Maths-
General
Easy

Question

y greater or equal than negative 2 x plus 11
y greater than 3 x minus 9
In the xy-plane, point A is contained in the graph of the solution set of the system of inequalities above. Which of the following could be the coordinates of point A?

  1. (2,1)
  2. (4,1)
  3. (4,5)
  4. (6,6)

hintHint:

Hint:
We are given two inequalities in the xy-plane. We need to check if each of the co-ordinates given in the options satisfies the inequalities given in the question. If any one of the inequalities is not satisfied by the given co-ordinate, then A will not be that point.

The correct answer is: (4,5)


    A) (2, 1)
    Putting this point in the first inequality,
    y greater or equal than negative 2 x plus 11
    1 greater or equal than negative 2.2 plus 11
    1 greater or equal than negative 4 plus 11
    1 greater or equal than 7
    But this is not true as1 less than 7 .
    Option A) is not correct
    B) (4 , 1)
    Putting this point in the first inequality,
    y greater or equal than negative 2 x plus 11
    1 greater or equal than negative 2.4 plus 11
    1 greater or equal than negative 8 plus 11
    1 greater or equal than 3
    But this is not true because 1 < 3
    C) (4 , 5)
    Putting this point in the first inequality,
    y greater or equal than negative 2 x plus 11
    5 greater or equal than negative 2.4 plus 11
    5 greater or equal than negative 8 plus 11
    5 greater or equal than 3
    This is true
    Next, putting this point in the second inequality
    y greater than 3 x minus 9
    5 greater than 3.4 minus 9
    5 greater than 12 minus 9
    5 greater than 3
    This is also true.
    Thus, we find that point (4, 5) satisfies both the given inequalities.
    Hence, the point A is (4, 5)
    The correct option is C)

    Note:
    An alternate way to find the solution is to plot the given inequalities in the xy-plane. Each inequality denotes either side of the line given by putting equal sign instead of the inequality. To find which side of the line satisfies the inequality, check with point (0, 0) and shade the region satisfied by the inequality. After that, check if each of the points given in the options satisfies the region shaded in the xy-plane.

    Related Questions to study

    General
    Maths-

    Solve for x : 3x - 2 = 46 - x

    Solve for x : 3x - 2 = 46 - x

    Maths-General
    General
    Maths-

    H equals 1.88 L plus 32.01
    The formula above can be used to approximate the height H, in inches, of an adult male based on the length L, in inches, of his femur. What is the meaning of  1.88 in this  context?

    H equals 1.88 L plus 32.01
    The formula above can be used to approximate the height H, in inches, of an adult male based on the length L, in inches, of his femur. What is the meaning of  1.88 in this  context?

    Maths-General
    General
    Maths-

    Find the square root of 149.8176 by division method.

    Find the square root of 149.8176 by division method.

    Maths-General
    parallel
    General
    Maths-

    Find the square root of 741321 by division method.

    Find the square root of 741321 by division method.

    Maths-General
    General
    Maths-

    Find the square root of 68121 by division method ?

    Find the square root of 68121 by division method ?

    Maths-General
    General
    Maths-

    Which of the following expressions is equivalent to x squared plus 10 x plus 21?

    Note:
    Observe that the expressions in the incorrect options is slightly different than the correct one, so there is a high chance of making a mistake while finding the product of two linear factors.
    In the options, if only the product of two linear factors was given, without the extra term, then we would find the solution by middle term factorization and there was no need to break 21 into 12 and 9 .

    Which of the following expressions is equivalent to x squared plus 10 x plus 21?

    Maths-General

    Note:
    Observe that the expressions in the incorrect options is slightly different than the correct one, so there is a high chance of making a mistake while finding the product of two linear factors.
    In the options, if only the product of two linear factors was given, without the extra term, then we would find the solution by middle term factorization and there was no need to break 21 into 12 and 9 .

    parallel
    General
    Maths-

    In an auditorium , the number of columns equal to the number of chairs in a each column. If the capacity of an auditorium is 16129. How many chair are there in each column ?

    In an auditorium , the number of columns equal to the number of chairs in a each column. If the capacity of an auditorium is 16129. How many chair are there in each column ?

    Maths-General
    General
    Maths-

    Find the least square numbers exactly divisible by each one of numbers 6, 9, 15 and
    20.

    Find the least square numbers exactly divisible by each one of numbers 6, 9, 15 and
    20.

    Maths-General
    General
    Maths-

    2 over 3 left parenthesis 9 x minus 6 right parenthesis minus 4 equals 9 x minus 6
    Based on the equation above, what is the value of 3x - 2 ?

    2 over 3 left parenthesis 9 x minus 6 right parenthesis minus 4 equals 9 x minus 6
    Based on the equation above, what is the value of 3x - 2 ?

    Maths-General
    parallel
    General
    Maths-

    If a peregrine falcon dove at its maximum speed for half a mile to catch prey, how many seconds would the dive take? (Round your answer to the nearest second.)

    The concepts of speed, time, and distance are frequently used in questions about motion in a straight line, circular motion, boats and streams, races, clocks, and so on. Therefore, aspirants should comprehend the interdependence of speed, distance, and time.
    Relationship between speed, time, and distance
    • Speed = Distance/Time: This indicates how slowly or quickly an object moves. It shows the distance traveled divided by the time taken to cover the distance.
    Distance is directly proportional to speed, and time is inversely proportional to speed.
    • Distance = Speed x Time, and
    • Time = Distance / Speed; as speed increases, the time taken will decrease, and vice versa.
    Any basic problem can be solved using these formulas. However, the correct usage of units is also important while using formulas.

    If a peregrine falcon dove at its maximum speed for half a mile to catch prey, how many seconds would the dive take? (Round your answer to the nearest second.)

    Maths-General

    The concepts of speed, time, and distance are frequently used in questions about motion in a straight line, circular motion, boats and streams, races, clocks, and so on. Therefore, aspirants should comprehend the interdependence of speed, distance, and time.
    Relationship between speed, time, and distance
    • Speed = Distance/Time: This indicates how slowly or quickly an object moves. It shows the distance traveled divided by the time taken to cover the distance.
    Distance is directly proportional to speed, and time is inversely proportional to speed.
    • Distance = Speed x Time, and
    • Time = Distance / Speed; as speed increases, the time taken will decrease, and vice versa.
    Any basic problem can be solved using these formulas. However, the correct usage of units is also important while using formulas.

    General
    Maths-

    Which of the following is the graph of the equation y = 3x - 2 in the x y-plane?

    Note:
    We can also solve this question by eliminating the options.
    The first option A) is not correct because the line passes through the origin and so it must satisfy the equation, which is not true as 0not equal to- 2
    Then C) is not correct as the line passes through (0, -3), but this point does not satisfy the equation. Similarly, for option D) the point (0, 2) lies on the graph, but does not satisfy the equation.

    Which of the following is the graph of the equation y = 3x - 2 in the x y-plane?

    Maths-General

    Note:
    We can also solve this question by eliminating the options.
    The first option A) is not correct because the line passes through the origin and so it must satisfy the equation, which is not true as 0not equal to- 2
    Then C) is not correct as the line passes through (0, -3), but this point does not satisfy the equation. Similarly, for option D) the point (0, 2) lies on the graph, but does not satisfy the equation.

    General
    Maths-

    What is a peregrine falcon's maximum speed while diving to catch prey, in feet per second? (Round your answer to the nearest whole number 1 mile = 5280 feet)

    What is a peregrine falcon's maximum speed while diving to catch prey, in feet per second? (Round your answer to the nearest whole number 1 mile = 5280 feet)

    Maths-General
    parallel
    General
    Maths-

    Keith modeled the growth over several hundred years of a tree population by estimating the number of the trees' pollen grains per square centimeter that were deposited each year within layers of a lake's sediment. He estimated there were 310 pollen grains per square centimeter the first year the grains were deposited, with a 1%  annual increase in the number of grains per square centimeter thereafter. Which of the following functions models p(t), the number of pollen grains per square centimeter t years after the first year the grains were deposited?

    Keith modeled the growth over several hundred years of a tree population by estimating the number of the trees' pollen grains per square centimeter that were deposited each year within layers of a lake's sediment. He estimated there were 310 pollen grains per square centimeter the first year the grains were deposited, with a 1%  annual increase in the number of grains per square centimeter thereafter. Which of the following functions models p(t), the number of pollen grains per square centimeter t years after the first year the grains were deposited?

    Maths-General
    General
    Maths-

    In the xy-plane, a line that has the equation y = c for some constant c intersects a parabola at exactly one point. If the parabola has the equation y equals negative x squared plus 5 x, what is the value of  c ?

    In the xy-plane, a line that has the equation y = c for some constant c intersects a parabola at exactly one point. If the parabola has the equation y equals negative x squared plus 5 x, what is the value of  c ?

    Maths-General
    General
    Maths-

    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 2.4 x minus 1.5 y equals 0.3 end cell row cell 1.6 x plus 0.5 y equals negative 1.3 end cell end table
    The system of equations above is graphed in the xy  -plane. What is the x -coordinate of the intersection  point ( x, y) of the system?

    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 2.4 x minus 1.5 y equals 0.3 end cell row cell 1.6 x plus 0.5 y equals negative 1.3 end cell end table
    The system of equations above is graphed in the xy  -plane. What is the x -coordinate of the intersection  point ( x, y) of the system?

    Maths-General
    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.