fractions. Highlight the common terms. Cancel out the common terms. Simplify. So simplifies to . In other words, where , , , , or (these are the restrictions to avoid division by zero).

Rational-functions/188591: Multiply. State any restrictions on the variable. x^2+6x-7/x^2+5x times 3x^2+16x+5/2x^2+7x-9 1 solutions Answer 141467 by jim_thompson5910(28476)   on 2009-03-27 21:51:17 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor to get . Factor to get . Factor to get . Factor to get . Combine the fractions. Highlight the common terms. Cancel out the common terms. Simplify. So simplifies to . In other words, where , , , or (these are the restrictions to avoid dividing by zero).

logarithm/188597: Evaluate each logarithm. key: () means that number is the base.. thanks please do these.. i had like 50 to do and these are the most confusin one and i just cant figure out.. thanks log(5)125 log(1/2)1/4 log(3)729 log(9)1/3 log(1/4)16 log(8)1/256 1 solutions Answer 141445 by jim_thompson5910(28476)   on 2009-03-27 18:19:05 (Show Source): You can put this solution on YOUR website! I'll do the first three to get you started I'm using the identities: and # 1 So -------------------------------------------------------- # 2 So -------------------------------------------------------- # 3 So

Radicals/188648: . Rationalize the denominator: 2____ √[6] – √[5] It came out fuzzy I will retype it 2/sqrt[6]-[5] . Simplify the rational expression: x2 – 3x – 10 find the gcf of the polynomial x2 – x – 20 . Simplify: √[144x10y12z18] 1 solutions Answer 141444 by jim_thompson5910(28476)   on 2009-03-27 18:05:46 (Show Source): You can put this solution on YOUR website! # 1 Start with the given expression. Multiply both the numerator and denominator by (the conjugate of the denominator). This will rationalize the denominator FOIL Square each term. Subtract Reduce Distribute So # 2 Start with the given expression. Factor to get . Factor to get . Highlight the common terms. Cancel out the common terms. Note: the GCF is and is canceled out. Simplify. So simplifies to . In other words, where or # 3 Start with the given expression. Factor into 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 . Take the square root of to get . Rearrange and multiply the terms. ================================================== Answer: So simplifies to In other words, where every variable is non-negative.

Complex_Numbers/188637: True or False.... 1 + 3/(2 − i) = 5 - i Can you provide a detailed explanation of how you found the solution? 1 solutions Answer 141442 by jim_thompson5910(28476)   on 2009-03-27 17:21:03 (Show Source): You can put this solution on YOUR website! Start with the left side of the given equation. Multiply the fraction by (this is to make the denominator a real number) FOIL Plug in Rewrite the denominator Add Distribute Multiply the first term 1 by Combine the fractions Combine like terms. Break up the fraction Since and , this means that So consequently So the statement is false.

Rational-functions/188590: Simplify. State any restrictions on the variable[thanks for your wonderful help] x^2+x-6/x^2+3x 4x^2-25/2x^2+3x-20 1 solutions Answer 141417 by jim_thompson5910(28476)   on 2009-03-27 13:42:58 (Show Source): You can put this solution on YOUR website! Start with the given expression Factor the numerator Factor the denominator Cancel out the common terms. Simplify So where or (these are the restrictions). Note: These restrictions are made to avoid division by zero. ------------------------------------------------------------------------ Start with the given expression Factor the numerator Factor the denominator Cancel out the common terms. Simplify So where or (these are the restrictions). Note: These restrictions are made to avoid division by zero.

