Maths-
General
Easy

Question

Draw a quadrilateral that is not regular.

Hint:

A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices, and four angles.

The correct answer is: We have to draw an irregular quadrilateral that are: rectangle, trapezoid, parallelogram, kite, rhombus


    Explanation:
    • We have been given information in the question to draw a quadrilateral that is not regular.
    We have to draw an irregular quadrilateral that are: rectangle, trapezoid, parallelogram, kite, rhombus.

    Related Questions to study

    General
    Maths-

    Which of the statements is TRUE?

    Explanation:
    • We have been given four statements in the question from which we have to choose which statement is true.
    • In the given four statements we have been given information about the semicircle, concave polygon, triangle and regular polygon.
    Step 1 of 1:
    Option A:
    A semicircle is a polygon.
    No this is not true, because polygon only contain straight lines.
    Option B:
    A concave polygon is regular
    It is not necessary that a concave polygon is regular.
    So, it is not true
    Option C:
    A regular polygon is equiangular
    Yes this is true, a regular polygon is equiangular and equilateral.
    Option D:
    Every triangle is regular
    This is not true, because mant triangles are not regulat.
    Hence, Option C is correct.

    Which of the statements is TRUE?

    Maths-General
    Explanation:
    • We have been given four statements in the question from which we have to choose which statement is true.
    • In the given four statements we have been given information about the semicircle, concave polygon, triangle and regular polygon.
    Step 1 of 1:
    Option A:
    A semicircle is a polygon.
    No this is not true, because polygon only contain straight lines.
    Option B:
    A concave polygon is regular
    It is not necessary that a concave polygon is regular.
    So, it is not true
    Option C:
    A regular polygon is equiangular
    Yes this is true, a regular polygon is equiangular and equilateral.
    Option D:
    Every triangle is regular
    This is not true, because mant triangles are not regulat.
    Hence, Option C is correct.
    General
    Maths-

    The length of each side of a nonagon is 8 in. Find its perimeter

    Solution:
    Hint:
    • A nonagon is a polygon with nine sides and nine angles which can be regular, irregular, concave or convex depending upon its sides and interior angles.
    Explanation:
    • We have been given the length of each side of a nonagon that is 8 in.
    • We have to find the perimeter of the given nonagon.
    Step 1 of 1:
    We have length of each side of a nanagon 8in
    Now the perimeter will be
    9 × 8in
    72in
    Hence, Option C is correct.

    The length of each side of a nonagon is 8 in. Find its perimeter

    Maths-General
    Solution:
    Hint:
    • A nonagon is a polygon with nine sides and nine angles which can be regular, irregular, concave or convex depending upon its sides and interior angles.
    Explanation:
    • We have been given the length of each side of a nonagon that is 8 in.
    • We have to find the perimeter of the given nonagon.
    Step 1 of 1:
    We have length of each side of a nanagon 8in
    Now the perimeter will be
    9 × 8in
    72in
    Hence, Option C is correct.
    General
    Maths-

    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.

    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 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

    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.

    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 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
    parallel
    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

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