Find the values of a and b in each of the following -Maths 9th

Find the values of a and b in each of the following -Maths 9th
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Find the values of a and b in each of the following -Maths 9th

Description : Find the values of a and b in each of the following -Maths 9th

Last Answer : Value of a and b .

If x = 3 and y = -1, find the values of each of the following using in identity: -Maths 9th

Description : If x = 3 and y = -1, find the values of each of the following using in identity: -Maths 9th

Last Answer : Formula, (a+b+c)2=a2+b2+c2+2ab+2bc+2ca Given, (2+x−2y)2=22+(x)2+(−2y)2+2(2)(x)+2(x)(−2y)+2(2)(−2y) =4+x2+4y2+4x−4xy−8y

In the figure, ABCD is a rhombus, whose diagonals meet at 0. Find the values of x and y. -Maths 9th

Description : In the figure, ABCD is a rhombus, whose diagonals meet at 0. Find the values of x and y. -Maths 9th

Last Answer : Since diagonals of a rhombus bisect each other at right angle . ∴ In △AOB , we have ∠OAB + ∠x + 90° = 180° ∠x = 180° - 90° - 35° [∵ ∠ OAB = 35°] = 55° Also, ∠DAO = ∠BAO = 35° ∴ ∠y + ∠DAO + ∠BAO + ∠x ... 180° ⇒ ∠y = 180° - 125° = 55° Hence the values of x and y are x = 55°, y = 55°.

Find the median of the values 37, 31, 42, 43, 46, 25, 39, 45, 32. -Maths 9th

Description : Find the median of the values 37, 31, 42, 43, 46, 25, 39, 45, 32. -Maths 9th

Last Answer : Arranging the data in ascending order, we have 25, 31, 32, 37, 39, 42, 43, 45, 46 Here, number of observations = 9 (odd) Median = value of (9+1 / 2)th Observation = Value of 5th Observation = 39

For what value of c, the linear equation 2x + cy = 8 has equal values of x and y for its solution? -Maths 9th

Description : For what value of c, the linear equation 2x + cy = 8 has equal values of x and y for its solution? -Maths 9th

Last Answer : The given linear equation is 2x + cy= 8. …(i) Now, by condition, x and y-coordinate of given linear equation are same, i.e., x = y. Put y = x in Eq. (i), we get

In the figure, ABCD is a rhombus, whose diagonals meet at 0. Find the values of x and y. -Maths 9th

Description : In the figure, ABCD is a rhombus, whose diagonals meet at 0. Find the values of x and y. -Maths 9th

Last Answer : Since diagonals of a rhombus bisect each other at right angle . ∴ In △AOB , we have ∠OAB + ∠x + 90° = 180° ∠x = 180° - 90° - 35° [∵ ∠ OAB = 35°] = 55° Also, ∠DAO = ∠BAO = 35° ∴ ∠y + ∠DAO + ∠BAO + ∠x ... 180° ⇒ ∠y = 180° - 125° = 55° Hence the values of x and y are x = 55°, y = 55°.

Find the median of the values 37, 31, 42, 43, 46, 25, 39, 45, 32. -Maths 9th

Description : Find the median of the values 37, 31, 42, 43, 46, 25, 39, 45, 32. -Maths 9th

Last Answer : Arranging the data in ascending order, we have 25, 31, 32, 37, 39, 42, 43, 45, 46 Here, number of observations = 9 (odd) Median = value of (9+1 / 2)th Observation = Value of 5th Observation = 39

For what value of c, the linear equation 2x + cy = 8 has equal values of x and y for its solution? -Maths 9th

Description : For what value of c, the linear equation 2x + cy = 8 has equal values of x and y for its solution? -Maths 9th

Last Answer : The given linear equation is 2x + cy= 8. …(i) Now, by condition, x and y-coordinate of given linear equation are same, i.e., x = y. Put y = x in Eq. (i), we get

For what value of c, the linear equation 2x + cy = 8 has equal values of x and y as its solution? -Maths 9th

Description : For what value of c, the linear equation 2x + cy = 8 has equal values of x and y as its solution? -Maths 9th

Last Answer : Solution :-

The solutions of a linear equation in two variables always take integral values .True / false -Maths 9th

Description : The solutions of a linear equation in two variables always take integral values .True / false -Maths 9th