Polynomials-and-rational-expressions/188535: 24x^2-37-5 my teacher taugt us lIke multi:AC then subtract to get -37 0k so 24*5=120 then she said see what all goes into that number then when u found it see if it is the same is B which is -37.. i got -40+3 is -37 but when i put it all together 24x^2-40x+3x-5 4x(6x-10)+1(3x-5) and Its suppose to be the same i get lost can u help me im hopin u can understand wat im sayin thats the best way i can explain it 1 solutions Answer 141366 by jim_thompson5910(28476)   on 2009-03-26 22:52:08 (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 : 1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120 -1,-2,-3,-4,-5,-6,-8,-10,-12,-15,-20,-24,-30,-40,-60,-120 Note: list the negative of each factor. This will allow us to find all possible combinations. These factors pair up and multiply to . 1*(-120) 2*(-60) 3*(-40) 4*(-30) 5*(-24) 6*(-20) 8*(-15) 10*(-12) (-1)*(120) (-2)*(60) (-3)*(40) (-4)*(30) (-5)*(24) (-6)*(20) (-8)*(15) (-10)*(12) 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 -120 1+(-120)=-119 2 -60 2+(-60)=-58 3 -40 3+(-40)=-37 4 -30 4+(-30)=-26 5 -24 5+(-24)=-19 6 -20 6+(-20)=-14 8 -15 8+(-15)=-7 10 -12 10+(-12)=-2 -1 120 -1+120=119 -2 60 -2+60=58 -3 40 -3+40=37 -4 30 -4+30=26 -5 24 -5+24=19 -6 20 -6+20=14 -8 15 -8+15=7 -10 12 -10+12=2 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 . Note: you can check the answer by FOILing to get or by graphing the original expression and the answer (the two graphs should be identical).

Polynomials-and-rational-expressions/188463: Factor the polynomial completly: x^3y+2x^2y^2+xy^3 Factor the polinomial completly: 32x^2y-2y^3 Use grouping to factor the polynomial completly: x^3+x^2-x-1 Use grouping to factor the polynomial completly" y^3-5y^2+8y-40 1 solutions Answer 141354 by jim_thompson5910(28476)   on 2009-03-26 21:50:33 (Show Source): You can put this solution on YOUR website! I'll do the first two to get you started # 1 Start with the given expression Factor out the GCF Now let's focus on the inner expression ------------------------------------------------------------ Looking at we can see that the first term is and the last term is where the coefficients are 1 and 1 respectively. Now multiply the first coefficient 1 and the last coefficient 1 to get 1. Now what two numbers multiply to 1 and add to the middle coefficient 2? Let's list all of the factors of 1: Factors of 1: 1 -1 ...List the negative factors as well. This will allow us to find all possible combinations These factors pair up and multiply to 1 1*1 (-1)*(-1) note: remember two negative numbers multiplied together make a positive number Now which of these pairs add to 2? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 2 First Number Second Number Sum 1 1 1+1=2 -1 -1 -1+(-1)=-2 From this list we can see that 1 and 1 add up to 2 and multiply to 1 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 ) note: is equivalent to since the term occurs twice. So also factors to ------------------------------------------------------------ So our expression goes from and factors further to ------------------ Answer: So completely factors to # 2 Start with the given expression Factor out the GCF Rewrite as Factor to get (use the difference of squares) So completely factors to

Equations/188517: (5x+4)^2=100 1 solutions Answer 141352 by jim_thompson5910(28476)   on 2009-03-26 21:44:44 (Show Source): You can put this solution on YOUR website! Start with the given equation. 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 Subtract from both sides. or Combine like terms. or Divide both sides by to isolate . -------------------------------------- Answer: So the solutions are or .

Exponents-negative-and-fractional/188525: Simplify expression showing work (25y^2)^1/2 (fraction 1/2) 1 solutions Answer 141350 by jim_thompson5910(28476)   on 2009-03-26 21:43:08 (Show Source): You can put this solution on YOUR website! Start with the given expression. Convert to radical notation. Break up the square root using the identity . Take the square root of to get . Take the square root of to get . ================================================== Answer: So simplifies to In other words, where

test/188526: Find the Vertex I did the problem but I still dont really get how to do this that much and I dont know if this is right either. y = x2+6x+8 a=1 b=6 x= b = 6 = -6 = -3 _ _____ _ _____ ____ 2a 2(1) 2 y = x2+6x+8 = 1(-3)2+6(-3)+8 = 9-18+8 = 1 Vertex= (-3 ,1 ) 1 solutions Answer 141349 by jim_thompson5910(28476)   on 2009-03-26 21:40:31 (Show Source): You can put this solution on YOUR website! 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 . Divide. 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. Note: 9-18=-9 and -9+8=-1 So the y-coordinate of the vertex is . So the vertex is . So you were off by a sign.

Square-cubic-other-roots/188434: simplify the square root of 144+25 1 solutions Answer 141302 by jim_thompson5910(28476)   on 2009-03-26 17:47:28 (Show Source): You can put this solution on YOUR website! Is it ??? If so, then OR... Is it ??? If so, then

Expressions-with-variables/188342: This question is from textbook n- 2/3= 3/4 1 solutions Answer 141203 by jim_thompson5910(28476)   on 2009-03-25 22:00:20 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply EVERY term by the LCD to clear any fractions. Multiply and simplify. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . ---------------------------------------------------------------------- Answer: So the answer is which approximates to .

