Maths-
General
Easy

Question

The lengths (in inches) of two sides of a regular pentagon are represented by the expressions 4x + 7 and x + 16. Find the length of a side of the pentagon.

Hint:

A regular pentagon is a polygon that has 5 sides all of same length and all the angles of the same measure.

The correct answer is: 19


    Explanation:
    • We have been given the two sides of a regular pentagon in the form of expressions that is -  
    • 4x + 7 and x + 16
    • We have to find the length of a side of the pentagon.
    Step 1 of 1:
    The length of the two sides of a regular pentagon is represented by x + 16; 4x + 7
    Now, We know that all sides of regular polygon are equal.
    So,

    X + 16 = 4x + 7
    3x = 16 - 7
    3x = 9
    x = 3
    And the measure of length will be

    = x + 16
    = 3 + 16
    = 19

    Related Questions to study

    General
    Maths-

    Two angles of a regular polygon are given to be left parenthesis 2 x plus 27 right parenthesis to the power of ring operator text  and  end text left parenthesis 3 x minus 3 right parenthesis to the power of ring operator Find the value of  and measure of each angle.

    Solution:
    Hint:
    • A polygon whose length of all sides is equal with equal angles at each vertex is called regular polygon.
    Explanation:
    • We have been given the two sides of a regular polygon that is - (2𝑥 + 27)° 𝑎𝑛𝑑 (3𝑥 − 3)°
    • We have to find the value of x and measure of each angle.
    Step 1 of 1:
    We know that a regulat polygon is equiangular
    So,
    2x + 27 = 3x - 3
    x = 27 + 3
    x = 30
    And the value of each angle will be
    = 2x + 27
    = 2(30) + 27
    = 87

    Two angles of a regular polygon are given to be left parenthesis 2 x plus 27 right parenthesis to the power of ring operator text  and  end text left parenthesis 3 x minus 3 right parenthesis to the power of ring operator Find the value of  and measure of each angle.

    Maths-General
    Solution:
    Hint:
    • A polygon whose length of all sides is equal with equal angles at each vertex is called regular polygon.
    Explanation:
    • We have been given the two sides of a regular polygon that is - (2𝑥 + 27)° 𝑎𝑛𝑑 (3𝑥 − 3)°
    • We have to find the value of x and measure of each angle.
    Step 1 of 1:
    We know that a regulat polygon is equiangular
    So,
    2x + 27 = 3x - 3
    x = 27 + 3
    x = 30
    And the value of each angle will be
    = 2x + 27
    = 2(30) + 27
    = 87
    General
    Maths-

    Solve the equation. Write a reason for each step.
    8(−x − 6) = −50 − 10x

    Hint :- using the additive property and subtraction property ,division property on both sides .solve for x.
    Ans:- x = 1
    Explanation :-
    Given ,8(-x − 6) = -50-10x.
    By left distributive property - 8x − 48 = - 50 -10x
    Adding 48 on both sides by additive property of equality both sides remain equal.
    - 8x − 48 + 48 = - 50 -10x + 48
    - 8x = -10x - 2
    Adding 10x on both sides by additive property of equality both sides remain equal.
    - 8x +10x = -10x - 2 +10x
    2x = - 2
    Dividing 2  left parenthesis not equal to 0 right parenthesis by division property of equality both sides remains equal.
    fraction numerator 2 x over denominator 2 end fraction equals fraction numerator negative 2 over denominator 2 end fraction
    x = -1
    ∴ x = -1

    Solve the equation. Write a reason for each step.
    8(−x − 6) = −50 − 10x

    Maths-General
    Hint :- using the additive property and subtraction property ,division property on both sides .solve for x.
    Ans:- x = 1
    Explanation :-
    Given ,8(-x − 6) = -50-10x.
    By left distributive property - 8x − 48 = - 50 -10x
    Adding 48 on both sides by additive property of equality both sides remain equal.
    - 8x − 48 + 48 = - 50 -10x + 48
    - 8x = -10x - 2
    Adding 10x on both sides by additive property of equality both sides remain equal.
    - 8x +10x = -10x - 2 +10x
    2x = - 2
    Dividing 2  left parenthesis not equal to 0 right parenthesis by division property of equality both sides remains equal.
    fraction numerator 2 x over denominator 2 end fraction equals fraction numerator negative 2 over denominator 2 end fraction
    x = -1
    ∴ x = -1
    General
    Maths-

    Find the measure of each angle of an equilateral triangle using base angle theorem.

