Find the following products: (i) (3x + 2y) (9X2 – 6xy + Ay2) (ii) (4x – 5y) (16x2 + 20xy + 25y2) (iii) (7p4 + q) (49p8 – 7p4q + q2) -Maths 9th

Find the following products: (i) (3x + 2y) (9X2 – 6xy + Ay2) (ii) (4x – 5y) (16x2 + 20xy + 25y2) (iii) (7p4 + q) (49p8 – 7p4q + q2) -Maths 9th
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Find the following products: (i) (3x + 2y + 2z) (9x2 + 4y2 + 4z2 – 6xy – 4yz – 6zx) (ii) (4x -3y + 2z) (16x2 + 9y2+ 4z2 + 12xy + 6yz – 8zx) (iii) (2a – 3b – 2c) (4a2 + 9b2 + 4c2 + 6ab – 6bc + 4ca) (iv) (3x -4y + 5z) (9x2 + 16y2 + 25z2 + 12xy- 15zx + 20yz) -Maths 9th

Description : Find the following products: (i) (3x + 2y + 2z) (9x2 + 4y2 + 4z2 – 6xy – 4yz – 6zx) (ii) (4x -3y + 2z) (16x2 + 9y2+ 4z2 + 12xy + 6yz – 8zx) (iii) (2a – 3b – 2c) (4a2 + 9b2 + 4c2 + 6ab – 6bc + 4ca) (iv) (3x -4y + 5z) (9x2 + 16y2 + 25z2 + 12xy- 15zx + 20yz) -Maths 9th

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If 9x2 + 25y2 = 181 and xy = -6, find the value of 3x + 5y. -Maths 9th

Description : If 9x2 + 25y2 = 181 and xy = -6, find the value of 3x + 5y. -Maths 9th

Last Answer : answer:

Compute the value of 9x2 + 4y2 if xy = 6 and 3x + 2y = 12. -Maths 9th

Description : Compute the value of 9x2 + 4y2 if xy = 6 and 3x + 2y = 12. -Maths 9th

Last Answer : Consider the equation 3x + 2y = 12 Now, square both sides: (3x + 2y)2 = 122 => 9x2 + 12xy + 4y2 = 144 =>9x2 + 4y2 = 144 – 12xy From the questions, xy = 6 So, 9x2 + 4y2 = 144 – 72 Thus, the value of 9x2 + 4y2 = 72

A pair of linear equations which has a unique solution x = 2, y = -3 is (a) x + y = -1 ; 2x – 3y = -5 (b) 2x + 5y = -11 ; 4x + 10y = -22(c) 2x – y = 1 ; 3x + 2y = 0 (d) x – 4y – 14 = 0 ;5x – y – 13 = 0

Description : A pair of linear equations which has a unique solution x = 2, y = -3 is (a) x + y = -1 ; 2x – 3y = -5 (b) 2x + 5y = -11 ; 4x + 10y = -22(c) 2x – y = 1 ; 3x + 2y = 0 (d) x – 4y – 14 = 0 ;5x – y – 13 = 0

Last Answer : (d) x – 4y – 14 = 0 ;5x – y – 13 = 0

If 3x -7y = 10 and xy = -1, find the value of 9x2 + 49y2 -Maths 9th

Description : If 3x -7y = 10 and xy = -1, find the value of 9x2 + 49y2 -Maths 9th

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Find the value of 27X3 + 8y3 if (i) 3x + 2y = 14 and xy = 8 (ii) 3x + 2y = 20 and xy = 149 -Maths 9th

Description : Find the value of 27X3 + 8y3 if (i) 3x + 2y = 14 and xy = 8 (ii) 3x + 2y = 20 and xy = 149 -Maths 9th

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Solve these following equations: (i) 3x + 3 = 15 (ii) 2y + 7 =19 -Maths 9th

Description : Solve these following equations: (i) 3x + 3 = 15 (ii) 2y + 7 =19 -Maths 9th

Last Answer : answer:

Write any two solutions of the linear equation 3x + 2y =9. -Maths 9th

Description : Write any two solutions of the linear equation 3x + 2y =9. -Maths 9th

Last Answer : Solution :-

Draw a graph of the equation x + Y = 5 & 3x - 2y =0 on the same graph paper. Find the coordinates of the point whose two lines intersect. -Maths 9th

Description : Draw a graph of the equation x + Y = 5 & 3x - 2y =0 on the same graph paper. Find the coordinates of the point whose two lines intersect. -Maths 9th

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Draw a graph of the equation x+ y=5 & 3x -2y=0 in the same graph paper find the coordinates of the point whose two two lines intersect. -Maths 9th

