Maths-
General
Easy

Question

The set of ordered pairs (1,19)(2,23) (3,23) (4,29)(5,31) represents the number of tickets sold to a fundraiser. The input values represents the day and the output values represents the number of tickets sold on that day.
a) Make an arrow diagram that represents the relation
b) Is the relation a function ? Explain.

Hint:

An ordered pair is represented as (INPUT, OUTPUT)
A function from set A to the set B is a relation which associates every element of a set A to unique element of set B.

The correct answer is: {19 , 23 , 29 , 31}


    We have given the set of ordered pairs (1,19)(2,23) (3,23) (4,29)(5,31) which represents the number of tickets sold to a fundraiser
    We have data as
    (1,19)(2,23) (3,23) (4,29)(5,31)
    Domain (Day) :- {1, 2 , 3 , 4 , 5}
    Co- domain(tickets sold) :- {19 , 23 , 29 , 31}
    a)    Arrow diagram of the given data is


    b) From the given data we can analyse that each element in the domain input set has exactly one output.
    The members in the domain set has its square as a output in the co-domain set
    Therefore, the given data is a function.

    All functions are relations but all relations are not functions.

    Related Questions to study

    General
    Maths-

    The perimeter of a regular dodecagon is 108 . Find the length of each side.

    Solution:
    Hint:
    • A dodecagon is a polygon with 12 sides, 12 vertices and 12 angles. Dodecagon can be regular in which all the sides and interior angles are equal in measure.
    Explanation:
    • We have been given the perimeter of dodecagon in the question that is 108
    • We have to find the length of each side of the dodecagon.
    Step 1 of 1:
    We have given a perimeter of a regular dodecagon 108.
    A dodecagon has 12 sides.
    Let the length of the side be a
    So,
    12a = 108
    a = 9
    So, The length of the side is
    Hence, Option C is correct.

    The perimeter of a regular dodecagon is 108 . Find the length of each side.

    Maths-General
    Solution:
    Hint:
    • A dodecagon is a polygon with 12 sides, 12 vertices and 12 angles. Dodecagon can be regular in which all the sides and interior angles are equal in measure.
    Explanation:
    • We have been given the perimeter of dodecagon in the question that is 108
    • We have to find the length of each side of the dodecagon.
    Step 1 of 1:
    We have given a perimeter of a regular dodecagon 108.
    A dodecagon has 12 sides.
    Let the length of the side be a
    So,
    12a = 108
    a = 9
    So, The length of the side is
    Hence, Option C is correct.
    General
    Maths-

    Solve x plus 3 over 4 equals 3 over 8 x minus 1 half. Write a reason for each step.

    Ans:- x = -2
    Given ,x plus 3 over 4 equals 3 over 8 x minus 1 half.
    Subtract 3 over 8 X  from both sides by subtraction property of equality both sides remain equal.

        x plus 3 over 4 minus 3 over 8 x equals 3 over 8 x minus 1 half minus 3 over 8 x

        5 over 8 x plus 3 over 4 equals negative 1 half.
    Subtract 3 over 4 from both sides by subtraction property of equality both sides remain equal.

       5 over 8 x plus 3 over 4 minus 3 over 4 equals negative 1 half minus 3 over 4

       5 over 8 x equals negative 5 over 4.
    Divide both side with 5 over 8 left parenthesis not equal to 0 right parenthesis by division property of equality both sides remain equal.

      fraction numerator 5 over 8 x over denominator begin display style 5 over 8 end style end fraction equals fraction numerator negative 5 over 4 over denominator begin display style 5 over 8 end style end fraction not stretchy rightwards double arrow space x space equals fraction numerator negative 5 over denominator 4 end fraction cross times 8 over 5

       x =  - 2

    ∴ x  = - 2

    Solve x plus 3 over 4 equals 3 over 8 x minus 1 half. Write a reason for each step.

    Maths-General
    Ans:- x = -2
    Given ,x plus 3 over 4 equals 3 over 8 x minus 1 half.
    Subtract 3 over 8 X  from both sides by subtraction property of equality both sides remain equal.

        x plus 3 over 4 minus 3 over 8 x equals 3 over 8 x minus 1 half minus 3 over 8 x

        5 over 8 x plus 3 over 4 equals negative 1 half.
    Subtract 3 over 4 from both sides by subtraction property of equality both sides remain equal.

       5 over 8 x plus 3 over 4 minus 3 over 4 equals negative 1 half minus 3 over 4

       5 over 8 x equals negative 5 over 4.
    Divide both side with 5 over 8 left parenthesis not equal to 0 right parenthesis by division property of equality both sides remain equal.

      fraction numerator 5 over 8 x over denominator begin display style 5 over 8 end style end fraction equals fraction numerator negative 5 over 4 over denominator begin display style 5 over 8 end style end fraction not stretchy rightwards double arrow space x space equals fraction numerator negative 5 over denominator 4 end fraction cross times 8 over 5

       x =  - 2

    ∴ x  = - 2

    General
    Maths-

    Is the relation shown below a function ? Explain
    (4,16)(5,25)(3,9)(6,36)(2,4)(1,1)

    We have given the data as
    (4,16)(5,25)(3,9)(6,36)(2,4)(1,1)
    Domain:-  {  4, 5 , 3 , 6 , 2 , 1  }
    Co- Domain:- { 16, 25 , 9 , 36 , 4 , 1}
    From the given data we can analyse that each element in the domain input set has exactly one output.
    The members in the domain set has its square as a output in the co-domain set
    Therefore, the given data is a function.

    Is the relation shown below a function ? Explain
    (4,16)(5,25)(3,9)(6,36)(2,4)(1,1)

    Maths-General
    We have given the data as
    (4,16)(5,25)(3,9)(6,36)(2,4)(1,1)
    Domain:-  {  4, 5 , 3 , 6 , 2 , 1  }
    Co- Domain:- { 16, 25 , 9 , 36 , 4 , 1}
    From the given data we can analyse that each element in the domain input set has exactly one output.
    The members in the domain set has its square as a output in the co-domain set
    Therefore, the given data is a function.
    parallel
    General
    Maths-

    Is the relation shown below a function ? Explain

    We have given the data in the arrow diagram format.
    We will convert the given data into points
    As (5, 10), (10, 20) , (15, 30) , (20, 40) , (20, 50)
    Domain:-  { 5 , 10 , 15 , 20 }
    Co- Domain:- { 10, 20, 30 , 40 , 50 }
    From the given data we can analyse that the member in the domain set i.e.20 has two images i.e. 40 and 50 in the co-domain .
    We know that in a function one member in the domain set cannot have two images in the co-domain set.
    Therefore, the given relation is not a function.

    Is the relation shown below a function ? Explain

    Maths-General
    We have given the data in the arrow diagram format.
    We will convert the given data into points
    As (5, 10), (10, 20) , (15, 30) , (20, 40) , (20, 50)
    Domain:-  { 5 , 10 , 15 , 20 }
    Co- Domain:- { 10, 20, 30 , 40 , 50 }
    From the given data we can analyse that the member in the domain set i.e.20 has two images i.e. 40 and 50 in the co-domain .
    We know that in a function one member in the domain set cannot have two images in the co-domain set.
    Therefore, the given relation is not a function.
    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 given a figure with three unknown angles x, y, z.
    • We have to find the value of x, y, z.
    Step 1 of 1:
    We have given figure,

    In , A B C comma A C equals B C
    straight angle B A C equals straight angle C A B equals 25 to the power of ring operator
    Now, By Exterior angle theorem of triangle,
    straight angle B A C plus straight angle C A B equals straight angle A C D
    So,
    straight angle A C D equals straight angle B A C plus straight angle C A B
    straight angle A C D equals 25 plus 25
    = 50
    So, x = 500
    Since, AC = AD
    Then
    y = x = 500
    Now, y and z form linear pair then,
    y plus z equals 180 to the power of ring operator
    500 + z = 1800
    z = 1300
    So,
    x = 500
    y = 500

    z = 1300

    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 given a figure with three unknown angles x, y, z.
    • We have to find the value of x, y, z.
    Step 1 of 1:
    We have given figure,

    In , A B C comma A C equals B C
    straight angle B A C equals straight angle C A B equals 25 to the power of ring operator
    Now, By Exterior angle theorem of triangle,
    straight angle B A C plus straight angle C A B equals straight angle A C D
    So,
    straight angle A C D equals straight angle B A C plus straight angle C A B
    straight angle A C D equals 25 plus 25
    = 50
    So, x = 500
    Since, AC = AD
    Then
    y = x = 500
    Now, y and z form linear pair then,
    y plus z equals 180 to the power of ring operator
    500 + z = 1800
    z = 1300
    So,
    x = 500
    y = 500

    z = 1300
    General
    Maths-

    Is the relation shown below a function ? Explain.

    We have given the data in the tabular format
    We will convert it into point format
    As (3,4) , (4, 6) , (1, 2) , (5, 8) , (2, 5)
    Domain:-  {  3, 4, 1 , 5 , 2 }
    Co- Domain:- { 4, 6 , 2 , 8 , 5 }
    From the given data we can analyse that each element in the domain input set has exactly one output.
    Therefore, the given data is a function.

    Is the relation shown below a function ? Explain.

    Maths-General
    We have given the data in the tabular format
    We will convert it into point format
    As (3,4) , (4, 6) , (1, 2) , (5, 8) , (2, 5)
    Domain:-  {  3, 4, 1 , 5 , 2 }
    Co- Domain:- { 4, 6 , 2 , 8 , 5 }
    From the given data we can analyse that each element in the domain input set has exactly one output.
    Therefore, the given data is a function.
    parallel
    General
    Maths-

    Six more than eight times a number is forty-six. Find the number.

    Hint :- assume the number and frame the equation to solve from the condition and solve it to get the number .
    Ans:- the number is 5.
    Explanation :-
    Let the number be x
    Six more than eight times a number is forty-six
    6+ 8x = 46
    8x = 46 -6
    8x = 40
    x equals 40 over 8 equals 5
    ∴The unknown Number is 5

    Six more than eight times a number is forty-six. Find the number.

    Maths-General
    Hint :- assume the number and frame the equation to solve from the condition and solve it to get the number .
    Ans:- the number is 5.
    Explanation :-
    Let the number be x
    Six more than eight times a number is forty-six
    6+ 8x = 46
    8x = 46 -6
    8x = 40
    x equals 40 over 8 equals 5
    ∴The unknown Number is 5
    General
    Maths-

    Sravs and her parents are going to an art museum for the day. The Parking garage near the museum charges the rates shown here below:

    a) Is the cost to park a function of time ? Explain .
    b) If they stay at the museum for 6 hours , Should they expect to pay more than $25.

    We have given the two data of Time and Cost.
    We will convert the given data into points
    As (1,5), (2,10) , (3,15) , (4,20) , (5,25)
    Domain:-  { 1, 2, 3, 4, 5 }
    Co- Domain:- { 5, 10, 15, 20, 25 }
    From the given data we can analyse that the every member in the domain set has unique image in the co-domain set .
    It is an identity function.
    We can represent the given function as

    y = 5 x
    where x is time and y is cost
    a) Yes, because as the time increases the cost increases 5 times the cost.
    b) If they stay at museum for 6 hours then x = 6

    y = 5 x = 5 (6)

    = 30
    Which is greater than $25
    So they have to pay more than $25.
    Note: All functions are relations but all relations are not functions

    Sravs and her parents are going to an art museum for the day. The Parking garage near the museum charges the rates shown here below:

    a) Is the cost to park a function of time ? Explain .
    b) If they stay at the museum for 6 hours , Should they expect to pay more than $25.

    Maths-General
    We have given the two data of Time and Cost.
    We will convert the given data into points
    As (1,5), (2,10) , (3,15) , (4,20) , (5,25)
    Domain:-  { 1, 2, 3, 4, 5 }
    Co- Domain:- { 5, 10, 15, 20, 25 }
    From the given data we can analyse that the every member in the domain set has unique image in the co-domain set .
    It is an identity function.
    We can represent the given function as

    y = 5 x
    where x is time and y is cost
    a) Yes, because as the time increases the cost increases 5 times the cost.
    b) If they stay at museum for 6 hours then x = 6

    y = 5 x = 5 (6)

    = 30
    Which is greater than $25
    So they have to pay more than $25.
    Note: All functions are relations but all relations are not functions

    General
    Maths-

    Is the following ordered pairs forms a function ?
    (54,9)( 54, 10 )(61,17) (45, 10)(65,11) (50 , 12)

    We have given the data in the form of ordered pairs.
    We will convert the given data into points
    As (54, 9), (54, 10) , (61, 17) , (45, 10) , (65, 11) , (50 , 12)
    Domain:-  { 54 , 61 ,45, 65 , 50 }
    Co- Domain:- { 9, 10,17 , 11,12 }
    From the given data we can analyse that the member in the domain set i.e.54 has two images i.e. 9 and 10 in the co-domain .
    We know that in a function one member in the domain set cannot have two images in the co-domain set.
    Therefore, the given relation is not a function.
    Note: All functions are relations but all relations are not functions.

