Maths-
General
Easy

Question

Let A and B two sets such that n( AxB)= 6 . If three elements of AXB are ( 3,2)(7,5)(8,5), then

  1. A= {3,7,8}
  2. {2,5,7}
  3. {3,5}
  4. None of the above

Hint:

Hint:- Cartesian product of A and B is denoted by A X B and it is defined as set og all ordered pairs (a, b) such that and

The correct answer is: A= {3,7,8}


    We have given the two sets A and B
    And n( A x B)= 6
    Therefore, the one set should contain 3 and one should contain 2 elements
    Since, {(3,2),(7,5),(8,5)} are the elements of A×B.
    It follows that the elements of
    set A={3,7,8}
    and B={2,5}
    Hence,
    A × B = {(3,2),(3,5),(7,2),(7,5),(8,2),(8,5)}
    Therefore the correct option is a) A= {3,7,8}

    Related Questions to study

    General
    Maths-

    Find the number of diagonals of a 50-gon

    Solution:
    Hint:
    • A 50-gon is a fifty-sided polygon also known as pentacontagon.
    • The sum of the interior angles of a 50-gon is 8640 degrees.
    Explanation:
    • We have been given in the question about a polygon that is 50-gon.
    • We have to find the number of diagonals of a 50-gon from the four options provided.
    Step 1 of 1:
    We have to find the number of diagonals of a 50-gon
    We know that the number of diagonal in n - side polygon equalsfraction numerator n left parenthesis n minus 3 right parenthesis over denominator 2 end fraction
    Here, n = 50
    So, Number of diagonals will be
    equals fraction numerator n left parenthesis n minus 3 right parenthesis over denominator 2 end fraction
    equals fraction numerator 50 left parenthesis 50 minus 3 right parenthesis over denominator 2 end fraction
    = 25 × 47
    = 1175

    Find the number of diagonals of a 50-gon

    Maths-General
    Solution:
    Hint:
    • A 50-gon is a fifty-sided polygon also known as pentacontagon.
    • The sum of the interior angles of a 50-gon is 8640 degrees.
    Explanation:
    • We have been given in the question about a polygon that is 50-gon.
    • We have to find the number of diagonals of a 50-gon from the four options provided.
    Step 1 of 1:
    We have to find the number of diagonals of a 50-gon
    We know that the number of diagonal in n - side polygon equalsfraction numerator n left parenthesis n minus 3 right parenthesis over denominator 2 end fraction
    Here, n = 50
    So, Number of diagonals will be
    equals fraction numerator n left parenthesis n minus 3 right parenthesis over denominator 2 end fraction
    equals fraction numerator 50 left parenthesis 50 minus 3 right parenthesis over denominator 2 end fraction
    = 25 × 47
    = 1175
    General
    Maths-

    Find the GCF (GCD) of the given pair of monomials.
    10 x space straight & space 25

    Solution:
    Hint:
    • The highest number that divides exactly into two or more numbers is known as GCF.
    • An algebraic expression consisting only one term is called monomial.
    Explanation:
    • We have been given a monomial in the question
    • We have to find the GCF of the given pair of monomials.
    Step 1 of 1:
    We have given two monomials 10 x space comma space 25.
    10 x equals 5 cross times 2 cross times x
    25 equals 5 cross times 5
    The highest factor in these two monomial is 5.
    So, The GCF 10x , 25 is 5.

    Find the GCF (GCD) of the given pair of monomials.
    10 x space straight & space 25

    Maths-General
    Solution:
    Hint:
    • The highest number that divides exactly into two or more numbers is known as GCF.
    • An algebraic expression consisting only one term is called monomial.
    Explanation:
    • We have been given a monomial in the question
    • We have to find the GCF of the given pair of monomials.
    Step 1 of 1:
    We have given two monomials 10 x space comma space 25.
    10 x equals 5 cross times 2 cross times x
    25 equals 5 cross times 5
    The highest factor in these two monomial is 5.
    So, The GCF 10x , 25 is 5.
    General
    Maths-

    Find the number of diagonals of a 100-gon.