Last Answer : answer:

Express the equation –x + 3y = -2/3 in the form of ax + by + c =0 and identify the values of a,b and c. -Maths 9th

Description : Express the equation –x + 3y = -2/3 in the form of ax + by + c =0 and identify the values of a,b and c. -Maths 9th

Last Answer : answer:

If nCr : nCr+1 = 1 : 2 and nCr+1 : nCr+2 = 2 : 3 determine the values of n and r. -Maths 9th

Description : If nCr : nCr+1 = 1 : 2 and nCr+1 : nCr+2 = 2 : 3 determine the values of n and r. -Maths 9th

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Find the range of values of x for which (x^2+x+1)/(x^2+2)<1/3, x being real. -Maths 9th

Description : Find the range of values of x for which (x^2+x+1)/(x^2+2)

Last Answer : answer:

Find the range of values of x which satisfy x^2 + 6x – 27 > 0, –x^2 + 3x + 4 > 0 simultaneously. -Maths 9th

Description : Find the range of values of x which satisfy x^2 + 6x – 27 > 0, –x^2 + 3x + 4 > 0 simultaneously. -Maths 9th

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The set of values for which x^3 + 1 > x^2 + x is -Maths 9th

Description : The set of values for which x^3 + 1 > x^2 + x is -Maths 9th

Last Answer : answer:

What values of x satisfy x^(2/3) + x^(1/3) – 2 < 0? -Maths 9th

Description : What values of x satisfy x^(2/3) + x^(1/3) – 2 < 0? -Maths 9th

Last Answer : answer:

Which of the following values of x do not satisfy the inequality x^2 – 3x + 2 > 0 at all. -Maths 9th

Description : Which of the following values of x do not satisfy the inequality x^2 – 3x + 2 > 0 at all. -Maths 9th

Last Answer : answer:

Find the range of real values of x for which (x-1)/(4x+5)<(x-3)/(4x-3). -Maths 9th

Description : Find the range of real values of x for which (x-1)/(4x+5)

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Find the complete set of values that satisfy the inequalities | |x| – 3 | < 2 and | |x| – 2| < 3. -Maths 9th

Description : Find the complete set of values that satisfy the inequalities | |x| – 3 | < 2 and | |x| – 2| < 3. -Maths 9th

Last Answer : answer:

The number of positive integral values of m satisfying the inequalities 8m + 35 > 75 and 5m + 18 < 53 is -Maths 9th

Description : The number of positive integral values of m satisfying the inequalities 8m + 35 > 75 and 5m + 18 < 53 is -Maths 9th

Last Answer : answer:

Find the set of values of x satisfying |(5-x)/3|< 2 -Maths 9th

Description : Find the set of values of x satisfying |(5-x)/3|< 2 -Maths 9th

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The set of values of x for which the inequalities x^2 – 3x – 10 < 0, 10x – x^2 – 16 > 0 hold simultaneously is -Maths 9th

Description : The set of values of x for which the inequalities x^2 – 3x – 10 < 0, 10x – x^2 – 16 > 0 hold simultaneously is -Maths 9th

Last Answer : answer:

If (cos x)/(1 + cosec x) + (cos x)/(cosec x - 1)= 2which one of the following is one of the values of x ? -Maths 9th

Description : If (cos x)/(1 + cosec x) + (cos x)/(cosec x - 1)= 2which one of the following is one of the values of x ? -Maths 9th

Last Answer : answer:

Find the values of k for which the equations x^2 – kx – 21 = 0 and x^2 – 3kx + 35 = 0 will have a common root? -Maths 9th

Description : Find the values of k for which the equations x^2 – kx – 21 = 0 and x^2 – 3kx + 35 = 0 will have a common root? -Maths 9th

Last Answer : Let the common root be α ⟹α2−kα−21=0......(1) α2−3kα+35=0........(2) (1)−(2)⟹2kα=56⟹α=k28​Substituting α=k28​ in (1) (k28​)2−28−21=0 ⟹k=±4

When (x^3 – 2x^2 + px – q) is divided by (x^2 – 2x – 3), the remainder is (x – 6), What are the values of p and q respectively ? -Maths 9th

Description : When (x^3 – 2x^2 + px – q) is divided by (x^2 – 2x – 3), the remainder is (x – 6), What are the values of p and q respectively ? -Maths 9th

