Maths-
General
Easy

Question

Graph the following functions by filling out the X/Y chart using the given inputs
Y equals square root of X plus 7 end root
X -7 -6 -3 2 9
Y          

Hint:

First, we complete the table by calculating the values of y corresponding to each value of x from the given equation. To make the graph of the function, we draw perpendicular lines, x axis and y axis; then we plot the ordered points in the xy plane and join the points by a smooth curve to get the required graph.

The correct answer is: 0,1,2,3,4


    Step by step solution:
    The given equation is
    Y equals square root of X plus 7 end root
    Putting x = -7 in the above equation, we get the value of y as
    y equals square root of negative 7 plus 7 end root equals 0
    Similarly, putting x = -6, we get
    y equals square root of negative 6 plus 7 end root equals square root of 1 equals 1
    Putting x = -3 we have
    y equals square root of negative 3 plus 7 end root equals square root of 4 equals 2
    Putting x = 2 we have
    y equals square root of 2 plus 7 end root equals square root of 9 equals 3
    Finally, putting x = 9, we have
    y equals square root of 9 plus 7 end root equals square root of 16 equals 4
    Completing the table, we have
    x
    -7
    -6
    -3
    2
    9
    y
    0
    1
    2
    3
    4
    We plot these points on the xy plane

    After plotting the points, we join them with a smooth curve to get the graph of the equation.

    We can find the tabular values for any points of x and then plot them on the graph. But we usually choose values for which calculating y is easier. Either way, we need points satisfying the equation to plot its graph.

    Related Questions to study

    General
    Maths-

    Make and test a conjecture about the square of even numbers.

    SOLUTION:
    HINT: Take general form and check.
    Complete step by step solution:
    The square of an even number is always an even number.
    We know that the even number is always of the form 2n
    Let some N = 2n
    On squaring both the sides, we get N squared equals left parenthesis 2 n right parenthesis squared
    not stretchy rightwards double arrow N squared equals 4 n squared
    On taking common from RHS part, we get N squared equals 2 open parentheses 2 n squared close parentheses equals 2 m
    So we get that the square of an even number is always even.

    Make and test a conjecture about the square of even numbers.

    Maths-General
    SOLUTION:
    HINT: Take general form and check.
    Complete step by step solution:
    The square of an even number is always an even number.
    We know that the even number is always of the form 2n
    Let some N = 2n
    On squaring both the sides, we get N squared equals left parenthesis 2 n right parenthesis squared
    not stretchy rightwards double arrow N squared equals 4 n squared
    On taking common from RHS part, we get N squared equals 2 open parentheses 2 n squared close parentheses equals 2 m
    So we get that the square of an even number is always even.
    General
    Maths-

    Graph the following functions by filling out the X/Y chart using the given inputs
    straight Y equals square root of X plus 9 end root
    X -9 -8 -5 0 7
    Y          

    Step by step solution:
    The given equation is
    straight Y equals square root of X plus 9 end root
    Putting x = -9 in the above equation, we get the value of y as
    y equals square root of negative 9 plus 9 end root equals 0
    Similarly, putting x = -8, we get
    y equals square root of negative 8 plus 9 end root equals square root of 1 equals 1
    Putting x = -5 we have
    y equals square root of negative 5 plus 9 end root equals square root of 4 equals 2
    Putting x = 0 we have
    y equals square root of 0 plus 9 end root equals square root of 9 equals 3
    Finally, putting x = 7, we have
    y equals square root of 7 plus 9 end root equals square root of 16 equals 4
    Completing the table, we have
    x
    -9
    -8
    -5
    0
    7
    y
    0
    1
    2
    3
    4
    We plot these points on the xy plane

    After plotting the points, we join them with a smooth curve to get the graph of the equation.

