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Inequalities/119513: how would you solve this -3 > 7y-3 > -24 1 solutions Answer 87565 by jim_thompson5910(28598)   on 2008-01-10 15:39:30 (Show Source): You can put this solution on YOUR website! Start with the given compound inequality Reverse the compound inequality by switching the outer sides and reversing the inequality signs Add 3 to all sides Divide every side by 7 to isolate y. So the solution in interval notation is: (-3,0) Now let's graph the solution set Note: at there is a open circle (which means this point is excluded) and at there is a open circle (which means this point is excluded)

expressions/119518: I really need help with these questions. Evaluate each function for x= -2,0,and 5. 1.) y = 9 + x 2.) y = x^2 - 1 Please help me because I need to get this to my teacher tommorrow. 1 solutions Answer 87562 by jim_thompson5910(28598)   on 2008-01-10 15:34:29 (Show Source): You can put this solution on YOUR website! #1 Let's evaluate Start with the given function. Plug in . In other words, replace each x with -2. Multiply 1 and -2 to get -2 Now combine like terms -----------Now let's evaluate another value--------- Let's evaluate Start with the given function. Plug in . In other words, replace each x with 0. Multiply 1 and 0 to get 0 Now combine like terms -----------Now let's evaluate another value--------- Let's evaluate Start with the given function. Plug in . In other words, replace each x with 5. Multiply 1 and 5 to get 5 Now combine like terms #2 Let's evaluate Start with the given function. Plug in . In other words, replace each x with -2. Evaluate to get 4. Now combine like terms -----------Now let's evaluate another value--------- Let's evaluate Start with the given function. Plug in . In other words, replace each x with 0. Evaluate to get 0. Now combine like terms -----------Now let's evaluate another value--------- Let's evaluate Start with the given function. Plug in . In other words, replace each x with 5. Evaluate to get 25. Now combine like terms

Linear-equations/119501: Find the slope and y-intercept. -4x + 5y = 25 1 solutions Answer 87549 by jim_thompson5910(28598)   on 2008-01-10 13:17:02 (Show Source): You can put this solution on YOUR website! Solved by pluggable solver: Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa) Start with the given equation Add to both sides Multiply both sides by Distribute Multiply Rearrange the terms Reduce any fractions So the equation is now in slope-intercept form () where (the slope) and (the y-intercept)

Radicals/119510: Find the distance between each pair of points. 1. (0,8)and(0,-4) 2. (2,6)and(-3,4) I'm lost on where to start on this type of problem. 1 solutions Answer 87548 by jim_thompson5910(28598)   on 2008-01-10 13:15:12 (Show Source): You can put this solution on YOUR website! #1 Start with the given distance formula where is the first point and is the second point Plug in , , , Evaluate to get 0. Evaluate to get 12. Square each value Add Simplify the square root (note: If you need help with simplifying the square root, check out this solver) So the distance between (0,8) and (0,-4) is 12 units #2 Start with the given distance formula where is the first point and is the second point Plug in , , , Evaluate to get 5. Evaluate to get 2. Square each value Add So the distance approximates to which rounds to 5.39 So the distance between (2,6) and (-3,4) is approximately 5.39 units

Quadratic_Equations/119461: This question is from textbook Trigonometry Solve the equation by extracting square roots - list both the exact solution and the decimal solution rounded to two decimal places. (x+13)^2 = 25 1 solutions Answer 87506 by jim_thompson5910(28598)   on 2008-01-10 00:36:18 (Show Source): You can put this solution on YOUR website! Start with the given equation Take the square root of both sides Simplify the square root (note: If you need help with simplifying the square root, check out this solver) Subtract 13 from both sides to isolate x. Break down the expression into two parts: or Now combine like terms for each expression: or ----------------------------------- Answer: So our solution is or Notice when we graph the equations and we get: graph of (red) and (green) Here we can see that the two equations intersect at x values of and , so this verifies our answer.

Quadratic_Equations/119411: Use the quadratic formula to solve the equation. -2x^2+x+8=0 Solve the equation. x^2+18x+81=25 Simplify (square root of -175) using the imaginary number i. 1 solutions Answer 87480 by jim_thompson5910(28598)   on 2008-01-09 19:18:32 (Show Source): You can put this solution on YOUR website! #1 Let's use the quadratic formula to solve for x: Starting with the general quadratic the general solution using the quadratic equation is: So lets solve ( notice , , and ) Plug in a=-2, b=1, and c=8 Square 1 to get 1 Multiply to get Combine like terms in the radicand (everything under the square root) Simplify the square root (note: If you need help with simplifying the square root, check out this solver) Multiply 2 and -2 to get -4 So now the expression breaks down into two parts or Now break up the fraction or Simplify or So these expressions approximate to or So our solutions are: or Notice when we graph , we get: when we use the root finder feature on a calculator, we find that and .So this verifies our answer #2 Start with the given equation Subtract 25 from both sides Combine like terms Let's use the quadratic formula to solve for x: Starting with the general quadratic the general solution using the quadratic equation is: So lets solve ( notice , , and ) Plug in a=1, b=18, and c=56 Square 18 to get 324 Multiply to get Combine like terms in the radicand (everything under the square root) Simplify the square root (note: If you need help with simplifying the square root, check out this solver) Multiply 2 and 1 to get 2 So now the expression breaks down into two parts or Lets look at the first part: Add the terms in the numerator Divide So one answer is Now lets look at the second part: Subtract the terms in the numerator Divide So another answer is So our solutions are: or Notice when we graph , we get: and we can see that the roots are and . This verifies our answer Solved by pluggable solver: Simplifying Square Roots (whole numbers only) Start with the given expression Factor out a negative 1 Break up the square roots using the identity Replace with (remember ) Now lets simplify : The goal of simplifying expressions with square roots is to factor the radicand into a product of two numbers. One of these two numbers must be a perfect square. When you take the square root of this perfect square, you will get a rational number. So let's list the factors of 175 Factors: 1, 5, 7, 25, 35, 175 Notice how 25 is the largest perfect square, so lets factor 175 into 25*7 Factor 175 into 25*7 Break up the square roots using the identity Take the square root of the perfect square 25 to get 5 So the expression simplifies to --------------------- Answer: So the expression simplifies to (just reintroduce back in)

Rational-functions/119412: Use the quadratic formula to solve the equation. -2x^2+x+8=0 Solve the equation. x^2+18x+81=25 Simplify (square root of -175) using the imaginary number i. 1 solutions Answer 87479 by jim_thompson5910(28598)   on 2008-01-09 19:17:33 (Show Source): You can put this solution on YOUR website! #1 Let's use the quadratic formula to solve for x: Starting with the general quadratic the general solution using the quadratic equation is: So lets solve ( notice , , and ) Plug in a=-2, b=1, and c=8 Square 1 to get 1 Multiply to get Combine like terms in the radicand (everything under the square root) Simplify the square root (note: If you need help with simplifying the square root, check out this solver) Multiply 2 and -2 to get -4 So now the expression breaks down into two parts or Now break up the fraction or Simplify or So these expressions approximate to or So our solutions are: or Notice when we graph , we get: when we use the root finder feature on a calculator, we find that and .So this verifies our answer #2 Start with the given equation Subtract 25 from both sides Combine like terms Let's use the quadratic formula to solve for x: Starting with the general quadratic the general solution using the quadratic equation is: So lets solve ( notice , , and ) Plug in a=1, b=18, and c=56 Square 18 to get 324 Multiply to get Combine like terms in the radicand (everything under the square root) Simplify the square root (note: If you need help with simplifying the square root, check out this solver) Multiply 2 and 1 to get 2 So now the expression breaks down into two parts or Lets look at the first part: Add the terms in the numerator Divide So one answer is Now lets look at the second part: Subtract the terms in the numerator Divide So another answer is So our solutions are: or Notice when we graph , we get: and we can see that the roots are and . This verifies our answer Solved by pluggable solver: Simplifying Square Roots (whole numbers only) Start with the given expression Factor out a negative 1 Break up the square roots using the identity Replace with (remember ) Now lets simplify : The goal of simplifying expressions with square roots is to factor the radicand into a product of two numbers. One of these two numbers must be a perfect square. When you take the square root of this perfect square, you will get a rational number. So let's list the factors of 175 Factors: 1, 5, 7, 25, 35, 175 Notice how 25 is the largest perfect square, so lets factor 175 into 25*7 Factor 175 into 25*7 Break up the square roots using the identity Take the square root of the perfect square 25 to get 5 So the expression simplifies to --------------------- Answer: So the expression simplifies to (just reintroduce back in)