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If the expression (px^3 + x^2 – 2x – q) is divisible by (x – 1) and (x + 1), then the values of p and q respectively are ? -Maths 9th

Description : If the expression (px^3 + x^2 – 2x – q) is divisible by (x – 1) and (x + 1), then the values of p and q respectively are ? -Maths 9th

Last Answer : Let f(x)=px3+x2−2x−q Since f(x) is divisible by (x−1) and (x+1) so x=1 and −1 must make f(x)=0. Therefore, p+1−2−q=0, i.e., p−q=1; and −p+1+2−q=0, i.e., p+q=3 Thus p=2 and q=1

The values of a, b and c respectively for the expression f(x) = x^3 + ax^2 + bx + c, if f(1) = f(2) = 0 and f(4) = f(0) are : -Maths 9th

Description : The values of a, b and c respectively for the expression f(x) = x^3 + ax^2 + bx + c, if f(1) = f(2) = 0 and f(4) = f(0) are : -Maths 9th

Last Answer : f′(x)=3x2+2ax+6 f(x)⇒f′(x)≥0 3x2+2ax+6≥0 ⇒D≤0 4[a2−3b]≤0 a2≤3b ∴P=6×6×6(16)×6​=3616​=94​ Answer.

If logy x = (a. logz y) = (b. logxz) = ab, then which of the following pairs of values for (a, b) is not possible ? -Maths 9th

Description : If logy x = (a. logz y) = (b. logxz) = ab, then which of the following pairs of values for (a, b) is not possible ? -Maths 9th

Last Answer : answer:

If the points A(a, –11), B(5, b), C(2, 15) and D(1, 1) are the vertices of a parallelogram ABCD, find the values of a and b. -Maths 9th

Description : If the points A(a, –11), B(5, b), C(2, 15) and D(1, 1) are the vertices of a parallelogram ABCD, find the values of a and b. -Maths 9th

Last Answer : Let the x-axis divide the line joining the points (-2, 5) and (1, -9) in the ratio k : 1. Let the point of division on x-axis is P Then,\(x\) = \(rac{k-2}{k+1}\), y = \(rac{-9k+ ... (rac{5}{9}\)k being positive, the division is internal. ∴ x-axis divides the given line internally in the ratio 5 : 9.

Prove that a2 + b2 + c2 – ab – bc – ca is always non-negative for all values of a, b and c. -Maths 9th

Description : Prove that a2 + b2 + c2 – ab – bc – ca is always non-negative for all values of a, b and c. -Maths 9th

Last Answer : Sol-2(a2+b2+c2-ab-bc-ca)/2 multiplying & dividing by 2 ...

Find the values of x and y, if two ordered pairs (x – 3, – 6) and (4, x + y) are equal. -Maths 9th

Description : Find the values of x and y, if two ordered pairs (x – 3, – 6) and (4, x + y) are equal. -Maths 9th

Last Answer : hope its clear

Hameed has built a cubical water tank with lid for his house, with each other edge 1.5m long. -Maths 9th

Description : Hameed has built a cubical water tank with lid for his house, with each other edge 1.5m long. -Maths 9th

Last Answer : Edge of cubical tank = 1.5 m ∴ Area of 4 walls = 4 (side)² = 4(1.5)² m² = 4 x 225 = 9 m² Area of floor = (1.5)² = 2.25 m² ∴ Total surface area = 9 + 2.25 = 11.25 m² Edge of square tile = 25 m = 0.25 m² ∴ Area of 1 tile = (0.25)2 = .0625 m²

A kite in the shape of a square with a diagonal 32 cm and an isosceles triangle of base 8 cm and sides 6 cm each is to be made of three different shades as shown in figure. -Maths 9th

Description : A kite in the shape of a square with a diagonal 32 cm and an isosceles triangle of base 8 cm and sides 6 cm each is to be made of three different shades as shown in figure. -Maths 9th

Last Answer : Each shade of paper is divided into 3 triangles i.e., I, II, III 8 cm For triangle I: ABCD is a square [Given] ∵ Diagonals of a square are equal and bisect each other. ∴ AC = BD = 32 cm Height of AABD ... are: Area of shade I = 256 cm2 Area of shade II = 256 cm2 and area of shade III = 17.92 cm2

