Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions: y < 2x − 7 y is greater than or equal to negative 1 over 2 times x plus 3 part a: describe the graph of the system, including shading and the types of lines graphed. provide a description of the solution area. part b: is the point (3, −7) included in the solution area for the system? justify your answer mathematically.

Solution-

The given inequalities are,

Part A

As the former inequality is only '<' so it will be represented as dotted line, but in case of the later inequality there is '≥' so it will be represented as a solid line.

This happens because in only '<, >' the values must be either lesser or greater than y, they can't take the values of y, but in case of '≤, ≥' the values can be equal to y.

Taking origin (0, 0) and putting in the first inequality.

As the equation does not satisfy, so the shaded area will be on the other side of the origin.

Again taking origin (0, 0) and putting in the second inequality.

As the equation does not satisfy, so the shaded area will be on the other side of the origin.

The second attachment contains the feasible region.

Part B

In order to know whether the point (3, −7) is included in the solution area for the system or not, we must put it in both the equations, if it satisfies both then only it is within the solution area.

As the point (3, -7) only satisfies first inequality, but not the second inequality so this point won't be in the solution area.

Part A: The graph of given system of inequalities shown below.

Part B: (3,-7) is not included in the solution area.

Step-by-step explanation:

The given system of equations is

        .... (1)

        ... (2)

Part A:

The related equations are

              .... (3)

       ... (4)

Table of values

For equation 3.

x      y

0     -7

3.5   0

For equation 4.

x      y

0     3

6     0

Plot these ordered pairs on a coordinate planes and connect corresponding lines to draw the straight lines.

Check each inequality by (0,0).

 (False)

   (False)

It means (0,0) is not included in the shaded region of any of these inequalities.

is dotted line.

is a solid line.

Therefore, the graph of given system of inequalities shown below.

Part B:

Check each each inequality by (3,-7).

      (True)

    (False)

Since second inequality is not satisfied by the point (3,-7), therefore (3,-7) is not included in the solution area.

19.side- angle- side

20. angle- side- angle

step-by-step explanation:

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}