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Please Help Me Solve This Book 4 Quantitative Reasoning Problem / Maths Guru Please Help Me Solve This Simultaneous Equations For My Young(photo) / Can U Solve This Primary 6 Quantitative Reasoning (2) (3) (4)
Please Help Me Solve This by Nobody: 9:53am On Jan 12, 2018 |
I would like it if u can help ne solve it by snapping ur solution with ur phone or typing it here cos i know the answer but i need to know how to solve it. X+3/X-2 - 1-X/x =17/4 that is x+3 over x-2 then minus 1-x over x = 17 over 4 thank you. |
Re: Please Help Me Solve This by Nobody: 11:17am On Jan 12, 2018 |
Frenzy007: |
Re: Please Help Me Solve This by Nobody: 11:21am On Jan 12, 2018 |
Frenzy007:cc MIKEZURUKI NEXTPRINCE |
Re: Please Help Me Solve This by Nobody: 11:22am On Jan 12, 2018 |
Frenzy007:cc MIKEZURUKI NEXTPRINCE tempest01 Biafraisdead raintaker tanx |
Re: Please Help Me Solve This by Raintaker(m): 11:43am On Jan 12, 2018 |
Frenzy007:too long .. x+3/x-2-1-x/x=17/4 Two solutions were found : x =(33-√897)/8= 0.381 x =(33+√897)/8= 7.869 Rearrange: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : x+3/x-2-1-x/x-(17/4)=0 Step by step solution : Step 1 : 17 Simplify —— 4 Equation at the end of step 1 : 3 x 17 ((((x+—)-2)-1)-—)-—— = 0 x x 4 Step 2 : x Simplify — x Equation at the end of step 2 : 3 17 ((((x+—)-2)-1)-1)-—— = 0 x 4 Step 3 : 3 Simplify — x Equation at the end of step 3 : 3 17 ((((x + —) - 2) - 1) - 1) - —— = 0 x 4 Step 4 : Rewriting the whole as an Equivalent Fraction : 4.1 Adding a fraction to a whole Rewrite the whole as a fraction using x as the denominator : x x • x x = — = ————— 1 x Equivalent fraction : The fraction thus generated looks different but has the same value as the whole Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator Adding fractions that have a common denominator : 4.2 Adding up the two equivalent fractions Add the two equivalent fractions which now have a common denominator Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible: x • x + 3 x2 + 3 ————————— = —————— x x Equation at the end of step 4 : (x2 + 3) 17 (((———————— - 2) - 1) - 1) - —— = 0 x 4 Step 5 : Rewriting the whole as an Equivalent Fraction : 5.1 Subtracting a whole from a fraction Rewrite the whole as a fraction using x as the denominator : 2 2 • x 2 = — = ————— 1 x Polynomial Roots Calculator : 5.2 Find roots (zeroes) of : F(x) = x2 + 3 Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0 Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient In this case, the Leading Coefficient is 1 and the Trailing Constant is 3. The factor(s) are: of the Leading Coefficient : 1 of the Trailing Constant : 1 ,3 Let us test .... P Q P/Q F(P/Q) Divisor -1 1 -1.00 4.00 -3 1 -3.00 12.00 1 1 1.00 4.00 3 1 3.00 12.00 Polynomial Roots Calculator found no rational roots Adding fractions that have a common denominator : 5.3 Adding up the two equivalent fractions (x2+3) - (2 • x) x2 - 2x + 3 ———————————————— = ——————————— x x Equation at the end of step 5 : (x2 - 2x + 3) 17 ((————————————— - 1) - 1) - —— = 0 x 4 Step 6 : Rewriting the whole as an Equivalent Fraction : 6.1 Subtracting a whole from a fraction Rewrite the whole as a fraction using x as the denominator : 1 1 • x 1 = — = ————— 1 x Trying to factor by splitting the middle term 6.2 Factoring x2 - 2x + 3 The first term is, x2 its coefficient is 1 . The middle term is, -2x its coefficient is -2 . The last term, "the constant", is +3 Step-1 : Multiply the coefficient of the first term by the constant 1 • 3 = 3 Step-2 : Find two factors of 3 whose sum equals the coefficient of the middle term, which is -2 . -3 + -1 = -4 -1 + -3 = -4 1 + 3 = 4 3 + 1 = 4 Observation : No two such factors can be found !! Conclusion : Trinomial can not be factored Adding fractions that have a common denominator : 6.3 Adding up the two equivalent fractions (x2-2x+3) - (x) x2 - 3x + 3 ——————————————— = ——————————— x x Equation at the end of step 6 : (x2 - 3x + 3) 17 (————————————— - 1) - —— = 0 x 4 Step 7 : Rewriting the whole as an Equivalent Fraction : 7.1 Subtracting a whole from a fraction Rewrite the whole as a fraction using x as the denominator : 1 1 • x 1 = — = ————— 1 x Trying to factor by splitting the middle term 7.2 Factoring x2 - 3x + 3 The first term is, x2 its coefficient is 1 . The middle term is, -3x its coefficient is -3 . The last term, "the constant", is +3 Step-1 : Multiply the coefficient of the first term by the constant 1 • 3 = 3 Step-2 : Find two factors of 3 whose sum equals the coefficient of the middle term, which is -3 . -3 + -1 = -4 -1 + -3 = -4 1 + 3 = 4 3 + 1 = 4 Observation : No two such factors can be found !! Conclusion : Trinomial can not be factored Adding fractions that have a common denominator : 7.3 Adding up the two equivalent fractions (x2-3x+3) - (x) x2 - 4x + 3 ——————————————— = ——————————— x x Equation at the end of step 7 : (x2 - 4x + 3) 17 ————————————— - —— = 0 x 4 Step 8 : Trying to factor by splitting the middle term 8.1 Factoring x2-4x+3 The first term is, x2 its coefficient is 1 . The middle term is, -4x its coefficient is -4 . The last term, "the constant", is +3 Step-1 : Multiply the coefficient of the first term by the constant 1 • 3 = 3 Step-2 : Find two factors of 3 whose sum equals the coefficient of the middle term, which is -4 . -3 + -1 = -4 That's it Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -3 and -1 x2 - 3x - 1x - 3 Step-4 : Add up the first 2 terms, pulling out like factors : x • (x-3) Add up the last 2 terms, pulling out common factors : 1 • (x-3) Step-5 : Add up the four terms of step 4 : (x-1) • (x-3) Which is the desired factorization Calculating the Least Common Multiple : 8.2 Find the Least Common Multiple The left denominator is : x The right denominator is : 4 Number of times each prime factor appears in the factorization of: Prime Factor Left Denominator Right Denominator L.C.M = Max {Left,Right} 2022 Product of all Prime Factors 144 Number of times each Algebraic Factor appears in the factorization of: Algebraic Factor Left Denominator Right Denominator L.C.M = Max {Left,Right} x 101 Least Common Multiple: 4x Calculating Multipliers : 8.3 Calculate multipliers for the two fractions Denote the Least Common Multiple by L.C.M Denote the Left Multiplier by Left_M Denote the Right Multiplier by Right_M Denote the Left Deniminator by L_Deno Denote the Right Multiplier by R_Deno Left_M = L.C.M / L_Deno = 4 Right_M = L.C.M / R_Deno = x Making Equivalent Fractions : 8.4 Rewrite the two fractions into equivalent fractions Two fractions are called equivalent if they have the same numeric value. For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well. To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier. L. Mult. • L. Num. (x-1) • (x-3) • 4 —————————————————— = ————————————————— L.C.M 4x R. Mult. • R. Num. 17 • x —————————————————— = —————— L.C.M 4x Adding fractions that have a common denominator : 8.5 Adding up the two equivalent fractions (x-1) • (x-3) • 4 - (17 • x) 4x2 - 33x + 12 ———————————————————————————— = —————————————— 4x 4x Trying to factor by splitting the middle term 8.6 Factoring 4x2 - 33x + 12 The first term is, 4x2 its coefficient is 4 . The middle term is, -33x its coefficient is -33 . The last term, "the constant", is +12 Step-1 : Multiply the coefficient of the first term by the constant 4 • 12 = 48 Step-2 : Find two factors of 48 whose sum equals the coefficient of the middle term, which is -33 . -48 + -1 = -49 -24 + -2 = -26 -16 + -3 = -19 -12 + -4 = -16 -8 + -6 = -14 -6 + -8 = -14 For tidiness, printing of 14 lines which failed to find two such factors, was suppressed Observation : No two such factors can be found !! Conclusion : Trinomial can not be factored Equation at the end of step 8 : 4x2 - 33x + 12 —————————————— = 0 4x Step 9 : When a fraction equals zero : 9.1 When a fraction equals zero ... Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero. Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator. Here's how: 4x2-33x+12 —————————— • 4x = 0 • 4x 4x Now, on the left hand side, the 4x cancels out the denominator, while, on the right hand side, zero times anything is still zero. The equation now takes the shape : 4x2-33x+12 = 0 Parabola, Finding the Vertex : 9.2 Find the Vertex of y = 4x2-33x+12 Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 4 , is positive (greater than zero). Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions. Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex. For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 4.1250 Plugging into the parabola formula 4.1250 for x we can calculate the y -coordinate : y = 4.0 * 4.13 * 4.13 - 33.0 * 4.13 + 12.0 or y = -56.063 Parabola, Graphing Vertex and X-Intercepts : Root plot for : y = 4x2-33x+12 Axis of Symmetry (dashed) {x}={ 4.13} Vertex at {x,y} = { 4.13,-56.06} x -Intercepts (Roots) : Root 1 at {x,y} = { 0.38, 0.00} Root 2 at {x,y} = { 7.87, 0.00} Solve Quadratic Equation by Completing The Square 9.3 Solving 4x2-33x+12 = 0 by Completing The Square . Divide both sides of the equation by 4 to have 1 as the coefficient of the first term : x2-(33/4)x+3 = 0 Subtract 3 from both side of the equation : x2-(33/4)x = -3 Now the clever bit: Take the coefficient of x , which is 33/4 , divide by two, giving 33/8 , and finally square it giving 1089/64 Add 1089/64 to both sides of the equation : On the right hand side we have : -3 + 1089/64 or, (-3/1)+(1089/64) The common denominator of the two fractions is 64 Adding (-192/64)+(1089/64) gives 897/64 So adding to both sides we finally get : x2-(33/4)x+(1089/64) = 897/64 Adding 1089/64 has completed the left hand side into a perfect square : x2-(33/4)x+(1089/64) = (x-(33/) • (x-(33/) = (x-(33/)2 Things which are equal to the same thing are also equal to one another. Since x2-(33/4)x+(1089/64) = 897/64 and x2-(33/4)x+(1089/64) = (x-(33/)2 then, according to the law of transitivity, (x-(33/)2 = 897/64 We'll refer to this Equation as Eq. #9.3.1 The Square Root Principle says that When two things are equal, their square roots are equal. Note that the square root of (x-(33/)2 is (x-(33/)2/2 = (x-(33/)1 = x-(33/ Now, applying the Square Root Principle to Eq. #9.3.1 we get: x-(33/ = √ 897/64 Add 33/8 to both sides to obtain: x = 33/8 + √ 897/64 Since a square root has two values, one positive and the other negative x2 - (33/4)x + 3 = 0 has two solutions: x = 33/8 + √ 897/64 or x = 33/8 - √ 897/64 Note that √ 897/64 can be written as √ 897 / √ 64 which is √ 897 / 8 Solve Quadratic Equation using the Quadratic Formula 9.4 Solving 4x2-33x+12 = 0 by the Quadratic Formula . According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by : - B ± √ B2-4AC x = ———————— 2A In our case, A = 4 B = -33 C = 12 Accordingly, B2 - 4AC = 1089 - 192 = 897 Applying the quadratic formula : 33 ± √ 897 x = —————— 8 √ 897 , rounded to 4 decimal digits, is 29.9500 So now we are looking at: x = ( 33 ± 29.950 ) / 8 Two real solutions: x =(33+√897)/8= 7.869 or: x =(33-√897)/8= 0.381 Supplement : Solving Quadratic Equation Directly Solving x2-4x+3 = 0 directly Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula Parabola, Finding the Vertex : 10.1 Find the Vertex of y = x2-4x+3 Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 1 , is positive (greater than zero). Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions. Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex. For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 2.0000 Plugging into the parabola formula 2.0000 for x we can calculate the y -coordinate : y = 1.0 * 2.00 * 2.00 - 4.0 * 2.00 + 3.0 or y = -1.000 Parabola, Graphing Vertex and X-Intercepts : Root plot for : y = x2-4x+3 Axis of Symmetry (dashed) {x}={ 2.00} Vertex at {x,y} = { 2.00,-1.00} x -Intercepts (Roots) : Root 1 at {x,y} = { 1.00, 0.00} Root 2 at {x,y} = { 3.00, 0.00} Solve Quadratic Equation by Completing The Square 10.2 Solving x2-4x+3 = 0 by Completing The Square . Subtract 3 from both side of the equation : x2-4x = -3 Now the clever bit: Take the coefficient of x , which is 4 , divide by two, giving 2 , and finally square it giving 4 Add 4 to both sides of the equation : On the right hand side we have : -3 + 4 or, (-3/1)+(4/1) The common denominator of the two fractions is 1 Adding (-3/1)+(4/1) gives 1/1 So adding to both sides we finally get : x2-4x+4 = 1 Adding 4 has completed the left hand side into a perfect square : x2-4x+4 = (x-2) • (x-2) = (x-2)2 Things which are equal to the same thing are also equal to one another. Since x2-4x+4 = 1 and x2-4x+4 = (x-2)2 then, according to the law of transitivity, (x-2)2 = 1 We'll refer to this Equation as Eq. #10.2.1 The Square Root Principle says that When two things are equal, their square roots are equal. Note that the square root of (x-2)2 is (x-2)2/2 = (x-2)1 = x-2 Now, applying the Square Root Principle to Eq. #10.2.1 we get: x-2 = √ 1 Add 2 to both sides to obtain: x = 2 + √ 1 Since a square root has two values, one positive and the other negative x2 - 4x + 3 = 0 has two solutions: x = 2 + √ 1 or x = 2 - √ 1 Solve Quadratic Equation using the Quadratic Formula 10.3 Solving x2-4x+3 = 0 by the Quadratic Formula . According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by : - B ± √ B2-4AC x = ———————— 2A In our case, A = 1 B = -4 C = 3 Accordingly, B2 - 4AC = 16 - 12 = 4 Applying the quadratic formula : 4 ± √ 4 x = ———— 2 Can √ 4 be simplified ? Yes! The prime factorization of 4 is 2•2 To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root). √ 4 = √ 2•2 = ± 2 • √ 1 = ± 2 So now we are looking at: x = ( 4 ± 2) / 2 Two real solutions: x =(4+√4)/2=2+= 3.000 or: x =(4-√4)/2=2-= 1.000 Two solutions were found : x =(33-√897)/8= 0.381 x =(33+√897)/8= 7.869 Processing ends successfully 1 Like |
Re: Please Help Me Solve This by Nobody: 1:23pm On Jan 12, 2018 |
[quote author=Raintaker post=64126880]too long .. x+3/x-2-1-x/x=17/4 Two solutions were found : x =(33-√897)/8= 0.381 x =(33+√897)/8= 7.869 Rearrange: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : x+3/x-2-1-x/x-(17/4)=0 Step by step solution : Step 1 : 17 Simplify —— 4 Equation at the end of step 1 : 3 x 17 ((((x+—)-2)-1)-—)-—— = 0 x x 4 Step 2 : x Simplify — x Equation at the end of step 2 : 3 17 ((((x+—)-2)-1)-1)-—— = 0 x 4 Step 3 : 3 Simplify — x Equation at the end of step 3 : 3 17 ((((x + —) - 2) - 1) - 1) - —— = 0 x 4 Step 4 : Rewriting the whole as an Equivalent Fraction : 4.1 Adding a fraction to a whole Rewrite the whole as a fraction using x as the denominator : x x • x x = — = ————— 1 x Equivalent fraction : The fraction thus generated looks different but has the same value as the whole Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator Adding fractions that have a common denominator : 4.2 Adding up the two equivalent fractions Add the two equivalent fractions which now have a common denominator Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible: x • x + 3 x2 + 3 ————————— = —————— x x Equation at the end of step 4 : (x2 + 3) 17 (((———————— - 2) - 1) - 1) - —— = 0 x 4 Step 5 : Rewriting the whole as an Equivalent Fraction : 5.1 Subtracting a whole from a fraction Rewrite the whole as a fraction using x as the denominator : 2 2 • x 2 = — = ————— 1 x Polynomial Roots Calculator : 5.2 Find roots (zeroes) of : F(x) = x2 + 3 Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0 Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient In this case, the Leading Coefficient is 1 and the Trailing Constant is 3. The factor(s) are: of the Leading Coefficient : 1 of the Trailing Constant : 1 ,3 Let us test .... P Q P/Q F(P/Q) Divisor -1 1 -1.00 4.00 -3 1 -3.00 12.00 1 1 1.00 4.00 3 1 3.00 12.00 Polynomial Roots Calculator found no rational roots Adding fractions that have a common denominator : 5.3 Adding up the two equivalent fractions (x2+3) - (2 • x) x2 - 2x + 3 ———————————————— = ——————————— x x Equation at the end of step 5 : (x2 - 2x + 3) 17 ((————————————— - 1) - 1) - —— = 0 x 4 Step 6 : Rewriting the whole as an Equivalent Fraction : 6.1 Subtracting a whole from a fraction Rewrite the whole as a fraction using x as the denominator : 1 1 • x 1 = — = ————— 1 x Trying to factor by splitting the middle term 6.2 Factoring x2 - 2x + 3 The first term is, x2 its coefficient is 1 . The middle term is, -2x its coefficient is -2 . The last term, "the constant", is +3 Step-1 : Multiply the coefficient of the first term by the constant 1 • 3 = 3 Step-2 : Find two factors of 3 whose sum equals the coefficient of the middle term, which is -2 . -3 + -1 = -4 -1 + -3 = -4 1 + 3 = 4 3 + 1 = 4 [\quote]wat did you use is it an application or u solved it urself |
Re: Please Help Me Solve This by biafraisdead(m): 3:04pm On Jan 12, 2018 |
Frenzy007:x=4 or x=-2/9. it's a simple quadratic equation. 1 Like
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Re: Please Help Me Solve This by Raintaker(m): 3:48pm On Jan 12, 2018 |
[quote author=Frenzy007 post=64129929][/quote]I used Google |
Re: Please Help Me Solve This by Nobody: 7:14pm On Jan 12, 2018 |
biafraisdead:My guy i no see the pics well but i asked someone to solve it. Tnx anyways as usual it was one simple thing that made ne fail it 1 Like |
Re: Please Help Me Solve This by Deicide: 10:08pm On Jan 12, 2018 |
The answers are in surd/decimal forms sha the last eqn after simplifying is: -9x2 + 10x + 8 = 0 |
Re: Please Help Me Solve This by biafraisdead(m): 8:29am On Jan 13, 2018 |
Deicide:not true, after simplifying u would have: 9x2 - 34x - 8= 0. Let me give u a friendly tips; firstly assuming ur simplification above was correct don't u think it would make more sense to write it as this: 9x2 - 10x - 8 =0 rather than as: -9x2 + 10x + 8 = 0. secondly always verify ur answers by substituting ur aswers into the original equation and see if it makes sense. |
Re: Please Help Me Solve This by ugonna1054(m): 11:15am On Jan 13, 2018 |
Raintaker:mhen, tf.......this shii too long |
Re: Please Help Me Solve This by Deicide: 3:22pm On Jan 13, 2018 |
biafraisdead:Lol na lazy ness make me leave am like that |
Re: Please Help Me Solve This by freemandgenius(m): 4:35pm On Jan 13, 2018 |
Raintaker:wrong sir |
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