    Is the following ordered pairs forms a function ?
    (54,9)( 54, 10 )(61,17) (45, 10)(65,11) (50 , 12)

    Maths-General
    We have given the data in the form of ordered pairs.
    We will convert the given data into points
    As (54, 9), (54, 10) , (61, 17) , (45, 10) , (65, 11) , (50 , 12)
    Domain:-  { 54 , 61 ,45, 65 , 50 }
    Co- Domain:- { 9, 10,17 , 11,12 }
    From the given data we can analyse that the member in the domain set i.e.54 has two images i.e. 9 and 10 in the co-domain .
    We know that in a function one member in the domain set cannot have two images in the co-domain set.
    Therefore, the given relation is not a function.
    Note: All functions are relations but all relations are not functions.
    parallel
    General
    Maths-

    • We have been given in the question that △ 𝑋𝑌𝑍, 𝑥 = 𝑦 = 𝑧 represent the three equal sides
    • We have to find out △ 𝑋𝑌Z from the given four options.
    Step 1 of 1:
    We have given in XYZ

     x = y = z
    We know that, when all side of a triangle are equal, then it is equilateral triangle.
    So,
    XYZ is equilateral triangle.
    Also,
    In equilateral triangle, all angles are equal.
    So, It is also called as equiangular
    Hence, Option A&B is correct.
    Or
    Option C is correct.

    Maths-General
    • We have been given in the question that △ 𝑋𝑌𝑍, 𝑥 = 𝑦 = 𝑧 represent the three equal sides
    • We have to find out △ 𝑋𝑌Z from the given four options.
    Step 1 of 1:
    We have given in XYZ

     x = y = z
    We know that, when all side of a triangle are equal, then it is equilateral triangle.
    So,
    XYZ is equilateral triangle.
    Also,
    In equilateral triangle, all angles are equal.
    So, It is also called as equiangular
    Hence, Option A&B is correct.
    Or
    Option C is correct.

    General
    Maths-

    Rita uses a table to record the ages and heights of the six students he tutors . Is the relation a function ? Explain .

    We have given the two data of Age and Height.
    We will convert the given data into points
    As (9, 54), (10, 54) , (9, 61) , (8, 45) , (12, 65) , (8 , 50)
    Domain:-  { 9 , 10 , 8 , 12 }
    Co- Domain:- { 54, 61, 45 , 65 , 50 }
    From the given data we can analyse that the member in the domain set i.e.8 has two images i.e. 45 and 50 in the co-domain .
    We know that in a function one member in the domain set cannot have two images in the co-domain set.
    Therefore, the given relation is not a function.
    Note: All functions are relations but all relations are not functions.

    Rita uses a table to record the ages and heights of the six students he tutors . Is the relation a function ? Explain .

    Maths-General
    We have given the two data of Age and Height.
    We will convert the given data into points
    As (9, 54), (10, 54) , (9, 61) , (8, 45) , (12, 65) , (8 , 50)
    Domain:-  { 9 , 10 , 8 , 12 }
    Co- Domain:- { 54, 61, 45 , 65 , 50 }
    From the given data we can analyse that the member in the domain set i.e.8 has two images i.e. 45 and 50 in the co-domain .
    We know that in a function one member in the domain set cannot have two images in the co-domain set.
    Therefore, the given relation is not a function.
    Note: All functions are relations but all relations are not functions.
    General
    Maths-

    Solve 3(5x + 1) = 2(x + 21). Write a reason for each step.

    Ans:- x = 3
    Given ,3(5x + 1) = 2(x + 21).
    By left distributive property 15x + 3  =  2x + 42
    Subtract 2x from both sides by subtraction property of equality both sides remains equal.
    15x - 2x + 3 = 2x + 42 - 2x
    13x + 3 = 42
    Subtract 3 from both sides by subtraction property of equality both sides remains equal.
    13x + 3 - 3 = 42 - 3
    13x  =  39
    Dividing 9left parenthesis not equal to 0 right parenthesis by division property of equality both sides remains equal.
    fraction numerator 13 x over denominator 13 end fraction equals 39 over 13
    x = 3

    Solve 3(5x + 1) = 2(x + 21). Write a reason for each step.