Polynomials-and-rational-expressions/119393: FACTOR EACH EXPRESSION: 40- 5T CUBED 1 solutions Answer 87473 by jim_thompson5910(28598)   on 2008-01-09 18:32:08 (Show Source): You can put this solution on YOUR website! Start with the given expression Factor out the GCF Now let's focus on the inner expression Start with the inner expression. Rewrite as . Rewrite as . Now factor by using the difference of cubes formula. Remember the difference of cubes formula is Multiply So factors to . Now reintroduce the GCF So factors to

Polynomials-and-rational-expressions/119396: factor each expression: 4t^5-32T^2 1 solutions Answer 87472 by jim_thompson5910(28598)   on 2008-01-09 18:28:35 (Show Source): You can put this solution on YOUR website! Start with the given expression Factor out the GCF Now let's focus on the inner expression Start with the inner expression. Rewrite as . Rewrite as . Now factor by using the difference of cubes formula. Remember the difference of cubes formula is Multiply So factors to . Now reintroduce the GCF So factors to

Polynomials-and-rational-expressions/119394: factor compeletly: 2x cubed + x squared - 72x -36 1 solutions Answer 87470 by jim_thompson5910(28598)   on 2008-01-09 18:25:17 (Show Source): You can put this solution on YOUR website! Start with the given expression Group like terms Factor out the GCF out of the first group. Factor out the GCF out of the second group Since we have the common term , we can combine like terms Factor by use of the difference of squares So factors to

Polynomials-and-rational-expressions/119397: factor each expression: x^3 + 64 1 solutions Answer 87469 by jim_thompson5910(28598)   on 2008-01-09 18:21:53 (Show Source): You can put this solution on YOUR website! Start with the given expression. Rewrite as . Rewrite as . Now factor by using the sum of cubes formula. Remember the sum of cubes formula is Multiply So factors to . In other words,

Polynomials-and-rational-expressions/119398: Factor Each expression: x^3 +x^2 -x -1 1 solutions Answer 87468 by jim_thompson5910(28598)   on 2008-01-09 18:21:11 (Show Source): You can put this solution on YOUR website! Start with the given expression Group like terms Factor out the GCF out of the first group. Factor out the GCF out of the second group Since we have the common term , we can combine like terms Now factor by using the difference of squares Multiply So factors to

Polynomials-and-rational-expressions/119400: factor each expression: 8x^3 + 4x^2 - 2X-1 1 solutions Answer 87467 by jim_thompson5910(28598)   on 2008-01-09 18:19:36 (Show Source): You can put this solution on YOUR website! Start with the given expression Group like terms Factor out the GCF out of the first group. Factor out the GCF out of the second group Since we have the common term , we can combine like terms So factors to

Polynomials-and-rational-expressions/119401: factor each expression: 8-m^6 1 solutions Answer 87466 by jim_thompson5910(28598)   on 2008-01-09 18:18:31 (Show Source): You can put this solution on YOUR website! Start with the given expression. Rewrite as . Rewrite as . Now factor by using the difference of cubes formula. Remember the difference of cubes formula is Multiply So factors to . In other words,

Polynomials-and-rational-expressions/119395: Factor Completely: 9x^9 -16x^7 + 9x^6 -16x^4 1 solutions Answer 87465 by jim_thompson5910(28598)   on 2008-01-09 18:17:38 (Show Source): You can put this solution on YOUR website! Start with the given expression Factor out the GCF Now let's focus on the inner expression Start with the inner expression Group like terms Factor out the GCF out of the first group. Factor out the GCF out of the second group Since we have the common term , we can combine like terms Now factor by using the sum of cubes to get and factor by using the difference of squares to get Reintroduce the GCF So factors to

Inequalities/119350: This question is from textbook Algebra and Trigonmertry structure and method graph the set of solution of each open sentence 1.)|2t+5|<7 2.)|w-5|>3 1 solutions Answer 87463 by jim_thompson5910(28598)   on 2008-01-09 18:11:54 (Show Source): You can put this solution on YOUR website! #1 Start with the given inequality Break up the absolute value (remember, if you have , then and ) and Break up the absolute value inequality using the given rule Combine the two inequalities to get a compound inequality Subtract 5 from all sides Divide all sides by 2 to isolate t ---------------------------------------------------- Answer: So our answer is which looks like this in interval notation if you wanted to graph the solution set, you would get Graph of the solution set in blue and the excluded values represented by open circles #2 Start with the given inequality Break up the absolute value (remember, if you have , then or ) or Break up the absolute value inequality using the given rule Now lets focus on the first inequality Start with the given inequality Add 5 to both sides Combine like terms on the right side Now lets focus on the second inequality Start with the given inequality Add 5 to both sides Combine like terms on the right side ---------------------------------------------------- Answer: So our answer is or which looks like this in interval notation if you wanted to graph the solution set, you would get Graph of the solution set in blue and the excluded values represented by open circles

