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 Equations/178327: -1/6(x-12)+1/2(x+2)=x+151 solutions Answer 133280 by jim_thompson5910(28504)   on 2009-01-24 18:37:06 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply every term (that's not in a set of parenthesis) by the LCD 12 to clear the fractions. Distribute. Combine like terms on the left side. 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 answer is
 Equations/178310: 11/x+2=5/x1 solutions Answer 133260 by jim_thompson5910(28504)   on 2009-01-24 17:29:16 (Show Source): You can put this solution on YOUR website!Is the equation ??? Start with the given equation. Cross multiply Distribute. Subtract from both sides. Combine like terms on the left side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the answer is which approximates to . ============================= Or.... Is the equation ??? Start with the given equation. Multiply every term by the LCD "x" to clear the fractions. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the answer is
 absolute-value/178311: This question is from textbook Find the value of s if the perimeter of the square is 36 inches. (s+4)1 solutions Answer 133259 by jim_thompson5910(28504)   on 2009-01-24 17:26:10 (Show Source): You can put this solution on YOUR website! Start with the perimeter of a square formula Plug in Divide both sides by 4 to isolate "s" Reduce So the side length of the square is
 Polynomials-and-rational-expressions/178309: "Area of a painting. A rectangular painting with a width of x centimeters has an area of x2 + 50x square centimeters.Find a binomial that represents the length. See the accompanying figure." 1 solutions Answer 133258 by jim_thompson5910(28504)   on 2009-01-24 17:15:16 (Show Source): You can put this solution on YOUR website! Start with the area of a rectangle formula Plug in and Factor out the GCF "x" Divide both sides by "x" to isolate "L". Notice how the "x" terms cancel. Simplify ----------------------------------------------- Answer: So the length is
 Linear-systems/178302: This is actually solve by elimination problem. 7r - 6s = 22 6r +7s = 31 (this is what I have (32/85,?/85) can you file in the blank for me please? Thank you for your help!1 solutions Answer 133257 by jim_thompson5910(28504)   on 2009-01-24 16:59:18 (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 7. Distribute and multiply. Multiply the both sides of the second equation by 6. 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. --------------------------------------------- Answer: So the solutions are and which form the ordered pair This means that the system is consistent and independent.
 Equations/178305: 6-4x=7x-9x-41 solutions Answer 133255 by jim_thompson5910(28504)   on 2009-01-24 16:57:06 (Show Source): You can put this solution on YOUR website! Start with the given equation. Combine like terms on the right side. 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 answer is
 Equations/178301: 6x=5x-51 solutions Answer 133254 by jim_thompson5910(28504)   on 2009-01-24 16:56:22 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Combine like terms on the left side. ---------------------------------------------------------------------- Answer: So the answer is
 Inequalities/178299: 1/4(8y+4)-34<-1/3(9y-6)1 solutions Answer 133253 by jim_thompson5910(28504)   on 2009-01-24 16:55:53 (Show Source): You can put this solution on YOUR website! Start with the given inequality Multiply EVERY term (that's not in a set of parenthesis) by the LCD 12 to clear the fractions. Distribute. Combine like terms on the left side. Add to 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 answer is So the answer in interval notation is Also, the answer in set-builder notation is Here's the graph of the solution set on the number line:
 Linear-systems/178292: 5x + 2y = -36 x = 6 - 7y1 solutions Answer 133252 by jim_thompson5910(28504)   on 2009-01-24 16:53:23 (Show Source): You can put this solution on YOUR website! Start with the first equation. Plug in . In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown. Distribute Combine like terms on the left side Subtract 30 from both sides Combine like terms on the right side Divide both sides by -33 to isolate y Divide Now that we know that , we can plug this into to find Move onto the second equation. Plug in Multiply Combine like terms. So our answer is and which form the ordered pair Notice if we graph the two equations, we can see that their intersection is at . So this verifies our answer. Graph of (red) and (green)
 Functions/178298: d=1/2 mq m=1 solutions Answer 133251 by jim_thompson5910(28504)   on 2009-01-24 16:47:54 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply both sides by 2. Divide both sides by "q" to isolate "m". So the solution is
 Inequalities/178293: x>1 1 solutions Answer 133249 by jim_thompson5910(28504)   on 2009-01-24 16:46:39 (Show Source): You can put this solution on YOUR website!Do you want the interval and set-builder notation? Interval notation: Set-builder notation:
 Quadratic_Equations/178294: A rectangular patio is 7 feet longer than it is wide. Determine the dimensions of the patio if it measures 13 feet diagonally.1 solutions Answer 133248 by jim_thompson5910(28504)   on 2009-01-24 16:45:37 (Show Source): You can put this solution on YOUR website!Length: and Width: Start with Pythagorean's Theorem Plug in , , and Square 13 to get 169 FOIL Subtract 169 from both sides. Combine like terms. Factor or Set each factor equal to zero (we'll ignore this one) or Solve for "x" So the width of the patio is 5 ft. This makes the length 12 ft (add 7 to the width)
 Expressions-with-variables/178295: 5/2x + 1/4x = 9/4 + x ( this one I just gave up on, could not for the life of me even come close to the right answer) Please help. Thank you!1 solutions Answer 133247 by jim_thompson5910(28504)   on 2009-01-24 16:44:34 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply both sides by the LCD to clear any fractions. Distribute and multiply. Combine like terms on the left side. Subtract from both sides. Combine like terms on the left side. Divide both sides by to isolate . ---------------------------------------------------------------------- Answer: So the answer is which approximates to .
 Equations/178296: -(6y+2)-(-5y-5)=-51 solutions Answer 133246 by jim_thompson5910(28504)   on 2009-01-24 16:43:45 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Combine like terms on the left side. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the answer is
 Quadratic_Equations/178284: A photo is 4 inches longer than it is wide. A 3 inch border is placed around the photo making the total area of the photo and border 165 inches. What are the dimensions of the photo? 1 solutions Answer 133244 by jim_thompson5910(28504)   on 2009-01-24 16:02:28 (Show Source): You can put this solution on YOUR website!Length of photo+frame: Width of photo+frame: Area of photo+frame: Start with the given equation. Plug in FOIL Subtract 165 from both sides. Factor or Set each factor equal to zero (we'll toss this solution) or Solve for "x" So the width of the photo is 5 inches which means that the length of the photo is 9 inches (just add 4 to the width).
 Quadratic_Equations/178286: Three consecutive even integers are such that the square of the third is 100 more than the square of the second. Find the three integers.1 solutions Answer 133243 by jim_thompson5910(28504)   on 2009-01-24 16:01:12 (Show Source): You can put this solution on YOUR website! Consecutive even integers are of the form , , , etc... So the word problem translates to Start with the given equation. FOIL Get all terms to the left side. Combine like terms. Add to both sides. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the answer is which means that the numbers are So the numbers are 22, 24, and 26
 logarithm/178281: This question is from textbook college algebras Thanks in advance for your help evaluating this expression log(3) 243 1 solutions Answer 133238 by jim_thompson5910(28504)   on 2009-01-24 15:01:26 (Show Source): You can put this solution on YOUR website! Start with the given logarithm. Rewrite 243 as . Note: . The key here is the base is 3 and the base of the log is 3 Rewrite the expression using the identity Evaluate the log base 3 of 3 to get 1. Note: where Multiply So
 Triangles/178260: This question is from textbook Geometry Two vertical poles have heights 6ft and 12ft. A rope is stretched from the top of each pole to the bottom of the other. How far above the ground do the ropes cross? Please spell out steps!1 solutions Answer 133237 by jim_thompson5910(28504)   on 2009-01-24 14:56:56 (Show Source): You can put this solution on YOUR website!If we draw a picture, we get Now let the horizontal distance from the poles be the value "a" (this variable is needed, but as you will soon see, it does not change the final answer). Also, label the top and bottom of both poles with coordinates (draw some coordinate axis if necessary) So to find the height of the point where the ropes cross, we first need to find the equations of the lines (the red and blue lines) Equation of the first line from (0,12) to (a,0) (red line) Slope: So the slope of the red line is Start with the slope-intercept general equation Plug in , and (since the red line goes through the point (0,12)) Multiply Simplify So the first equation (the equation of the red line) is ----------------------------------------------------------- Equation of the second line from (0,0) to (a,6) (blue line) Slope: So the slope of the blue line is Start with the slope-intercept general equation Plug in , and (since the blue line goes through the point (0,0)) Multiply Simplify So the second equation (the equation of the blue line) is ----------------------------------------------------------- Now equate the two equations and Multiply EVERY term by the LCD "a" to clear the fractions. Add 12x to both sides. Combine like terms. Divide both sides by 18 to isolate "a". Reduce. Note: this tells us that no matter what the value of "a" is, the crossing point will ALWAYS be of the horizontal length Go back to the second equation Plug in Multiply Reduce So the point of intersection of the red and blue lines is for any value of "a" Since the y-coordinate is 4, this means that the height of the crossing point is 4 ft. ================================================== Answer: So the ropes cross 4 ft above the ground regardless of the horizontal distance between the two poles.