    Solution:
    Hint:
    • the base angle theorem states that if the sides of a triangle are congruent then the angles opposite these sides are congruent.
    • An equilateral triangle is a triangle with all the three sides of equal length.
    Explanation:
    • We have to find the measure of each angle of an equilateral triangle using base angle theorem.
    Step 1 of 1:
    Let a triangle be ABC

    Here,
    AB = AC
    Using base angle theorem
    straight angle B equals straight angle C
    And, B C equals A C
    So, straight angle A equals straight angle B
    Therefore,
    straight angle A equals straight angle B equals straight angle C
    Step 2 of 2:
    We know that the sum of all angles of a triangle is 1800.
    Now,
    straight angle A plus straight angle B plus straight angle C equals 180 to the power of ring operator
    straight angle straight A plus straight angle straight A plus straight angle straight A equals 180 to the power of ring operator
    3 straight angle A equals 180 to the power of ring operator
    straight angle A equals 60 to the power of ring operator
    So,
    straight angle A equals straight angle B equals straight angle C equals 60 to the power of ring operator

    Find the measure of each angle of an equilateral triangle using base angle theorem.

    Maths-General
    Solution:
    Hint:
    • the base angle theorem states that if the sides of a triangle are congruent then the angles opposite these sides are congruent.
    • An equilateral triangle is a triangle with all the three sides of equal length.
    Explanation:
    • We have to find the measure of each angle of an equilateral triangle using base angle theorem.
    Step 1 of 1:
    Let a triangle be ABC

    Here,
    AB = AC
    Using base angle theorem
    straight angle B equals straight angle C
    And, B C equals A C
    So, straight angle A equals straight angle B
    Therefore,
    straight angle A equals straight angle B equals straight angle C
    Step 2 of 2:
    We know that the sum of all angles of a triangle is 1800.
    Now,
    straight angle A plus straight angle B plus straight angle C equals 180 to the power of ring operator
    straight angle straight A plus straight angle straight A plus straight angle straight A equals 180 to the power of ring operator
    3 straight angle A equals 180 to the power of ring operator
    straight angle A equals 60 to the power of ring operator
    So,
    straight angle A equals straight angle B equals straight angle C equals 60 to the power of ring operator
    parallel
    General
    Maths-

    The length of each side of a regular pentagon is . Find the value of  if its perimeter is .

    Solution:
    Hint:
    • A regular pentagon is a polygon that has 5 sides all of same length and all the angles of the same measure.
    Explanation:
    • We have been given in the question the length of each side of a regular pentagon which is (x+5) cm
    • We have also been given the perimeter that is 50 cm.
    • We have to find the value of x.
    Step 1 of 1:
    We have given a perimeter of a regular pentaogn 50.
    A pentagon has  sides.
    The length of the side is  x+5
    So,
    5(x + 5) = 50
    x + 5 = 10
    x = 5
    Hence, Option A is correct.

    The length of each side of a regular pentagon is . Find the value of  if its perimeter is .

    Maths-General
    Solution:
    Hint:
    • A regular pentagon is a polygon that has 5 sides all of same length and all the angles of the same measure.
    Explanation:
    • We have been given in the question the length of each side of a regular pentagon which is (x+5) cm
    • We have also been given the perimeter that is 50 cm.
    • We have to find the value of x.
    Step 1 of 1:
    We have given a perimeter of a regular pentaogn 50.
    A pentagon has  sides.
    The length of the side is  x+5
    So,
    5(x + 5) = 50
    x + 5 = 10
    x = 5
    Hence, Option A is correct.
    General
    Maths-

    Name the property of equality the statement illustrates.
    Every segment is congruent to itself.

    Hint :- The reflexive property states that any real number, a, is equal to itself i.e a = a.
    Ans :- Option A
    Explanation :-
    The reflexive property states that any real number, a, is equal to itself. That is, a = a.
    Similarly the segment is congruent to itself .
    ∴Option A

    Name the property of equality the statement illustrates.
    Every segment is congruent to itself.