    Maths-General
    Ans:- x = 3
    Given ,3(5x + 1) = 2(x + 21).
    By left distributive property 15x + 3  =  2x + 42
    Subtract 2x from both sides by subtraction property of equality both sides remains equal.
    15x - 2x + 3 = 2x + 42 - 2x
    13x + 3 = 42
    Subtract 3 from both sides by subtraction property of equality both sides remains equal.
    13x + 3 - 3 = 42 - 3
    13x  =  39
    Dividing 9left parenthesis not equal to 0 right parenthesis by division property of equality both sides remains equal.
    fraction numerator 13 x over denominator 13 end fraction equals 39 over 13
    x = 3
    parallel
    General
    Maths-

    ABCDE is a regular polygon. Find the length of each side.

    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 a regular polygon figure named ABCDE. and also, the length of two sides that is – AB and DC.
    • We have to find the length of each side of the polygon.
    Step 1 of 1:
    We have given a regular polygon
    We know that a regular polygon has all sides equal.
    So,
    4x + 7 = 5x - 2
    x = 7 + 2
    x = 9
    Now put this value in any of the side
    5x - 2
    5(9) - 2
    43
    Hence, The length of the side is 43.

    ABCDE is a regular polygon. Find the length of each side.

    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 a regular polygon figure named ABCDE. and also, the length of two sides that is – AB and DC.
    • We have to find the length of each side of the polygon.
    Step 1 of 1:
    We have given a regular polygon
    We know that a regular polygon has all sides equal.
    So,
    4x + 7 = 5x - 2
    x = 7 + 2
    x = 9
    Now put this value in any of the side
    5x - 2
    5(9) - 2
    43
    Hence, The length of the side is 43.
    General
    Maths-

    Srinu needs to advertise his company . he Considers several different brochures of different lengths and areas. He presents the data as ordered pairs (4,24) (5,35 )(8,24) (2,20) (9,27).
    Represent it in an arrow diagram and explain whether it is a function or not .

    We have given the following data of Srinu’s company
    (4,24) (5,35 )(8,24) (2,20) (9,27)
    Arrow diagram for the given data will be

    We have drawn the arrow diagram of the given data
    From the given data we can analyse that each element in the domain set A has exactly one output.
    Therefore, the given data is a function.
    Note: All functions are relations but all relations are not functions.

    Srinu needs to advertise his company . he Considers several different brochures of different lengths and areas. He presents the data as ordered pairs (4,24) (5,35 )(8,24) (2,20) (9,27).
    Represent it in an arrow diagram and explain whether it is a function or not .

    Maths-General
    We have given the following data of Srinu’s company
    (4,24) (5,35 )(8,24) (2,20) (9,27)
    Arrow diagram for the given data will be

    We have drawn the arrow diagram of the given data
    From the given data we can analyse that each element in the domain set A has exactly one output.
    Therefore, the given data is a function.
    Note: All functions are relations but all relations are not functions.
    General
    Maths-

    Solve 3(x − 7) = 2(x − 3). Write a reason for each step.

    Hint :- using the additive property and subtraction property ,division property on both sides .solve for x.
    Ans:- x = 15
    Explanation :-
    Given ,3(x − 7) = 2(x -3).
    By left distributive property 3x - 21 = 2x - 6
    Adding 21 on both sides by additive property of equality both sides remain equal.
    3x - 21 + 21 = 2x - 6 + 21
    3x = 2x + 15
    Subtract 2x from both sides by subtraction property of equality both sides remains equal.
    3x - 2x = 2x +15 - 2x
    x = 15
    ∴x = 15

    Solve 3(x − 7) = 2(x − 3). Write a reason for each step.

    Maths-General
    Hint :- using the additive property and subtraction property ,division property on both sides .solve for x.
    Ans:- x = 15
    Explanation :-
    Given ,3(x − 7) = 2(x -3).
    By left distributive property 3x - 21 = 2x - 6
    Adding 21 on both sides by additive property of equality both sides remain equal.
    3x - 21 + 21 = 2x - 6 + 21
    3x = 2x + 15
    Subtract 2x from both sides by subtraction property of equality both sides remains equal.
    3x - 2x = 2x +15 - 2x
    x = 15
    ∴x = 15
    parallel

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