Description : Draw a graph of the equation x+ y=5 & 3x -2y=0 in the same graph paper find the coordinates of the point whose two two lines intersect. -Maths 9th

Last Answer : From x + y = 5, If x = 0 0 + y = 5 y = 5 Therefore (0,5) If x = 1 1 + y = 5 y =5 - 1 y = 4 Therefore (1,4) Draw a graph for this And From 3x - 2y = 0 If x = 0 3 (0) - 2y = 0 0 - ... 2y = 0 -2y = -6 y = -6/-2 y = 3 Therefore (2,3) Draw a graph for these points And the point of intersection is (2,3)

Find the equation of the straight line passing through the point (4, 5) and perpendicular to 3x – 2y + 5 = 0. -Maths 9th

Description : Find the equation of the straight line passing through the point (4, 5) and perpendicular to 3x – 2y + 5 = 0. -Maths 9th

Last Answer : There are two ways to prove it. 1st way: Area of triangle formed by the given points = 0 if they are collinear.∴ \(rac{1}{2}\) [\(x\)(2 - (y + 1) ) + 1((y + 1) - 1) + 0(1 - 2)] = 0⇒ \(rac{1}{2}\) [2\(x\) - \(x\)y - \( ... y - \(x\)y - 1 + \(x\) ⇒ x + y = \(x\)y ⇒ \(rac{1}{x}\) + \(rac{1}{y}\) = 1.

What is the angle between the lines whose equations are: 3x + y – 7 = 0 and x + 2y + 9 = 0. -Maths 9th

Description : What is the angle between the lines whose equations are: 3x + y – 7 = 0 and x + 2y + 9 = 0. -Maths 9th

Last Answer : (c) (8, 6)Let AB be the given line 4x + 3y = 25 Let O′(a, b) be the image of O in the given line AB. Let O O′ cut AB in point P. Also OP ⊥ AB and P is the mid-point of OO′. ∴ Co-ordinates of P are \(\bigg( ... 4 imes6}{3}\) = 8∴ The image of the point O(0, 0) in the line 4x + 3y - 25 = 0 is (8, 6).

If 3x – 2y= 11 and xy = 12, find the value of 27x3 – 8y3. -Maths 9th

Description : If 3x – 2y= 11 and xy = 12, find the value of 27x3 – 8y3. -Maths 9th

Last Answer : Given, (a−b)3=a3−3ab(a−b)−b3 (3x−2y)3=27x3−8y3−3(3x)(2y)(3x−2y) 113=27x3−8y3−18(12)(11) 27x3−8y3=3707

What must be substract from x(to the power 4) + 3x(cube) + 4x(square) - 3x - 6 to get 3x(cube) + 4x(square) - x + 3? -Maths 9th

Description : What must be substract from x(to the power 4) + 3x(cube) + 4x(square) - 3x - 6 to get 3x(cube) + 4x(square) - x + 3? -Maths 9th

Last Answer : Solution :-

For what value of m will the expression 3x^3 + mx^2 + 4x – 4m be divisible by x + 2 ? -Maths 9th

Description : For what value of m will the expression 3x^3 + mx^2 + 4x – 4m be divisible by x + 2 ? -Maths 9th

Last Answer : f(x) = 3x3 + mx2 + 4x – 4m f(x) is divisible by (x + 2) if f(–2) = 0 Now f(–2) = 3(–2)3 + m(–2)2 + 4(–2) – 4m = – 24 + 4m – ... ; 4m = – 32 ≠ 0 ∴ No such value of m exists for which (x + 2) is a factor of the given expression

For what value of k, will the expression (3x^3 – kx^2 + 4x + 16) be divisible by (x – k/2) ? -Maths 9th

Description : For what value of k, will the expression (3x^3 – kx^2 + 4x + 16) be divisible by (x – k/2) ? -Maths 9th

Last Answer : Given f(x) = 3x³ - kx² + 4x + 16. Since (x - k/2) is a factor of polynomial. This means x = k/2 is the zero of the given polynomial. ⇒ f(k/2) = 3(k/2)³ - k(k/2)² + 4(k/2) + 16 ⇒ 0 ... - 4k + 32) + 4(k² - 4k + 32) ⇒ 0 = (k + 4)(k² - 4k + 32) ⇒ k = -4.