    Graph the following functions by filling out the X/Y chart using the given inputs
    straight Y equals square root of X plus 9 end root
    X -9 -8 -5 0 7
    Y          

    Maths-General
    Step by step solution:
    The given equation is
    straight Y equals square root of X plus 9 end root
    Putting x = -9 in the above equation, we get the value of y as
    y equals square root of negative 9 plus 9 end root equals 0
    Similarly, putting x = -8, we get
    y equals square root of negative 8 plus 9 end root equals square root of 1 equals 1
    Putting x = -5 we have
    y equals square root of negative 5 plus 9 end root equals square root of 4 equals 2
    Putting x = 0 we have
    y equals square root of 0 plus 9 end root equals square root of 9 equals 3
    Finally, putting x = 7, we have
    y equals square root of 7 plus 9 end root equals square root of 16 equals 4
    Completing the table, we have
    x
    -9
    -8
    -5
    0
    7
    y
    0
    1
    2
    3
    4
    We plot these points on the xy plane

    After plotting the points, we join them with a smooth curve to get the graph of the equation.
    General
    General

    Choose the synonym for 'Present’?

    Correct answer a) Current.
    Explanation- "Present - Existing or happening now”

    Choose the synonym for 'Present’?

    GeneralGeneral
    Correct answer a) Current.
    Explanation- "Present - Existing or happening now”
    parallel
    General
    Maths-

    Make and test a conjecture about the square of odd numbers.

    HINT: Take general form and check.
    Complete step by step solution:
    The square of an odd number is always an odd number.
    We know that the odd number is always of the form 2n+1
    Let some N = 2n + 1
    On squaring both the sides, we get N squared equals open parentheses 2 n plus 1 close parentheses squared
    not stretchy rightwards double arrow N squared equals 4 n squared plus 4 n plus 1
    On taking common from RHS part, we get N squared equals 2 n left parenthesis 2 n plus 1 right parenthesis plus 1
    not stretchy rightwards double arrow N squared equals 2 n left parenthesis N right parenthesis plus 1 left parenthesis text  since  end text N equals 2 n plus 1 right parenthesis
    not stretchy rightwards double arrow N equals 2 n plus 1
    So we get that the square of an odd number is always odd.
    Note: We can take the form of N = 2n - 1 and then find the square and then also
    we get that the square of an odd number is always odd.

    Make and test a conjecture about the square of odd numbers.

    Maths-General
    HINT: Take general form and check.
    Complete step by step solution:
    The square of an odd number is always an odd number.
    We know that the odd number is always of the form 2n+1
    Let some N = 2n + 1
    On squaring both the sides, we get N squared equals open parentheses 2 n plus 1 close parentheses squared
    not stretchy rightwards double arrow N squared equals 4 n squared plus 4 n plus 1
    On taking common from RHS part, we get N squared equals 2 n left parenthesis 2 n plus 1 right parenthesis plus 1
    not stretchy rightwards double arrow N squared equals 2 n left parenthesis N right parenthesis plus 1 left parenthesis text  since  end text N equals 2 n plus 1 right parenthesis
    not stretchy rightwards double arrow N equals 2 n plus 1
    So we get that the square of an odd number is always odd.
    Note: We can take the form of N = 2n - 1 and then find the square and then also
    we get that the square of an odd number is always odd.
    General
    General

    Complete the sentences with a subordinating cogs Rehire, at trough once. since

    Complete the sentences with a subordinating cogs Rehire, at trough once. since

    GeneralGeneral
    General
    Maths-

    Graph the following functions by filling out the X/Y chart using the given inputs
    straight Y equals x over 3 plus 2
    X -6 -3 0 3 6
    Y          

    Step by step solution:
    The given equation is
    y equals x over 3 plus 2
    Putting X = -6 in the above equation, we get the value of y as
    y equals fraction numerator negative 6 over denominator 3 end fraction plus 2 equals negative 2 plus 2 equals 0
    Similarly, putting X = -3 we get
    y equals fraction numerator negative 3 over denominator 3 end fraction plus 2 equals negative 1 plus 2 equals 1
    Putting X = 0 in the above equation, we have
    y equals 0 over 3 plus 2 equals 0 plus 2 equals 2
    Putting X = 3 in the above equation, we have
    y equals 3 over 3 plus 2 equals 1 plus 2 equals 3
    Finally, putting X = 6 in the above equation, we have
    y equals 6 over 3 plus 2 equals 2 plus 2 equals 4
    Completing the table, we get
    x
    -6
    -3
    0
    3
    6
    y
    0
    1
    2
    3
    4
    We plot these points on the xy plane.