Systems-of-equations/188362: Hi need help please in solving all values of x and y and can you please show me each step this is another one 1. x^2 - 3y^2 = 13 x - 2y = 1 1 solutions Answer 141202 by jim_thompson5910(28476)   on 2009-03-25 21:58:35 (Show Source): You can put this solution on YOUR website! Start with the second equation. Add 2y to both sides to isolate "x". ----------------- Move onto the first equation Plug in FOIL Subtract 13 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 y 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 answers for "y" are or Now simply plug each solution of "y" into to find "x" Plug in So one set of solutions is and giving us the ordered pair (or point of intersection) (5,2) ------------------- Plug in This means that another set of solutions is and giving us the ordered pair (or point of intersection) (-11,-6) Here's a graph to visually confirm the answer: Graph of (red) and (blue) with the intersection points (-11,-6) and (5,2) (black points)

Trigonometry-basics/188358: I need help solving the following question. 1. Solve the equation: tan3x=1 1 solutions Answer 141199 by jim_thompson5910(28476)   on 2009-03-25 21:49:23 (Show Source): You can put this solution on YOUR website! Start with the given equation. Take the arctangent of both sides (to eliminate the tangent on the left side) Evaluate the arctangent of 1 to get (use the unit circle). Remember to add (to account for all of the solutions). Note: is an integer Divide both sides by 3. Break up the fraction and simplify So the solutions are where "n" is an integer.

Systems-of-equations/188361: Hi need help please in solving all values of x and y and can you please show me each step 1. 5x + 2y =16 3x - 5y =-9 1 solutions Answer 141198 by jim_thompson5910(28476)   on 2009-03-25 21:44:00 (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 5. Distribute and multiply. Multiply the both sides of the second 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-equations/188360: Linear Equations: I need help on how to undersatnd this because i don't get non of this. The tuter thing i just saw didn't help me at all. I'm only 14 years old. 1 solutions Answer 141197 by jim_thompson5910(28476)   on 2009-03-25 21:42:56 (Show Source): You can put this solution on YOUR website! Please post a problem so we can walk you through it. Thanks.

Inverses/188359: Pre-Algebra- I think..not sure. This problem is from Contemporary's Number Power Algebra 3 by Robert Mitchell TERMS ON BOTH SIDES OF AN EQUATION: and *** this one I tried, but kept getting the wrong answer etc.. here is the problem*** Any help would be greatly appreciated, as I am studying for a test in Pre-algebra/algebra, and need to attain a score of 55+ in Pre-algebra, and a score of 30+ in algebra. This test is on Saturday, (28th March), and I have been studying, religiously, but then..somewhere along the way, I become hopelessly lost, and end up with answerrs that are so-far out in left field, that I am not even sure I am in the same class etc....I should mention, that I am a returning adult...and not fresh out of High-School. My last algebra class was twenty-five+ years ago etc..... Thank-you for your time, and any helpful suggestions..other than do not enter school would be greatly appreciated!!!! (the above joke was a lame attempt at keeping/finding humour in this stressful aspiration!!!) Thanx~ John 1 solutions Answer 141196 by jim_thompson5910(28476)   on 2009-03-25 21:42:03 (Show Source): You can put this solution on YOUR website! 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 . ---------------------------------------------------------------------- Answer: So the answer is which in decimal form is . # 2 Is the equation ??? Start with the given equation. Multiply EVERY term by the LCD to clear the fractions. Multiply and simplify. 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 answer is

Radicals/188343: Which expression is equivalent to 7(radical)90 a)16(radical)10 b)21(radical)10 c)70(radical)9 d)(radical)630 please tell me who you got this . 1 solutions Answer 141184 by jim_thompson5910(28476)   on 2009-03-25 20:03:45 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor into Break up the square root. Take the square root of 9 to get 3 Multiply So

Polynomials-and-rational-expressions/188334: Please help solve the following equation: 600 = 0.9x^ - 26.5x + 290 Thanks. 1 solutions Answer 141177 by jim_thompson5910(28476)   on 2009-03-25 19:06:38 (Show Source): You can put this solution on YOUR website! I'm assuming that the equation should be Start with the given equation. Multiply EVERY term by 10 to make every number a whole number Subtract 6000 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 . Simplify the square root or Break up the expression. So the answers are or which approximate to or