An umbrella is made by stitching 10 triangular pieces of cloth of two different colours (see figure), each piece measuring 20 cm, 50 cm and 50 cm. -Maths 9th

Description : An umbrella is made by stitching 10 triangular pieces of cloth of two different colours (see figure), each piece measuring 20 cm, 50 cm and 50 cm. -Maths 9th

Last Answer : Let the sides of each triangular piece be a = 20 cm, b = 50 cm, c = 50 cm

A rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30 m and its longer diagonal is 48 m, how much area of grass field will each cow be getting? -Maths 9th

Description : A rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30 m and its longer diagonal is 48 m, how much area of grass field will each cow be getting? -Maths 9th

Last Answer : Here, each side of the rhombus = 30 m. Let ABCD be the given rhombus and the diagonal, BD = 48 m Sides ∆ABC are a = AB = 30m, b = AD = 30m, c = BD = 48m Since, a diagonal divides the rhombus into ... Area of grass for 18 cows to graze = 864 m2 ⇒ Area of grass for 1 cow to graze = 86418 m2 = 48 m2

Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases: (i) p(x) = 2x3+x2–2x–1, g(x) = x+1 -Maths 9th

Description : Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases: (i) p(x) = 2x3+x2–2x–1, g(x) = x+1 -Maths 9th

Last Answer : Solution: p(x) = 2x3+x2–2x–1, g(x) = x+1 g(x) = 0 ⇒ x+1 = 0 ⇒ x = −1 ∴Zero of g(x) is -1. Now, p(−1) = 2(−1)3+(−1)2–2(−1)–1 = −2+1+2−1 = 0 ∴By factor theorem, g(x) is a factor of p(x

A bus stop is barricaded from the remaining part of the road, by using 50 hollow cones made of recycled cardboard. Each cone has a base diameter of 40 cm and height 1 m. -Maths 9th

Description : A bus stop is barricaded from the remaining part of the road, by using 50 hollow cones made of recycled cardboard. Each cone has a base diameter of 40 cm and height 1 m. -Maths 9th

Last Answer : Given: Radius of cone, r = diameter/2 = 40/2 cm = 20cm = 0.2 m Height of cone, h = 1m Slant height of cone is l, and l2 = (r2+h2) Using given values, l2 = (0.22+12) = (1.04) Or l ... (32.028 12) = Rs.384.336 = Rs.384.34 (approximately) Therefore, the cost of painting all these cones is Rs. 384.34.

A cubical box has each edge 10 cm and another cuboidal box is 12.5cm long, 10 cm wide and 8 cm high -Maths 9th

Description : A cubical box has each edge 10 cm and another cuboidal box is 12.5cm long, 10 cm wide and 8 cm high -Maths 9th

Last Answer : From the question statement, we have Edge of a cube = 10cm Length, l = 12.5 cm Breadth, b = 10cm Height, h = 8 cm (i) Find the lateral surface area for both the figures Lateral surface ... . Therefore, the total surface area of the cubical box is smaller than that of the cuboidal box by 10 cm2

1. Draw different pairs of circles. How many points does each pair have in common? What is the maximum number of common points? -Maths 9th

Description : 1. Draw different pairs of circles. How many points does each pair have in common? What is the maximum number of common points? -Maths 9th

Last Answer : As we can see from the figure, that two circles have two points in common. Two circles cannot intersect each other at more than two points. Let us assume that two circles cut each other at ... circle can pass. So, two circles if intersect each other will intersect at maximum two points.

6. Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other. -Maths 9th

Description : 6. Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other. -Maths 9th

Last Answer : Solution: Let ABCD be a quadrilateral and P, Q, R and S are the mid points of AB, BC, CD and DA respectively. Now, In ΔACD, R and S are the mid points of CD and DA respectively. , ... , PQRS is parallelogram. PR and QS are the diagonals of the parallelogram PQRS. So, they will bisect each other.

5. Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square. -Maths 9th

Description : 5. Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square. -Maths 9th

Last Answer : Solution: Given that, Let ABCD be a quadrilateral and its diagonals AC and BD bisect each other at right angle at O. To prove that, The Quadrilateral ABCD is a square. Proof, In ΔAOB and ΔCOD, AO = ... right angle. Thus, from (i), (ii) and (iii) given quadrilateral ABCD is a square. Hence Proved.

