Bonita is testing prototype model rocket engines. to be considered a successful launch, the rocket must reach a height of at least 24 ft and must go a horizontal distance of no more than 10 ft. the vertical height must be at least three times as high as the horizontal distance. no rocket should go higher than 33 ft. the graph shows the feasible region, where x represents the horizontal distance and y represents the vertical distance. which ordered pairs meet all the constraints for a successful launch and make sense in context of the situation? select each correct answer. (0, 33) (4, 36) (4.8, 30.5) (9, 26) (2, 22)

Let

x--------> the horizontal distance in feet

y--------> the vertical height in feet

we know that

The constraints are

1)

2)

3)

Let's verify each case to determine the solution to the problem.

case A) point

Substitute the values of x and y in each of the constraints

constraint 1

---------> is true

constraints 2

-------> is true

constraints 3

--------> is true

therefore

the ordered pair   meet all the constraints for a successful launch

case B) point

Substitute the values of x and y in each of the constraints

constraint 1

---------> is true

constraints 2

-------> is not true

constraints 3

--------> is true

therefore

the ordered pair   does not meet all restrictions for a successful launch

case C) point

Substitute the values of x and y in each of the constraints

constraint 1

---------> is true

constraints 2

-------> is true

constraints 3

--------> is true

therefore

the ordered pair   meet all the constraints for a successful launch

case D) point

Substitute the values of x and y in each of the constraints

constraint 1

---------> is not true

constraints 2

-------> is true

constraints 3

--------> is true

therefore

the ordered pair   does not meet all restrictions for a successful launch

case E) point

Substitute the values of x and y in each of the constraints

constraint 1

---------> is true

constraints 2

-------> is not true

constraints 3

--------> is true

therefore

the ordered pair does not meet all restrictions for a successful launch

the answer is

The ordered pairs that  meet all the constraints for a successful launch and make sense in context of the situation are:

            (0,33) and  (4.8,30.5)

Step-by-step explanation:

Here x represent the horizontal distance and y represent the vertical distance.

From the given information in the question we can make the following inequalities:

                                      y ≥ 24

                        and        x ≤ 10

             i.e.       y ≥ 3x

               i.e.           y ≤ 33

Hence, after combining all the inequalities we have:

                          x ≤ 10

                     24 ≤ y ≤ 33

       and               y ≥ 3x

1)

(0, 33)

As (0,33) satisfies all the constraints of the given problem.

Hence, this ordered pair will lie in the feasible region.

2)

(4, 36)

As the height that is the y-value has to be less than 33.

Hence, the ordered pair (4,36) does not lie in the feasible region.

3)

(4.8, 30.5)

It satisfies all the inequalities of a successful launch.

Hence, this ordered pair will lie in the feasible region.

4)

(9, 26)

As the property that y ≥ 3x mjust be satisfied.

But here at x=9

              y ≥ 27

but we are given y=26.

Hence, this ordered pair also does not lie  in the feasible region.

5)

(2, 22)

As the minimum vertical distance must be 24.

But here we are given y=22.

Hence, this ordered pair does not lie in the feasible region.

c

step-by-step explanation: