Maths-
General
Easy

Question

Is the relation forms a linear function ?

Use the graph to support your answer.

Hint:

An equation of the form y = f(x) is called a function if there is a unique value of y for every value of x. In other words, every value of x must have one value of y. We can check if the graph is a function by the vertical line test. A graph represents a function if any vertical line in the xy plane cuts the graph at maximum one point. A function is linear if the graph of the function is a straight line.

The correct answer is: function is linear


    Step by step solution:
    Let us denote the week by x.
    Let us denote the number of students by y.
    The given table is
    x
    0
    1
    2
    3
    4
    5
    y
    300
    250
    200
    150
    100
    50
    We draw a graph from the above table.

    From the graph, we can observe that, the curve drawn is a straight line.
    Hence the function is linear.

    There are other ways to determine whether a function is linear or not, like, checking if the slope is equal between each of the points or if the equation can be written in the form of y = ax + b, where a and b are constants.

    Related Questions to study

    General
    Maths-

    Solve 2x-5<5x-22, then graph the solution

    Hint:
    Linear inequalities are expressions where any two values are compared by the inequality symbols<,>,≤&≥ .
    We are asked to solve the inequality and graph the solution.
    Step 1 of 2:
    Rearrange and solve the inequality,
    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 2 x minus 5 less than 5 x minus 22 end cell row cell 22 minus 5 less than 5 x minus 2 x end cell row cell 17 less than 3 x end cell row cell 17 over 3 less than x end cell end table
    Step 2 of 2:
    Graph the inequality using the solution;

    Note:
    Whenever we use the inequality symbol < or> we do not include the end point.

    Solve 2x-5<5x-22, then graph the solution

    Maths-General
    Hint:
    Linear inequalities are expressions where any two values are compared by the inequality symbols<,>,≤&≥ .
    We are asked to solve the inequality and graph the solution.
    Step 1 of 2:
    Rearrange and solve the inequality,
    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 2 x minus 5 less than 5 x minus 22 end cell row cell 22 minus 5 less than 5 x minus 2 x end cell row cell 17 less than 3 x end cell row cell 17 over 3 less than x end cell end table
    Step 2 of 2:
    Graph the inequality using the solution;

    Note:
    Whenever we use the inequality symbol < or> we do not include the end point.
    General
    Maths-

    Write the solutions to the given equation.
    Rewrite them as the linear-quadratic system of equations and graph them to solve.
    5 minus 0.5 x squared equals negative 0.5 x plus 2

    Hint:
    A quadratic equation is when the polynomial has a degree two. A graph is a geometrical representation of an equation.
    We are asked to solve the equation graphically by arranging them in a linear-quadratic equation.
    Step 1 of 2:
    The given equation is 5 minus 0.5 x squared equals negative 0.5 x plus 2.
    Re arranging them, we get:
    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 5 minus 0.5 x squared equals negative 0.5 x plus 2 end cell row cell 0.5 x squared minus 0.5 x plus 2 minus 5 equals 0 end cell row cell 0.5 x squared minus 0.5 x minus 3 equals 0 end cell row cell 5 x squared minus 5 x minus 30 equals 0 end cell row cell x squared minus x minus 6 equals 0 end cell end table
    Here, once we rearrange it, we multiply the equation with ten to remove the decimal. Then, take out five to factorize into the simplest form.
    Step 2 of 2:
    Graph the equation to get the solution:
    .
    Thus, the solution of the equation is:
    x equals negative 2 straight & x equals 3.
    Note:
    A lot of the quadratic equations can be solved using identities and factorization. You would get a maximum of two solutions for each quadratic equation.

    Write the solutions to the given equation.
    Rewrite them as the linear-quadratic system of equations and graph them to solve.
    5 minus 0.5 x squared equals negative 0.5 x plus 2

    Maths-General
    Hint:
    A quadratic equation is when the polynomial has a degree two. A graph is a geometrical representation of an equation.
    We are asked to solve the equation graphically by arranging them in a linear-quadratic equation.
    Step 1 of 2:
    The given equation is 5 minus 0.5 x squared equals negative 0.5 x plus 2.
    Re arranging them, we get:
    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 5 minus 0.5 x squared equals negative 0.5 x plus 2 end cell row cell 0.5 x squared minus 0.5 x plus 2 minus 5 equals 0 end cell row cell 0.5 x squared minus 0.5 x minus 3 equals 0 end cell row cell 5 x squared minus 5 x minus 30 equals 0 end cell row cell x squared minus x minus 6 equals 0 end cell end table
    Here, once we rearrange it, we multiply the equation with ten to remove the decimal. Then, take out five to factorize into the simplest form.
    Step 2 of 2:
    Graph the equation to get the solution:
    .
    Thus, the solution of the equation is:
    x equals negative 2 straight & x equals 3.
    Note:
    A lot of the quadratic equations can be solved using identities and factorization. You would get a maximum of two solutions for each quadratic equation.
    General
    Maths-

    Prove the following statement.
    The length of any one median of a triangle is less than half the perimeter of the triangle.