    Maths-General
    Hint :- The reflexive property states that any real number, a, is equal to itself i.e a = a.
    Ans :- Option A
    Explanation :-
    The reflexive property states that any real number, a, is equal to itself. That is, a = a.
    Similarly the segment is congruent to itself .
    ∴Option A
    General
    Maths-

    Solution:
    Hint:
    • the base angle theorem states that if the sides of a triangle are congruent then the angles opposite these sides are congruent.
    Explanation:
    • We have been given a diagram of a triangle in the question named ABC we have also been given 𝑚∠𝐵 = 55°.
    • We have to find out 𝑚∠A.
    Step 1 of 1:
    We have given figure

    Here, AB = AC
    It means the given triangle is an isosceles triangle.
    Now,
    By base angle theorem straight angle B equals straight angle C.
    And it is given straight angle B equals 55 to the power of ring operator
    So, straight angle B equals straight angle C equals 55 to the power of ring operator
    Step 2 of 2:
    We know that the sum of angle of a triangle is 1800
    straight angle A plus straight angle B plus straight angle C equals 180 to the power of ring operator
    straight angle A plus straight angle B plus straight angle B equals 180 to the power of ring operator
    straight angle A plus 2 straight angle B equals 180 to the power of ring operator
    straight angle A plus 2 open parentheses 55 to the power of ring operator close parentheses equals 180 to the power of ring operator
    straight angle A equals 70 to the power of ring operator

    Maths-General
    Solution:
    Hint:
    • the base angle theorem states that if the sides of a triangle are congruent then the angles opposite these sides are congruent.
    Explanation:
    • We have been given a diagram of a triangle in the question named ABC we have also been given 𝑚∠𝐵 = 55°.
    • We have to find out 𝑚∠A.
    Step 1 of 1:
    We have given figure

    Here, AB = AC
    It means the given triangle is an isosceles triangle.
    Now,
    By base angle theorem straight angle B equals straight angle C.
    And it is given straight angle B equals 55 to the power of ring operator
    So, straight angle B equals straight angle C equals 55 to the power of ring operator
    Step 2 of 2:
    We know that the sum of angle of a triangle is 1800
    straight angle A plus straight angle B plus straight angle C equals 180 to the power of ring operator
    straight angle A plus straight angle B plus straight angle B equals 180 to the power of ring operator
    straight angle A plus 2 straight angle B equals 180 to the power of ring operator
    straight angle A plus 2 open parentheses 55 to the power of ring operator close parentheses equals 180 to the power of ring operator
    straight angle A equals 70 to the power of ring operator
    parallel
    General
    Maths-

    If f(x) satisfies the relation 2f(x) +f(1-x) = x2 for all real x , then f(x) is

    Solution:-
    We have given that
    2f(x) +f(1-x) = x2     - - -- - - - - -(i)
    We have to find the value of f(x)
    By replacing x by (1-x) in equation (i)we get,
    2f(1-x) + f(x) = (1-x)2
    2f(1-x) + f(x) = 1 + x2 – 2x         - - - - - -(ii)
    Multiplying the equation(i) by 2 we get,
    4f(x) + 2f(1-x) = 2x2                - - - - - - (iii)
    Subtracting equation (ii) from (iii)
    3f(x) = x2 + 2x -1
    So,
    f left parenthesis x right parenthesis equals fraction numerator x squared plus 2 x minus 1 over denominator 3 end fraction
    Therefore option (b) is correct.

    If f(x) satisfies the relation 2f(x) +f(1-x) = x2 for all real x , then f(x) is

    Maths-General
    Solution:-
    We have given that
    2f(x) +f(1-x) = x2     - - -- - - - - -(i)
    We have to find the value of f(x)
    By replacing x by (1-x) in equation (i)we get,
    2f(1-x) + f(x) = (1-x)2
    2f(1-x) + f(x) = 1 + x2 – 2x         - - - - - -(ii)
    Multiplying the equation(i) by 2 we get,
    4f(x) + 2f(1-x) = 2x2                - - - - - - (iii)
    Subtracting equation (ii) from (iii)
    3f(x) = x2 + 2x -1
    So,
    f left parenthesis x right parenthesis equals fraction numerator x squared plus 2 x minus 1 over denominator 3 end fraction
    Therefore option (b) is correct.
    General
    Maths-

    If f:R->R be a function whose inverse is (𝑥+5)/3 , then what is the value of f(x)

    We have given that inverse of the function f(x)

    f-1(x) = (x+5)/3
    For solving this let us take

    y = f-1(x)

    y = (x+5)/3
    Further solving we get,

    x = 3y – 5

    f(y) = 3y – 5
    Therefore,

    f(x) = 3x – 5

    If f:R->R be a function whose inverse is (𝑥+5)/3 , then what is the value of f(x)