    After plotting the points, we join them with a line to get the graph of the equation.

    Graph the following functions by filling out the X/Y chart using the given inputs
    straight Y equals x over 3 plus 2
    X -6 -3 0 3 6
    Y          

    Maths-General
    Step by step solution:
    The given equation is
    y equals x over 3 plus 2
    Putting X = -6 in the above equation, we get the value of y as
    y equals fraction numerator negative 6 over denominator 3 end fraction plus 2 equals negative 2 plus 2 equals 0
    Similarly, putting X = -3 we get
    y equals fraction numerator negative 3 over denominator 3 end fraction plus 2 equals negative 1 plus 2 equals 1
    Putting X = 0 in the above equation, we have
    y equals 0 over 3 plus 2 equals 0 plus 2 equals 2
    Putting X = 3 in the above equation, we have
    y equals 3 over 3 plus 2 equals 1 plus 2 equals 3
    Finally, putting X = 6 in the above equation, we have
    y equals 6 over 3 plus 2 equals 2 plus 2 equals 4
    Completing the table, we get
    x
    -6
    -3
    0
    3
    6
    y
    0
    1
    2
    3
    4
    We plot these points on the xy plane.

    After plotting the points, we join them with a line to get the graph of the equation.
    parallel
    General
    Maths-

    Make and test a conjecture about the sign of the product of any two negative integers.

    SOLUTION:
    HINT: Use an example to prove it.
    Complete step by step solution:
    Take 2 negative numbers to be -3 and -4
    So, product of - 3 and - 4 = - 3×- 4 = 12
    We get that, the product of 2 negative numbers is always a positive number.

    Make and test a conjecture about the sign of the product of any two negative integers.

    Maths-General
    SOLUTION:
    HINT: Use an example to prove it.
    Complete step by step solution:
    Take 2 negative numbers to be -3 and -4
    So, product of - 3 and - 4 = - 3×- 4 = 12
    We get that, the product of 2 negative numbers is always a positive number.
    General
    General

    Choose whether the following is a simile or a metaphor
    "Busy as a bee"?

    Correct answer a) Simile
    Explanation - Simile- Compares two different things. Something is like or as something else
    Example - She swam like a fish.
    Metaphor - Compares two different things. Something is something else
    Example- Time is money.

    Choose whether the following is a simile or a metaphor
    "Busy as a bee"?

    GeneralGeneral
    Correct answer a) Simile
    Explanation - Simile- Compares two different things. Something is like or as something else
    Example - She swam like a fish.
    Metaphor - Compares two different things. Something is something else
    Example- Time is money.
    General
    Maths-

    Mark has $100 gift card to buy apps for his smart phone .Each week he buys one new app for $4.99
    a) Write an equation that relates the amount left on the card ,y , over time x.
    b) Make a graph of the function

    Step by step solution:
    Let the amount left on the gift card be denoted by y.
    Let the time (in weeks) be denoted by x.
    The initial amount on the gift card = $100
    Amount spent each week = $4.99
    Thus, we can say that
    Rate of change of amount left in the gift card with respect to time (in weeks), m = - 4.99
    The value is negative as the amount is decreasing.
    Initial value, c = 100
    Using the slope intercept form of an equation
    y = mx + c
    We get
    y = -4.99x + 100
    The above equation relates the amount left on the card over time
    Next, we construct a table with different values of x and corresponding values of y.
    Putting x = 0 in the above equation, we will get, y = 100
    Similarly, putting x = 1, in the above equation, we get y = 95.01
    Continuing this way, we have
    For x = 2, we get y = 90.02
    For x = 3, we get y = 85.03
    For x = 4, we get y = 80.04
    Making a table of all these points, we have
    x
    0
    1
    2
    3
    4
    y
    100
    95.01
    90.02
    85.03
    80.04
    Now we plot these points on the graph.

    This is the required graph.