    Answer:
    • Hints:
      • Triangle inequality theorem
      • According to this theorem, in any triangle, sum of two sides is greater than third side,
      • a < b + c
    b < a + c
    c < a + b
      • The line segment which joins the vertex of triangle to midpoint of opposite side is called the ‘median’.
      • Perimeter of triangle is sum of sides.
      • Perimeter = a + b + c
    • To prove: 
      • The length of any one median of a triangle is less than half the perimeter of the triangle.

    solution:

    • Step 1:
    Let,
    Side AB = a
    Side BC = b
    Side AC = c

    And median AM be Ma
    • Step 2:
    In △ABM,
    AM is median so M is midpoint of BC
    BM = b over 2
    So, according to triangle inequality theorem,
    Ma < a + b over 2 ---- eq. 1
    In △ACM,
    AM is median so M is midpoint of BC
    MC = b over 2
    So, according to triangle inequality theorem,
    Ma < c + b over 2 ---- eq. 2

    Add eq. 1 and eq. 2.
    Ma + Ma < a + b over 2 + c + b over 2
    2Ma < a + b + c
    Mafraction numerator a plus b plus c over denominator 2 end fraction
    • Final Answer: 
    Hence, proved.

    Prove the following statement.
    The length of any one median of a triangle is less than half the perimeter of the triangle.

    Maths-General
    Answer:
    • Hints:
      • Triangle inequality theorem
      • According to this theorem, in any triangle, sum of two sides is greater than third side,
      • a < b + c
    b < a + c
    c < a + b
      • The line segment which joins the vertex of triangle to midpoint of opposite side is called the ‘median’.
      • Perimeter of triangle is sum of sides.
      • Perimeter = a + b + c
    • To prove: 
      • The length of any one median of a triangle is less than half the perimeter of the triangle.

    solution:

    • Step 1:
    Let,
    Side AB = a
    Side BC = b
    Side AC = c

    And median AM be Ma
    • Step 2:
    In △ABM,
    AM is median so M is midpoint of BC
    BM = b over 2
    So, according to triangle inequality theorem,
    Ma < a + b over 2 ---- eq. 1
    In △ACM,
    AM is median so M is midpoint of BC
    MC = b over 2
    So, according to triangle inequality theorem,
    Ma < c + b over 2 ---- eq. 2

    Add eq. 1 and eq. 2.
    Ma + Ma < a + b over 2 + c + b over 2
    2Ma < a + b + c
    Mafraction numerator a plus b plus c over denominator 2 end fraction
    • Final Answer: 
    Hence, proved.
    parallel
    General
    General

    Select the three most common text features

    Correct answer a) Title, 6) Table of Content d) Picture of and Captions
    Explanations - Text features refer to parts of a text but don't necessarily appear directly within the main body

    Select the three most common text features

    GeneralGeneral
    Correct answer a) Title, 6) Table of Content d) Picture of and Captions
    Explanations - Text features refer to parts of a text but don't necessarily appear directly within the main body
    General
    Maths-

    Solve 3.5x+19≥1.5x-7

    Hint:
    Linear inequalities are expressions where any two values are compared by the inequality symbols<,>,≤&≥ .
    We are asked to solve the inequality.
    Step 1 of 1:
    Rearrange and solve the inequality,
    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 3.5 x plus 19 greater or equal than 1.5 x minus 7 end cell row cell 3.5 x minus 1.5 x greater or equal than negative 7 minus 19 end cell row cell 2 x greater or equal than negative 26 end cell row cell x greater or equal than fraction numerator negative 26 over denominator 2 end fraction end cell row cell x greater or equal than negative 13 end cell end table
    Note:
    Whenever we use the symbol ≤ or ≥ , we use the endpoint as well. We could also solve the inequality by graphing it.

    Solve 3.5x+19≥1.5x-7

    Maths-General
    Hint:
    Linear inequalities are expressions where any two values are compared by the inequality symbols<,>,≤&≥ .
    We are asked to solve the inequality.
    Step 1 of 1:
    Rearrange and solve the inequality,
    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 3.5 x plus 19 greater or equal than 1.5 x minus 7 end cell row cell 3.5 x minus 1.5 x greater or equal than negative 7 minus 19 end cell row cell 2 x greater or equal than negative 26 end cell row cell x greater or equal than fraction numerator negative 26 over denominator 2 end fraction end cell row cell x greater or equal than negative 13 end cell end table
    Note:
    Whenever we use the symbol ≤ or ≥ , we use the endpoint as well. We could also solve the inequality by graphing it.
    General
    Maths-

    Determine whether each graph represents a function ?

    Step by step solution:
    We consider the first graph.

    We can observe that any vertical line drawn on the graph cuts the line at exactly one point
    Hence, this graph represents a function.
    The second graph is

    Again, we can observe that any vertical line drawn cuts the graph at exactly one point.
    Hence, this graph is also a function.
    Finally, consider the third graph.

    If we draw a vertical line at the origin, that is, the y-axis, we can see that it cuts the graph at two points.
    Thus, this graph is not a function.

    Determine whether each graph represents a function ?

    Maths-General
    Step by step solution:
    We consider the first graph.