20 POINTS AND BRAINLIEST A line passes through the points (k, 4) and (3,-6). The line is perpendicular to the graph of 5y + 4x = 8. What is the value of k? 11
2
-1.6
-9.5

hjhj

Step-by-step explanation:

There are 87 students signed up for Humanities course only

Step-by-step explanation:

* Lets explain how to solve the problem

- Its easy to solve this problem using Venn-diagram

- We start with drawing a rectangle and three intersected circles

 inscribed in the rectangle

- The rectangle represents all the students courses

- Circle labeled M for mathematics course

- Circle labeled L for Language Arts course

- Circle labeled H for Humanities course

- There are 74 students had signed up for a Math course

- 51 students had signed up for a Language Arts course

- 20 students had signed up for both a Math and Language Arts course

- 10 students had signed up for both a Math and Humanities course

- 5 students had signed up for both a Language Arts and Humanities

 course

- 3 students had signed up for all three courses

- 20 students did not sign up for any of these classes

- x students had signed up for Humanities course only

* Lets put these numbers in the venn-diagram

∵ There are 20 students did not sign up for any of these classes

∴ Put 20 inside the rectangle but outside the circles

∵ There are 3 students had signed up for all three courses

∴ Put 3 in the common region between the three circles

∵ There are 5 students had signed up for both a Language Arts and

   Humanities course

- 3 student of them are already put in the common part of the 3 circles

∴ Put 5 - 3 = 2 in the common part between circles L and H only

∵ There are 10 students had signed up for both a Math and

   Humanities course

- 3 student of them are already put in the common part of the 3 circles

∴ There are 10 - 3 = 7 in the common part between circles M and

   H only

∵ There are 20 students had signed up for both a Math and

   Language Arts course

- 3 student of them are already put in the common part of the 3 circles

∴ Put 20 - 3 = 17 in the common par between the circles M and L only

∵ 51 students had signed up for a Language Arts course

- We already put 3 + 17 + 2  = 22

∴ Put 51 - 22 = 29 in the empty part of circle L not intersected

  with any other circle

∵ There are 74 students had signed up for a Math course

- We already put 3 + 17 + 7  = 27

∴ Put 74 - 27 = 47 in the empty part of circle M not intersected

  with any other circle

∵ There are x students had signed up for Humanities course only

∴ Put x in the empty part of circle H not intersected with any other

  circle

* Now lets add all the numbers inside the diagram (Bold number)

 and then equate them by the total number of the students

∵ The sum of the students in the venn-diagram is:

  20 + 3 + 2 + 7 + 17 + 29 + 47 + x = 125 + x

∵ There are 212 SPC students was taken at registration

∴ 125 + x = 212

- Subtract 125 from both sides

∴ x = 87

∵ x represents the students had signed up for Humanities

  course only

∴ There are 87 students signed up for Humanities course only

* Look to the attached file for more understand