    Mark has $100 gift card to buy apps for his smart phone .Each week he buys one new app for $4.99
    a) Write an equation that relates the amount left on the card ,y , over time x.
    b) Make a graph of the function

    Maths-General
    Step by step solution:
    Let the amount left on the gift card be denoted by y.
    Let the time (in weeks) be denoted by x.
    The initial amount on the gift card = $100
    Amount spent each week = $4.99
    Thus, we can say that
    Rate of change of amount left in the gift card with respect to time (in weeks), m = - 4.99
    The value is negative as the amount is decreasing.
    Initial value, c = 100
    Using the slope intercept form of an equation
    y = mx + c
    We get
    y = -4.99x + 100
    The above equation relates the amount left on the card over time
    Next, we construct a table with different values of x and corresponding values of y.
    Putting x = 0 in the above equation, we will get, y = 100
    Similarly, putting x = 1, in the above equation, we get y = 95.01
    Continuing this way, we have
    For x = 2, we get y = 90.02
    For x = 3, we get y = 85.03
    For x = 4, we get y = 80.04
    Making a table of all these points, we have
    x
    0
    1
    2
    3
    4
    y
    100
    95.01
    90.02
    85.03
    80.04
    Now we plot these points on the graph.

    This is the required graph.
    parallel
    General
    General

    Chore the correct synonym for the word 'text'.

    Correct answer a) words
    Explanation - text  the words of something writer

    Chore the correct synonym for the word 'text'.

    GeneralGeneral
    Correct answer a) words
    Explanation - text  the words of something writer
    General
    General

    Choose the synonym for "Jumped”

    Correct answer a) leaped
    Explanation - to push yourself suddenly off the ground into and go over something.

    Choose the synonym for "Jumped”

    GeneralGeneral
    Correct answer a) leaped
    Explanation - to push yourself suddenly off the ground into and go over something.
    General
    Maths-

    Use the function Y = 1.5X + 3 to complete the table of values.
    X        
    Y 9 6 0 -3

    Step by step solution:
    The given equation is
    Y = 1.5x + 3
    We rewrite this equation with ‘x’ on one side of the equation so that it is easy to find its value.
    table attributes columnspacing 1em end attributes row cell 1.5 x equals y minus 3 end cell row cell not stretchy rightwards double arrow x equals fraction numerator 1 over denominator 1.5 end fraction left parenthesis y minus 3 right parenthesis end cell end table
    Using , we get
    x equals 2 over 3 left parenthesis y minus 3 right parenthesis
    Now, we calculate x for the given values of y.
    Putting y = 9, in the above equation, we get,
    x equals 2 over 3 left parenthesis 9 minus 3 right parenthesis equals 2 over 3 times 6 equals 4
    Similarly, putting y = 6 in the above equation,
    x equals 2 over 3 left parenthesis 6 minus 3 right parenthesis equals 2 over 3 times 3 equals 2
    Putting y = 0 in the above equation,
    x equals 2 over 3 left parenthesis 0 minus 3 right parenthesis equals 2 over 3 left parenthesis negative 3 right parenthesis equals negative 2
    Finally, putting y = -3, we get
    x equals 2 over 3 left parenthesis negative 3 minus 3 right parenthesis equals 2 over 3 left parenthesis negative 6 right parenthesis equals negative 4
    Thus, we complete the table as
    X
    4
    2
    -2
    -4
    y
    9
    6
    0
    -3

    Use the function Y = 1.5X + 3 to complete the table of values.
    X        
    Y 9 6 0 -3

    Maths-General
    Step by step solution:
    The given equation is
    Y = 1.5x + 3
    We rewrite this equation with ‘x’ on one side of the equation so that it is easy to find its value.
    table attributes columnspacing 1em end attributes row cell 1.5 x equals y minus 3 end cell row cell not stretchy rightwards double arrow x equals fraction numerator 1 over denominator 1.5 end fraction left parenthesis y minus 3 right parenthesis end cell end table
    Using , we get
    x equals 2 over 3 left parenthesis y minus 3 right parenthesis
    Now, we calculate x for the given values of y.
    Putting y = 9, in the above equation, we get,
    x equals 2 over 3 left parenthesis 9 minus 3 right parenthesis equals 2 over 3 times 6 equals 4
    Similarly, putting y = 6 in the above equation,
    x equals 2 over 3 left parenthesis 6 minus 3 right parenthesis equals 2 over 3 times 3 equals 2
    Putting y = 0 in the above equation,
    x equals 2 over 3 left parenthesis 0 minus 3 right parenthesis equals 2 over 3 left parenthesis negative 3 right parenthesis equals negative 2
    Finally, putting y = -3, we get
    x equals 2 over 3 left parenthesis negative 3 minus 3 right parenthesis equals 2 over 3 left parenthesis negative 6 right parenthesis equals negative 4
    Thus, we complete the table as
    X
    4
    2
    -2
    -4
    y
    9
    6
    0
    -3
    parallel
    General
    General