    Solution:
    Hint:
    • A hundred-sided polygon is known as 100-gon or hectogon. The sum of exterior angle of a 100-gon is 360 degrees.
    Explanation:
    • We have been given in the question the information about a polygon that is 100-gon having 100 sides
    • We have to find the number of diagonals of the 100-gon from the four options provided.
    Step 1 of 1:
    We have to find the number of diagonals of a 100-gon
    We know that the number of diagonal in n - side polygon =fraction numerator n left parenthesis n minus 3 right parenthesis over denominator 2 end fraction
    Here, n = 100
    So, Number of diagonals will be
    equals fraction numerator n left parenthesis n minus 3 right parenthesis over denominator 2 end fraction
    equals fraction numerator 100 left parenthesis 100 minus 3 right parenthesis over denominator 2 end fraction
    equals 50 cross times 97
    = 4850

    Find the number of diagonals of a 100-gon.

    Maths-General
    Solution:
    Hint:
    • A hundred-sided polygon is known as 100-gon or hectogon. The sum of exterior angle of a 100-gon is 360 degrees.
    Explanation:
    • We have been given in the question the information about a polygon that is 100-gon having 100 sides
    • We have to find the number of diagonals of the 100-gon from the four options provided.
    Step 1 of 1:
    We have to find the number of diagonals of a 100-gon
    We know that the number of diagonal in n - side polygon =fraction numerator n left parenthesis n minus 3 right parenthesis over denominator 2 end fraction
    Here, n = 100
    So, Number of diagonals will be
    equals fraction numerator n left parenthesis n minus 3 right parenthesis over denominator 2 end fraction
    equals fraction numerator 100 left parenthesis 100 minus 3 right parenthesis over denominator 2 end fraction
    equals 50 cross times 97
    = 4850
    parallel
    General
    Maths-

    Factor out the GCF from the given polynomial.
    negative 16 y to the power of 6 plus 28 y to the power of 4 minus 20 y cubed

    Solution:
    Hint:
    • The highest number that divides exactly into two or more numbers is known as GCF.
    • A polynomial is a type of algebraic expression in which the exponents of all variable should be a whole number.
    Explanation:
    • We have been given a polynomial in the question
    • We have to factor out the GCF of the given polynomial.
    Step 1 of 1:
    We have to find the GCD of the given polynomial negative 16 y to the power of 6 plus 28 y to the power of 4 minus 20 y cubed.
    Now we will factorize the given polynomial and extract the greatest factor from it.
    So,
    equals negative 16 y to the power of 6 plus 28 y to the power of 4 minus 20 y cubed
    equals 4 y cubed open parentheses negative 4 y cubed plus 7 y minus 5 close parentheses
    So, The GCD of this polynomial will be 4y3.

    Factor out the GCF from the given polynomial.
    negative 16 y to the power of 6 plus 28 y to the power of 4 minus 20 y cubed

    Maths-General
    Solution:
    Hint:
    • The highest number that divides exactly into two or more numbers is known as GCF.
    • A polynomial is a type of algebraic expression in which the exponents of all variable should be a whole number.
    Explanation:
    • We have been given a polynomial in the question
    • We have to factor out the GCF of the given polynomial.
    Step 1 of 1:
    We have to find the GCD of the given polynomial negative 16 y to the power of 6 plus 28 y to the power of 4 minus 20 y cubed.
    Now we will factorize the given polynomial and extract the greatest factor from it.
    So,
    equals negative 16 y to the power of 6 plus 28 y to the power of 4 minus 20 y cubed
    equals 4 y cubed open parentheses negative 4 y cubed plus 7 y minus 5 close parentheses
    So, The GCD of this polynomial will be 4y3.
    General
    Maths-

    Factor out the GCF from the given polynomial.
    x cubed plus 5 x squared minus 22 x

    Solution:
    Hint:
    • The highest number that divides exactly into two or more numbers is known as GCF.
    • A polynomial is a type of algebraic expression in which the exponents of all variable should be a whole number.
    Explanation:
    • We have been given a polynomial in the question
    • We have to factor out the GCF of the given polynomial.
    Step 1 of 1:
    We have to find the GCD of the given polynomial x cubed plus 5 x squared minus 22 x.
    Now we will factorize the given polynomial and extract the greatest factor from it.
    So,
    x cubed plus 5 x squared minus 22 x
    x open parentheses x squared plus 5 x minus 22 close parentheses
    So, The GCD of this polynomial will be x.