If the polynomials ax^3 + 4x^2 + 3x – 4 and x^3 – 4x + a leave the same remainder when divided by (x – 3), the value of a is : -Maths 9th

Description : If the polynomials ax^3 + 4x^2 + 3x – 4 and x^3 – 4x + a leave the same remainder when divided by (x – 3), the value of a is : -Maths 9th

Last Answer : Given ax^3 + 4x^2 + 3x - 4 and x^3 - 4x + a leave the same remainder when divided by x - 3. Let p(x) = ax^3 + 4x^2 + 3x - 4 and g(x) = x^3 - 4x + a By remainder theorem, if f(x) is divided by (x − a) then ... 4 27a+41 g(3)=27-4(3)+a 15+a f(3)=G(3) 27a+41=15+a 26a=15-41 a=15-41/26 a=-26/26 a=-1

What is the equation of the line joining the origin with the point of intersection of the lines 4x + 3y = 12 and 3x + 4y = 12 ? -Maths 9th

Description : What is the equation of the line joining the origin with the point of intersection of the lines 4x + 3y = 12 and 3x + 4y = 12 ? -Maths 9th

Last Answer : (b) (5, 6)Let the foot of the perpendicular be M(x1, y1) Slope of line AB, i.e., y = -x + 11 = -1 Slope of line PM = \(rac{y_1-3}{x_1-2}\)Now, PM ⊥ AB⇒ \(\bigg(rac{y_1-3}{x_1-2}\bigg)\) x - ... get 2x1 = 10 ⇒ x1 = 5 Putting x1 in (ii), we get y1 = 6. ∴ Required foot of the perpendicular M is (5, 6).

Find the value of m, so that 2x -1 be a factor of 8x4 +4x3 -16x2 +10x+07. -Maths 9th

Description : Find the value of m, so that 2x -1 be a factor of 8x4 +4x3 -16x2 +10x+07. -Maths 9th

Last Answer : Solution of this question

Find the value of m, so that 2x -1 be a factor of 8x4 +4x3 -16x2 +10x+07. -Maths 9th

Description : Find the value of m, so that 2x -1 be a factor of 8x4 +4x3 -16x2 +10x+07. -Maths 9th

Last Answer : Solution of this question

If the equation `3x^(2)+6xy+my^(2)=0` represents a pair of coincident straight lines, then `(3m)/2` is equal to

Description : If the equation `3x^(2)+6xy+my^(2)=0` represents a pair of coincident straight lines, then `(3m)/2` is equal to

Last Answer : If the equation `3x^(2)+6xy+my^(2)=0` represents a pair of coincident straight lines, then `(3m)/2` is equal to

Factorise the following : 9x2 -12x+ 3 -Maths 9th

Description : Factorise the following : 9x2 -12x+ 3 -Maths 9th

Last Answer : Factorise the following :

Factorise the following : 9x2 +4y2 + 16z2 +12xy-16yz -24xz -Maths 9th

Description : Factorise the following : 9x2 +4y2 + 16z2 +12xy-16yz -24xz -Maths 9th

Last Answer : Factorise the following

Factorise the following : 9x2 -12x+ 3 -Maths 9th

Description : Factorise the following : 9x2 -12x+ 3 -Maths 9th

Last Answer : Factorise the following :

Factorise the following : 9x2 +4y2 + 16z2 +12xy-16yz -24xz -Maths 9th

Description : Factorise the following : 9x2 +4y2 + 16z2 +12xy-16yz -24xz -Maths 9th

Last Answer : Factorise the following

Find the values of x for which the following functions are maximum or minimum: (i) ` x^(3)- 3x^(2) - 9x ` (ii) ` 4x^(3)-15x^(2)+12x+1` (iii) ` 1-x-x^(

Description : Find the values of x for which the following functions are maximum or minimum: (i) ` x^(3)- 3x^(2) - 9x ` (ii) ` 4x^(3)-15x^(2)+12x+1` (iii) ` 1-x-x^(

Last Answer : Find the values of x for which the following functions are maximum or minimum: (i) ` x^(3)- 3x^(2) - 9x ` (ii) ` 4x ... (v) `(x^(2)-x+1)/(x^(2)+x+1)`

Solve for `x` `(i) |x+1|=4x+3` `(ii) |x+1|=|x+3|` `(iii) 7|x-2|-|x-7|=5` `(iv) ||x-1|-2|=6x+8` `(v) |2x^(2)-3x+1|=|x^(2)+x-3|`

Description : Solve for `x` `(i) |x+1|=4x+3` `(ii) |x+1|=|x+3|` `(iii) 7|x-2|-|x-7|=5` `(iv) ||x-1|-2|=6x+8` `(v) |2x^(2)-3x+1|=|x^(2)+x-3|`

Last Answer : Solve for `x` `(i) |x+1|=4x+3` `(ii) |x+1|=|x+3|` `(iii) 7|x-2|-|x-7|=5` `(iv) ||x-1|-2|=6x+8` `(v) |2x^(2)-3x+1|=|x^(2)+x-3|`

what is the difference of the two polynomials? (9x2 + 8x) – (2x2 + 3x) -General Knowledge

Description : what is the difference of the two polynomials? (9x2 + 8x) – (2x2 + 3x) -General Knowledge

Last Answer : (9x^2 + 8x) - (2x^2 + 3x) = 7x^2 + 5x.