    Rewrite the sentences using possessive nouns

    Explanation 7
    Possessive Nouns - A noun that possesses something. has something. In most cases, a possessive known is formed by adding an apostrophe  to the  noun the noun is plural and already and already exists ends in S, only an apes trope needs be added.

    Rewrite the sentences using possessive nouns

    GeneralGeneral
    Explanation 7
    Possessive Nouns - A noun that possesses something. has something. In most cases, a possessive known is formed by adding an apostrophe  to the  noun the noun is plural and already and already exists ends in S, only an apes trope needs be added.
    General
    General

    Choose the synonym 6 ‘auditory'

    Correct answer  a) acoustic
    Explanation - relating to the sense of hearing.

    Choose the synonym 6 ‘auditory'

    GeneralGeneral
    Correct answer  a) acoustic
    Explanation - relating to the sense of hearing.
    General
    Maths-

    You have an ant form with 22 ants. The population of ants in your farm doubles every 3 months.
    a) Complete the table .

    b) Is the relation forms a function ? If so , is it a linear function or non linear function ? Explain.

    Step by step solution:
    Given,
    Population of the ant farm initially = 22
    The population doubles every 3 months.
    Rate at which the population of the ant farm increases per month = 3 over 2
    We know, the slope intercept form of the equation is y = mx + c, where m is the slope and c is the y intercept.
    Here, m = 3 over 2 = 1.5 and c=22
    Thus, the equation representing the relationship between the ant population with respect to the number of months is
    y = 1.5x + 22
    We use this equation to complete the table.
    We can see that for x = 0, we get y = 22
    Putting x = 3 in the above equation, we get
    y = 1.5 cross times3 + 22 = 4.5 + 22 = 26.5
    Similarly, putting  in the above equation, we get
    y = 15 cross times 6 + 22 = 9 + 22 = 31
    Finally, putting  in the above equation, we have
    y = 1.5 cross times 9 + 22 = 13.5 + 22 = 35.5
    Putting these values in the table, we have
    No. of months (x)
    0
    3
    6
    9
    Ant population (y)
    22
    26.5
    31
    35.5
    The above relation forms a function as there is a unique value of y for every value of x.
    It is also a linear function as the rate of change of ant population or the slope of the equation is a constant value 1.5.

    You have an ant form with 22 ants. The population of ants in your farm doubles every 3 months.
    a) Complete the table .

    b) Is the relation forms a function ? If so , is it a linear function or non linear function ? Explain.

    Maths-General
    Step by step solution:
    Given,
    Population of the ant farm initially = 22
    The population doubles every 3 months.
    Rate at which the population of the ant farm increases per month = 3 over 2
    We know, the slope intercept form of the equation is y = mx + c, where m is the slope and c is the y intercept.
    Here, m = 3 over 2 = 1.5 and c=22
    Thus, the equation representing the relationship between the ant population with respect to the number of months is
    y = 1.5x + 22
    We use this equation to complete the table.
    We can see that for x = 0, we get y = 22
    Putting x = 3 in the above equation, we get
    y = 1.5 cross times3 + 22 = 4.5 + 22 = 26.5
    Similarly, putting  in the above equation, we get
    y = 15 cross times 6 + 22 = 9 + 22 = 31
    Finally, putting  in the above equation, we have
    y = 1.5 cross times 9 + 22 = 13.5 + 22 = 35.5
    Putting these values in the table, we have
    No. of months (x)
    0
    3
    6
    9
    Ant population (y)
    22
    26.5
    31
    35.5
    The above relation forms a function as there is a unique value of y for every value of x.
    It is also a linear function as the rate of change of ant population or the slope of the equation is a constant value 1.5.
    parallel

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