Polynomials-and-rational-expressions/119390: FACTOR EACH EXPRESSION: 8z squared - 4z +10z -5 1 solutions Answer 87461 by jim_thompson5910(28598)   on 2008-01-09 18:08:05 (Show Source): You can put this solution on YOUR website! Start with the given expression Group like terms Factor out the GCF out of the first group. Factor out the GCF out of the second group Since we have the common term , we can combine like terms So factors to

Polynomials-and-rational-expressions/119389: Factor Each Expression: 3p cubed - 21 p squared-p+7 1 solutions Answer 87460 by jim_thompson5910(28598)   on 2008-01-09 18:06:49 (Show Source): You can put this solution on YOUR website! Start with the given expression Group like terms Factor out the GCF out of the first group. Factor out the GCF out of the second group Since we have the common term , we can combine like terms So factors to

Polynomials-and-rational-expressions/119323: x^5/y^3 / x^2/y^8 1 solutions Answer 87408 by jim_thompson5910(28598)   on 2008-01-09 14:06:16 (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 Combine the fractions Remember when you divide monomials, you subtract their corresponding exponents. For instance Simplify. -------------------------------------------- Answer: So simplifies to . In other words, .

Quadratic_Equations/119297: What is the standard form for y=1/2x^2+4x-3 ? 1 solutions Answer 87399 by jim_thompson5910(28598)   on 2008-01-09 13:22:27 (Show Source): You can put this solution on YOUR website! Solved by pluggable solver: Completing the Square to Get a Quadratic into Vertex Form Start with the given equation Add to both sides Factor out the leading coefficient Take half of the x coefficient to get (ie ). Now square to get (ie ) Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of does not change the equation Now factor to get Distribute Multiply Now add to both sides to isolate y Combine like terms Now the quadratic is in vertex form where , , and . Remember (h,k) is the vertex and "a" is the stretch/compression factor. Check: Notice if we graph the original equation we get: Graph of . Notice how the vertex is (,). Notice if we graph the final equation we get: Graph of . Notice how the vertex is also (,). So if these two equations were graphed on the same coordinate plane, one would overlap another perfectly. So this visually verifies our answer.

Polynomials-and-rational-expressions/119313: x-2 / 3 + 5x/2 = -3/5 1 solutions Answer 87397 by jim_thompson5910(28598)   on 2008-01-09 13:19:17 (Show Source): You can put this solution on YOUR website! Start with the given equation Multiply both sides by the LCM of 30. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver) Distribute and multiply the LCM to each side Combine like terms on the left side Add 20 to both sides Combine like terms on the right side Divide both sides by 105 to isolate x Reduce -------------------------------------------------------------- Answer: So our answer is (which is approximately in decimal form)

Equations/119317: 25=5/9(x+32) 1 solutions Answer 87396 by jim_thompson5910(28598)   on 2008-01-09 13:18:20 (Show Source): You can put this solution on YOUR website! Start with the given equation Multiply both sides by the LCM of 9. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver) Distribute and multiply the LCM to each side Distribute Subtract 225 from both sides Subtract 5x from both sides Combine like terms on the right side Divide both sides by -5 to isolate x Divide -------------------------------------------------------------- Answer: So our answer is

Equations/119318: 35=5/9(x+32) 1 solutions Answer 87395 by jim_thompson5910(28598)   on 2008-01-09 13:17:49 (Show Source): You can put this solution on YOUR website! Start with the given equation Multiply both sides by the LCM of 9. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver) Distribute and multiply the LCM to each side Distribute Subtract 315 from both sides Subtract 5x from both sides Combine like terms on the right side Divide both sides by -5 to isolate x Divide -------------------------------------------------------------- Answer: So our answer is

Expressions-with-variables/119253: This question is from textbook Algebra 1 4x -7 = 3x, I can't figure it out 1 solutions Answer 87352 by jim_thompson5910(28598)   on 2008-01-08 22:41:45 (Show Source): You can put this solution on YOUR website! Start with the given equation Add 7 to both sides Subtract 3x from both sides Combine like terms on the left side -------------------------------------------------------------- Answer: So our answer is