    Maths-General
    We have given that inverse of the function f(x)

    f-1(x) = (x+5)/3
    For solving this let us take

    y = f-1(x)

    y = (x+5)/3
    Further solving we get,

    x = 3y – 5

    f(y) = 3y – 5
    Therefore,

    f(x) = 3x – 5

    General
    Maths-

    Solution:
    Hint:
    • The base angle theorem states that if the sides of a triangle are congruent then the angles opposite these sides are congruent.
    Explanation:
    • We have been given in the question a diagram of a triangle named ABC and 𝑚∠𝐴 = 60°.
    • We have to find the 𝑚∠𝐴 𝑎𝑛𝑑 𝑚∠𝐶.
    Step 1 of 1:
    In the given figure, AB = AC.
    So, ABC is an isosceles triangle.
    So, According to base-angle theorem, the angles opposite the congruent sides are congruent.
    So,
    straight angle B equals straight angle C
    Step 2 of 2:
    Now we know that the sum of angle of triangle is equal to 1800.
    So,
    straight angle A plus straight angle B plus straight angle C equals 180 to the power of ring operator
    Since,straight angle B equals straight angle C
    So,
    straight angle A plus straight angle B plus straight angle C equals 180 to the power of ring operator
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell straight angle A plus straight angle C plus straight angle C equals 180 to the power of ring operator end cell end table
    60 plus 2 straight angle C equals 180 to the power of ring operator
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank row blank row cell 2 straight angle C equals 120 to the power of ring operator end cell row blank end table
    straight angle C equals 60 to the power of ring operator
    Therefore,
    straight angle C equals 60 to the power of ring operator straight &
    straight angle A equals 60 to the power of ring operator

    Maths-General
    Solution:
    Hint:
    • The base angle theorem states that if the sides of a triangle are congruent then the angles opposite these sides are congruent.
    Explanation:
    • We have been given in the question a diagram of a triangle named ABC and 𝑚∠𝐴 = 60°.
    • We have to find the 𝑚∠𝐴 𝑎𝑛𝑑 𝑚∠𝐶.
    Step 1 of 1:
    In the given figure, AB = AC.
    So, ABC is an isosceles triangle.
    So, According to base-angle theorem, the angles opposite the congruent sides are congruent.
    So,
    straight angle B equals straight angle C
    Step 2 of 2:
    Now we know that the sum of angle of triangle is equal to 1800.
    So,
    straight angle A plus straight angle B plus straight angle C equals 180 to the power of ring operator
    Since,straight angle B equals straight angle C
    So,
    straight angle A plus straight angle B plus straight angle C equals 180 to the power of ring operator
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell straight angle A plus straight angle C plus straight angle C equals 180 to the power of ring operator end cell end table
    60 plus 2 straight angle C equals 180 to the power of ring operator
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank row blank row cell 2 straight angle C equals 120 to the power of ring operator end cell row blank end table
    straight angle C equals 60 to the power of ring operator
    Therefore,
    straight angle C equals 60 to the power of ring operator straight &
    straight angle A equals 60 to the power of ring operator
    parallel
    General
    Maths-

    Let A= {x, y, z} and B= { p, q, r, s}, What is the number of distinct relations from B to A ?

    We have given the two sets A and B
    A= {x, y, z}
    B= { p, q, r, s},
    For finding the district relations from B to A we have to take the cartesian product of B and A
    B×A = {p, q, r, s} × {x, y, z}
    = {(p, x) , (p, y) , (p, z) , (q, x) , (q, y), (q, z) , (r, x) , (r, y), (r, z) , (s, x), (s, y), (s, z)}
    Therefore there are 12 distinct relations .

    Let A= {x, y, z} and B= { p, q, r, s}, What is the number of distinct relations from B to A ?

    Maths-General
    We have given the two sets A and B
    A= {x, y, z}
    B= { p, q, r, s},
    For finding the district relations from B to A we have to take the cartesian product of B and A
    B×A = {p, q, r, s} × {x, y, z}
    = {(p, x) , (p, y) , (p, z) , (q, x) , (q, y), (q, z) , (r, x) , (r, y), (r, z) , (s, x), (s, y), (s, z)}
    Therefore there are 12 distinct relations .
    General
    Maths-

    Let f, g : R→R be defined, respectively by f(x) = x + 1, g(x) = 2x – 3. Find f + g, f – g and f(g)