6x^+17xy+5y^ -Maths 9th

Description : 6x^+17xy+5y^ -Maths 9th

Last Answer : what we have to do to this question??? we have to factorise or do something else?

Simplify (2x- 5y)3 – (2x+ 5y)3. -Maths 9th

Description : Simplify (2x- 5y)3 – (2x+ 5y)3. -Maths 9th

Last Answer : (2x -5y)3 - (2x + 5y)3 = [(2x)3 - (5y)3 - 3(2x)(5y)(2x - 5y)] -[(2x)3 + (5y)3 + 3(2x)(5y)(2x+5y)] [using identity, (a - b)3 = a3 -b3 - 3ab and (a + b)3 =a3 +b3 + 3ab] = (2x)3 - (5y)3 - ... 2x)3- (5y)3 - 30xy (2x + 5y) = -2 (5y)3 - 30xy(2x - 5y + 2x + 5y) = -2 x 125y3 - 30xy(4x) = -250y3 -120x2y

The linear equation 2x – 5y = 7 has -Maths 9th

Description : The linear equation 2x – 5y = 7 has -Maths 9th

Last Answer : (c) In the given equation 2x – 5y = 7, for every value of x, we get a corresponding value of y and vice-versa. Therefore, the linear equation has infinitely many solutions.

The equation 2x+ 5y = 7 has a unique solution, if x and y are -Maths 9th

Description : The equation 2x+ 5y = 7 has a unique solution, if x and y are -Maths 9th

Last Answer : (a) In natural numbers, there is only one pair i.e., (1, 1) which satisfy the given equation but in positive real numbers, real numbers and rational numbers there are many pairs to satisfy the given linear equation.

6x^+17xy+5y^ -Maths 9th

Description : 6x^+17xy+5y^ -Maths 9th

Last Answer : what we have to do to this question??? we have to factorise or do something else?

Simplify (2x- 5y)3 – (2x+ 5y)3. -Maths 9th

Description : Simplify (2x- 5y)3 – (2x+ 5y)3. -Maths 9th

Last Answer : (2x -5y)3 - (2x + 5y)3 = [(2x)3 - (5y)3 - 3(2x)(5y)(2x - 5y)] -[(2x)3 + (5y)3 + 3(2x)(5y)(2x+5y)] [using identity, (a - b)3 = a3 -b3 - 3ab and (a + b)3 =a3 +b3 + 3ab] = (2x)3 - (5y)3 - ... 2x)3- (5y)3 - 30xy (2x + 5y) = -2 (5y)3 - 30xy(2x - 5y + 2x + 5y) = -2 x 125y3 - 30xy(4x) = -250y3 -120x2y

The linear equation 2x – 5y = 7 has -Maths 9th

Description : The linear equation 2x – 5y = 7 has -Maths 9th

Last Answer : (c) In the given equation 2x – 5y = 7, for every value of x, we get a corresponding value of y and vice-versa. Therefore, the linear equation has infinitely many solutions.

The equation 2x+ 5y = 7 has a unique solution, if x and y are -Maths 9th

Description : The equation 2x+ 5y = 7 has a unique solution, if x and y are -Maths 9th

Last Answer : (a) In natural numbers, there is only one pair i.e., (1, 1) which satisfy the given equation but in positive real numbers, real numbers and rational numbers there are many pairs to satisfy the given linear equation.

Expand using suitable identity (-2x + 5y - 3z) to the whole square. -Maths 9th

Description : Expand using suitable identity (-2x + 5y - 3z) to the whole square. -Maths 9th

Last Answer : Solution :-

Simplify: (2x–5y)3 – (2x + 5y)3 -Maths 9th

Description : Simplify: (2x–5y)3 – (2x + 5y)3 -Maths 9th

Last Answer : Solution :-

How many solutions does the equation 2x +5y=8 has? -Maths 9th

Description : How many solutions does the equation 2x +5y=8 has? -Maths 9th

Last Answer : Solution :- Infinitely many solutions.

ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA (see Fig 8.29). AC is a diagonal. Show that: (i) SR || AC and SR = 1/2 AC (ii) PQ = SR (iii) PQRS is a parallelogram. -Maths 9th

Description : ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA (see Fig 8.29). AC is a diagonal. Show that: (i) SR || AC and SR = 1/2 AC (ii) PQ = SR (iii) PQRS is a parallelogram. -Maths 9th

Last Answer : . Solution: (i) In ΔDAC, R is the mid point of DC and S is the mid point of DA. Thus by mid point theorem, SR || AC and SR = ½ AC (ii) In ΔBAC, P is the mid point of AB and Q is the mid point of BC. ... ----- from question (ii) ⇒ SR || PQ - from (i) and (ii) also, PQ = SR , PQRS is a parallelogram.

4x + 5y?

Description : 4x + 5y?

Last Answer : 9

What is the minimum value of 3x plus 5y in the feasible region?

Description : What is the minimum value of 3x plus 5y in the feasible region?

Last Answer : It is 18.

What are the points of intersection between the equations of 3x -5y equals 16 and xy equals 7?

Description : What are the points of intersection between the equations of 3x -5y equals 16 and xy equals 7?

Last Answer : If 3x -5y = 16 and xy = 7 then by combining both equations into a single quadratic equation and solving it then the points of intersection are at (-5/3, -21/5) and (7, 1)

Elimination (-3x-15y=-17) and (-x+5y=-13)?

Description : Elimination (-3x-15y=-17) and (-x+5y=-13)?

Last Answer : Elimination is the removal of undigested food (solid waste) from the body.

Give the geometric interpretations of 5x + 3 = 3x – 7 as an equation (i) in one variable (ii) in two variables. -Maths 9th

Description : Give the geometric interpretations of 5x + 3 = 3x – 7 as an equation (i) in one variable (ii) in two variables. -Maths 9th

Last Answer : Solution :-

Find the remainder when y3 + y2 - 2y + 5 is divided by y - 5. -Maths 9th

Description : Find the remainder when y3 + y2 - 2y + 5 is divided by y - 5. -Maths 9th

Last Answer : Remainder = 145 Again, we should evaluate p(5) Let p(y) = y3 + y2 - 2y + 5 ∴ p(5) = 53 + 52 - 2 x 5 + 5 = 125 + 25 - 10 + 5 = 145 Thus , we find that p(5) is the remainder when p(y) is divided by y - 5 .

Without finding the cubes, factorise (x- 2y)3 + (2y – 3z)3 + (3z – x)3. -Maths 9th

Description : Without finding the cubes, factorise (x- 2y)3 + (2y – 3z)3 + (3z – x)3. -Maths 9th

Last Answer : We know that, a3 + b3 + c3 – 3 abc = (a + b + c)(a2 + b2 + c2 -ab-bc-ca) Also, if a + b + c = 0, then a3 + b3 + c3 = 3abc Here, we see that (x-2y) +(2y-3z)+ (3z-x) = 0 Therefore, (x-2y)3 + (2y-3z)3 + (3z-x)3 = 3(x-2y)(2y-3z)(3z-x).

Multiply x2 + 4y2 + z2 + 2xy + xz – 2yz by (-z + x-2y). -Maths 9th

Description : Multiply x2 + 4y2 + z2 + 2xy + xz – 2yz by (-z + x-2y). -Maths 9th

Last Answer : Multiply this question

Find the solution of the linear equation x+2y = 8 which represents a point on -Maths 9th

Description : Find the solution of the linear equation x+2y = 8 which represents a point on -Maths 9th

Last Answer : We have, x + 2y = 8 ,..(i) (i) When the point is on the X-axis, then put y = 0 in Eq. (i), we get x+2 (0)=8 ⇒ x = 8 Hence, the required point is (8, 0). (ii) When the point is on the Y-axis, then put x = 0 in Eq. (i), we get 0 + 2y = 8 ⇒ y = 8/2 = 4 Hence, the required point is (0, 4).

Find the remainder when y3 + y2 - 2y + 5 is divided by y - 5. -Maths 9th

Description : Find the remainder when y3 + y2 - 2y + 5 is divided by y - 5. -Maths 9th

Last Answer : Remainder = 145 Again, we should evaluate p(5) Let p(y) = y3 + y2 - 2y + 5 ∴ p(5) = 53 + 52 - 2 x 5 + 5 = 125 + 25 - 10 + 5 = 145 Thus , we find that p(5) is the remainder when p(y) is divided by y - 5 .