    Factor out the GCF from the given polynomial.
    x cubed plus 5 x squared minus 22 x

    Maths-General
    Solution:
    Hint:
    • The highest number that divides exactly into two or more numbers is known as GCF.
    • A polynomial is a type of algebraic expression in which the exponents of all variable should be a whole number.
    Explanation:
    • We have been given a polynomial in the question
    • We have to factor out the GCF of the given polynomial.
    Step 1 of 1:
    We have to find the GCD of the given polynomial x cubed plus 5 x squared minus 22 x.
    Now we will factorize the given polynomial and extract the greatest factor from it.
    So,
    x cubed plus 5 x squared minus 22 x
    x open parentheses x squared plus 5 x minus 22 close parentheses
    So, The GCD of this polynomial will be x.
    General
    Maths-

    text  Find m end text straight angle A text .  end text

    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 diagram of a triangle named ABC where ∠ABC=60.
    • We have to find out angle A.
    Step 1 of 1:
    We have a given figure

    In this figure,
    3 x equals 7 x minus 20
    4x = 20
    x = 50
    So,
    straight angle B equals 3 x
    = 150
    And
    straight angle C equals 7 x minus 20
    7(5) - 20
    = 150
    Now, we know that the sum of angle of triangle is 1800.
    So,
    straight angle A plus straight angle B plus straight angle C equals 180 to the power of ring operator
    straight angle A plus 15 to the power of 0 plus 15 to the power of 0 equals 180 to the power of ring operator
    straight angle A plus 30 to the power of 0 equals 180 to the power of ring operator
    straight angle A equals 150 to the power of ring operator

    text  Find m end text straight angle A text .  end text

    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 diagram of a triangle named ABC where ∠ABC=60.
    • We have to find out angle A.
    Step 1 of 1:
    We have a given figure

    In this figure,
    3 x equals 7 x minus 20
    4x = 20
    x = 50
    So,
    straight angle B equals 3 x
    = 150
    And
    straight angle C equals 7 x minus 20
    7(5) - 20
    = 150
    Now, we know that the sum of angle of triangle is 1800.
    So,
    straight angle A plus straight angle B plus straight angle C equals 180 to the power of ring operator
    straight angle A plus 15 to the power of 0 plus 15 to the power of 0 equals 180 to the power of ring operator
    straight angle A plus 30 to the power of 0 equals 180 to the power of ring operator
    straight angle A equals 150 to the power of ring operator
    parallel
    General
    Maths-

    Use Symmetric Property of Equality: If x = y, then

    Hint :- The symmetric property states that for any real numbers, a and b, if a = b then b = a.
    Ans :- Option B
    Explanation :- The symmetric property states that for any real numbers, a and b, if a = b then b = a.
    Similarly with x and y  If x = y, then y = x
    ∴ Option B

    Use Symmetric Property of Equality: If x = y, then

    Maths-General
    Hint :- The symmetric property states that for any real numbers, a and b, if a = b then b = a.
    Ans :- Option B
    Explanation :- The symmetric property states that for any real numbers, a and b, if a = b then b = a.
    Similarly with x and y  If x = y, then y = x
    ∴ Option B
    General
    Maths-

    If m straight angle B equals left parenthesis 5 x plus 7 right parenthesis to the power of 0 and m straight angle C equals left parenthesis 2 x plus 34 right parenthesis to the power of ring operator , find the value of x and m straight angle A text .  end text

    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 that if 𝑚∠𝐵 = (5𝑥 + 7) ° and 𝑚∠𝐶 = (2𝑥 + 34) °
    • We have to find the value of x and 𝑚∠A
    Step 1 of 1:
    In the given figure,

    straight angle B equals straight angle C
    So,
    5 x plus 7 equals 2 x plus 34
    3 x equals 27
    x = 9
    So,
    straight angle B equals 5 x plus 7
    = 5(9) + 7
    = 520
    And,
    straight angle C equals 2 x plus 34
    = 2(9) + 34
    = 520
    Now we know that the sum of angle of triangle is 1800.
    So,
    straight angle A plus straight angle B plus straight angle C equals 180 to the power of ring operator
    straight angle A plus 52 to the power of 0 plus 52 to the power of 0 equals 180 to the power of ring operator
    straight angle A plus 104 to the power of 0 equals 180 to the power of ring operator
    straight angle A equals 76 to the power of ring operator