    We have given the function

    f(x) = x + 1

    g(x) = 2x – 3
    We have to find the value of

    i) f(x) + g(x)

    ii) f(x) – g(x)

    iii) f(g(x))
    Therefore,

    i) f(x) + g(x) = x + 1 + 2x – 3

    = 3x – 2

    ii f(x) – g(x) = x + 1 – (2x – 3)

    = x + 1 – 2x + 3

    = 4 – x

    iii) f(g(x)) = f(2x -3)

    = (2x – 3) + 1

    = 2x – 2
    Therefore, f+g = 3x – 2

    f – g = 4 – x

    f(g) = 2x – 2

    Let f, g : R→R be defined, respectively by f(x) = x + 1, g(x) = 2x – 3. Find f + g, f – g and f(g)

    Maths-General
    We have given the function

    f(x) = x + 1

    g(x) = 2x – 3
    We have to find the value of

    i) f(x) + g(x)

    ii) f(x) – g(x)

    iii) f(g(x))
    Therefore,

    i) f(x) + g(x) = x + 1 + 2x – 3

    = 3x – 2

    ii f(x) – g(x) = x + 1 – (2x – 3)

    = x + 1 – 2x + 3

    = 4 – x

    iii) f(g(x)) = f(2x -3)

    = (2x – 3) + 1

    = 2x – 2
    Therefore, f+g = 3x – 2

    f – g = 4 – x

    f(g) = 2x – 2

    General
    Maths-

    Name the property of equality the statement illustrates.
    If ∠P ≅ ∠Q, then ∠Q ≅ ∠P.

    Ans :- Option B
    The symmetric property states that for any real numbers, a and b, if a = b then b = a. Similarly with angles  If ∠P ≅ ∠Q, then ∠Q ≅ ∠P.
    ∴Option B

    Name the property of equality the statement illustrates.
    If ∠P ≅ ∠Q, then ∠Q ≅ ∠P.

    Maths-General
    Ans :- Option B
    The symmetric property states that for any real numbers, a and b, if a = b then b = a. Similarly with angles  If ∠P ≅ ∠Q, then ∠Q ≅ ∠P.
    ∴Option B
    parallel
    General
    Maths-

    Let f = {(1,1), (2,3), (0,–1), (–1, –3)} be a function from Z to Z defined by f(x) = ax + b, for some integers a, b. Determine a, b.

    We have given a function from Z to Z

     f = {(1,1), (2,3), (0,–1), (–1, –3)}
    And also we have given that

    f(x) = ax + b
    We have to find the value of a and b .
    First of all if the f is a function then its points will satisfy f(x) = ax + b

    f(1) = 1

    f(2) = 3

    f(0) = -1

    f(-1) = -3

    i) (1,1)

    f(1) = a (1) + b

    1 = a + b

    ii) (2,3)

    f(2) = a (2) + b

    3 = 2a + b

    Subtract equation (i) from (ii)

    2a – a + b – b = 3 – 1

    a = 2
    Putting this value in equation (i)

    1 = 2 + b

    b = 1 – 2

    b = -1
    Therefore, value of a = 2 and b = -1 .

    Let f = {(1,1), (2,3), (0,–1), (–1, –3)} be a function from Z to Z defined by f(x) = ax + b, for some integers a, b. Determine a, b.

    Maths-General
    We have given a function from Z to Z

     f = {(1,1), (2,3), (0,–1), (–1, –3)}
    And also we have given that

    f(x) = ax + b
    We have to find the value of a and b .
    First of all if the f is a function then its points will satisfy f(x) = ax + b

    f(1) = 1

    f(2) = 3

    f(0) = -1

    f(-1) = -3

    i) (1,1)

    f(1) = a (1) + b

    1 = a + b

    ii) (2,3)

    f(2) = a (2) + b

    3 = 2a + b

    Subtract equation (i) from (ii)

    2a – a + b – b = 3 – 1

    a = 2
    Putting this value in equation (i)

    1 = 2 + b

    b = 1 – 2

    b = -1
    Therefore, value of a = 2 and b = -1 .