 Inequalities/178273: Translate to an inequality. The average speed, s, was between 90 and 120 mph. Translateion 90 _____ s _______ 1201 solutions Answer 133236 by jim_thompson5910(28504)   on 2009-01-24 14:28:23 (Show Source): You can put this solution on YOUR website!Since the "average speed, s, was between 90 and 120 mph.", this means that the average speed was faster than (or the same speed as) 90 mph AND was slower than (or the same speed as) 120 mph. Mathematically, this means that the average speed "s" is both greater than or equal to 90 mph AND less than or equal to 120 mph So the inequality is
 Polynomials-and-rational-expressions/178262: This question is from textbook Algebra and Trigonometry Structure and Method book 2 I have been struggling to figure out this math problem and I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!! Binomials Containing Radicals Simplify. Assume that each radical represents a real number. (√w)/(√w+1)+(√w)/(√w-1) 1 solutions Answer 133235 by jim_thompson5910(28504)   on 2009-01-24 14:25:17 (Show Source): You can put this solution on YOUR website! Start with the given expression. Take note that the LCD is Multiply the first fraction by to get the denominator equal to the LCD Combine and multiply the fractions Multiply the second fraction by to get the denominator equal to the LCD Combine and multiply the fractions Distribute Multiply Square to get "w" Combine the fractions (this is possible since the denominators are equal) Combine like terms. FOIL the denominator (use the difference of squares formula) Square to get "w". Square 1 to get 1 ============================================================== Answer: So where
 Inequalities/178191: -9-3m-m<9m-91 solutions Answer 133234 by jim_thompson5910(28504)   on 2009-01-24 14:14:09 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Combine like terms on the left side. 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 . note: Remember, the inequality sign flips when we divide both sides by a negative number. Reduce. ---------------------------------------------------------------------- Answer: So the answer is So the answer in interval notation is Also, the answer in set-builder notation is Here's the graph of the solution set on the number line: Graph of the solution set where there is an open circle at the endpoint
 Polynomials-and-rational-expressions/178266: This question is from textbook Algebra and Trigonometry Structure and Method book 2 I have been struggling to figure out this math problem and I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!! Binomials Containing Radicals Simplify. Assume that each radical represents a real number. (√(a-√a) *√(a+√a) )/( √(a-1)) 1 solutions Answer 133233 by jim_thompson5910(28504)   on 2009-01-24 14:08:16 (Show Source): You can put this solution on YOUR website!First, let's simplify the numerator Let Start with the given expression. Plug in Combine the roots using the identity FOIL Plug in Square to get "a" Factor out the GCF "a" Break up the square root using the identity (this just the reverse of the previous identity) So the numerator simplifies to ------------------------------------------------ Now let's go back to the main problem: So the expression simplifies to (see steps above) Highlight the common terms. Cancel out the common terms. Simplify ========================================================== Answer: So where
 Equations/178264: 7r+1=7s solve for r1 solutions Answer 133227 by jim_thompson5910(28504)   on 2009-01-24 13:54:31 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Divide both sides by to isolate . ---------------------------------------------------------------------- Answer: So the answer is