    If m straight angle B equals left parenthesis 5 x plus 7 right parenthesis to the power of 0 and m straight angle C equals left parenthesis 2 x plus 34 right parenthesis to the power of ring operator , find the value of x and m straight angle A text .  end text

    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 that if 𝑚∠𝐵 = (5𝑥 + 7) ° and 𝑚∠𝐶 = (2𝑥 + 34) °
    • We have to find the value of x and 𝑚∠A
    Step 1 of 1:
    In the given figure,

    straight angle B equals straight angle C
    So,
    5 x plus 7 equals 2 x plus 34
    3 x equals 27
    x = 9
    So,
    straight angle B equals 5 x plus 7
    = 5(9) + 7
    = 520
    And,
    straight angle C equals 2 x plus 34
    = 2(9) + 34
    = 520
    Now we know that the sum of angle of triangle is 1800.
    So,
    straight angle A plus straight angle B plus straight angle C equals 180 to the power of ring operator
    straight angle A plus 52 to the power of 0 plus 52 to the power of 0 equals 180 to the power of ring operator
    straight angle A plus 104 to the power of 0 equals 180 to the power of ring operator
    straight angle A equals 76 to the power of ring operator
    General
    Maths-

    Use Substitution Property of Equality: If PQ = 10 cm , then PQ + RS =

    Hint :- substitute the given value and choose the option .
    Ans :- Option C
    Explanation :-
    If PQ = 10 cm
    then PQ + RS  = 10 cm + RS
    ∴ Option C

    Use Substitution Property of Equality: If PQ = 10 cm , then PQ + RS =

    Maths-General
    Hint :- substitute the given value and choose the option .
    Ans :- Option C
    Explanation :-
    If PQ = 10 cm
    then PQ + RS  = 10 cm + RS
    ∴ Option C
    parallel
    General
    Maths-

    Find the length of each side of the given regular dodecagon.

    Solution:
    Hint:
    • A regular dodecagon has 12 sides equal in length and all the angles have equal measures, all the 12 vertices are equidistant from the center of dodecagon.
    • A regular dodecagon is a symmetrical polygon.
    Explanation:
    • We have been given in the question figure of a regular dodecagon
    • We have also been given the two sides of it that is -
    • We have to find length of each side of the regular dodecagon.

    We have given a regular dodecagon with sides represented as x squared plus 2 x minus 1 semicolon x squared plus 9 x plus 15
    Since, It is regular, then all sides are equal
    So,
    x squared plus 2 x minus 1 equals x squared plus 9 x plus 15
    2x - 1 = 9x + 15
    7x = - 16
    X can not be negative
    Wrong data

    Find the length of each side of the given regular dodecagon.

    Maths-General
    Solution:
    Hint:
    • A regular dodecagon has 12 sides equal in length and all the angles have equal measures, all the 12 vertices are equidistant from the center of dodecagon.
    • A regular dodecagon is a symmetrical polygon.
    Explanation:
    • We have been given in the question figure of a regular dodecagon
    • We have also been given the two sides of it that is -
    • We have to find length of each side of the regular dodecagon.

    We have given a regular dodecagon with sides represented as x squared plus 2 x minus 1 semicolon x squared plus 9 x plus 15
    Since, It is regular, then all sides are equal
    So,
    x squared plus 2 x minus 1 equals x squared plus 9 x plus 15
    2x - 1 = 9x + 15
    7x = - 16
    X can not be negative
    Wrong data
    General
    Maths-

    Draw a quadrilateral that is not regular.

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

    Draw a quadrilateral that is not regular.

    Maths-General
    Solution:
    Hint:
    • A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices, and four angles.
    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.
    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.
    parallel
    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
    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
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.