Trigonometry-basics/188286: If a person bends at the waist with a straight back making an abgle of theta degrees with the horizontal, the the force F exerted on the back muscles can be modeled by the equation... F = .6Wsin(theta + 90degrees)/ sin 12 where W is the weight of the person. Use an identity to show that F is approximately equal to 2.9W cos theta. I had no clue how to do this one. 1 solutions Answer 141175 by jim_thompson5910(28476)   on 2009-03-25 18:56:38 (Show Source): You can put this solution on YOUR website! One of the many trig identities is ... Start with the given equation. ... Use the identity given above ... Evaluate the cosine of 90 degrees to get 0. Evaluate the sine of 90 degrees to get 1. ... Multiply ... Simplify ... Evaluate the sine of 12 degrees to get approximately 0.2079 ... Divide to get roughly 2.8858 ... Round to the nearest tenth

Equations/188275: Multiply and write in simplest form 4 1/5 x 10/21 x 9/20? I have no clue on where to begin. Thank you. Michelle 1 solutions Answer 141174 by jim_thompson5910(28476)   on 2009-03-25 18:47:16 (Show Source): You can put this solution on YOUR website! In order to multiply fractions, they must either be normal fractions like or or they must be improper fractions. So we must convert into an improper fraction Remember, where "a" is the whole part of the fraction, "b" is the numerator, and "c" is the denominator. So this means that In short which means that the mixed fraction 4 and one fifth is the same as the improper fraction -------------------------- ... Start with the given expression. ... Replace with ... Factor 20 into ... Cancel out the common terms. ... Simplify ... Multiply ... Combine the fractions. ... Multiply So

test/188326: Ineed help solving the following binomial expression: 4x^2+12x+9 1 solutions Answer 141169 by jim_thompson5910(28476)   on 2009-03-25 18:24:08 (Show Source): You can put this solution on YOUR website! I'm assuming that you want to factor this right? Note: is NOT a binomial, it is a trinomial. 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 2*18 3*12 4*9 6*6 (-1)*(-36) (-2)*(-18) (-3)*(-12) (-4)*(-9) (-6)*(-6) 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=37 2 18 2+18=20 3 12 3+12=15 4 9 4+9=13 6 6 6+6=12 -1 -36 -1+(-36)=-37 -2 -18 -2+(-18)=-20 -3 -12 -3+(-12)=-15 -4 -9 -4+(-9)=-13 -6 -6 -6+(-6)=-12 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 Condense the terms. --------------------------------------------- Answer: So factors to . Note: you can check the answer by FOILing to get or by graphing the original expression and the answer (the two graphs should be identical).

Numbers_Word_Problems/188302: The product of two consecutive numbers is 72. Find the smaller of the numbers 1 solutions Answer 141168 by jim_thompson5910(28476)   on 2009-03-25 18:19:07 (Show Source): You can put this solution on YOUR website! I'm assuming that you want the numbers to be positive. "The product of two consecutive numbers is 72" translates to Start with the given equation. Distribute Subtract 72 from both sides. 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 . Take the square root of to get . or Break up the expression. or Combine like terms. or Simplify. So the answers are or However, we only want the positive numbers. So the only answer is This means that the smaller number is 8.

Polynomials-and-rational-expressions/188277: Perform the indicated operations (4x-3)-(7x-2)+(-5x+8) 1 solutions Answer 141167 by jim_thompson5910(28476)   on 2009-03-25 18:15:56 (Show Source): You can put this solution on YOUR website! Start with the given expression. Distribute Rearrange and group like terms. Combine like terms. So

Polynomials-and-rational-expressions/188278: Perform the indicated operations (4x-3)-(7x-2)+(-5x+8) 1 solutions Answer 141166 by jim_thompson5910(28476)   on 2009-03-25 18:15:32 (Show Source): You can put this solution on YOUR website! Start with the given expression. Distribute Rearrange and group like terms. Combine like terms. So

Polynomials-and-rational-expressions/188281: perform the indication operation (4x-3)-(7x-2)+(-5x+8) 1 solutions Answer 141165 by jim_thompson5910(28476)   on 2009-03-25 18:14:36 (Show Source): You can put this solution on YOUR website! Start with the given expression. Distribute Rearrange and group like terms. Combine like terms. So