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  1. Asked: In:

    In Fig. 6.13, lines AB and CD intersect at O.

    Best Answer
    bhoomi889

    Given: Lines AB and CD intersects at O such that ∠BOD = 40° and ∠AOC + ∠BOE = 70° ...(1) ∠AOC = ∠BOD [∵ Vertically Opposite Angles] Hence, ∠AOC = 40° [∵ ∠BOD = 40°] Therefore, from the equation (1), we have, 40° + ∠BOE = 70° ⇒ ∠BOE = 70° - 40° = 30° Here, ∠AOC + ∠BOE + ∠COE = 180° [∵ AOB is a straigRead more

    Given: Lines AB and CD intersects at O such that ∠BOD = 40° and
    ∠AOC + ∠BOE = 70° …(1)
    ∠AOC = ∠BOD [∵ Vertically Opposite Angles]
    Hence, ∠AOC = 40° [∵ ∠BOD = 40°]
    Therefore, from the equation (1), we have,
    40° + ∠BOE = 70°
    ⇒ ∠BOE = 70° – 40° = 30°
    Here, ∠AOC + ∠BOE + ∠COE = 180° [∵ AOB is a straight line]
    ⇒ 70° + ∠COE = 180° [From the equation (1)]
    ⇒ ∠COE = 180° – 70° = 110° and
    Relex ∠COE = 360° – ∠COE = 360° – 110° = 250°

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  2. Asked: In:

    Why is Axiom 5, in the list of Euclid’s axioms, considered a ‘universal truth’? (Note that the question is not about the fifth postulate.)

    Best Answer
    bhoomi889

    Axiom 5: The whole is greater than the part. Since this is true for anything in any part of the world, this is a universal truth.

    Axiom 5:
    The whole is greater than the part.
    Since this is true for anything in any part of the world, this is a universal truth.

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  3. Asked: In:

    Draw the graph of each of the following linear equations in two variables: 3 = 2x + y

    Best Answer
    bhoomi889

    (iv) 3 = 2x +y ⇒ y = 3 - 2x Putting x = 0, we have, y = 3 - 2 × 0 = 3 Putting x = 1, we have, y = 3 - 2 × 1 = 1 Hence, G(0,3) and H(1,1) are the solutions of the equation.

    (iv) 3 = 2x +y
    ⇒ y = 3 – 2x
    Putting x = 0, we have, y = 3 – 2 × 0 = 3
    Putting x = 1, we have, y = 3 – 2 × 1 = 1
    Hence, G(0,3) and H(1,1) are the solutions of the equation.

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  4. Asked: In:

    Give the equations of two lines passing through (2, 14). How many more such lines are there, and why?

    Best Answer
    bhoomi889

    Equation of two lines passing through (2, 14) are given by: x + y = 16 and 8x - y = 2. There are infinite number of lines that can pass through (2, 4) as infinite number of lines passes through a point.

    Equation of two lines passing through (2, 14) are given by: x + y = 16 and 8x – y = 2.
    There are infinite number of lines that can pass through (2, 4) as infinite number of lines passes through a point.

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  6. Asked: In:

    If the point (3, 4) lies on the graph of the equation 3y = ax + 7, find the value of a.

    Best Answer
    bhoomi889

    Given equation of line: 3y = ax + 7. Putting x = 3 and y = 4, we have, 3 x 4 = a x3 +7 ⇒ 12 = 3a + 7 ⇒ 12 - 7 = 3a ⇒ a = 5/3

    Given equation of line: 3y = ax + 7.
    Putting x = 3 and y = 4, we have, 3 x 4 = a x3 +7
    ⇒ 12 = 3a + 7 ⇒ 12 – 7 = 3a
    ⇒ a = 5/3

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  7. Asked: In:

    The taxi fare in a city is as follows: For the first kilometre, the fare is Rs 8 and for the subsequent distance it is Rs 5 per km. Taking the distance covered as x km and total fare as Rs y, write a linear equation for this information, and draw its graph.

    bhoomi889

    Given that: Distance travelled = x km and total fare = ₹ y Total fare = Fare for first km + Fare for remaining distance Therefore, the equation: y = 8 + 5 × (x - 1) ⇒ y = 5x +3 For the graph: Putting x = 1, we have, y = 5 × 1 + 3 = 8 Putting x = 2, we have, y = 5 × 2 + 3 = 13 Putting x = 3, we have,Read more

    Given that: Distance travelled = x km and total fare = ₹ y
    Total fare = Fare for first km + Fare for remaining distance
    Therefore, the equation: y = 8 + 5 × (x – 1) ⇒ y = 5x +3
    For the graph:
    Putting x = 1, we have, y = 5 × 1 + 3 = 8
    Putting x = 2, we have, y = 5 × 2 + 3 = 13
    Putting x = 3, we have, y = 5 × 3 + 3 = 18
    Hence, A(1, 8), B(2, 13) and C[3, 18) are solutions of the equation.

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  8. Asked: In:

    The taxi fare in a city is as follows: For the first kilometre, the fare is Rs 8 and for the subsequent distance it is Rs 5 per km. Taking the distance covered as x km and total fare as Rs y, write a linear equation for this information, and draw its graph.

    bhoomi889
    • 1
  9. Asked: In:

    Use suitable identities to find the following products: (x + 4) (x + 10)

    Best Answer
    bhoomi889

    (i) (x + 4)(x + 10) = x² + (4 + 10)x + 4 × 10 [∵ (x + a)(x + b) = x² + (a + b)x + ab ] = x² + 14x + 40

    (i) (x + 4)(x + 10)
    = x² + (4 + 10)x + 4 × 10 [∵ (x + a)(x + b) = x² + (a + b)x + ab ]
    = x² + 14x + 40

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  11. Asked: In:

    Use suitable identities to find the following products: (x + 8) (x – 10)

    Best Answer
    bhoomi889

    (ii) (x + 8)(x + -10) = x² + (8 - 10)x + 8 × (-10) [∵ (x + a)(x + b) = x² + (a + b)x + ab ] = x² - 2x - 80

    (ii) (x + 8)(x + -10)
    = x² + (8 – 10)x + 8 × (-10) [∵ (x + a)(x + b) = x² + (a + b)x + ab ]
    = x² – 2x – 80

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  12. Asked: In:

    Use suitable identities to find the following products: (3x + 4) (3x – 5)

    Best Answer
    bhoomi889

    (iii) (3x + 4)(3x - 5) = (3x)² + (4 - 5)3x + 4 × (-5) [∵ (x + a)(x + b) = x² + (a + b)x + ab ] = 9x² - 3x - 20

    (iii) (3x + 4)(3x – 5)
    = (3x)² + (4 – 5)3x + 4 × (-5) [∵ (x + a)(x + b) = x² + (a + b)x + ab ]
    = 9x² – 3x – 20

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