 Polynomials-and-rational-expressions/178268: This question is from textbook Algebra and Trigonometry Structure and Method book 2 I have been struggling to figure out this math problem and I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!! Binomials Containing Radicals Simplify. Assume that each radical represents a real number. (√(n+1) +√n)( √(n+1) -√n)1 solutions Answer 133226 by jim_thompson5910(28504)   on 2009-01-24 13:53:19 (Show Source): You can put this solution on YOUR website!When trying to simplify or expand complicated expressions involving roots, you can try substitutions to get the expression into a cleaner form (it's not required, but I find that it helps you see the big picture). So if we let and , we can simplify to get (note: I just replaced every with "x" and every with "y") --------------------------------------------------- Now let's FOIL 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:. --------------------------------------------------- Now collect every term to make a single expression. Now combine like terms. So FOILs to . In other words, . --------------------------------------------------------- Start with the last equation Plug in (ie replace every "x" with ) Plug in (ie replace every "y" with ) Simplify Square to get (note: the square undoes the square root) Square to get (note: the square undoes the square root) Combine like terms. ===================================================================== Answer: So
 Equations/178265: (y-9)-(y+8)=10y1 solutions Answer 133224 by jim_thompson5910(28504)   on 2009-01-24 13:42:43 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Combine like terms on the left side. Divide both sides by to isolate . ---------------------------------------------------------------------- Answer: So the answer is which in decimal form is .
 Radicals/178229: Simplify 3 (^3√81a^3b^4) - 2a (^3√24b^4) 1 solutions Answer 133219 by jim_thompson5910(28504)   on 2009-01-24 12:54:51 (Show Source): You can put this solution on YOUR website! Start with the given expression. Simplify the first cube root. Note: let me know if you need help simplifying cube roots. Multiply Simplify the second cube root. Multiply Factor out the GCF Combine like terms. Rearrange the terms. ================================================== Answer: So
 Radicals/178163: ^3√16x^4y^3 times ^3√12x^2y^41 solutions Answer 133117 by jim_thompson5910(28504)   on 2009-01-23 16:09:40 (Show Source): You can put this solution on YOUR website! Start with the given expression Combine the radicals Multiply Factor each term where at least one term is a perfect cube. Break up the cube root. Take the cube root of 64 to get 4. Take the cube root of to get "x". Take the cube root of to get "y". Rearrange the terms and multiply. ============================================ Answer: So
 Expressions-with-variables/178160: 44) x/(x^2 – 2x – 3) - 3x/(x^2 – 9) ......please i'm desperate and can you please show the steps, so i can see how u got the answer. Perform the operations or solve if it is an equation (= sign) 1 solutions Answer 133113 by jim_thompson5910(28504)   on 2009-01-23 16:02:44 (Show Source): You can put this solution on YOUR website! Start with the given expression Factor the first denominator Factor the second denominator Take note that the LCD is (the LCD is comprised of the unique factors of both denominators). So the goal is to get EVERY denominator equal to the LCD Multiply both the numerator and denominator of the first fraction by to get the denominator equal to the LCD Distribute Multiply both the numerator and denominator of the second fraction by to get the denominator equal to the LCD Distribute Now that EVERY denominator is equal to the LCD, we can subtract the fractions: Combine the fractions by subtracting the numerators over the common denominator. Distribute Combine like terms. Multiply the terms out in the denominator (this step is optional) ==================================================== Answer: So where , , or Or.. where , , or Note: both answers are the same, but the second one is if you decided to expand the denominator
 Equations/178143: I=Prt solve for t (can you explain step for step please)1 solutions Answer 133087 by jim_thompson5910(28504)   on 2009-01-23 13:07:45 (Show Source): You can put this solution on YOUR website! Start with the given equation Divide both sides by "P" Divide both sides by "r" Multiply the first fraction by the reciprocal of Multiply the fractions. ====================================== Answer: So the solution is
 Numbers_Word_Problems/178145: a+b+c=P solve for c (can you explain step by step please)1 solutions Answer 133084 by jim_thompson5910(28504)   on 2009-01-23 13:05:15 (Show Source): You can put this solution on YOUR website! Start with the given equation Subtract "a" from both sides Subtract "b" from both sides So the answer is