1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
zmey [24]
3 years ago
8

Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions:y >

2x + 3y is less than negative 3 over 2 times x minus 4Part A: Describe the graph of the system, including shading and the types of lines graphed. Provide a description of the solution area. (6 points)Part B: Is the point (â’4, 6) included in the solution area for the system? Justify your answer mathematically. (4 points)

Mathematics
2 answers:
swat323 years ago
8 0

Answer:

We are given the system of inequalities,

y>2x+3 and y

Part A: We have that the equations given are straight line which have the intersection point (-2,-1).

<em>According to 'Zero Test' which states that 'After substituting (0,0) in the inequalities. If the result is true, the solution region is towards the origin. If the result is false, the solution region is away from the origin'.</em>

So, from the graph we see that the solution region is away from the origin, which means both the given inequalities fails the 'Zero Test'.

i.e. y>2x+3 ⇒ 0 > 3, which is false and y ⇒ 0 < -4, which is also false.

Part B: We see that from the graph, that the point (4,6) lies outside the solution region.

Mathematically, we will substitute the value of x= 4 in the equality to check whether the value of y= 6.

So, y=2x+3 ⇒ y=2\times 4+3 ⇒ y=8+3 ⇒ y= 11

And, y=-\frac{3}{2}x-4 ⇒ y ⇒ y=-3\times 2-4 ⇒ y=-6-4 ⇒ y= -10.

Hence, we see that mathematically the point (4,6) does not lie in the solution region.

pantera1 [17]3 years ago
3 0

Answer:

Part A: The graph of given inequality is shown below.

Part B: The point (4,6) is not a solution of given system of inequalities.

Step-by-step explanation:

Part A:

The given inequalities are

y>2x+3

y

The related equation of given inequalities are

y=2x+3

y=-\frac{3}{2}x-4

Put x=0, to find the y-intercepts.

y=2(0)+3=3

y=-\frac{3}{2}(0)-4=-4

Put y=0, to find the x-intercepts.

0=2x+3\Rightarrow x=-\frac{3}{2}

0=-\frac{3}{2}x-4\Rightarrow x=-\frac{8}{3}

The x and y-intercepts of first line are (0,3) and (-1.5,0) respectively. The x and y-intercepts of second line are (0,-4) and (-2.667,0) respectively.

Check the given inequality by (0,0).

0>2(0)+3

0>3

This statement is false. It means (0,0) is not the solution of this inequality and the shaded region is opposite side of the origin.

0

0

This statement is false. It means (0,0) is not the solution of this inequality and the shaded region is opposite side of the origin.

The graph of given inequalities is shown below.

Part B:

We have to check whether (4,6) is a solution of the system of inequality or not.

Check the given inequality for the point (4,6).

(6)>2(4)+3

6>11

This statement is false. It means (4,6) is not the solution of given system of inequalities.

You might be interested in
What is the absolute value transformation of this function?
xxMikexx [17]

Answer:

k(x) = -|x + 2| + 3

Step-by-step explanation:

Parent function of the absolute function given in the graph,

f(x) = |x|

1). Function 'g' is reflected across the x-axis, then the image will be,

  h(x) = -f(x) = -|x|

2). Function 'h' the shifted 2 units left and 3 units upwards, image function will be,

  k(x) = h(x + 2) + 3

  k(x) = -|x + 2| + 3

Therefore, the transformed function is k(x) = -|x + 2| + 3.

6 0
3 years ago
ILLL markk brainliest i promise plsss helpp
SOVA2 [1]

Answer:

3

Step-by-step explanation:

8 0
3 years ago
Find the 15th term of the geometric sequence 2 , -8 , 32
marishachu [46]

Answer:

first term (a)= 2

second term (b) = -8

common ratio (r) = -8/2 = -4

15th term = ar^ (n-1)

                = 2* (-4)^ 14 =536870912

Step-by-step explanation:

5 0
3 years ago
For all the following, which ones represent y as a function of x, and how do you know?
earnstyle [38]
Only 25 and 28 are functions.

A function must have only one y value per x value. For 26, the y value of 0 and multiple others have two different y values. For 27, all x values less than 0 have multiple y values.
4 0
3 years ago
which of the following answer choices is equal to the sum of three consecutive odd integers? 153,154,155,156 or 157
Virty [35]
153 is the sum of 49, 51, and 53
6 0
3 years ago
Other questions:
  • WORTH 45 POINTS AND BRAINLIST NO FAKE ANSWERS AND PLAGIARIZING
    10·2 answers
  • Could someone explain to me how to answer this question.
    9·2 answers
  • Evaluate -4a + 8z if a=8 and z=3.​
    10·2 answers
  • What does the ratio difference in means divided by the mean absolute deviation tell you about how much visual overlap there is b
    14·1 answer
  • I need these numbers Least to greatest
    13·1 answer
  • Which equation has no solution?
    13·2 answers
  • Can you help meeeeeeeeeeeeeeeeeee
    5·1 answer
  • ⅕ + ⅕ + ⅕ +⅕ <br><br> 6 x ⅕ <br><br> Which is GREATER?
    10·1 answer
  • What type of transformation is shown mathematical experts or someone who’s taken the test please help!
    9·1 answer
  • A bird was sitting 9 meters from the base of an oak tree and flew 15 meters to reach the top of the tree. How tall is the tree?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!