Quadratic_Equations/119248: This question is from textbook Intermediate Algebra y2 - 16 = 0 1 solutions Answer 87341 by jim_thompson5910(28598)   on 2008-01-08 21:55:25 (Show Source): You can put this solution on YOUR website! Start with the given equation Factor the left side (note: if you need help with factoring, check out this solver) Now set each factor equal to zero: or or Now solve for y in each case So our answer is or

Rational-functions/119220: Perform the indication functions. 14x-7/x^2+3x-4 * x^2+6x+8/2x^2+5x-3 / x^2+2x/x^2+2x-3 1 solutions Answer 87339 by jim_thompson5910(28598)   on 2008-01-08 21:53:55 (Show Source): You can put this solution on YOUR website! Let's simplify the numerator Start with the given expression Factor to get Factor to get Factor to get Factor to get Combine the fractions Cancel like terms Simplify So simplifies to . In other words ------------------------------------------------------------------------------ So becomes Multiply the first fraction by the reciprocal of the second fraction Factor to get Factor to get Combine the fractions Cancel like terms Simplify ---------------------------- Answer: So simplifies to In other words,

Angles/119245: Find the measure of each unknown angle 1 solutions Answer 87336 by jim_thompson5910(28598)   on 2008-01-08 21:42:18 (Show Source): You can put this solution on YOUR website! Remember, supplementary angles add to 180. So these angles are the bottom left angles Start with the given equation Combine like terms on the left side Add 22 to both sides Combine like terms on the right side Divide both sides by 4 to isolate x Reduce -------------------------------------------------------------- Answer: So our answer is (which is approximately in decimal form) ------------------------------ Now plug in into to find the angle Plug in Simplify So the first interior angle is 129.5 degrees ------------------------------ Now plug in into to find the angle Plug in Simplify So the second interior angle is 91 degrees Now subtract that answer from 180 to solve for the exterior angle y So ------------------------------ Now into to find the angle Plug in Simplify So the third interior angle is 65.5 degrees Now subtract that answer from 180 to solve for the exterior angle z So ------------------------------ Since the sum of the 4 angles in any quadrilateral is 360 degrees, this means Angle1+Angle2+Angle3+Angle4=360 Plug in the given info. These are the angles that were previously solved for. Combine like terms Subtract 286 from both sides Combine like terms on the right side Now subtract that answer from 180 to solve for the exterior angle u So -------------------------------------------------------------- Answer: So our answer is So the fourth interior angle w is 74 degrees Summary: So we have the following angles: , , , , , and

Equations/119222: This question is from textbook Algebra 1 Write each equation in standard form using integers. just checking. is this right? y=5x-32 5y=(5x-32)5 5y= 25x-160 -25x -25x -25x+5y=-260 ??? i am having trouble on this. 30.)y= 7/3x + 25/3 thank you for reading this. i hope you reply as soon as possible! thanks again! 1 solutions Answer 87329 by jim_thompson5910(28598)   on 2008-01-08 21:06:47 (Show Source): You can put this solution on YOUR website! Solved by pluggable solver: Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa) Start with the given equation Subtract from both sides Rearrange Now the equation is in standard form where , , and Solved by pluggable solver: Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa) Start with the given equation Subtract from both sides Rearrange Multiply both sides by 3 Distribute Multiply Reduce Reduce2 Now the equation is in standard form where , , and

Angles/119221: hi1 i have a question but can send it by mail because it is a figure of a quadrilateral and we have to find the angles that are unknowm. please relply to me and give me your mail or what ever so i can send you the question. Its night here already thankyou. Desperatley seeking hope to hear from you soon.... 1 solutions Answer 87324 by jim_thompson5910(28598)   on 2008-01-08 20:43:01 (Show Source): You can put this solution on YOUR website! Go ahead and send me the picture at jim_thompson5910@hotmail.com

Equations/119218: x= 1/A + 1/B 1 solutions Answer 87322 by jim_thompson5910(28598)   on 2008-01-08 20:35:00 (Show Source): You can put this solution on YOUR website! Do you want to simplify? Start with the given equation Multiply the first fraction by and the second fraction by . Multiply the fractions Combine the fractions

Proportions/119219: im doing homework in pre-algebra and i am not sure if it is proportions the book doesnt say but the problem is -10=-2b and it says you have to find the value of "b" but i cant figure out how 1 solutions Answer 87320 by jim_thompson5910(28598)   on 2008-01-08 20:32:51 (Show Source): You can put this solution on YOUR website! Start with the given equation Divide both sides by 2 to isolate b Reduce So the answer is