4. Show that the diagonals of a square are equal and bisect each other at right angles. -Maths 9th

Description : 4. Show that the diagonals of a square are equal and bisect each other at right angles. -Maths 9th

Last Answer : Solution: Let ABCD be a square and its diagonals AC and BD intersect each other at O. To show that, AC = BD AO = OC and ∠AOB = 90° Proof, In ΔABC and ΔBAD, AB = BA (Common) ∠ABC = ∠BAD = ... = ∠COB ∠AOB+∠COB = 180° (Linear pair) Thus, ∠AOB = ∠COB = 90° , Diagonals bisect each other at right angles

3. Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus. -Maths 9th

Description : 3. Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus. -Maths 9th

Last Answer : Solution: Let ABCD be a quadrilateral whose diagonals bisect each other at right angles. Given that, OA = OC OB = OD and ∠AOB = ∠BOC = ∠OCD = ∠ODA = 90° To show that, if the ... a parallelogram. , ABCD is rhombus as it is a parallelogram whose diagonals intersect at right angle. Hence Proved.

In the given figure, if chords AB and CD of the circle intersect each other at right angles, then find x + y. -Maths 9th

Description : In the given figure, if chords AB and CD of the circle intersect each other at right angles, then find x + y. -Maths 9th

Last Answer : ∴ ∠CAO = ∠ODB = x [angles in same segment ] ---- (i) Now, in right angled ΔDOB , ∠ODB + ∠DOB + ∠OBD = 180° ⇒ x + 90° + y =180° (using equation i) ⇒ x + y = 90°

Two cubes of side 2 cm each are joined end to end. Find the volume of the cuboid so formed. -Maths 9th

Description : Two cubes of side 2 cm each are joined end to end. Find the volume of the cuboid so formed. -Maths 9th

Last Answer : When two cubes of side 2 cm each are joined end to end then, Length (l) = (2 + 2) = 4cm Breadth (b) = 2 cm; Height (h) = 2 cm ∴ Volume of cuboid = lbh = 4 x 2 x 2 = 16 cm3

A metallic sheet is of rectangular shape with dimensions 48 cm x 36 cm. From each of its corners, a square of 8 cm is cut-off and an open box is made of the remaining sheet. Find the volume of the box. -Maths 9th

Description : A metallic sheet is of rectangular shape with dimensions 48 cm x 36 cm. From each of its corners, a square of 8 cm is cut-off and an open box is made of the remaining sheet. Find the volume of the box. -Maths 9th

Last Answer : When squares of 8 cm is cutt-off from rectangulare sheet then, Length of box (l) = (98 - 8 - 8) = 32 cm Breadth of box (b) = (36 - 8 - 8) = 20 cm Height of box (h) = 8cm ∴ Volume of box = lbh = 32 x 20 x 8 = 5120 cm3

How many bricks will be required to construct a wall 8 m long, 6 m high and 22.5 cm thick, if each brick measures 25 cm x 11.25 cm x 6 cm? -Maths 9th

Description : How many bricks will be required to construct a wall 8 m long, 6 m high and 22.5 cm thick, if each brick measures 25 cm x 11.25 cm x 6 cm? -Maths 9th

Last Answer : ∵ Volume of one brick = (25 × 11.25 × 6) cm3 and volume of the wall = (800 × 600 × 22.5) cm3 ∴ Number of bricks = Volume of the walls / Volume of one brick = 800 × 600 × 22.5 / 25 × 11.25 × 6 = 6400

Express each of the following as a mixed surd in the simplest form : -Maths 9th

Description : Express each of the following as a mixed surd in the simplest form : -Maths 9th

Last Answer : MIxed surd in the simplest form

Express each of the following as a mixed surd in the simplest form : -Maths 9th

Description : Express each of the following as a mixed surd in the simplest form : -Maths 9th

Last Answer : Mixed surd in the simplest form

Factorise each of the following expressions: -Maths 9th

Description : Factorise each of the following expressions: -Maths 9th

Last Answer : (i) 48x3 - 36x2 = 12.4 x2 x - 12.3x2 = 12x2 (4x - 3) (ii) 5x2 - 15xy = 5x (x-3y) (iii) 15x3y2z - 25xy2z3 = 5xy2z(3x2 - 5z2)