    General
    Maths-

    Planet Wiener receives $2.25 for every hotdog sold. They spend $105 for 25 packages of hot dogs and 10 packages of buns. Think of the linear function that demonstrates the profit based on the number of hotdogs sold
    Rate of Change:___________
    Initial Value:______________
    Independent Variable:______
    Dependent Variable:________
    EQ of Line:________________

    HINT – $105 is an investment made before earning any profit.
    SOL – Let Dependent Variable : x given by no of hotdog sold
    Independent Variable : y given by profit earned
    It is given that Planet Wiener receives $2.25 for every hotdog sold.
    rightwards double arrow Rate of change : 2.25
    We know that Slope of the line = Rate of Change
    So, m  =  2.25                                             ---- (1)
    Planet Wiener spends $105 for 25 packages of hot dogs and 10 packages of buns. (See it as an investment made before earning any profit. So, these $105 will actually be considered in ‘-’)
    rightwards double arrow Initial Value : - 105
    This initial value is obtained when no of hotdogs sold, x = 0 i.e., it will act as y – intercept, c = - 105      ---- (2)
    Using slope intercept form equation of a line is given by
    y = mx + c where m is slope and c is y – intercept.
    rightwards double arrow Equation of line : y = 2.25x – 105       ( From (1) and (2) )

    Planet Wiener receives $2.25 for every hotdog sold. They spend $105 for 25 packages of hot dogs and 10 packages of buns. Think of the linear function that demonstrates the profit based on the number of hotdogs sold
    Rate of Change:___________
    Initial Value:______________
    Independent Variable:______
    Dependent Variable:________
    EQ of Line:________________

    Maths-General
    HINT – $105 is an investment made before earning any profit.
    SOL – Let Dependent Variable : x given by no of hotdog sold
    Independent Variable : y given by profit earned
    It is given that Planet Wiener receives $2.25 for every hotdog sold.
    rightwards double arrow Rate of change : 2.25
    We know that Slope of the line = Rate of Change
    So, m  =  2.25                                             ---- (1)
    Planet Wiener spends $105 for 25 packages of hot dogs and 10 packages of buns. (See it as an investment made before earning any profit. So, these $105 will actually be considered in ‘-’)
    rightwards double arrow Initial Value : - 105
    This initial value is obtained when no of hotdogs sold, x = 0 i.e., it will act as y – intercept, c = - 105      ---- (2)
    Using slope intercept form equation of a line is given by
    y = mx + c where m is slope and c is y – intercept.
    rightwards double arrow Equation of line : y = 2.25x – 105       ( From (1) and (2) )
    General
    Maths-

    Sketch a graph modelling a function for the following situation:
    A dog is sleeping when he hears the cat “meow” in the next room. He quickly runs to the next room where he slowly walks around looking for the cat. When he doesn’t find the cat, he sits down and goes back to sleep. Sketch a graph of a function of the dog’s speed in terms of time.

    HINT – Figure out slope of the graph with respect to situations given.
    SOL – Let dog’s speed = y
    Time taken = x
    Acc. to the question, dog was sleeping when time, x = 0 , speed, y = 0
    Then, he quickly runs to the next room i.e. speed is increasing over time. Since he moved quickly, implies that rate of change is very high.
    rightwards double arrow Slope is positive and line is very steep
    Then, he slowly walks around looking for the cat. i.e. there is a sudden decrease in the speed.
    rightwards double arrow A line parallel to y – axis will be drawn to a point where speed is less.
    And then he walks around looking for the cat i.e., speed is same over time
    rightwards double arrow A line parallel to x – axis is drawn
    Further, he sits down and goes back to sleep i.e. speed is 0
    Since speed suddenly drops to 0, so line x = 0 which is parallel to y – axis and then line y = 0 which is parallel to x – axis and has slope = 0

    Sketch a graph modelling a function for the following situation:
    A dog is sleeping when he hears the cat “meow” in the next room. He quickly runs to the next room where he slowly walks around looking for the cat. When he doesn’t find the cat, he sits down and goes back to sleep. Sketch a graph of a function of the dog’s speed in terms of time.

    Maths-General
    HINT – Figure out slope of the graph with respect to situations given.
    SOL – Let dog’s speed = y
    Time taken = x
    Acc. to the question, dog was sleeping when time, x = 0 , speed, y = 0
    Then, he quickly runs to the next room i.e. speed is increasing over time. Since he moved quickly, implies that rate of change is very high.
    rightwards double arrow Slope is positive and line is very steep
    Then, he slowly walks around looking for the cat. i.e. there is a sudden decrease in the speed.
    rightwards double arrow A line parallel to y – axis will be drawn to a point where speed is less.
    And then he walks around looking for the cat i.e., speed is same over time
    rightwards double arrow A line parallel to x – axis is drawn
    Further, he sits down and goes back to sleep i.e. speed is 0
    Since speed suddenly drops to 0, so line x = 0 which is parallel to y – axis and then line y = 0 which is parallel to x – axis and has slope = 0
    parallel

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